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INTRODUCTION {#s1} ============ With the ever increasing cost and time-consuming process of drug development, new strategies for drug development are highly demanded. Drug repurposing, which aims for identifying novel indications for existing drugs, attracts a lot of attention since the toxicity of known drugs is already understood \\[[@R1]\\]. For example, Metformin has been widely used for more than 30 years for the treatment of type 2 diabetes, but extensive preclinical and clinical studies over the past decade have demonstrated the antitumor effects of the drug \\[[@R2]\\]. It has been reported that Metformin was able to lower the risk of cancer mortality and incidence in patients with diabetes \\[[@R3]\\]. Nowadays, drug repurposing has been considered as an effective approach in drug development. However, identifying novel indications with drug repurposing is highly challenging since the novel indications of one drug may have no obvious relationship with its initial purpose. During the past decade, much effort has been made to develop new computational approaches for the purpose of repositioning drugs and elucidating the molecular mechanisms of drugs. For example, Wang *et al* proposed a novel method to predict drug target proteins based on drug-domain interactions \\[[@R4]\\], and Zhang *et al* constructed a post-translational regulatory network to explore network motifs as potential drug targets which can help design multi-component or combinatorial drugs \\[[@R5]\\]. With the popular deep learning (DL) techniques, Kadurin *et al* proposed a DL-based model for screening potential anti-cancer compounds \\[[@R6]\\]. Recently, the network pharmacology approaches have been widely employed for understanding the mechanisms of drug actions, resistance and side effects \\[[@R7]--[@R9]\\]. At the same time, some network pharmacology approaches have been proposed to predict the associations between drugs and diseases. For instance, Martinez *et al* developed DrugNet to prioritize drugs for certain diseases by integrating complex associations among disease, drugs and proteins \\[[@R10]\\]. Besides, Alaimo *et al* also introduced a method that can be used to integrate biological knowledge and bipartite interaction network to predict new indications of drugs \\[[@R11]\\]. As multi-target or multi-component therapies gain increasing attention recently, Traditional Chinese Medicines (TCMs) are being re-evaluated and becoming important resources for the discovery of alternative treatments for certain diseases, where various network pharmacology approaches have been proposed for this purpose \\[[@R12]--[@R15]\\]. For example, Qing Luo Yin (QLY) is an effective formula in the treatment of arthritis and antiangiogenic. With the target network of QLY, not only the diseases related key biological processes including angiogenesis, inflammatory and immune response were revealed, but also the active ingredients and synergistic combinations of this herbal formula were identified \\[[@R16]\\]. Another example is Liuwei Dihuang Wan (LDW), which shows potential for regulating the imbalance of hormones and metabolism \\[[@R17]\\]. Therefore, the network pharmacology approaches are capable of providing insights into the mechanisms of actions of known drugs and identifying new indications of those drugs \\[[@R18]--[@R20]\\]. However, current network pharmacology methods for repurposing drugs are mainly based on the target proteins of active compounds, whereas the target information may not be indicative of diseases that the drugs can be used for. In this paper, we investigate the mechanisms of drug actions based on the pathways modulated by the drugs. By further integrating pathway profiles with chemical structures as well as disease phenotypes, we present a network pharmacology approach namely PINA (Predicting new Indications of compounds with a Network pharmacology Approach) as shown in Figure [1](#F1){ref-type="fig"}, to predict potential indications of old drugs. Benchmark results on FDA approved drugs have proven the superiority of our method over traditional network pharmacology approaches, as regard to revealing new associations between compounds and diseases. We further extend PINA to predict the novel indications of Traditional Chinese Medicines (TCMs) with Liuwei Dihuang Wan (LDW) as a case study. The predicted indications, including immune system disorders and tumor, are validated by expert knowledge and evidences from literature, demonstrating the effectiveness of our proposed computational approach. {#F1} RESULTS {#s2} ======= Identification of the pathway profiles associated with diseases {#s2_1} --------------------------------------------------------------- In this work, given a disease, we assume that the compounds that can significantly affect the pathway profiles associated with the disease can be used for the disease. With 4,774 known drug-disease associations composed of 928 compounds and 608 diseases extracted from CTD database \\[[@R21]\\], we first identified the pathways that are dysfunctional in diseases. Assuming that diseases with similar pathway profiles should have similar mechanisms, based on the pathways we identified a disease-disease association network was constructed, where two diseases were linked if they shared at least one pathway. We further detected modules from the network with density-based MCODE \\[[@R22]\\] tool ([Supplementary Figure 2](#SD1){ref-type="supplementary-material"}). Table [1](#T1){ref-type="table"} listed the 14 modules and the corresponding average similarities among diseases within the module as well as the most enriched disease class. [Supplementary Table 2](#SD3){ref-type="supplementary-material"} has shown the detailed information of the 14 modules. If the pathway profiles we identified are indeed associated with diseases, we expected that the diseases belonging to the same module should have similar mechanisms. It could be seen that the diseases grouped into the same module based on pathway profiles tended to have similar symptoms, where the disease similarity was calculated as described in \\[[@R23]\\]. Furthermore, the diseases can be grouped into 22 classes based on the physiological systems affected by the diseases as defined in \\[[@R24]\\]. By investigating the diseases belonging to same module, we found that the diseases in the same module tend to be in the same class as shown in Table [1](#T1){ref-type="table"}, indicating that the diseases from the same module have similar mechanisms. In addition, by investigating the number of disease classes that the pathway profiles were associated with, we found that each of more than 79% pathways was associated with only one specific disease class, implying that each pathway profile is specifically associated with a certain type of diseases ([Supplementary Figure 3](#SD1){ref-type="supplementary-material"}). ###### The modules detected by MCODE from the disease association network generated with disease related pathway profiles Modules Number of diseases Average similarity^\\#^ Disease class (Coverage)^\\*^ --------- -------------------- ------------------------ ------------------------------------- 1 16 0.1623 Psychiatric (0.625) 2 9 0.3210 Neurological (0.67) 3 7 0.2448 Ophthamological (0.71) 4 5 0.3294 Connective tissue (0.6) 5 5 0.6367 Cardiovascular (1.0) 6 4 0.4166 Endocrine (1.0) 7 4 0.2861 Neurological (0.5), Metabolic (0.5) 8 4 0.2427 Neurological (0.5), Cancer (0.5) 9 3 0.5193 Neurological (1.0) 10 3 0.3635 Bone (1.0) 11 3 0.2281 Immunological (1.0) 12 3 0.4612 Metabolic (1.0) 13 3 0.4284 Multiple (1.0) 14 3 0.5407 Gastrointestinal (1.0) ^\\#^Average similarity means the average of similarities over all disease pairs in each module detected in disease associated network. ^\\*^Coverage means the number of the diseases in the most enriched class divided by the number of disease in the module. By further investigating the pathway profiles that were associated with one disease class, we found that those pathways were indeed related to the disease class. For instance, the calcium signaling pathway played a crucial role in the control of neuronal functions and plasticity by regulating members of the neuronal calcium sensor (NCS) proteins \\[[@R25]\\]. It was reported that the deregulation of calcium signaling pathway was one of the key processes in the pathogenesis of neurodegenerative disorders \\[[@R26]\\]. In our study, the neurological class consists of 48 diseases while the calcium signaling pathway was predicted to be related with 18 out of them. Besides, the transmission across chemical synapses pathway we identified was related to more than 20% of neurological diseases, where the chemical synapses were specialized junctions used for communications between neuron \\[[@R27]\\]. Furthermore, the GPCR ligand binding pathway was predicted to be associated with all psychiatric diseases, where the G protein-coupled receptors have been found to play important roles in major psychiatric disorders, such as depression and schizophrenia \\[[@R28]\\]. From the findings shown above, we can see that the pathway profiles identified here are indeed related to the corresponding diseases. Prediction of potential indications for FDA approved drugs {#s2_2} ---------------------------------------------------------- With the pathway profiles identified above, the potential associations between compounds and diseases could be predicted. Based on the FDA approved drugs with target information and their known associations with diseases obtained from the CTD database, PIPP, NP~\\_C~ and NP~\\_D~ were respectively applied to predict potential compound-disease associations. By comparing the three approaches, we noticed that many of the predictions by pathway profile approach (PIPP) could be validated with those predicted by chemical structures and disease similarities based on the 'guilt by association' rule, where drugs with similar structures were assumed to be able to treat the same disease while similar diseases could be treated with the same drug. For example, the compound Nortriptyline (CID: 4543) was originally used as an anti-depressive agent \\[[@R2]\\], and it was predicted for the treatment of schizophrenia (OMIM: 603176) with a score of 0.9985 by PIPP. In fact, the drug Nortriptyline had similar structure with Amitriptyline (CID: 2160), which was used for schizophrenia \\[[@R9]\\], with a similarity score of 0.92. On the other hand, schizophrenia was similar with Attention Deficit Hyperactivity (ADH) disorder (OMIM: 143465), and Nortriptyline have already been reported for treating ADH in the CTD database, which validated that Nortriptyline could be used for schizophrenia. Moreover, we noticed that the pathway profile approach could successfully recover known associations that were missed by the chemical or disease similarity based approach. For example, the compound Retinoic Acid was used for femur head necrosis, which was successfully identified by our pathway profile method with a score of 1.0. However, the nearest profile approach based on chemical and disease similarity failed to identify this association with scores of 0.0 and 0.27, respectively. The results shown above demonstrate that the pathway profile approach can complement with other approaches, e.g. chemical or disease similarity based ones, very well. Therefore, we further proposed an ensemble approach named as PINA that combines the pathway profile method with chemical and disease similarity based methods to predict potential compound-disease associations. The novel potential indications of all compounds are list in [Supplementary Table 4](#SD5){ref-type="supplementary-material"}. We also compared PINA with three existing methods from literature, including DrugNet \\[[@R10]\\], HGBI \\[[@R29]\\] and NBI \\[[@R30]\\]. DrugNet is a network-based drug repositioning method, which integrates the information of diseases, drugs and proteins to prioritize drug-disease associations. HGBI and NBI have been originally developed for predicting drug-protein interactions, and can also be used for the prediction of drug-disease associations. HGBI predicts the drug-disease associations with the guilt-by-association principle based on the drug-disease heterogeneous graph, while NBI can predict new drug-disease associations based on a two-step diffusion model on a drug-disease bipartite graph. To evaluate the performance of our approach, PINA was compared with the other three approaches on the same benchmark drug-disease associations from the Comparative Toxicogenomics Database, where the same pre-process was used for all the four computational approaches. The chemical similarities between compounds were calculated based on their fingerprints by using the Single Linkage algorithm \\[[@R31]\\] while the disease similarities were defined as described in \\[[@R23]\\]. All the four approaches were evaluated with 5-fold cross-validations. Table [2](#T2){ref-type="table"} shows the performances of different methods, from which we can see that PINA has the highest AUC (0.8969) and F1 (0.3833) and significantly outperforms the other approaches. ###### The performances of different methods which were obtained with 5-fold cross-validation Method AUC Precision Recall F1 score ------------- ------------ ------------ ------------ ------------ *PIPP* 0.8515 0.1517 0.4899 0.2313 *NP*~*\\_C*~ 0.8132 0.0873 **0.6511** 0.1539 *NP*~*\\_D*~ 0.8633 0.3005 0.4760 0.3684 *PINA* **0.8969** **0.4325** 0.3446 **0.3833** *DrugNet* 0.8034 0.3411 0.3923 0.3568 *HGBI* 0.8125 0.3867 0.3639 0.3752 *NBI* 0.7983 0.3297 0.3321 0.3308 AUC - Area under ROC curve; Precision - TP/(TP+FP), positive predictive value; Recall - TP/(TP+FN), true positive rate; F1 score - Harmonic mean of precision and recall. Prediction of potential indications for LDW {#s2_3} ------------------------------------------- In this part, we further extended PINA to predict the novel indications of Traditional Chinese Medicines (TCMs) with Liuwei Dihuang Wan (LDW) as a case study. With the known compound-disease associations from the CTD database, we built a model as described in Equation [(4)](#eq004){ref-type="disp-formula"} and identified 59 diseases that LDW can be used for. Among the 156 compound components of LDW, only the eight compounds that can be found new indications with PINA were considered here, where the eight compounds were further required to be drug-like. Table [3](#T3){ref-type="table"} shows the detailed information about the eight compounds. By investigating the indications of the eight compounds obtained from CTD, we found that LDW, as a mixture of multiple compounds, achieves its therapeutic effects through its individual components. For example, LDW was used for anti-aging, delayed development and blurred vision, whereas Retinol, also known as vitamin A, plays an essential role in anti-aging, promoting bone growth and the treatment of various eye conditions. Moreover, it was found that LDW was useful for decreasing blood sugar, suppressing blood pressure and improving the renal function. Another compound component Quercetin, an antioxidant, was reported to treat many LDW associated disease, such as acute kidney injury, diabetes mellitus and hypertension. The combination of Nicotinamide and Retinol could be effective for acne treatment for which LDW has been used for \\[[@R32]\\]. ###### The detail information about eight compounds belonging to LDW Compound ID Name FDA Status Part of known indications obtained from CTD database ---------------- -------------- -------------- -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- CID000445354 Retinol Approved Acne Vulgaris; Acute Kidney Injury; Adrenal Insufficiency; Carcinoma, Hepatocellular; Colonic Neoplasms; Diabetes Mellitus, Type 1; Fatty Liver; Hypertension, Portal; Hypertriglyceridemia; Liver Cirrhosis; Nephrosis; CID000024360 Camptothecin Experimental Neoplasms; Leukemia, Lymphoid CID027237R1936 Nicotinamide Experimental Diabetes Mellitus, Type 2; Hypercholesterolemia; Hyperglycemia; Hyperlipoproteinemias; Hypertension; Hypertriglyceridemia; Kidney Diseases; Nerve Degeneration; Ventricular Dysfunction, Left; CID000006137 L-methionine Approved Carcinoma, Hepatocellular; Fatty Liver; Kidney Diseases; Memory Disorders; CID005280343 Quercetin Experimental Acute Kidney Injury; Autoimmune Diseases; Breast Neoplasms; Cognition Disorders; Diabetes Mellitus; Fatty Liver; Hypertension; Kidney Diseases; Memory Disorders; Ovarian Neoplasms; Prostatic Neoplasms; CID000005641 Urethane Withdrawn Arrhythmias, Cardiac; Hypertension; Liver Neoplasms; Ovarian Neoplasms; CID027237R1305 Choline Approved Amnesia; Cognition Disorders; Fatty Liver; Memory Disorders; CID027237R1681 Dopamine Approved Acute Kidney Injury; Arrhythmias, Cardiac; Central Nervous System Diseases; Heart Failure; Hypertension; Learning Disorders; Nerve Degeneration; Nervous System Diseases; Parkinson Disease; With the findings above, we assumed that the new indications we predicted for LDW can be validated with the indications of its component compounds. Figure [2](#F2){ref-type="fig"} shows a compound-disease association network constructed with the associations between diseases and compounds we have predicted, where the 59 diseases that LDW has been predicted to be used for were linked to the eight individual compounds based on PINA. Among the 104 compound-disease associations shown in Figure [2](#F2){ref-type="fig"}, 21 of them have been reported in CTD. For example, Quercetin could inhibit the growth of MCF-7 breast cancer cell line and promoted apoptosis by reducing G0/G1 phase arrest \\[[@R33], [@R34]\\]. Besides, it was widely accepted that the compound could be used to treat a certain disease if it targeted the disease related genes. With the known target and disease genes information, we also found there are another 27 predicted compound-disease associations which can be validated by sharing same genes. For instance, dopamine D2 receptor (DRD2) played an essential role in dopamine signaling which was strongly implicated in the etiology of schizophrenia (SZ) \\[[@R35]\\], and was also one of the targets of Dopamine. By targeting the gene DRD2, Dopamine may be used for schizophrenia. As a result, 48 compound-disease associations can be validated by difference evidence while the rest associations need further experimental validation. {#F2} By considering the indications (59 diseases) we predicted for LDW, we further investigated whether LDW has been reported to be effective for some of these diseases in literature by expert knowledge. As a result, 14 of them have been known to be associated with LDW as shown in [Supplementary Table 3](#SD4){ref-type="supplementary-material"}. For example, it was found that LDW could significantly inhibit the breast cancer tumor growth and progression, and promoted the recovery of breast ducts in mice \\[[@R36], [@R37]\\]. Likewise, LDW decoction could exert therapeutic effects on liver cancer in mice by affecting tumor cell cycle and down-regulate serum VEGF level \\[[@R38]\\]. Moreover, it was well accepted that LDW could counteract the adverse effect of steroid and immunosuppressive agents, significantly improving the therapeutic effectiveness in the treatment of Systemic Lupus Erythematosus (SLE) \\[[@R39]\\]. Besides, many other predicted diseases, i.e. diabetes mellitus, hypertension and so on \\[[@R40]--[@R43]\\], were also known to be associated with LDW. Previously, Li *et al* predicted new indications for LDW based on drug targets and disease genes \\[[@R17]\\]. We further investigated how many of our predictions could be validated by those reported in their work, and the new indications found by both works for LDW would be more convincing. Consequently, 7 of our predictions were also reported by Li *et al,* including atherosclerosis, retinoblastoma, rheumatoid arthritis, esophageal neoplasms, uterine cervical neoplasms, familial combined hyperlipidemia and panic disorder. For example, it was found that LDW had already been reported for treating esophageal neoplasms \\[[@R44]\\]. In addition, studies have shown that LDW pills could effectively inhibit the expression of IL-beta, MMP-1 and MMP-3, thus protecting and repairing the articular cartilage which had significant therapeutic effects on Osteoarthritis \\[[@R45]\\]. Moreover, we also performed text mining by querying the PubMed database to see whether LDW have been reported effective for the rest of our predictions. As a result, except the diseases mentioned above, 12 diseases have been reported to be treated by LDW in literature as listed in [Supplementary Table 3](#SD4){ref-type="supplementary-material"}. For instance, it was found that LDW could simultaneously disturb the regulations of apoptosis and protein ubiquitination among biological processes, such as RPS6KA1, FHIT and AMFR, which may be the therapeutic targets of Alzheimer Disease \\[[@R46], [@R47]\\]. Moreover, traditional Chinese doctors have already used LDW to treat asthma patients based on the cytokine gene expression perturbed by LDW \\[[@R48]\\]. Taken together, 33 out of 59 diseases we predicted to be treated by LDW have been validated in different ways, where the known indications with direct evidences tend to rank top. These results demonstrate that LDW can really work for those diseases. The detailed results with corresponding evidences were presented in [Supplementary Table 3](#SD4){ref-type="supplementary-material"}. DISCUSSION {#s3} ========== Repurposing old drugs has drawn increasing attention, since they could serve as the effective and cost-saving strategies for drug discovery. In this study, we first introduce pathway profiles associated with diseases and affected by compounds. By integrating the pathway profiles with chemical structure as well as disease phenotype, we present PINA to predict new indications of compounds. Benchmark results on FDA approved drugs have demonstrated the predictive power of PINA. We further extended PINA to predict the potential indications of traditional Chinese medicine with LDW as a case study. The new indications we predicted for LDW have been validated with expert knowledge and evidences from literature. We also noticed that improvement of our PINA approach is possible when predicting novel indications of TCMs. For example, a TCM formula is typically composed of multiple herbs or hundreds of chemical compounds. Here, the indications of a TCM formula were predicted with a Bayesian model, where the compound components were regarded to be independent with each other. Although the synergistic effects among compounds cannot be explicitly described in the Bayesian model, the good performance on LDW shows the effectiveness of the model. In the future, more efficient models should be developed to take into account the synergistic effects among compounds. Another concern is that many compound components of TCMs are not known while it is expensive and time-consuming to determine all bioactive compounds of TCMs, a comprehensive knowledgebase about compound components of TCMs is highly demanded. MATERIALS AND METHODS {#s4} ===================== Data sources {#s4_1} ------------ The FDA approved human drugs used in our study were retrieved from the DrugBank database (Version 4.3) \\[[@R49]\\], of which we only focused on the 932 compounds that had target information according to the DrugBank and STITCH databases (Version 4) \\[[@R50]\\] which provides a confidence score for each interaction. Here, a score of 700 was used as threshold to choose the high-confidence interactions \\[[@R51]\\]. Specifically, the interactions marked with prediction or text mining were removed to make sure high-quality interactions used in this paper. The LDW was composed of *Rehmannia glutinosa Libosch.*, *Cornus officinalis Sieb. et Zucc., Paeonia suffruticosa Andr., Dioscorea opposita Thunb., Poria cocos (Schw.) Wolf and Alisma orientalis (Sam.) Juzep.* In our work, the chemical constituents of LDW were mainly obtained from the TCM Database\\@Taiwan \\[[@R52]\\] by searching the herb names. Meanwhile, the other constituents were also collected manually from published articles by text mining. Then we transformed all constituents into mol2 format with ChemDraw software (<http://www.cambridgesoft.com/software/ChemDraw/>), and the chemicals were then converted into the canonical SMILES format. We downloaded all known chemicals with each of them annotated with PubChem identity from STITCH database (version 4.0). By querying the known compounds with the chemical SMILES files, the chemical constituents of LDW can be identified. Here, we only picked up the chemicals that had target information according to DrugBank and STITCH databases. Consequently, 156 compounds of LDW ([Supplementary Table 1](#SD2){ref-type="supplementary-material"}) were finally collected. The disease-gene associations were obtained from the Comparative Toxicogenomics Database (CTD) \\[[@R21]\\]. As a result, the associations between 4937 diseases and 8536 genes were collected. We further collected compound-disease associations from the CTD database, and the 4774 associations with direct evidence (therapeutic/maker) between 928 compounds and 608 diseases were used as the positive set while the other possible compound-disease associations were used as the negative set. All predefined biological pathways used in this study were obtained from the Molecular Signatures Database (Version 5.0) \\[[@R17]\\], where the canonical pathways from the curated (c2) gene sets were adopted. The physical protein-protein interactions were obtained from HPRD \\[[@R53]\\], BioGRID \\[[@R54]\\], IntAct \\[[@R55]\\], MINT \\[[@R56]\\] and DIP \\[[@R57]\\] databases. Predicting new indications of compounds with a network pharmacology approach {#s4_2} ---------------------------------------------------------------------------- ### Predicting indications of compounds based on pathway profile {#s4_2_1} We assumed that the occurrence of a disease was due to the aberrant functions of certain pathways. Accordingly, to treat a disease, the drugs should affect the dysfunctional pathways that were associated with the disease. With this assumption, for each drug and its related disease, the pathways linking the pair of drug and disease were firstly identified. For this, the pathway profiles associated with a drug and a disease were respectively identified, where the drug related pathways were enriched by its target proteins while the disease associated pathways were enriched by its related genes \\[[@R58]\\]. Given a pair of pathways respectively associated with a drug and a disease, we only considered the pathways that met one of the following conditions: (1) the two pathways are the same one (common pathway); (2) the two pathways share at least one gene (cross-talking pathways); (3) there are protein interactions between the two pathways (interacting pathways) (As shown in [Supplementary Figure 1](#SD1){ref-type="supplementary-material"}). To avoid possible false positives, the cross-talking or interacting pathways were required to have correlated activities based on the gene expression data obtained from 36 normal tissues \\[[@R59]\\]. Here, the pathway activity in a tissue was defined as the average expression value of all genes within the pathway and only the pathway pairs with a significant correlation coefficient (p-value \\<0.01) in 36 tissues were kept for further analysis. Here, the pathway profile method named PIPP (predicting indications based on pathways profile) were proposed. Given one disease and related drugs as well as the pathways associated with any pair of drug and disease as defined above, the score of a pathway pair associating a drug with the disease it could be used for was defined as follows:$$P\\left( {p_{i}\\_ D} \\right) = \\frac{N\\left( C \\middle| p_{i} \\right)}{N\\left( C^{\\prime} \\middle| D \\right)}$$where *N*(*C* \\| *p*~*i*~) is the number of compounds treating disease *D* and the pathway pair *p*~*i*~ is the one that occurs commonly between compound set C and the disease D, and *N*(*C*′ \\| *D*) is the number of all compounds used for disease *D*. If *P*(*p*~*i*~\\_*D*) is above a certain threshold, the pathway pair *p*~*i*~will be regarded as the pathway profiles for associating a disease with the drugs treating the disease. Given a new drug, the score of the drug used for treating the disease D can be defined as below:$$P\\left( {C_{i}\\_ D} \\right) = 1{\\sum\\limits_{m = 1}^{3}{\\alpha_{m}{\\prod\\left( {1 - P\\left( {p_{m}\\_ D} \\right)} \\right)}}}$$where *m* represents one of the three types of pathway profiles, i.e. common, cross-talking and interacting pathway(s), *P*(*p*~*m*~\\_*D*) is the score of the *m*th type of pathway profiles associated with disease *D,* and *α*~*m*~ is the weight for the *m*th type of pathway profiles. To determine the weights for the three types of pathway profiles, the 5-fold cross validation was employed and the AUC was used to choose the proper values. As a result, the weights in Equation [(2)](#eq002){ref-type="disp-formula"} were determined as: *α*~1~ = 0.5, *α*~2~ = 0.3, *α*~3~ = 0.2, where the best results were obtained. ### Predicting new indications of compounds based on the nearest neighbor profile {#s4_2_2} It has been found that similar drugs tend to have similar mechanism and can be used to treat similar diseases, and *vice versa* \\[[@R24]\\]. Therefore, given a new drug, the new indications of the drug can be predicted based on its similarity with other drugs. Here, the nearest neighbor profile approach proposed by Yamanishi *et al* \\[[@R26]\\], *i.e.* nearest profile based on chemical similarity and nearest profile based on disease similarity we named as NP\\_~C~ and NP\\_~D~, was adopted to predict whether a new drug could be used for a certain disease. The chemical similarity between compounds is calculated based on their fingerprints by using the Single Linkage algorithm \\[[@R31]\\]. The disease similarities are defined in \\[[@R23]\\], where the similarity was calculated based on disease descriptions from the OMIM database \\[[@R60]\\]. ### Predicting new indications of compounds based on an ensemble method {#s4_2_3} The three independent methods mentioned above, i.e. PIPP, NP~\\_C~ and NP~\\_D~, showed different performance on different datasets. Here, we further proposed an ensemble approach named PINA to predict the compound-disease associations by integrating the pathway profile, chemical similarity and disease similarity. In particular, a weight was set for each method based on its performance on a benchmark dataset, and the ensemble learner was constructed as follows:$$P\\left( {C\\_ D} \\right) = {\\sum\\limits_{i = 1}^{n}{W_{i} \\cdot M_{i}}}$$where *w*~*i*~ is the weight for each method, and *M*~*i*~ is the output of the *i*th method. Here, the weight for each method is set to the AUC (area under the curve) score of a receiver operating characteristic (ROC) curve. For a given compound, we can use the ensemble approach to predict whether the drug can be used for the disease. ### Predicting new indications of LDW {#s4_2_4} To evaluate the performance of our proposed approach, the PINA method was applied to infer the therapeutic indications of TCM and investigate the curative effect between TCM and its individual components. To this end, we chose the LDW as a case study since its chemical constituents and indications were well known. Subsequently, we proposed PINA to the 156 chemical constituents to predict compound-disease associations, where a score was calculated based on Equation [(3)](#eq003){ref-type="disp-formula"} as the confidence score of the prediction. To determine the threshold above which a prediction is regarded as positive, the 5-fold cross-validation was employed on the known drug-disease associations, i.e. training set. Especially, the threshold that can lead to the highest F1 score was chosen, where the F1 score can evaluate the overall performance of the learner and is a tradeoff between Precision and Recall. Here, the threshold of 0.6 that can lead to the highest F1 score in the cross-validation was chosen. Then we defined an efficacy score for LDW to a certain disease by considering the synergistic effect of all compounds based on Bayesian models. The efficacy score could be described as follows:$$P\\left( {LWDH\\_ D} \\right) = 1 - {\\prod\\limits_{C_{i} \\in LWDHW}\\left( {1 - P\\left( {C_{i}\\_ D} \\right)} \\right)}$$where *C*~*i*~ is the component of LDW. *P*(*C*~*i*~\\_*D*) is the association score between compound *C*~*i*~ and disease *D* calculated with Equation [(3)](#eq003){ref-type="disp-formula"}. SUPPLEMENTARY MATERIALS FIGURES AND TABLES {#s5} ========================================== **Author contributions** Y.Y.W. and X.M.Z. conceived and designed the study. Y.Y.W. and R.Z. conducted the data analysis. Y.Y.W. and K.N. drafted the manuscript. X.M.Z., H.Y. and H.B. revised the manuscript. All authors contributed to writing and finalizing the manuscript. **CONFLICTS OF INTEREST** The authors declare no conflicts of interest. **FUNDING** This work was partly supported by National Nature Science Foundation of China (61772368, 61572363, 91530321, 61602347, 81573702 and 31671374), Ministry of Science and Technology's high-tech (863) grant (2014AA021502), Sino-German Research Center grant (GZ878), and China Postdoctoral Science Foundation Funded Project (2016M601647), and City University of Hong Kong (Project 7004707). [^1]: These authors have contributed equally to this work

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Amy E. Keating We are studying the specificity of protein-protein interactions in a research program that combines bioinformatic analysis, structural modeling, computational design and experimental characterization. Our aim is to understand, at a high level of detail, how the interaction properties of proteins are encoded in their sequences and structures. Most of our work is focused on two protein families that are important for human health: the α-helical coiled coil and the Bcl-2 family of apoptosis-regulating proteins. Protein-protein interactions establish the architecture of the cell, regulate biological signaling, underlie the assembly of macromolecular machines and mediate chemical transformations. Although we now have fairly complete lists of the proteins found in various organisms, our knowledge of which proteins interact with one another, as well as how and why they interact as they do, is limited. In the Keating lab, we are particularly interested in the question of interaction specificity, i.e. how a protein selects a particular interaction partner out of a large number of closely related alternatives. Both computational and experimental methods are needed to accelerate discovery and understanding in this area. Our lab integrates both approaches, tackling the complex problems of characterizing, analyzing, designing and predicting protein-protein interaction specificity by studying domains with relatively simple structures. Three goals are: (1) to develop and apply techniques to assess the interaction specificity of biologically interesting protein families in vitro, (2) to achieve an understanding of how specificity is encoded biophysically, through the analysis of protein sequence and structure, and (3) to develop and test computational methods for predicting and designing specific protein-protein interactions. Coiled coils The α-helical coiled coil is the simplest of all protein-protein interaction motifs. Coiled coils consist of two or more α-helices that wrap around each other with a superhelical twist. They are characterized by a repeating sequence of seven amino acids, (abcdefg)n, in which the a- and d-position residues are predominantly hydrophobic and the e- and g-position residues are usually polar or charged. The regular sequence makes it possible to predict the occurrence of coiled coils in genomic sequence data. We estimate that >5% of all proteins in S. cerevisiae, C. elegans,A. thaliana and D. melanogaster contain a coiled-coil region. It is likely that many of these coiled coils mediate protein-protein interactions or oligomerization. An important, unanswered question about coiled coils is how their interaction specificity is encoded in their sequences. We call this the “partnering problem” for coiled coils and are studying it using both computational and experimental approaches. Our experimental approach to the partnering problem started with an analysis of human bZIP transcription factor interactions. In these proteins, the coiled-coil region determines the homo- or heterodimerization specificity of the transcription factor, which in turn influences its DNA-binding properties and biological function. To determine how sequence encodes interaction preferences in the bZIPs, we used protein microarray technology to measure all of the pair-wise interactions between 48 human and 10 yeast bZIP peptides. We found that the interactions are very specific, and that interaction profiles are largely, but not universally, conserved within bZIP subfamilies. This work established the protein microarray as a powerful method for generating large amounts of high quality interaction specificity data. We continue to develop techniques that can increase the throughput and improve the reliability of protein-protein interaction measurements. In addition to providing a wealth of data about important transcription factor interactions, the bZIP microarray data provided an opportunity to test and improve computational models. We have used this information to develop and/or test several different methods for predicting coiled-coil interactions. A machine-learning algorithm trained on the literature shows excellent performance in detecting correct bZIP pairings. We have also used structure-based methods for prediction. Because the coiled coil has a very simple structure, it is particularly amenable to molecular modeling. We have shown that structural modeling can be used in conjunction with learning models to provide good predictions of bZIP coiled-coil interactions. We are now applying structure-based methods more broadly to the problem of predicting interaction specificity, with recent work focused on predicting parallel vs antiparallel helix orientation preferences. Another way to understand factors that mediate protein association is through the process of design. The field of protein design has seen exciting advances in the past ten years with the application of fast search algorithms to the problem of side-chain selection and positioning. This has allowed the design of proteins with new folds and functions. We are applying methods developed for the computational design of stable protein folds to the study of protein interaction specificity. In one study we designed and characterized a mini-protein heterotetramer in collaboration with Barbara Imperiali’s group at MIT. More recently, we have designed coiled-coil peptides that bind specifically to native bZIP transcription factor targets, and validated these using the protein microarray assay. Designed coiled coils could not only serve as research tools for probing the cell and disrupting native interactions, but also hold significant promise for applications in the emerging area of synthetic biology. Bcl-2 family proteins The Bcl-2 family comprises ~25 proteins important for controlling apoptosis. Critical junctures that govern cellular life-vs-death decisions are regulated by specific interactions among pro- and anti-apoptotic members of this family. The delicate balance between these is often disrupted in cancers. Five mammalian anti-apoptotic family members have a conserved structure with a surface binding cleft, and all known family members share a weakly conserved short BH3 (Bcl-2 homology 3) sequence. Peptides corresponding to the BH3 region have been shown in several instances to bind as alpha helices into the hydrophobic groove on the surface of the anti-apoptotic proteins (see figure). We are interested in how the interaction specificity of Bcl-2 family proteins is determined by sequence and structure and are exploring this using x-ray crystallography, mutational analysis, selection experiments and computational protein design. Using new computational methods for varying the backbone structure of α-helices, we designed several novel ligands to bind the anti-apoptotic protein Bcl-xL. Solution binding studies confirm that many of these designed peptides bind with low- to mid- nanomolar affinity and have specificity profiles that differ from those of known native BH3s. More recently we have solved crystal structures that provide additional insights into the structural plasticity of Bcl-2 complexes, and we have selected BH3 peptides with novel sequences and specific binding behaviors out of libraries. Computational methodology We apply a wide range of computational tools to the analysis of protein interactions, including structure-based modeling, sequence analysis and machine learning. Some projects in the lab are focused on developing or improving computational methods, and a recent exciting advance was our collaboration with the Ceder group (MIT Materials Science) to adapt the technique of cluster expansion for use in protein modeling. Cluster expansion allows the energy of a protein folded into a certain structure to be expressed directly as a function of sequence. The approach brings dramatic speed-ups to modeling calculations while retaining many of the benefits of physical, structure-based approaches. We have also explored many methodological aspects of computational protein design (including the use of cluster expansion in design).

The invention relates to an apparatus for detecting objects formed by labels on a carrier material, and sheets, particularly sheets of paper. An apparatus of this type is known from German Patent DE-PS 195 21 129. This apparatus includes a capacitive sensor having two adjacent capacitor elements, which are spaced from one another opposite a capacitor plate. The carrier material with the labels is guided in the air gap between the capacitor plate and the capacitor elements. For detecting the labels on the carrier material, a timing element that generates a pulse sequence and a low-pass filter are disposed downstream of each capacitor element. The outputs of the low-pass filters are guided to the inputs of a differential amplifier. This circuit can detect labels on the carrier material, even if the labels and the carrier material comprise transparent materials. A disadvantage, however, is that such apparatuses are extremely sensitive to temperature influences, and humidity in particular. They also encounter difficulties in detecting metallized materials. Furthermore, the two capacitor elements can only detect the signal flanks occurring in the detection of a label edge. A prerequisite of this is that the labels and the carrier material be moved past the capacitor elements at a predetermined speed. Static detection with a stationary carrier material is not possible. A further drawback is that a reliable label detection is only possible if the label edges travel along a straight line transverse to the transport direction of the carrier material, so that an at least approximately constant spacing between adjacent labels must be maintained over the label width.

U NITED S TATES AIR F ORCE C OURT OF C RIMINAL APPEALS ________________________ No. ACM S32554 ________________________ UNITED STATES Appellee v. Eric R. PROCTOR Technical Sergeant (E-6), U.S. Air Force, Appellant ________________________ Appeal from the United States Air Force Trial Judiciary Decided 4 June 2020 ________________________ Military Judge: Christina M. Jimenez. Approved sentence: Bad-conduct discharge and reduction to E-3. Sen- tence adjudged 24 August 2018 by SpCM convened at Schriever Air Force Base, Colorado. For Appellant: Major David A. Schiavone, USAF. For Appellee: Lieutenant Colonel Joseph J. Kubler, USAF; Lieutenant Colonel Brian C. Mason, USAF; Major Jessica L. Delaney, USAF; Mary Ellen Payne, Esquire. Before J. JOHNSON, POSCH, and KEY, Appellate Military Judges. Judge POSCH delivered the opinion of the court, in which Chief Judge J. JOHNSON and Judge KEY joined. ________________________ This is an unpublished opinion and, as such, does not serve as precedent under AFCCA Rule of Practice and Procedure 30.4. ________________________ POSCH, Judge: A special court-martial composed of officer and enlisted members found Ap- pellant guilty, contrary to his pleas, of six specifications of willfully disobeying a lawful command from his squadron commander, one specification of assault  United States v. Proctor, No. ACM S32554 consummated by a battery, and one specification of wrongfully communicating a threat, in violation of Articles 90, 128, and 134, Uniform Code of Military Justice (UCMJ), 10 U.S.C. §§ 890, 928, 934. 1 Appellant was sentenced to a bad- conduct discharge, hard labor without confinement for three months, and re- duction to the grade of E-3. The convening authority approved the bad-conduct discharge and the reduction in grade, and disapproved the hard labor without confinement. Appellant raises four issues on appeal: (1) whether the military judge erred when she found six no-contact orders to be lawful; (2) whether the military judge erred in denying Appellant’s request for an instruction on self-defense to the assault consummated by a battery offense; (3) whether the military judge’s failure to sua sponte instruct on defense of property as a defense to the assault consummated by a battery offense was plain error; and (4) whether there was evidence of unlawful command influence (UCI) when Appellant’s commander held a commander’s call to address his squadron’s noncommissioned officer (NCO) “problem” just over one year before Appellant’s court-martial. We find no prejudicial error and affirm. I. BACKGROUND Appellant’s convictions are the result of his conduct with Airmen who were assigned with Appellant to the security forces squadron at Schriever Air Force Base, Colorado, to include interactions he had with his girlfriend, Staff Ser- geant (SSgt) CM. Appellant, his three children, and SSgt CM shared an off-base apartment in Colorado Springs, Colorado. On Thanksgiving Day in 2016, SSgt CM invited SSgt AG and junior Airmen assigned to her flight to celebrate the holiday in her home. Appellant returned to the apartment after his shift and drove out the Airmen, angry that guests were in his home. While doing so, Appellant strangled SSgt AG by grabbing his throat with Appellant’s hand after SSgt AG came to the defense of an Airman whose presence Appellant found especially provoking. In a second incident, in December 2016, after SSgt CM and Appel- lant separately returned home from a squadron Christmas party, SSgt CM came towards Appellant with a knife and Appellant responded by drawing a gun before the incident deescalated. 1 All references in this opinion to the Uniform Code of Military Justice (UCMJ), Rules for Courts-Martial (R.C.M.), and Military Rules of Evidence are to the Manual for Courts-Martial, United States (MCM) (2016 ed.). 2  United States v. Proctor, No. ACM S32554 Appellant’s commander, Lieutenant Colonel (Lt Col) MS, was unaware of Appellant’s conduct on Thanksgiving and after his squadron’s Christmas party when he issued Appellant an order to refrain from having any contact or com- munication with SSgt CM. 2 That first no-contact order was given in February 2017 after Lt Col MS received a report from his NCOs that Appellant had strangled SSgt CM in their apartment and threatened to kill her. In time, Lt Col MS issued an additional six commands in succession, continuing his or- der that Appellant refrain from communicating and having contact with SSgt CM when a preceding order was about to expire. Appellant willfully disobeyed each of the six orders, including during the time that Lt Col MS had ordered Appellant into pretrial confinement, and after Appellant’s release from pretrial confinement over a year before trial. II. DISCUSSION A. Legality of the No-Contact Orders The Government charged Appellant with disobeying the six orders, and grouped the violations under six specifications, one for each order it alleged Appellant disobeyed. At trial, Appellant challenged the six orders claiming they did not serve a valid military purpose and were thus unlawful. The mili- tary judge found the orders were lawful and issued a written ruling denying Appellant’s motion to dismiss the six specifications. 3 Appellant renews his challenge in this appeal. 1. Additional Background In February 2017, SSgt CM contacted her supervisor because she and Ap- pellant were in a physical altercation and she needed help. Her supervisor and first sergeant, both senior NCOs, responded to the shared residence and ob- served Appellant was emotionally distraught. SSgt CM reported Appellant had strangled her and she had scratched Appellant’s face trying to get away. She further stated Appellant had threatened to kill her. Civilian law enforcement personnel were called to respond to the incident, but neither Appellant nor SSgt CM were willing to cooperate with the police. On 21 February 2017, their squadron commander, Lt Col MS, issued no-contact orders to both Appellant 2Lt Col MS issued a reciprocal order and subsequent orders to SSgt CM to refrain from all communication and contact with Appellant. 3Appellant was convicted of violating six orders issued on 22 March 2017, 19 May 2017, 19 June 2017, 1 August 2017, 31 August 2017, and 22 September 2017. 3  United States v. Proctor, No. ACM S32554 and SSgt CM. Appellant’s order expired on 7 March 20174 and was not con- tested at trial or on appeal. After the order expired, on 18 March 2017 local police responded to Appel- lant’s residence in response to an allegation that Appellant had choked or beaten SSgt CM’s nine-week-old puppy after she left for work. Lt Col MS was briefed on the incident by the NCOs and then spoke with SSgt CM. She related the February incident was “not the first time [Appellant] put his hands on [her]” and she “can’t count how many times that [Appellant] choked [her] out until [her] eyes were blood red.” Lt Col MS recalled seeing SSgt CM on duty and observing her eyes were unusually red, which at the time she attributed to a sneeze. 5 On 22 March 2017, Lt Col MS issued a second order to Appellant command- ing him to have no communication or contact with SSgt CM for two months. He based his decision to issue this and subsequent orders on his years of lis- tening to victims of domestic violence, concluding that SSgt CM was caught in a cycle of violence and Appellant would “harm things that are precious to [her]” such as her puppy. Lt Col MS saw a pattern whereby neither NCO was willing to cooperate with civilian police, and the harm done to SSgt CM’s puppy showed an “escalation of the domestic violence” in their relationship “and it’s just going to get worse.” Lt Col MS explained he issued the order for SSgt CM’s protection and for good order and discipline, noting he was aware of “two vio- lent interactions that are happening in [his] unit by two people that are sup- posed to be NCOs leading [his] [A]irmen.” Before the second no-contact order was set to expire on 22 May 2017, Lt Col MS learned Appellant posted a message on Facebook, sometime between 10 and 21 May 2017, that read: What ether should I drop first? Shots Fired or Officer Down? Once them shi[*]s drop then I’ll go ahead and drop that joint I got . . . . Had to kick Lee Lee out for flaugin and workin for 12. Appellant’s friend, SSgt JP, who was also a member of the squadron, saw Ap- pellant’s Facebook post and responded, “some mofos only got a few hours left” followed by an image of three skulls. After SSgt JP’s post, Appellant responded indicating he “liked” SSgt JP’s post via Facebook. 4Lt Col MS testified he allowed the order to expire because “there was no police action being taken downtown” or “other incidents of violence,” and he learned from NCOs in the squadron that Appellant and SSgt CM “were working through their situation.” 5 Lt Col MS acknowledged in his testimony that after he met with SSgt CM in regard to the puppy incident he had “seen her come to work with burst capillaries in her eyes.” 4  United States v. Proctor, No. ACM S32554 Lt Col MS did not initially understand Appellant’s Facebook post, but found it unusual that a security forces NCO would post “Shots Fired,” and “Officer Down.” He soon learned “Lee Lee” was the nickname for Mr. LA, a former Air- man and one-time friend of Appellant who was married to an NCO in his squadron. Lt Col MS was aware that Mr. LA, his wife, and several members of the squadron had written statements that were used as evidence in nonjudicial punishment proceedings alleging that Appellant had violated the second no- contact order. 6 Lt Col MS learned “flaugin” was slang for lying or snitching, and “workin for the 12” meant working for the police. Mr. LA’s wife understood “Shots Fired” and “Officer Down” as “referring to [her] husband” who was a civilian member of law enforcement. Mr. LA considered the posts to be a threat directed at him and was concerned to the point that he retrieved and loaded his gun and then stayed up late in the event that Appellant or someone on Appellant’s behalf might act on the threat. Lt Col MS understood the Facebook post as an escalation of threats towards members of his squadron for cooperating and making statements against Ap- pellant. On 19 May 2017, Lt Col MS continued the no-contact order and ex- panded its scope to include additional personnel. 7 Lt Col MS was concerned Appellant “would reach out to intimidate, threat[en] or harass either [SSgt CM] or any of these people if [Lt Col MS] didn’t have a no-contact order in place.” Around the same time he issued the expanded order, he learned of other allegations of violent acts that Appellant had committed against SSgt CM and threats Appellant made against others. This included the allegation of violence on Thanksgiving and that SSgt CM pulled a knife on Appellant and Appellant in turn pulled a gun on her after the squadron’s Christmas party. Lt Col MS had also heard that Appellant had made threats to “go after” members of the squadron who had made statements against Appellant. Lt Col MS continued the series of no-contact orders until Appellant’s legal proceedings concluded. 8 Lt Col MS testified he issued the orders because of the ongoing court-martial proceedings and to protect SSgt CM because “their toxic, 6Before the Facebook post, on 10 May 2017, Lt Col MS offered nonjudicial punishment to Appellant under Article 15, UCMJ, 10 U.S.C. § 815, for allegedly violating the sec- ond no-contact order on divers occasions. Appellant declined nonjudicial punishment and demanded trial by court-martial. 7Lt Col MS expanded the order to include ten named individuals for the preservation of good order and discipline of his unit. 8 Lt Col MS preferred the original charges on 7 June 2017. Although those charges were subsequently withdrawn and dismissed by the convening authority on 1 August 2017, he preferred charges anew on 14 August 2017; an additional charge was pre- ferred on 28 September 2017, and a second additional charge was preferred on 6 No- vember 2017. 5  United States v. Proctor, No. ACM S32554 violent relationship was affecting the good order and discipline in the unit.” Among the considerations in reissuing the orders was that Lt Col MS became aware of a reason SSgt CM gave to co-workers for continuing to violate recip- rocal orders he gave to SSgt CM to refrain from all communication and contact with Appellant. SSgt CM told others she felt that she had no choice but to vio- late Lt Col MS’s orders: “I have to stay with [Appellant]. I have to violate the orders, because my life is more important.” Lt Col MS believed that continuing the reciprocal orders would mitigate the violence in their relationship. Appellant acknowledged receipt and understanding of each order. 2. Law We review de novo the lawfulness of a military order. United States v. New, 55 M.J. 95, 106 (C.A.A.F. 2001) (citation omitted). The critical “attributes of a lawful order include: (1) issuance by competent authority—a person authorized by applicable law to give such an order; (2) communication of words that ex- press a specific mandate to do or not do a specific act; and (3) relationship of the mandate to a military duty.” United States v. Deisher, 61 M.J. 313, 317 (C.A.A.F. 2005) (citations omitted). Orders are presumed to be lawful, and an appellant bears the burden of demonstrating otherwise. New, 55 M.J. at 106 (citation omitted); United States v. Hughley, 46 M.J. 152, 154 (C.A.A.F. 1997) (citations omitted). Thus, “a sub- ordinate disobeys an order at his own peril,” though they may challenge the lawfulness of the order when it is given or in later proceedings. United States v. Kisala, 64 M.J. 50, 52 (C.A.A.F. 2006) (footnotes omitted). Our evaluation of the lawfulness of an order includes consideration of the criteria from the Man- ual for Courts-Martial, United States (2016 ed.) (MCM), pt. IV, ¶ 14.c.(2)(a)(iv), which states as follows: Relationship to military duty. The order must relate to military duty, which includes all activities reasonably necessary to ac- complish a military mission, or safeguard or promote the morale, discipline, and usefulness of members of a command and directly connected with the maintenance of good order in the service. The order may not, without such a valid military purpose, interfere with private rights or personal affairs. However, the dictates of a person’s conscience, religion, or personal philosophy cannot justify or excuse the disobedience of an otherwise lawful order. Disobedience of an order which has for its sole object the attain- ment of some private end, or which is given for the sole purpose of increasing the penalty for an offense which it is expected the accused may commit, is not punishable under this article. 6  United States v. Proctor, No. ACM S32554 To be presumed lawful, an order must also be clear, specific, and narrowly drawn. United States v. Moore, 58 M.J. 466, 468 (C.A.A.F. 2003) (citing United States v. Womack, 29 M.J. 88, 90 (C.M.A. 1989)). 3. Analysis At the outset, we reject Appellant’s assertion at trial that Lt Col MS was without authority to issue the six no-contact orders Appellant was convicted of violating without first obtaining Appellant’s and SSgt CM’s consent. 9 We find no authority for this assertion and Appellant cites none. So long as a com- mander relies on a “valid military purpose” in issuing an unambiguous no-con- tact order that is narrowly drawn, any consequential “interfere[nce] with pri- vate rights or personal affairs” is nonetheless lawful without more. MCM, pt. IV, ¶ 14.c.(2)(a)(iv); see also Moore, 58 M.J. at 467–68. On appeal, Appellant does not contest whether the six orders were issued by a competent authority or if they were sufficiently clear, specific, or narrowly drawn, see Moore, 58 M.J. at 468 (citing Womack, 29 M.J. at 90). Rather, Ap- pellant claims the orders served no valid military purpose because Lt Col MS’s justification for issuing the orders was inadequate. To this end, Appellant gives three bases for challenging lawfulness: (1) the orders appear to have been based on Lt Col MS’s dislike for the relationship between Appellant and SSgt CM, and a paternalistic belief that he knew what was best for SSgt CM; (2) “assuming arguendo that the altercation in February was a sufficient military purpose to justify the initial no-contact order, that justification dissipated quickly. Lt Col MS could point to no other acts of violence between Appellant and SSgt CM that occurred after February 2017;” and (3) the only purpose of the orders was to enhance Appellant’s punitive exposure. We consider each contention in turn including an examination of “the conduct at issue.” United States v. Padgett, 48 M.J. 273, 278 (C.A.A.F. 1998) (citing Womack, 29 M.J. at 91); see generally Moore, 58 M.J. at 468 (focusing on the “specific conduct at issue in the context of the purposes and language of the order”). As to Appellant’s first contention, Lt Col MS’s orders directed Appellant not to contact, communicate, or interact in any way with SSgt CM. As found by the military judge, each order “was thought out and thoughtful as to pur- pose and its parameters.” The military judge also found that Lt Col MS sought to ensure that Appellant did not tamper with or improperly influence SSgt CM, and thus the orders were “connected or related to military duty.” We find the 9The military judge asked defense counsel if it was “the [D]efense’s position that the commander was required to ask [Appellant] and/or [SSgt CM] whether or not they wanted a no-contact order?” Defense counsel replied it was “[i]f he’s going to interfere with their personal rights.” 7  United States v. Proctor, No. ACM S32554 military judge’s factfinding was not clearly erroneous. Thus, we decline to ac- cept Appellant’s contrary assertions that Lt Col MS’s purpose in issuing the orders was his dislike of Appellant’s relationship with SSgt CM or Lt Col MS being unduly protective of what he thought was in SSgt CM’s best interests. Lt Col MS was clear that it was not the relationship he disapproved of; rather, “[w]hat [he] disapprove[d] of [wa]s the violence in their relationship” and he “never interfered with their relationship . . . until [he] . . . was made aware of violence.” The evidence of record demonstrates Lt Col MS genuinely sought to prevent harm to SSgt CM and issued the series of orders to protect her safety, 10 see Padgett, 48 M.J. at 278 (upholding order intended to protect individuals from servicemember), as well as for the good order and discipline of his unit. He also sought to safeguard the ongoing investigation of Appellant. See United States v. Nieves, 44 M.J. 96, 99 (C.A.A.F. 1996) (citation omitted) (declining to find an order prohibiting discussions with witnesses unlawful, in part because there was “no evidence that appellant ever requested permission to interview [a wit- ness] or that such permission was denied”). Lt Col MS stated that he had a concern about Appellant contacting witnesses to threaten them or to influence their testimony. This was a valid concern, and was also related to Lt Col MS’s duty to maintain good order and discipline in his unit. As to Appellant’s second contention, Lt Col MS believed the no-contact or- ders reduced the level of violence between Appellant and SSgt CM even as he suspected Appellant of violating his orders. He also continued the orders, ex- panding them to apply to other named individuals, out of concern that Appel- lant would contact SSgt CM and witnesses to threaten them or influence their testimony. As the investigation of Appellant proceeded, Lt Col MS’s reasons for issuing the orders did not diminish. Under the circumstances, we conclude the commander possessed a valid military purpose for issuing the series of no- contact orders. Lastly, we reject Appellant’s third contention—that the only purpose of the orders was to enhance Appellant’s punitive exposure because contacting wit- nesses to influence an investigation is already prohibited by the UCMJ—as contrary to the military judge’s findings of fact. We recognize the “ultimate offense doctrine” prohibits “the escalation in severity of minor offenses ‘by charging them as violations of orders or the willful disobedience of superiors.’” United States v. Phillips, 74 M.J. 20, 22 (C.A.A.F. 2015) (quoting United States v. Hargrove, 51 M.J. 408, 409 (C.A.A.F. 1999)). Our superior court has similarly 10Lt Col MS explained there were “many reasons for the no-contact orders,” “[o]ne of them to protect [SSgt CM].” One of the commander’s concerns he related to SSgt CM early on was that he “d[id]n’t want to have a funeral in [his] unit.” 8  United States v. Proctor, No. ACM S32554 interpreted this doctrine to prohibit commanders from ordering a member to “follow the law” and to then punish the member for both the underlying crim- inal offense and the failure to follow the order. See Padgett, 48 M.J. at 278. However, Appellant was not charged with both obstruction of justice and the violation of a no-contact order. Thus, we find no reason to conclude that Lt Col MS issued no-contact orders to increase Appellant’s punitive exposure. B. Self-Defense and Defense of Property Appellant contends the military judge erred by failing to consider the pos- sibility that Appellant acted in self-defense and that the evidence raised de- fense of property when Appellant committed the offense of assault consum- mated by a battery against SSgt AG. 11 Appellant claims the military judge was required to instruct on self-defense because there was evidence Appellant’s contact with SSgt AG was a response to SSgt AG’s use of force against Appel- lant. Appellant also claims the military judge was required to instruct, sua sponte, on defense of property because there was evidence the conduct in issue was a result of Appellant’s attempt to lawfully remove trespassers from his home. 1. Additional Background a. Thanksgiving Day SSgt CM shared an off-base residence with Appellant and his children. In November of 2016, SSgt CM invited Airmen from her flight to her home for Thanksgiving dinner. Among the invited guests were SSgt AG, Senior Airman (SrA) JT, and SrA KJ, who testified at trial about an incident between Appel- lant and SSgt AG after dinner. Appellant was working a swing shift and was not at the apartment when guests arrived. When Appellant returned home at around 2300 hours, he changed his clothes and, according to SSgt AG, told her guests to “get the hell out of my crib.” Appellant turned off the music and eve- ryone began to leave. Appellant began cursing the Airmen, calling them “pu[**]ies,” and claiming “you guys are just waiting to f[**]k my girl,” in refer- ence to SSgt CM. SSgt AG testified he saw a “glare come across [Appellant’s] face” the mo- ment Appellant entered the residence. Appellant aired “frustration” that oth- ers were in his home, and his voice was loud enough to “mean[ ] business.” As others were making their way out, SSgt AG stayed back because he was one of the more senior-ranking Airmen and he wanted to make sure all of the other guests left first, including one of his troops, SrA JT, who was standing “right by the doorway.” As SrA JT was “about to leave” by crossing “the door seal or As charged in Specification 2 of Charge II, Appellant did “unlawfully strangle [SSgt 11 AG] by grabbing his throat with his hand.” 9  United States v. Proctor, No. ACM S32554 the doorway,” Appellant was yelling at SrA JT and “went charging right after him” with a movement that SSgt AG described “was like a really brisk walk in [SrA JT’s] direction,” and Appellant’s “hands were up” in the air. SSgt AG “stepped in between the two of them” and “was able to cut [Appellant] off right by the doorway.” SSgt AG intervened to prevent a fight as he knew there was a long history of “bad blood” between Appellant and SrA JT. SSgt AG further testified that as soon as he was between the two, Appel- lant’s “right hand immediately went straight toward [SSgt AG’s] throat and [Appellant’s] left hand went towards [SSgt AG’s] right arm to try and move [SSgt AG] out of the way.” Appellant’s grip on his throat “started getting tighter and tighter” as SSgt AG told Appellant to “relax” and “let go.” Appel- lant’s children were by the door and pleaded with Appellant to stop. SSgt AG stayed between Appellant and SrA JT, but as Appellant’s grip got tighter it was harder for him to breathe, and he knew he was “going to pass out” if he did not push back. He “decided to keep trying to push [Appellant] back into the household,” and as soon as he did, Appellant’s focus changed from SrA JT to SSgt CM, and Appellant let go of SSgt AG’s throat. SSgt AG departed after SrA JT and was the last guest to leave. SrA JT 12 testified the Thanksgiving dinner party was a “family” setting that ended the moment Appellant arrived home from his shift. While Appellant and SSgt CM spoke in private, the guests looked at each other and asked if anyone knew “[w]hat’s going on?” They wondered if they had offended Appel- lant and did not know what to do. Eventually, Appellant came out of a room and told SrA JT to “get the F out of [Appellant’s] house.” SrA JT understood the demand was addressed to him personally, but all of the flight members began leaving as SrA JT put on his hat and started making his way to the door. Appellant followed and SrA JT was “[r]ight outside the doorway” when he saw SSgt AG and a second guest “kind of holding [Appellant] back, stopping [Ap- pellant] from coming towards” SrA JT who at that point was “already outside.” SrA JT observed Appellant flailing his left arm “up and down” but did not ob- serve Appellant choking SSgt AG. Lastly, SrA KJ testified. She was among seven or eight Airmen from her flight whom SSgt CM invited to Thanksgiving dinner. SrA KJ was standing on a balcony outside the living area when Appellant arrived home. When she came back inside she noticed the mood of the party had changed for the worse. Ap- pellant and SrA JT “started arguing with each other” and “the situation got kind of heated, and everyone started to walk out.” Appellant was “looking di- rectly at” SrA JT, using profanity, and speaking in an angry tone of voice. SrA 12 SrA JT had separated from the military when he testified. 10  United States v. Proctor, No. ACM S32554 KJ was one of the first to leave. SrA JT “was walking out as well” when Appel- lant “charged toward” SrA JT with his hands raised. She observed SSgt AG get between Appellant and SrA JT to try to calm Appellant down and prevent harm to SrA JT and further escalation of the situation. From her vantage of about 20 to 30 feet outside the residence she looked back and saw SSgt AG holding back Appellant and the contact she witnessed lasted a matter of sec- onds. She did not see Appellant choking SSgt AG, but heard SSgt AG repeating in disbelief, “I can’t believe [Appellant] choked me. [Appellant] choked me.” b. Trial The evidence at trial did not touch on Appellant’s and SSgt CM’s property rights or, more generally, their respective legal interests in the residence they shared on Thanksgiving Day in 2016 when Appellant cast out SSgt CM’s guests. There was no testimony as to any verbal agreement, custom, or practice about the presence of guests in their home. However, in her trial testimony about violating their commander’s no-contact orders by remaining in the same residence four months later, on 22 March 2016, SSgt CM explained “[w]e both had our names on the lease, [and] it was both of our apartment.” Lt Col MS testified in findings that he was aware their lease expired on or about June 2017, but his testimony did not address when the lease began, its terms, or who was bound by the lease contract on Thanksgiving in 2016. 13 After the close of evidence, the military judge held an Article 39(a), UCMJ, 10 U.S.C. § 839(a), session with the parties and listed instructions she thought were raised by the evidence. The military judge acknowledged “there has been a great deal of discussion as to self-defense,” but defense of property was not among the instructions she identified. The military judge asked counsel for both parties if they had “[a]ny objections right now to those [instructions] as outlined,” noting counsel would have an opportunity to read her proposed in- structions and make objections later. Defense counsel replied, “Not at this time, Your Honor.” Later in the session the military judge asked counsel for both parties if there were “[a]ny other instructions” they wanted. Defense coun- sel mentioned only an unrelated instruction that no adverse inference should be drawn from Appellant’s pretrial confinement status when he was alleged to have violated one of the orders. After a short discussion, the military judge asked if there were “[a]ny additional special instructions, Defense Counsel?” who replied, “Not at this moment, Your Honor, thank you.” 13Although not admitted in findings, pages of a lease contract were included as attach- ments to Appellate Exhibits III and IV. The lease identified both SSgt CM and Appel- lant as tenants for the term 25 June 2016 through 25 June 2017. 11  United States v. Proctor, No. ACM S32554 Before instructing the members, counsel for both parties reviewed the mil- itary judge’s proposed instructions in another Article 39(a), UCMJ, session. Defense counsel asked for an instruction on “self-defense of others” that im- pacted a specification for which Appellant would be acquitted, but did not raise defense of property to the specification at issue. At the end of the session, the military judge asked, “Anything else, Defense?” and the defense counsel re- plied, “Nothing additional, Your Honor.” At the end of the session after a brief discussion about answering a member’s question, the military judge asked if there was “[a]nything else we need to take up in this [Article] 39(a), [UCMJ, session],” and defense counsel replied, “No, Your Honor.” After the military judge instructed the members on the law, and prior to argument, defense counsel asked for an Article 39(a), UCMJ, session and the members left the courtroom. During the session, and for the first time on the record, the Defense requested the military judge instruct on self-defense for the Thanksgiving incident; however, the Defense did not also request a defense of property instruction. The military judge denied the request for the self-de- fense instruction, the members were seated, and counsel for both parties pre- sented argument. At the conclusion of argument, the military judge instructed the members on the procedural rules for their deliberations and voting, and then asked whether “[c]ounsel object to the instructions given or request additional [in- struction]?” Defense counsel replied, “No, Your Honor.” The military judge re- cessed the court for the evening. The next morning, the military judge gave a copy of her instructions to each member and closed the court for deliberations and voting on findings. 2. Law “Whether a panel was properly instructed is a question of law reviewed de novo.” United States v. Medina, 69 M.J. 462, 465 (C.A.A.F. 2011) (citation omit- ted). “A military judge must instruct members on any affirmative defense that is ‘in issue.’” United States v. Schumacher, 70 M.J. 387, 389 (C.A.A.F. 2011) (quoting Rule for Courts-Martial (R.C.M.) 920(e)(3)). An affirmative defense is “‘in issue’ when ‘some evidence, without regard to its source or credibility, has been admitted upon which members might rely if they chose.’” Id. (quoting United States v. Lewis, 65 M.J. 85, 87 (C.A.A.F. 2007)). The Schumacher court explained “‘some evidence’ entitling an accused to an instruction, has not been presented until ‘there exists evidence sufficient for a reasonable jury to find in [the accused’s] favor.’” 70 M.J. at 389 (quoting Mathews v. United States, 485 U.S. 58, 63 (1988)). 12  United States v. Proctor, No. ACM S32554 a. Self-Defense Self-defense is an affirmative defense to a charge of assault consummated by a battery, see generally R.C.M. 916(a) and Discussion, and has two elements. First, the accused must have “[a]pprehended, upon reasonable grounds, that bodily harm was about to be inflicted wrongfully on” him; and second, the ac- cused must have believed that the force used was “necessary for protection against bodily harm” and “that the force used by the accused was less than force reasonably likely to produce death or grievous bodily harm.” See R.C.M. 916(e)(3); see also United States v. Yanger, 67 M.J. 56, 57 (C.A.A.F. 2008). Be- cause the defense involves more than one element of proof, the record must contain some evidence upon which members could reasonably rely to find each element before the military judge is required to instruct the members on it. Schumacher, 70 M.J. at 389–90. The right to self-defense is not available to an accused who “was an aggres- sor, engaged in mutual combat, or provoked the attack which gave rise to the apprehension, unless the accused had withdrawn in good faith after the ag- gression, combat, or provocation and before the offense alleged occurred.” R.C.M. 916(e)(4). However, an accused who starts an affray is entitled to use reasonable force in self-defense to defend against an opponent who escalates the level of the conflict. United States v. Dearing, 63 M.J. 478, 484 n.24 (C.A.A.F. 2006) (citations omitted). b. Defense of Property Defense of property is also an affirmative defense to a charge of assault consummated by a battery, although “it is more accurate to refer to defense of property as a ‘special defense,’ and that the prosecution continuously bears ‘the burden of proving beyond a reasonable doubt that the defense did not exist.’” 14 United States v. Davis, 73 M.J. 268, 271 n.3 (C.A.A.F. 2014) (quoting R.C.M. 916(b)(1)). Among the means by which an accused may lawfully defend his property, an accused has a right to eject a trespasser. Id. at 271–72. However, the right is circumscribed as an accused may only use as much force as is reasonably necessary to remove an individual from his property after requesting that the individual leave and then allowing a reasonable amount of time for the individual to leave. A person or invitee who refuses to leave after being rightfully asked to do so becomes a tres- passer and may not resist if only reasonable force is employed in 14Although the defense supposes an accused has a legal right to defend the property at issue, whether real or personal, it is not among the defenses that R.C.M. 701(b)(2) requires notice to the Government before the beginning of trial. 13  United States v. Proctor, No. ACM S32554 ejecting him. However, a property owner may not purposely pro- voke a disturbance on his property and then use his ownership of the property as an excuse for an unnecessary assault in eject- ing another person. If more force is used than is reasonably nec- essary to remove a trespasser, this force constitutes assault and battery. Id. at 272 (citing United States v. Regalado, 33 C.M.R. 12, 14 (C.M.A. 1963)) (additional citations and internal quotation marks omitted). A military judge has a duty to sua sponte instruct on the defense of property when “some evi- dence, without regard to its source or credibility, has been admitted upon which members might rely if they choose.” Id. (quoting R.C.M. 920(e), Discus- sion). c. Waiver “Whether an appellant has waived an issue is a legal question that this Court reviews de novo.” United States v. Rich, ___ M.J. ___, No. 19-0425, 2020 CAAF LEXIS 240, at *8 (C.A.A.F. 28 Apr. 2020) (citing United States v. Davis, 79 M.J. 329, 332 (C.A.A.F. 2020)). In United States v. Gutierrez, the Court of Appeals for the Armed Forces (CAAF) rejected plain error review of a required instruction under R.C.M. 920(e)(3), observing that its “jurisprudence allows af- firmative waiver of affirmative defenses.” 64 M.J. 374, 376 n.3 (C.A.A.F. 2007). The trial judge in Gutierrez stated “there doesn’t appear to be any mistake of fact instruction with regard to battery,” and then pointedly asked the Defense, “Are you requesting one?” Id. at 376. The court found waiver in defense coun- sel’s equally pointed response, “I simply do not want to request one for the battery.” Id. The Gutierrez court explained, “In making waiver determinations, we look to the record to see if the statements signify that there was a ‘purpose- ful decision’ at play.” Id. at 377 (citing United States v. Smith, 50 M.J. 451, 456 (C.A.A.F. 1999)). The court found waiver, reasoning, “[d]efense counsel was presented with the opportunity to request or decline the mistake of fact in- struction as to assault consummated by battery. He chose to decline it, and in doing so he affirmatively waived his right to the instruction.” Id. at 377–78. In Davis, the CAAF again rejected plain error review of a findings instruc- tion. 79 M.J. at 332. The Davis court found waiver when an appellant argued for the first time on appeal that the mens rea of “knowingly” applies to the consent element of Article 120c.(a)(2), UCMJ, 10 U.S.C. § 920c.(a)(2). Davis, 79 M.J. at 331–32. At trial, before instructing the members, the military judge identified the instructions he intended to give including the consent element that the appellant raised as an issue on appeal. Id. at 330. After instructing the members, the military judge “asked whether the defense had any objections or requests for additional instructions,” and the defense counsel replied, “No 14  United States v. Proctor, No. ACM S32554 changes, sir.” Id. After marking his written instructions as an appellate ex- hibit, the military judge again asked if there were any objections, and the de- fense counsel replied, “No, Your Honor.” Id. The Davis court found, “By ex- pressly and unequivocally acquiescing to the military judge’s instructions, Ap- pellant waived all objections to the instructions, including in regards to the elements of the offense.” Id. at 331 (citations and internal quotation marks omitted). In Rich, the CAAF again found waiver of a mistake of fact defense instruc- tion as the court had found in Gutierrez, explaining “when counsel affirma- tively decline[s] to object and offer[s] no additional instructions, counsel ex- pressly and unequivocally acquiesce[s] to the military judge’s instructions, and his actions thus constitute waiver.” Rich, 2020 CAAF LEXIS 240, at *9 (alter- ations in original) (internal quotation marks omitted) (citing Davis, 79 M.J. at 332). In Davis, the CAAF observed, “[W]hile we review forfeited issues for plain error, ‘we cannot review waived issues at all because a valid waiver leaves no error for us to correct on appeal.’” Davis, 79 M.J. at 331 (quoting United States v. Campos, 67 M.J. 330, 332 (C.A.A.F. 2009)). Nonetheless, pursuant to Article 66(c), UCMJ, 10 U.S.C. § 866(c), the Courts of Criminal Appeals have the unique statutory responsibility to affirm only so much of the sentence that is correct and “should be approved.” Thus, we retain the authority to address er- rors raised for the first time on appeal despite waiver at trial. See, e.g., United States v. Hardy, 77 M.J. 438, 442–43 (C.A.A.F. 2018); United States v. Chin, 75 M.J. 220, 223 (C.A.A.F. 2016) (citation omitted) (addressing this court’s re- sponsibility to “assess the entire record to determine whether to leave an ac- cused’s waiver intact, or to correct the error”). 3. Analysis a. Self-Defense Although the three witnesses testified somewhat differently, the rapid on- set of violence at the Thanksgiving party is uncomplicated and the essential facts are not open to question. Appellant charged toward SrA JT 15 who was a guest in the home Appellant and his three children shared with SSgt CM. SrA JT’s presence, and possibly the presence of others, stirred Appellant’s anger, but there is no evidence of any particular words SrA JT uttered or conduct SrA JT engaged in that might cause Appellant to apprehend, upon reasonable 15 Appellant was not charged with assaulting SrA JT. “An ‘assault’ is an attempt or offer with unlawful force or violence to do bodily harm to another, whether or not the attempt or offer is consummated. It must be done without legal justification or excuse and without the lawful consent of the person affected.” MCM, pt. IV, ¶ 54.c.(1)(a). 15  United States v. Proctor, No. ACM S32554 grounds, that bodily harm was about to be inflicted wrongfully on Appellant, as might raise the defense of self-defense. R.C.M. 916(e)(3)(A). Appellant alludes to SrA KJ’s testimony that Appellant and SrA JT “started arguing with each other” and “the situation got kind of heated.” How- ever, Appellant cites no authority, and we are aware of none, that justifies a resort to violence and entitles an aggressor to a self-defense instruction from an argument in which the words that were exchanged, by whom, and the back- ground or context are not evident from the record. Considering SrA KT’s testi- mony alone or with the testimony of other witnesses, there is no evidence SrA JT manifested any threat of attack or intent to start a fight. There was no evidence upon which members might rely to find that either SSgt AG or SrA JT, and not Appellant, started the affray. See Schumacher, 70 M.J. at 389. It follows that SSgt AG’s intervention and physical contact with Appellant when he came to SrA JT’s defense was in every respect a response to an unjustified attack. 16 Appellant had no right to self-defense when he rushed at SrA JT be- cause the uncontradicted evidence at trial was that Appellant was the initial, unprovoked aggressor. R.C.M. 916(e)(4). As SSgt AG stepped between Appellant and SrA JT, and Appellant then made contact with SSgt AG’s body, Appellant’s assault consummated in bat- tery. 17 SSgt AG was legally justified to defend both himself, R.C.M. 916(e)(3), and SrA JT, R.C.M. 916(e)(5), with force necessary for protection against bodily harm under the principles of self-defense and defense of another. Only if SSgt AG used unlawful force, and thereby escalated the level of the conflict, would Appellant then be justified to use force to defend against the escalation. See generally Dearing, 63 M.J. at 484 n.24 (citing United States v. Cardwell, 15 M.J. 124, 126 (C.M.A. 1983)). This is so because “[e]ven a person who starts an affray is entitled to use self-defense when the opposing party escalates the level of the conflict.” Cardwell, 15 M.J. at 126 (citing United States v. Acosta-Vargas, 32 C.M.R. 388 (C.M.A. 1962); United States v. Straub, 30 C.M.R. 156 (C.M.A. 1961)) (“The theory of self-defense is protection and not aggression, and to keep the two in rough balance the force to repel should approximate the violence threatened.”). 16A bystander acts at his own peril when he “goes to the aid of an apparent assault victim” because he assumes the legal status of the defended person. R.C.M. 916(e)(5), Discussion. If, unbeknownst to the bystander, the apparent victim was in fact the ag- gressor, the bystander has no right to self-defense. Id. In the instant case, as discussed, there is no evidence on which a rational factfinder could conclude SrA JT was an ag- gressor or a provocateur. “A ‘battery’ is an assault in which the attempt or offer to do bodily harm is consum- 17 mated by the infliction of that harm.” MCM, pt. IV, ¶ 54.c.(2)(a). 16  United States v. Proctor, No. ACM S32554 Appellant was entitled to a self-defense instruction tailored to include the principle of escalation of force if there was “some evidence” in the record which the members could rely upon that placed escalation in issue. United States v. Stanley, 71 M.J. 60, 63–64 (C.A.A.F. 2012) (failure to instruct on the principle of escalation of force was not error because the record lacked any evidence that would trigger a duty to instruct). In the instant case, it was Appellant who abruptly escalated the level of force in the conflict and intensified the violence by immediately grabbing SSgt AG’s throat and using Appellant’s own power and strength to try to force his way around SSgt AG and threaten harm to SrA JT. While SSgt AG overcame Appellant’s force by holding Appellant back and stopping Appellant from reaching SrA JT, there is no evidence SSgt AG esca- lated his use of force beyond that which was necessary to fend off Appellant’s continued unlawful assault and battery. In particular, Appellant’s strangling SSgt AG at the same time Appellant continued to manifest unprovoked aggres- sion toward SrA JT was unnecessary for his own defense. See, e.g., United States v. Ginn, 4 C.M.R. 45, 50 (C.M.A. 1952) (“Self-defense is a defensive, not an offensive act; and it cannot exceed the bounds of mere protection of one’s self.”). We find the issue of self-defense was not reasonably raised by the evidence, see Schumacher, 70 M.J. at 389–90, and the military judge did not err in de- clining to instruct the members on self-defense or give a tailored instruction that included the principle of escalation of force in self-defense. b. Defense of Property Appellant also claims the military judge was required to instruct, sua sponte, on defense of property as a defense to Appellant strangling SSgt AG. The law recognizes that “individuals may protect their place of abode against unlawful intrusion. When one with the right to do so has ordered another from the premises, the latter has no right to refuse or resist.” Regalado, 33 C.M.R. at 15 (citing United States v Adams, 18 C.M.R. 187, 194 (C.M.A. 1955) (appel- lant occupying government tent had right to protect himself from trespasser); United States v Berry, 20 C.M.R. 354 (C.M.A. 1956)). We find Appellant affirmatively waived a defense of property instruction. We reach this conclusion from defense counsel’s discussions with the military judge in three Article 39(a), UCMJ, sessions held to discuss proposed findings instructions. Considered together, these sessions included a discussion of ap- plicable defenses to include self-defense as a complete defense to the specifica- tion at issue. In each session, defense counsel neither objected nor requested a defense of property instruction. After the conclusion of the findings arguments, the military judge again asked if the Defense had any objections or requests for additional instructions. The Defense replied it had no objections to the in- structions as given, and did not request any additional instructions. 17  United States v. Proctor, No. ACM S32554 On these facts, Appellant expressly and unequivocally acquiesced to find- ings instructions that did not include the defense of property instruction Ap- pellant claims should have been given. See Davis, 79 M.J. at 332 (citing United States v. Wall, 349 F.3d 18, 24 (1st Cir. 2003) (“[C]ounsel twice confirmed upon inquiry from the judge that he had ‘no objection and no additional requests [regarding the instructions].’ Having directly bypassed an offered opportunity to challenge and perhaps modify the instructions, appellant waived any right to object to them on appeal.” (alteration in original))). Appellant thus waived the objection he raises on appeal. We find no reason to pierce Appellant’s waiver in this case, see Hardy, 77 M.J. at 442–43; see also Chin, 75 M.J. at 223, because the military judge com- mitted no error. Appellant’s claim supposes he had a right to an instruction that he could oust SSgt CM’s guests from their shared residence. 18 However, Appellant points to no evidence at trial upon which members might have relied to find Appellant had a right he asserts for the first time on appeal. Appellant’s lease was not admitted in evidence. No evidence suggests Appellant’s property rights under Colorado law were superior to SSgt CM’s own, that Appellant was at liberty to force SSgt CM’s guests to leave, or that SSgt CM acceded to the removal of her guests on Appellant’s terms. Even if we were to assume Appellant had the requisite property rights and legal interest to demand SSgt CM’s guests leave their shared residence, the evidence does not suggest that Appellant gave them reasonably adequate time to comply and that Appellant used no more force than was reasonably neces- sary. Instead, the evidence indicates Appellant did what the law disallows: he “purposely provoke[d] a disturbance on his property and then use[d] his own- ership of the property as an excuse for an unnecessary assault in ejecting an- other person.” Davis, 73 M.J. at 272. Defense of property simply was not in issue given the facts of this case and the military judge did not err in failing to sua sponte instruct the members that it was. C. Allegation of Unlawful Command Influence Appellant renews his claim at trial that over a year before Appellant’s court-martial, Lt Col MS orchestrated a commander’s call message to discour- age Appellant’s coworkers from providing character letters or testifying on Ap- 18Appellant’s claim is, to some extent, contrary to the position taken by the civilian defense counsel who argued in findings that Appellant and SSgt CM “lived together,” “were on a lease together,” and “they both have rightful legal access to that property.” (Emphasis added). 18  United States v. Proctor, No. ACM S32554 pellant’s behalf. Appellant requests this court set aside and dismiss the find- ings and sentence on the basis of apparent UCI in the adjudicative stage of his court-martial. 1. Additional Background Lt Col MS released Appellant from pretrial confinement on 1 August 2017 after the convening authority withdrew and dismissed Appellant’s original charges, and before Lt Col MS preferred charges anew on 14 August 2017. A week earlier, on 7 August 2017, and just over a year before Appellant’s trial and sentencing, Lt Col MS held a commander’s call as was his practice every six months. The topics covered at the commander’s call included military awards and recognition, civilian achievements, sexual assault, and NCOs be- having poorly and making bad decisions. 19 Lt Col MS encouraged the squadron to “support” Airmen, no matter what process or difficulty the Airman may be going through, but not “enable” bad behavior. He also addressed the impropriety of spreading rumors, stating met- aphorically, “You guys may know what your friends are telling you, but you don’t have the big picture,” and that there was “more than one chapter in the book.” He testified, My goal was to get NCOs to start acting like NCOs, and other NCOs who were holding the line, to call the other NCOs out. They should be embarrassed when their NCOs are acting a cer- tain way and giving their corps a bad name. Just like we get embarrassed when officers misbehave. Lt Col MS told a story from when he was enlisted and a junior Airman under his supervision asked him to provide a character letter. The Airman was undergoing nonjudicial punishment proceedings for breaking curfew in a de- ployed location. At the commander’s call, Lt Col MS explained why he declined, reasoning that the Airman not only disobeyed the order of the mission com- mander, but Lt Col MS had looked the Airman in the eye and told him to make sure he was back on time. Lt Col MS related he was there to support the Air- man but that he could not write a letter advocating that his commander not take a stripe over the good order and discipline of the unit. Lt Col MS explained at the commander’s call about his “commitment to the Air Force” then, noting his commander at the time would question Lt Col MS’s judgment if Lt Col MS signed a letter advocating that the commander not take a stripe. 19Lt Col MS addressed the squadron, and afterwards the senior NCOs separately ad- dressed the NCOs to reinforce the commander’s message and answer questions. Ap- pellant was not in attendance at the commander’s call or the meeting of NCOs. 19  United States v. Proctor, No. ACM S32554 Lt Col MS’s comments did not mention anyone by name or reference alle- gations or incidents of misconduct in the unit. Even so, his remarks were prompted by knowledge of issues involving Appellant and SSgt CM, and other NCOs in the squadron. Lt Col MS was aware that Appellant’s friend, SSgt JP, had responded to Appellant’s Facebook post with a message that Lt Col MS viewed as a continuation of Appellant’s Facebook threat. The catalyst for mak- ing NCO behavior a topic of the commander’s call was SSgt JP’s reaction to Appellant’s recent release from pretrial confinement at the same time the orig- inal charges that Lt Col MS had preferred against Appellant were withdrawn and dismissed by the convening authority. Lt Col MS testified he knew at the time of the convening authority’s disposition he would prefer charges anew. 20 Around this time Lt Col MS learned from his NCOs that Appellant and SSgt CM continued to contact each other in violation of his orders, including during the time when Appellant was in pretrial confinement. He felt the squadron took a negative turn when charges were withdrawn and dismissed because the Airmen were wondering what was going on and had lost faith in the system. 21 Lt Col MS’s remarks were prompted also by matters unrelated to Appellant, including that SSgt JP had been found in his vehicle outside a club with over twice the legal limit of alcohol in his blood, an NCO had operated a motorcycle in a manner that caused injury to a junior Airman who was a passenger, and several NCOs had recently failed their physical fitness assessments. After the commander’s call, a junior NCO 22 who was Appellant’s friend asked to meet with the commander. Lt Col MS was aware that the NCO had previously given a statement to law enforcement stating he “thought that the unit and the Air Force were after [Appellant] and [Appellant] wasn’t that bad.” Lt Col MS met with the NCO who assured the commander he was friends with Appellant, but understood the commander’s perspective and “everything that’s 20Lt Col MS was concerned about the effect on his unit of SSgt JP “[w]alking around just talking real loud saying, ‘My homey’s getting released. He’s getting out. We are going to throw a barbecue,’” with the implication that Appellant was in the clear. Lt Col MS was concerned also because two individuals around whom SSgt JP revelled in Ap- pellant’s seeming good fortune were individuals SSgt JP disliked and were witnesses in the Government’s case. Lt Col MS believed SSgt JP knew they were witnesses be- cause SSgt JP was friends with Appellant. 21 Lt Col MS testified he knew of an instance of NCOs discussing Appellant’s orders violations in front of a junior Airman. He explained, “When you are in command . . . [y]ou can feel your unit start to question and doubt what is going on. Why is leadership not taking care of things?” In response to the military judge’s questions, he added, “A unit that had high morale and doing very well was starting to go flat.” 22The junior NCO did not testify at the hearings. However, Lt Col MS testified about their conversations. 20  United States v. Proctor, No. ACM S32554 going on.” Because the NCO was close friends with Appellant, Lt Col MS rein- forced his expectation “to support [Appellant] when he needs something. Just do not enable him.” Lt Col MS testified in general about other exchanges he had with the junior NCO in which the commander encouraged the NCO to con- tact Appellant’s defense counsel because the NCO was not following through on returning calls by Appellant’s defense counsel. Lt Col MS told him, “You call the defense” because “[t]hat’s part of the process. You call them. They are going to interview you. All I ever expect anybody to do in this unit is just tell the truth.” The squadron’s first sergeant testified he was aware the junior NCO was visiting Appellant when Appellant was in pretrial confinement, and thanked him for supporting Appellant every time the first sergeant and the NCO talked. Both the Defense and trial counsel called Airmen who were present for the commander’s call to testify on the motion. The Defense called SSgt JP and a senior airman, both of whom understood the commander’s message to be that those who support an NCO in trouble need to rethink their careers in the Air Force. 23 While SSgt JP initially understood that the commander’s message was to not support Appellant, when he sought clarification from a senior NCO, he was told that the message was not about avoiding the Defense or withholding support for Appellant. Ultimately, SSgt JP did not believe the commander’s message was to stay away from Appellant or avoid speaking with Appellant’s defense counsel. Two senior NCOs testified they understood the commander’s message to be to support, and not enable, Airmen in trouble. SSgt AG, who was later the victim of Appellant’s assault consummated by a battery, also attended the commander’s call. He understood the message to be: if you support certain individuals, you need to rethink your position in the Air Force. SSgt AG was confused by the message and believed Lt Col MS was not clear on what “sup- port” meant. He believed the overall message was to rethink one’s position in the Air Force so as not to follow a bad path. SSgt AG did not seek to clarify the message with anyone in his chain of command. Ultimately, he did not believe he would be punished for his testimony or that the commander threatened punishment if he supported troubled NCOs. 23The senior airman understood his commander’s message to be “[i]f you’re supporting an NCO that’s in trouble, you might want to rethink your career. . . . [I]t might put you in a negative light . . . or you might be looked at as the problem, also.” He testified he thought it might rub the commander the wrong way to write a character statement “because [Lt Col MS] never really made it clear what he meant by that statement, so he left a lot of room for imagination.” He believed there would not be ramifications to his testimony on the motion because he intended to separate from active duty. 21  United States v. Proctor, No. ACM S32554 2. Law “Allegations of unlawful command influence are reviewed de novo.” United States v. Salyer, 72 M.J. 415, 423 (C.A.A.F. 2013) (citations omitted). Where an assertion of unlawful command influence is litigated at trial, we review the military judge’s findings of fact for clear error, but we review de novo the legal question whether those facts constitute unlawful command influence. United States v. Ayers, 54 M.J. 85, 95 (C.A.A.F. 2000) (citing United States v. Wallace, 39 M.J. 284, 286 (C.M.A. 1994)). “On appeal, the accused bears the initial bur- den of raising unlawful command influence.” Salyer, 72 M.J. at 423. “Two types of unlawful command influence can arise in the military justice system: actual unlawful command influence and the appearance of unlawful command influence.” United States v. Boyce, 76 M.J. 242, 247 (C.A.A.F. 2017). Unlike actual UCI, a meritorious claim of an appearance of UCI does not re- quire prejudice to an accused. Boyce, 76 M.J. at 248 (footnote omitted). “[W]hen an appellant asserts there was an appearance of unlawful command influ- ence[,] [t]he appellant initially must show ‘some evidence’ that unlawful com- mand influence occurred.” Id. at 249 (quoting United States v. Stoneman, 57 M.J. 35, 41 (C.A.A.F. 2002)) (additional citation omitted). This initial showing requires an accused to demonstrate: (a) facts, which if true, constitute unlawful command influence; and (b) this unlawful command influence placed an intolerable strain on the public’s perception of the military justice system because an objective, disinterested observer, fully informed of all the facts and circumstances, would harbor a significant doubt about the fairness of the proceeding. Id. (internal quotation marks and citation omitted). Though the burden of this threshold showing on an accused is low, the evidence presented must consist of more than “mere allegation or speculation.” Salyer, 72 M.J. at 423 (citation omitted). “Once an appellant presents ‘some evidence’ of unlawful command influ- ence, the burden then shifts to the government to . . . prov[e] beyond a reason- able doubt that either the predicate facts proffered by the appellant do not ex- ist, or the facts as presented do not constitute unlawful command influence.” Boyce, 76 M.J. at 249 (citing Salyer, 72 M.J. at 423) (additional citation omit- ted). If the Government fails to rebut the appellant’s factual showing, it may still prevail if it proves “beyond a reasonable doubt that the unlawful command influence did not place ‘an intolerable strain’ upon the public’s perception of the military justice system and that ‘an objective, disinterested observer, fully informed of all the facts and circumstances, would [not] harbor a significant 22  United States v. Proctor, No. ACM S32554 doubt about the fairness of the proceeding.’” Id. at 249–50 (quoting Salyer, 72 M.J. at 423) (internal quotation marks omitted). 3. Analysis The military judge found Appellant did not meet his threshold burden to demonstrate “some evidence” of UCI and denied the motion. Boyce, 76 M.J. at 249. On appeal, Appellant asserts the Defense did present “some evidence” of at least an appearance of UCI in three respects, specifically: (1) that Lt Col MS made comments about his “NCO problem” in large part because of Appellant’s case; (2) that Lt Col MS attempted but failed to distinguish supporting Airmen from enabling Airmen; and (3) that Lt Col MS told the story about declining to provide a character letter for an Airman on deployment, because of the duty he felt to the Air Force and the negative consequences it could have had to his career. Appellant contends this evidence was a sufficient showing of apparent adjudicative UCI to shift the burden to the Government, which cannot prove beyond a reasonable doubt that the appearance did not create an intolerable strain on the public’s perception of the fairness of the military justice system. Accordingly, Appellant urges us to set aside and dismiss the findings and sen- tence. Although the record is unclear as to the exact words Lt Col MS spoke at the commander’s call or the message that was conveyed, we find Appellant met his initial showing of “some evidence” of apparent UCI. See Boyce, 76 M.J. at 249. Even if we accept the military judge’s factfinding that Lt Col MS did not or- chestrate a message to discourage members of his squadron from providing character letters or testifying on Appellant’s behalf as Appellant contends he did, there is no question Lt Col MS had Appellant in mind when he made his comments, and members of the squadron who knew Appellant well would rec- ognize Appellant was among the Airmen who were the focus of his remarks. The commander’s recitation of the personal story illustrated reasons not to pro- vide a requested character statement for an Airman facing discipline that was heavy on repercussions and less so on providing information to assist with dis- position and discipline of the offender. Lt Col MS knew he was going to reprefer charges on Appellant when he made his remarks. Nonetheless, we conclude that the evidence of apparent UCI was rebutted by the Government’s proof that there was no intolerable strain upon the pub- lic’s perception of the military justice system beyond a reasonable doubt. The commander’s call, held over a year before Appellant’s trial, addressed multiple topics; one of which was NCO misconduct, which the commander spoke about in general terms without identifying either Appellant, the facts underlying the investigation of Appellant’s misconduct, or repreferral of charges that would be forthcoming. While the commander told a personal story about refusing to write a character letter to an Airman who committed misconduct under his 23  United States v. Proctor, No. ACM S32554 supervision, importantly none of the witnesses testified that they understood his commander’s call message as one discouraging them from writing character letters for Appellant. Although charges were preferred one week after the commander’s call, trial on the merits was not held until more than a year later. No members of the squadron testified that Lt Col MS would take any action against them for their participation in the court-martial, and there is no evidence in the record that any Airman refused to testify or write a character letter in support of Appellant for sentencing. There is no evidence that a witness once supportive of Appel- lant later withdrew or changed any assurance of support. We conclude these facts demonstrate that the Government met its burden to demonstrate beyond a reasonable doubt that no fully-informed, disinterested, objective observer would doubt the fairness of Appellant’s court-martial. Boyce, 76 M.J. at 249– 50 (citation omitted). III. CONCLUSION The approved findings and sentence are correct in law and fact, and no er- ror materially prejudicial to the substantial rights of Appellant occurred. Arti- cles 59(a) and 66(c), UCMJ, 10 U.S.C. §§ 859(a), 866(c). Accordingly, the find- ings and the sentence are AFFIRMED. FOR THE COURT CAROL K. JOYCE Clerk of the Court 24 

package client // import "github.com/docker/docker/client" import ( "context" "net/url" "github.com/docker/docker/api/types" ) // NodeRemove removes a Node. func (cli *Client) NodeRemove(ctx context.Context, nodeID string, options types.NodeRemoveOptions) error { query := url.Values{} if options.Force { query.Set("force", "1") } resp, err := cli.delete(ctx, "/nodes/"+nodeID, query, nil) defer ensureReaderClosed(resp) return wrapResponseError(err, resp, "node", nodeID) }

Q: Scala Spark type missmatch found Unit, required rdd.RDD I am reading a table from a MySQL database in a spark project written in scala. It s my first week on it so I am really not so fit. When I am trying to run val clusters = KMeans.train(parsedData, numClusters, numIterations) I am getting an error for parsedData that says:"type mismatch; found : org.apache.spark.rdd.RDD[Map[String,Any]] required: org.apache.spark.rdd.RDD[org.apache.spark.mllib.linalg.Vector]" My parsed data is created above like this: val parsedData = dataframe_mysql.map(_.getValuesMap[Any](List("name", "event","execution","info"))).collect().foreach(println) where dataframe_mysql is the whatever is returned from sqlcontext.read.format("jdbc").option(....) function. How am I supposed to convert my unit to fit the requirements to pass it in the train function? According to documentation I am supposed to use something like this: data.map(s => Vectors.dense(s.split(' ').map(_.toDouble))).cache() Am I supposed to transform my values to double? because when I try to run the command above my project will crash. thank you! A: Remove the trailing .collect().foreach(println). After calling collect, you no longer have an RDD - it just turns into a local collection. Subsequently, when you call foreach it returns Unit - foreach is for doing side-effects like printing each element in a collection. etc.

The comedy film "Muppets Most Wanted" takes the entire Muppets gang on a global tour, selling out grand theaters in some of Europe’s most exciting destinations, including Berlin, Madrid and London. But mayhem follows the Muppets overseas, as they find themselves unwittingly entangled in an international crime caper headed by Constantine — the World’s Number One Criminal and a dead ringer for Kermit — and his dastardly sidekick Dominic, also known as Number Two, portrayed by Ricky Gervais. The film also stars Tina Fey as Nadya, a feisty prison guard, and Ty Burrell as Interpol agent Jean Pierre Napoleon. Here is what Gervais, Fey and Burrell said in interviews at the Los Angeles press junket for "Muppets Most Wanted.' Getty Images Interview With Ricky Gervais How would you describe your role in “Muppets Most Wanted”? Gervais: It’s about me and Constantine infiltrating those gullible Muppets. And I pretend to think they’re really brilliant. And I want to manage them and take them on a world tour, but really it’s just to get close to things like bank vaults and the crown jewels. That’s what happens when two master criminals. We [Constantine and I] working together in the movie. In real life, we’re sort of friends. We’re chums. In the movie, we’re sort of at each other’s throats. How long have you been a fan of the Muppets? Gervais: I’ve loved the Muppets for about 35 years … But when I met [Constantine], he is now my favorite Muppet of all time and one of my best pals, really. He had a really hard upbringing, born in the pond in Russia, one of eight siblings. What was your favorite part of filming “Muppets Most Wanted”? Gervais: My favorite was filming in Pinewood Studios in England. [Constantine] is amazing in the movie. He’s sings, dances, and is a great impressionist … Just wait for the sequel: “Muppets Least Wanted.” It’s just going to be us two. We’re going to get rid of all the other Muppets. Interview With Tina Fey How long have you been a fan of the Muppets? Fey: I have been a fan of the Muppets since I was a little girl. And then I really like the reboot movie that Disney did a few years ago. I thought it was really good, and I took my daughter to see it, and she really liked it. So I was just thrilled to be asked to continue on the tradition. How would you describe “Muppets Most Wanted”? Fey: “Muppets Most Wanted” is kind of a jewel-heist adventure caper. The Muppets get tricked by an evil frog named Constantine, who happens to look a lot like Kermit, except [Constantine] has a mole. He tells them he is Kermit and that he’s going to take them on a world tour, but he’s maybe secretly really robbing all the world’s greatest jewels. Meanwhile, poor Kermit has been put in jail, where Constantine should be, in Russia, and I am in charge of that jail. I portray a woman named Nadya, and I am a Russian Gulag warden. What was it like for you to sing and dance in “Muppets Most Wanted”? Fey: It was really fun to sing and dance in the movie. Bret McKenzie writes great songs, and he wrote all the songs from the [previous “Muppets”] movie. And, obviously, he was in Flight of the Conchords and stuff. And they were really fun, catchy songs. You get to pre-record the songs in the studio, so you get as many tries as you need to get it right. And then they fix it up a little more, and then you get to lip sync when you film it. It’s not so much hard. I’m not an amazing singer, so it was probably harder for Bret to listen to me sing then for me to try to do it. [Says jokingly] Do you have a crush on Kermit? Fey: I do. And I was able to channel through my character Nadya and pretend it wasn’t really me who has a crush on Kermit and pretend it was Nadya. [Says jokingly] Were you worried about getting the wrath of a jealous Miss Piggy? Fey: Miss Piggy and I shot only one day together, at the very end of the movie, n the roof of the Tower of London. My character enters, and she realizes that Kermit and I know each other, and she did shoot me the hot bacon look of death. Sizzling bacon dagger! Did you do anything special to prepare for Nadya’s Russian accent? Fey: I worked with a woman named Jill McCullough who is a dialect coach, who worked with me and Ty [Burrell]. She taught Ty his French dialect. She taught Ricky [Gervais] how to pretend to be English, because Ricky is actually from outer space. [She laughs.] So I would Skype with her, and she would actually go through the script with me before I went to London. And then when we went to London, she would be on set. She would talk to us in whatever dialect we were supposed to do. She’s a crazy, crazy dialect genius. What’s your first memory of the Muppets? Fey: My first memory of the Muppets is Kermit in his reporter’s outfit on “Sesame Street.” Why should people see “Muppets Most Wanted”? Fey: I think “Muppets Most Wanted” is a really, really funny movie. It has lots of heart, but it also has lots of great comedy in it. And it has really great music and adventure spirit. Interview With Ty Burrell How long have you been a fan of the Muppets? Burrell: I grew up watching the Muppets. I’m sure it’s subconscious, but I’m sure they had a huge influence on my sense of humor in general. It’s the same creative team as “Sesame Street.” Whatever eccentricities I have are due to the Muppets and “Sesame Street.” I was really giddy when I got a phone call about this [movie]. I definitely lost all my negotiating power immediately upon receiving this phone call, because I giggled and whooped and said, “It can’t be true!” Like many Americans or people all over the world, it [“The Muppet Show”] was just a huge part of my childhood. How did you feel about doing a French accent for your role in “Muppets Most Wanted”? Burrell: Luckily, I was given license for it to be terrible. I was like, “Well, gosh, I haven’t really done a French accent before, but I’m excited about getting a shot to do it. James [Bobin, the director of “Muppets Most Wanted”] was very nice from the very beginning. H just said, “Look, it’s the Muppets. We’re looking for a comedy version of an accent,” which was a huge amount of pressure off. But I also had a really good dialect coach called Jill McCullough, who was such a good sport and very kind to me as I botched this French accent. And also, I think it was a fun part of the process for me, because our running joke between Jean Pierre and Sam Eagle is that it’s a war of cultures between Europe and America. And the accent just a part of me getting a chance to be extremely smug and very self-righteous. What did you think of the Sam Eagle character? Burrell: We got along so well. I didn’t even so well until after the movie, but Sam Eagle is my favorite Muppet. He’ll sneak up on you. He’s that Muppet. There’s Miss Piggy, there’s Kermit, there’s Fozzie Bear. After spending a few months with Sam Eagle, you can’t not love him. He’s grumpy and sarcastic and also has a heart of gold. What advice would you give to any actor who’s going to do a “Muppets” movie? Burrell: Don’t be concerned with subtlety. Really, it was just a feeling that there’s nothing that the Muppets can’t hold. You can’t do anything too weird or broad that won’t fit into the Muppets. As long as it’s hopefully funny, which is just an awesome thing. It’s really an incredible thing. I don’t think “Modern Family” is the most subtle thing ever, but it’s attempting to kept things in the realm of reality. So getting a chance to do something where I’m essentially the closest thing to a Muppet that there is, I am barely a human in this [movie]. What was it like filming the “Interrogation Song” scene? Burrell: The “Interrogation Song” is basically a patter song. I didn’t have to hit too many notes. You’re welcome, America. It was challenging because that stuff is very fast and also super-technical. The folks with the Muppets are so used to that. It’s incredible. They’re the nicest, most patient people. And also, they’re good at it. They’re good at all the technical stuff, working out all the kinks. They’re used to shoots being long. I was the weak one. I was the one having to down fluids and stretch. I’m so spoiled on my show. But it was a very cool thing. It took a while to make that song, but it was a very cool experience. What’s your first memory of the Muppets? Burrell: My first memory of the Muppets is roughly Statler and Waldorf around the opening sequence and hearing my dad laugh at it, which is a cool memory, because there aren’t that many things that you watch with your parents when you’re that age. But hearing my dad laugh at that stuff, it’s a very fond memory. Can you compare and contrast 2011’s “The Muppets” to 2014’s “Muppets Most Wanted”? Burrell: I think the reboot was, in a way, perfectly true to the original. And I can’t even put my thumb on it, but there is its own style with what James [Bobin] and Bret McKenzie and what those guys have done with this new iteration. This one [“Muppets Most Wanted”] is an expansion of that. It’s an even bigger iteration of the last one. We’re going all over Europe. It’s an homage to the Muppet caper. But I just loved the [2011 “Muppets” movie] so much. I paid money to go see that movie with no kids. I just thought it was so funny. I think they are so funny and so smart, but [“Muppets Most Wanted"] also incorporates this huge European tour. Share this article Carla Hay has been an entertainment writer or editor at People magazine, Lifetime's website and Billboard magazine. Based in New York City, she is a graduate of Stanford University and the University of Southern California.

Big Bang experiment may reveal dark universe: CERN Geneva: Dark matter, which scientists believe makes up 25 percent of the universe but whose existence has never been proven, could be detected by the giant particle collider at CERN, the research center`s head said Monday. Rolf-Dieter Heuer told a news conference some evidence for the matter may emerge even in the shorter term from mega-power particle collisions aimed at recreating conditions at the "Big Bang" birth of the universe some 13.7 billion years ago. "We don`t know what dark matter is," said Heuer, Director-General of the European Organization for Nuclear Research on the Swiss-French border near Geneva. "Our Large Hadron Collider (LHC) could be the first machine to give us insight into the dark universe," he said. "We are opening the door to New Physics, to a discovery period." Astronomers and physicists say that only 5 percent of the universe is known currently, and that the invisible remainder consists of dark matter and dark energy, which make up some 25 percent and 70 percent, respectively. "If we can detect and understand dark matter, our knowledge will expand to encompass 30 percent of the universe, a huge step forward," Heuer said. The LHC, the world`s largest scientific experiment centered in a16.78 mile oval-shaped tunnel deep underground, is presently moving to colliding particles by the end of the month at the highest energy ever achieved. These multiple collisions at a total of 7 tera-electron volts, or TeV, will each create mini-Big Bangs, producing data that thousands of scientists at CERN and in laboratories around the globe will analyze. One widely publicized aim of the LHC is to try to find the theoretical particle that gave mass to the matter that spewed out after the primeval explosion and thereby made possible the emergence of stars, planets and eventually life -- on earth and perhaps elsewhere. The mysterious particle has been dubbed the Higgs boson after the Scottish physicist who three decades ago proposed it to explain the origin of mass in the universe. "We know everything about this particle. The only thing we don`t know is if it exists," said Heuer, a German physicist who took over at CERN 14 months ago. "And if it does not exist, we are bound to find something that is very much like it." Once collisions in the LHC are begun at 7 TeV, they will continue with only very brief breaks until the end of 2011, and then the machine will be shut down for a year to prepare it for years more of experiments at 14 TeV.

Market Segment by Regions (provinces), covering South China East China Southwest China Northeast China North China Central China Northwest China Split by product Type, with production, revenue, price, market share and growth rate of each type, can be divided into Portable Water Quality Analyzer Benchtop Water Quality Analyze Split by Application, this report focuses on consumption, market share and growth rate of Water Quality Analyzers in each application, can be divided into Laboratory Industrial Government Table of Contents China Water Quality Analyzers Market Research Report 2017 1 Water Quality Analyzers Market Overview 1.1 Product Overview and Scope of Water Quality Analyzers 1.2 Water Quality Analyzers Segment by Type 1.2.1 China Production Market Share of Water Quality Analyzers Type in 2015

The year 2019 started with an unusual trip. My girlfriend and I decided to visit the northern part of Norway, the Lofoten islands and the nordic city Tromso. I’d consider it an unusual destination as I don’t like spending my precious holidays in winter-cold countries or cities. As we already went through the winter curse in our country, which consisted of freezing nights and rainy days, we headed north-bound towards the arctic circle. I expected to take the best out of my recently bought Mavic Air drone and was looking forward to pet some reindeers. This all sounded too fancy, if it wouldn’t have been for the rain. We flew out from Brussels and had a 2-night stop in Bergen, the main city in the south-west of Norway. All I knew about Bergen, were the beautiful colored houses which I knew from google and the mountains surrounding the city center. It all seemed very “nordic” to me, because of the maritime vibe with all the ships, anchors and fishermen, therefor I was looking forward to finally discover Bergen. It turned out that city center wasn’t that attractive at all, and it ended up as a big disappointment. On tripadvisor we tried to find several tourist spots, which would allow us to kill the time. Sadly we couldn’t find any online. All you can do is get some fishy-food at the local fish market, grab a coffee or two, get on top of the mount “Fløyen” with its fancy funicalar. All this can be done in 4 hours. Besides that I really can’t give you any further tips. Bergen didn’t turn out as I expected it to be. At night, we didn’t find any awesome bars which would allow us to get to know some local folks, it all seemed very dead. I guess paying 10 euros/dollar for one beer or a shot of rum doesn’t sound very inviting. Sadly that’s the average price you gotta pay for booze in Norway. We were happy to move on towards the Lofoten in the early morning of our 3rd day in Norway. You can easily reach the city center of Begen from the airport by the local lightrail (one-way ticket costs about 3,5 euro/dollar, or the express busline “flybussen”, which takes about 25 min(the one-way ticket is about 10 euro/us$). Lofoten Islands: Reine, Sakrisoy, Henningsvær. We landed in Leknes, where one of the 3 airports of the Lofoten is located. It was the smallest airport that I’ve ever landed at. After jumping out of the airplane, we walked through a door, and immediately reached the luggage claim belt within a couple of meters. Right next to the luggage claim where two single booths of the rental car companies. After spending exactly 4 minutes at the desk, we got a descent upgrade for our car: a hybrid VW Golf, with automatic transmission, and spiked wheels. Prior our trip we booked a lovely wooden cabin in Sakrisøy, also known as “Rorbu” houses. Rorbuer are traditional fisher houses made out of wood and usually painted in red or yellow. It was one of the cheapest “chalets” we could find on booking.com, but it turned out to be exactly what were looking for. The check-in was flawless. The main entrance of the cabin was facing a big snow-covered mountain, right next to the water. A very basic kitchen station allowed us to prepare our dinners and breakfasts. Nearby the Sakrisoy houses was a “Coop” supermarket, and with 50 euro/us$, we could prepare our food for the upcoming 3 days. Expect to pay at least 60 euro/us$ while having dinner at a restaurant. Norway ain’t cheap! It was the first time I ever stayed in a wooden cabin. I loved brewing my fresh coffee every morning with my portable “Kalita Filter”. The living area and the wooden beds on the upper level of the house were very cosy. The wooden cabin was definitely an important part of our Lofoten experience, as we weren’t spoiled with the best weater. We spent 5 days / 4 nights on the Island. During our stay we only had two days of sunshine. The weather was changing constantly, it was mostly snowstorms, rain and fog. As it was my first trip where I would use my DJI MAVIC AIR drone, the weather didn’t allow us to fly it up, as the winds were way too strong. It’s really hard to kill the time on the Lofoten during bad weather, as there’s isn’t much to do. Because of the icy roads it takes quite a while to visit other cities. Driving from Reine to Svolvaer would easily take 3 hours. The center of Leknes hasn’t much too offer, except for a couple of coffee houses and an unattractive shopping mall. There’s one main road that leads across the Island, the E10. There aren’t barely any shortcuts, you won’t get lost on the Lofoten without a GPS, but you will use the same road over and over again to drive around. During our 4 days, we visited Reine, Leknes, Henningvaer and Svolvaer and we made it to the Unstad arctic surf beach. There are plenty of tiny villages that you will pass by within a couple of minutes. Different fishermen restaurants are spread out all over the Island. Besides having cake & coffee, taking lots and lots and lots of photographs, there’s not much to do in the Lofoten. The views are breathtaking! The landscape and mountains scenery is very unique, and you won’t be disappointed. Sadly we got also unlucky with the northern lights. We were using the iphone apps “Aurora Alerts” and “Aurora” to get informed about the optimal conditions of the northern lights. Every night around 22:00h (10pm) the green lights were right above our roof. Unluckily because of the clouded sky, we weren’t able to see them. One night we took our car and started driving around for an hour or two. No luck! Even later in Tromso, one of the best locations in Norway to witness the northern beauties in the sky, we were unlucky again. TROMSO. Tromso was the last destination on our norway trip. Initially we had planned to make it the most popular city in northern norway to visit e reindeer farm. You can several tours or reindeer sleeding, husky sledding, feeding the reindeers followed by a traditional sami dinner. All of that could have been, if it wasn’t for the rain & fog. After we landed in the late evening, the first glimpse at the city center was quite suprising. It looked like the center of fairy tale village, lots of inviting shops, packed restaurants and a handful of bars. On the next day we woke up with frustrations, the sky was gray, it was raining, and you could hear the wind through the room-window. We decided to walk across the main Tromso bridge and make it to the “Arctic Cathedral”. The beautiful A-shaped Cathedral was built in 1965, and to me it looked more like an Art-Center or Museum than a church. The shape of the building is actually very unusual for a religious building and it definitely looks like a recent construction. Never thought that the cathedral was over 50 years old. Obviously with all the bad luck on our side, the church was closed. There were way too many people outside to get a descent photograph. The winds were too strong to fly up the drone. The fog was so dense that we could barely see the other side of the bridge. Bummer! There wasn’t much to do in Tromso as well. We jumped from shop to the other, and tried too many coffees and cakes in the surrounding coffee-bars. Across our hotel was a lovely vinyl shop called “Backbeat Kaffe og Vinyl”. As the name of shop already reveals… you’ll find an interesting collection of vinyl (rock, indie, metal, soul, local bands) and can buy a fine cup of coffee, while browsing for new music. While in Norway, I had to buy the last album of “Kvelertak”, a gem of nordic rock music! As we planned on staying in Kerala for 8 nights, time realy wasn’t on our side. Distances in Kerala are quite significant, which we didn’t expect at all, considering Google-Maps showing us 120-150 km routes. Because of the traffic and the narrow roads, 120 km could easily take up to 5 hours of your prescious time. We landed in Trivandrum, as we were planning on spending New Years Eve on the beach, and we opted for Kovalam, because the surroundings and its red-white striped light house looked very charming. Kovalam. Kovalam’s beach was nice, nothing more nothing less. The restaurants at the beach front were quite alright for indian circumstances. However when you moved further away from the back alleys of the shore, the surroundings got pretty odd. There wasn’t an ATM nearby. You’d find plenty of roadstalls selling the usual stuff, chewing pan, sodas and biscuits. On New Years Eve, we were part of the few younger folks walking through the sand of the beach. Bars and restaurants were busy with older people, mostly europeans. There was nothing going on late at night. Selling alcoholic beverages was prohibited if the bar wouldn’t pay a pretty expensive authorization. Some bars would sell the booze under table and serve the wine, beer or spirits in coffee mugs. For half a bottle of red wine we paid 10 euros / dollars on NYE, which is insanely expensive for indian people. Of course we had to hide the bottle under the table, in case the cops would show up. Kovalam had its charming side, because only after one day, the locals would start recognizing you, and you’d get in lovely conversations with them. Of course always having in mind to win you as a customer in their shop or restaurant. The weather was flawless, even at night we had t-shirt temperatures. The water of the sea was pretty warm and the palmtrees bordering the shore made Kovalam a pretty place. One day we drove up to Varkara with a rental scooter, it took us 5 hours in total to do the roadtrip. Varkara looked different than Kovalam, less buildings, more greens. In the end I can’t tell you which beach I actually prefered. We enjoyed the scenery along the road while heading up north. But I guess the 5 hours driving weren’t worth it, to spend some hours on a beach. Initially we planned on staying 2 nights in Kovalam, but we extended our stay for one more night, as we didn’t want to rush with the usual check-out and packing our backpacks after the night of NYE. Honestly 3 nights in Kovalam is too long, as there isn’t much to do in the area. You can do daytrips to Varkara, the center of Trivandrum which gives you the feel of a city-vibe, or driving down south to the Vivekananda Rock Memorial (which we didn’t do, as it would take another 5 hours of driving in total). The scooter rental rate was a bargain, as we only paid 300 rupees per day (4 euros/dollars). Alleppey and its backwaters. After driving up north to Varkala, we figured out that Alleppey would be quite a ride. The distance between both cities is around 160 km which takes up to 5 hours driving. A local told us that you can reach Varkala by train, however the train only leaves in the early morning and only once a day. So we opted for a taxi, which would cost us only 40-50 euro/usd, hassslefree, with an A/C, and you can sleep in the back of the car. Easy! Alleppey is well known for its charming canals and its bigger lake on the northern side. That’s what we saw and what we got. In Alleppey we visited the city center, however the town looked like any other indian city. Our pleasant part of Alleppey was definitely our stay the “Bamboo Lagoon Resort”. The Bamboo Lagoon had the feel of a guesthouse, as there weren’t more than 10 to 12 rooms for rental. We had the chance to get one of the 3 rooms of a cottage that were very close to the river’s edge, facing the backwaters. Opening the doors in the morning was very beautiful as you could witness the beauty of the house boats passing by, watching the local fishermen in their canoos, or just observing the neighbours taking “a shower” in the river. It definitely felt more like India, than Kovalam’s beaches. There wasn’t much to do on the “island”, as you had to a 1 minute canoo-trip to reach mainland. For one day only it was very pleasant to saviour the quietness of the resort, spending an hour in a hammock and watching the boats passing by. You could book a boat from the hotel and do a canal trip through the back waters. The boat cost around 500 rupee an hour (5 euro/uds). It would lead you through different canals and offer you a scenic view of the neighbourhood. Unluckily on our first day we were told that on the following day, violent riots could take place in the city as there was an issue with a nearby temple, where women were granted access to use the temple for the first time ever. The radical religious fanatics obviously didn’t like that, and the use of violence was expected. So the only way to get to Munnar was to leave in the early morning at 01:00 or 02:00 am, or we would have to stay a second night, and spend all day at the resort, as driving with a taxi or buses was prohibited for security reasons. We decided to leave at night. However we were already pretty sure that we would stay one more night at the bamboo lagoon on our way back home to the airport. Munnar. Munnar was a contrasty destination in comparison to the backwaters and the beaches of Kerala’s coastal region. Munnar is a located in the mountainous area of Kerala. It looks very green and hilly and the temperatures tend to be much lower at night. Our roadtrip to Munnar was quite an experience. In the end we can have a good laugh about it, however the behaviour of our driver was rather dangerous than hilarious. The taxi driver picked us up at 01:30 in front of the bamboo lagoon resort. We put our stuff in the trunk and our journey began. After a couple of minutes the cab was stopped by the local police. They asked where we were heading, as it wasn’t allowed to drive out because of the riots that would high-probably happen that day. We were allowed to move on. On the road I noticed how the driving behaviour of our driver changed: accelerating, breaking, accelerating, breaking.. and it went on like this. I instantly knew he was too tired to hold the road. After having hit the sidewalk numerous times, the driver decided to have a break and sleep for 30 minutes. Later on he told us, that he hadn’t slept for almost 24 hours. We arrived in Munnar just before 07:00am. We stayed at the “Kaivalyam Wellness Retreat” for one night only. Before checking in we didn’t know that the resort had a fully-packed schedule with activities for their guests: free yoga classes, free tea tasting, early morning visits of the tea plantations, and many many more. They even gave free cooking classes 3 times a week. Obviously the cooking classes didn’t take place when we were visiting… as for myself, I’m always missing the best parts while traveling. Bummer! The Kaivalyam Retreat was most definitely a beautiful place. Surrounded by endless trees, different kind of plantations (black tea, cardomon), it felt so refreshing breathing in the mountain air with all those scents outside of your room. After having checked in, being led to our room, taking a shower… we notice the beautiful tree houses outside of our window. The lovely owner of the hotel, was so kind to give us a kind of upgrade, and let us move into one of the few tree houses that were available. Spending the night in a tree house was already worth the 5 hours we drove in a taxi to reach Munnar. We were looking forward to discover the mighty green hills that we found on Google. Sadly during our visit, most of the tuk-tuk drivers were off work, because of the on-going strike all across Kerala. So it wasn’t possible to get to those greeny landscapes, as they were located 15 kilometers away from our resort. Nevertheless, we were enjoying our 30 hours in Munnar. The 07:00 am yoga class was fun. It was interesting to witness the indian point of view about yoga, its flow, and how they practice it. We were executing all the asanas on traditional matt, rather a rug, and it kinda felt like I was doing yoga for the first time. This was pretty much our Kerala trip. So during a whole week, 7 days, we managed to visit 4 different cities: Kovalam, Varkara, Alleppey and Munnar (and we made it back to Alleppey and Kovalam on our last 2 days). Obviously we couldn’t experience all the parts of that beautiful state. But we experienced enough, to agree that it’s worth doing the drip. The whole trip changed my view of India, as it wasn’t actually that fun the first time I visited the country. If you’re a fan of Bali or Srilanka, you will love Kerala. Namaste to all the lovely people that crossed our path on this trip, … we met too many lovely ones! Most of my friends and relatives wouldn’t believe me, if I was telling them that I’d travel back to India. In 2017 I visited a couple of cities in the northern part of the country: Delhi, Agrar, Varanasi, Vrindavan. Back then, I wouldn’t hold myself back shouting out loud my disappointment about India on social-media, as I remembered the wise words of a friend “you either love or hate India, there’s nothing in between”. Follwing my India trip in 2017 I stood rather on the “hating” side, than among the appreciating crowds. However I had never argued about the fact that India’s culture had so much to offer: the mesmerizing colors, the scents of spices and flowers, the fascinating beliefs and rituals of the Hindu religion, the mouthwatering indian dishes… India has a lot to give, even though sometimes it can hit your nerves in the roughest way. Reaching the last days of the year on December 2018, I headed back to India. How did this happen? After my exhausting trip in 2017, I told myself, I would never again travel through India by myself. And the second condition would be the southern part of the country. I would give India a second chance, while visiting the south, famous for its beaches, palm trees, and yoga retreats. A quick stop in Delhi at the Humayun Tomb We decided to visit the state of Kerala on new years eve. The fact that my girlfriend is a total Sri Lanka aficionada, I felt like adding Varanasi to our India trip. Kerala doesn’t look that much different than Sri Lanka. Adding some contrast to our trip would make our journey across India more interesting and versatile. Varanasi. Writing a second blog-post about Varanasi would be pointless, as I mostly visited the same spots and areas as I did in 2017. We booked our 2 nights at the lovely Ganpati Guesthouse, the same guesthouse that I stayed at on my first trip. The room was flawless (for Indian standards)! On the first day we checked out the surrounding area of the guest house. The "burning ghat” was located very nearby. As the darkness kicked in, the scenes of the flames dancing over the dead bodies covered with piles of wood, was rather surreal. I knew that we weren’t allowed to take any photographs during the cremation of the deceased. Sometimes you gotta act very naive or stupid, to get lucky with photographs. As we were standing long enough at the bottom of the stairs, observing how the flames were decomposing the body, a family started asking where we were from. Obviously, like many indians do, one of them asked for a photograph with us. We agreed, and as a returning favor, I asked if I could take a couple of photos of the cremation. I respected the ritual in the deepest way, took out my camera and shot a couple of photos. I was kinda happy that I managed to get some descent snap of that holy place. The next early morning we headed to “assi ghat” around 05:45 am, to watch the sun rise, surrounded by chantings, pranayama sessions (breathing yoga) and watching the locals go wild during their morning rituals. 2017 I was blown away by the beauty of the sunrise and the diversity of the morning sounds that came with it (chantings, loud breaths during pranayamas, the fire ceremony, Bon Iver playing on my Ipod). All of this together made it to an unforgettable experience, as it felt like being ejected backwards in time. 2018 things had changed. “Assi ghat” looked less crowded. A peer down the river had been installed. The thing that blew me away this time, was the delicious masala chai that was served close to the main square. It was the best chai I’d ever had. Still being very cautious about what I eat and drink while traveling across India, I couldn’t hold myself back and bought 3 chais that day. The lovely gentleman explained us how to do the “best chai” in his own proper way. Just because of Varanasi I finally know how to brew the “best” masala tea. I also learned, that if you travel with the least expectations, you will enjoy your trip a lot more. I expected to be really annoyed by boats-men and local salesmen. They were less hard on tourist than my previous year. Eventhough Varanasi blew my mind the first time, I even enjoyed it more on my second visit. We passed by the “Vishnu’s Tea Emporium” as I read on trip-advisor it would offer a unique tea experience. I had the typical tea-shop image on my mind, the tidy western shops, with all kind of teas and smells. As we walked by the “Emporium” we missed it twice as it just looked like a small, dirty and untidy living room. It didn’t look like a tea shop at all. Following the recommendation of a friend, we stepped into the shop, and a couple minutes later Vishnu welcomed us. We got our second introduction how to make proper Masala tea, starting with a plain tea sample and adding each ingredient (ginger, cardamom, cloves, cinnamon..) step-by-step. After our initial shock of the tidiness of the room, we appreciated how much love Vishnu put into his tea ceremony. We bought two tea bags and a masala-spice-mix to thank him for his time and service. Varanasi is very picturesque old city that comes with “that special vibe”. You can feel the holy spirits within the city. You will see hundreds of very poor people, you will see too many smiles, you will hand out unlimited change and tips, some people will annoy you, others will make you happy with their grattitude, but in the end Varanasi will leave a unique memory within your heart. During a tea-break we had a short conversation with an older british lady, she told us that she’d stay in Varanasi for 2 weeks. I asked her if she could recommend us some hidden gems of the city, however all we got was the answer I had expected. She told us, that she would spend most of the day along the ghats next to the Ganges River. It was my second time in the city, and all we did, was spending time on the river-walk. That must be the magic of Varanasi, being happy with almost nothing, just enjoying the views and having a masala chai. While traveling as a couple, you will get used more easily to the poverty, the dirty streets, the endless honk sounds, after one day you will go with the flow, and witness the uniqueness of the probably oldest city on earth. Kerala. If you start talking about the south of india, about their beaches and yoga-beach-bums, Goa normally would pop up in most people’s heads. Kerala is just the state below Goa. The main reasons we were visiting South-India, were the summer-ish weather, the local cuisine, and the glimpse at the indian culture. It could have either been Goa or Kerala. We opted for Kerala as it seemed less touristic than Goa. And we could get a change of scenery within hours. Kovalam and Varkara are beach destinations, 150km further north you can explore the back-waters of Alleppey, from Alleppey heading north-east you’ll reach the greenish hills and mountains of Munnar. All this sounded very convenient for a 10-day trip through India. I decided to write a seperate blog-post about the single stops on our journey through Kerala. Writing down our experiences in Varanasi took more lines that I expected. Briefly I can summarize Kerala as a wonderful experience, as my expectations of India were very low. After bumping into too many rude and unwelcoming indian people in the north, I witnessed how lovely the indian people can be in the south of India. During our 10 days we didn’t experience one single unpleasant moment while interacting with numerous locals. The local people we bumped into, were very friendly, welcoming, generous and helpful. Especially taxi-drivers were super friendly. Their job wasn’t the easiest, as traffic in india can be a severe pain in the ass. Some of the drivers had to drive 5 hours straight to drop us at our next destination. The drives were chaotic, the cab-driver had to stay attentive during those 5 hours. And the maximum we paid for 4 to 5 hours rides was 4500 indian rupees {50 euros/dollars}. We decided the use taxis to move inside the state of Kerala. Besides doing shorter trips with a rental scooter, taxis would be the quickest way of transportation and we wouldn’t lose much time during our 8 days in the south. Obviously bus and train rides would have been cheaper and would have offered much more of a backpacker-feel, however some trains only leave once a day (early in the morning) and the rides would take up to 9 hours. As we wanted to visit 4-5 different areas within 8 days, taxis with a driver, was the optimal choice. Prior our departure, I was convinced that we’d rent a car and do a roadtrip on our own across Kerala. I knew that traffic could be very harsh in Delhi and Mumbai. I didn’t expect this to be the case in Kerala. The main roads weren’t as congested as in the north, however the streets in Kerala were at some points very narrow. While driving around on our rental-scooter, we had to swerve buses driving on our lane towards the oppostive driving direction. Animals and peoples were sharing the road with us. Long story cut short, driving in india is very adventerous and be quite dangerous sometimes. As we reached the middle of our trip, we were involved in an accident. That moment I thought that we would get in serious trouble, because it actually was our fault, that someone got injured. Surprisingly the police officers that showed up didn’t even ask for our passports. The locals surrounding the spot of the accident almost ignored us. Without any hesitation we paid cash for the damage we caused, and the taxi driver moved on and dropped us in Alleppey. In Trivandrum we met up my friend Vinoy’s family. They picked us up and dropped us at the airport, they invited us to their house were we got cooked a delicious indian dinner. The whole family was very welcoming. We even got presents after leaving their house. During our whole stay in Kerala we felt like - King & Queen. The hospitality of the locals was out of this world. Taiwan isn’t the usual destination that you’d go for while planning to visit Asia. Most people would choose Thailand, Japan or Vietnam over Taiwan in a heartbeat. However choosing the perfect summer holidays during the months of July & August isn’t the easiest part, because most asian countries are hit by the summer monsoons. Thailand and Bali are well known for their rain-season during the european summer months. While circling around the asian continent on a world-map with my finger, the tip of my index, landed on Taiwan. Two of my friends used to live in Taiwan, that’s why I only heard good things about the country. But I aslo gotta admit that I barely didn’t know anything about Taiwan, except for the city-name of Taipei and its skyscraper the “Taipei 101” building. After finding out that there are several national parks spread all over the country and that there’s a pretty coast called Kenting which is also know for its surfing spots, Taiwan sounded very inviting. And chances of getting wet was less probably compared to other popular asian countries. Taipei. When I heard Taipei, I thought Hong-Kong. From several photos and videos that I’ve seen form the capital of Taiwan, it pretty much reminded me of the fascinating city of Hong-Kong. Hell, I was wrong. In my opinion both cities are totally different. Hong-Kong is such a photogenic city, that you will get endless opportunities to take beautiful shots with your camera or phone. You can hop from cabs to subways and land on a boat and just cross the river within a couple of minutes. Hong-Kong has a bustling nightlife. Get on a funicular and make it to Lantau Island. Temples, skyscrapers… HK got it all. After my first two days in Taipei I still couldn’t feel the vibe of the capital. There were a couple of dull temples spread all over the different areas of the city. Blocks that were packed with shopping malls, the 101-Skyscraper that you could stare at from further distances. The shopping streets were very busy from the early after-noon until the late evening. Streetfood-markets are very popular, you’ll find quite a few and get all kind of dishes that costs about a dollar or a euro. At the food markets we only bumped into locals. The pannels were written in chinese and it was pretty hard to figure out what we were eating, as many of the taiwanese people don’t speak a word of english. Even though the streetfood wasn’t the best one, the foodstalls weren’t the cleanest, I still enjoyed watching people strolling over the market and observing the “chefs” preparing their food. To be honest, there wasn’t one single tourist attractioni in the city that I really enjoyed. Good nightlife spots were very hard to find, as the popular bars are spread widely appart. So you always gotta use a taxi or public transportation to make it to a busy bar or club. We spent two nights at the gay-district as it was easy to spot and you could buy an “all-you-can-drink” ticket for 15 bucks. While staying in Taipei we drove to several parcs and suburbs with a rental-scooter. The rides were fun, but the trips weren’t really worth it. Especially after having visited amazing cities likes Osaka, Tokyo, Hanoi, HK, Bangkok… We were often asked by taiwanese people “why are you vistigin our country?”. I seemed like the locals weren’t used to see a lot of tourists in their city. On our last day in Taipei we crossed a very laid back, but huge american guy, he stared at us, raised his hand, put a smile on his face and yelled at us “hello white people!”. That was pretty funny, because we realized that he was actually right. During our 10 days in Taiwan we met less than a handful caucasians. Keelung. Keelung is a city closer to the northern coast of Taiwan. It took us a little more than an hour to reach Keelung by train from Taipei Mainstation. After getting off at the final stop, Keelung instantly felt different than the capital. There weren’t any skyscrapers, no fancing shopping malls, it all looked more laid back. Obviously the city center looked more “taiwanese” than the capital. Right in the heart of Keelung, there was a harbor, a canal with many bridges and the famous Keelung street market. At first sight I was more attracted and impressed by Keelung than Taipei. As we planned to spend 5-6 nights in Keelung, quickly it turned out as a bad idea. There was even less going on at night than in Taipei. Keelung definitely beats Taipei with its beautiful coast, and its scenic road that surrounds the northern tip of the island. You easily could do a couple of daytrips from Keelung. We rented an electric scooter and visited Shifen and Jiufen. Shifen is a tiny village, located south-east of Keelung. It takes about 40 minutes to reach it by scooter. The special spot that makes Shifen pretty popular among tourists is its “Shifen Old Street”. A tiny alley, reserved for pedestrians, on which a railway-road passes straight through it. As soon as the train passes, tourists jump on the rails, trying to release their sky lantern. Visitors can buy a blank lantern for 5-10 euro/usd. They will write or paint their wish onto the 4 blank sides of the lantern. The vendor will put a gasoline-soaked cloth on the inside of the lantern, lit it on, and with a light handpush, the landern will fly towards the sky. It actually was a lovely place watching all the lantern flying high. You could see it as a cheap way to make good money. However, as for myself, it was the first time that I had the opportunity to release a lantern. Not far away from “Old Street” there was a hanging-bridge and cute little train-station. While being in Shifen, get back on the scooter and visit the Shifen waterfalls. Nothing impressive, however as there’s not that much to do in the area, it’s worth the trip. Jiufen is another village, located in the mountains, not too far away from Keelung. You might have seen beautiful nightshots on Instagram with uncountable red lanterns, that photo was high-probably taken in Jiufen. Depending on the weather you can get a jaw-dropping scenic view of the northern coast from the outskirt of the village. We visited Juifen twice, once at night, and once during the rain. It was hard to get descent photos of the views that the vista-point had to offer. The most famous part of Jiufen definitely is the covered streetmarket, seperated on different levels. Upstairs, downstairs, all the alleys lead to food, drinks, tea- & souvenirshops. The place is crammed with visitors. Hard to guess if it’s a tourist-trap or an authentic market, as we were the only white folks among the crowds. Considering the food, both of us got tired of the street food. After a couple of days we got bored and slightly disgusted by the smell of greasy food, seeing living frogs in a glass-jar waiting to get thrown onto the grill, the scents of stinky tofu. It was fun on the first day, after having bought some fresh fruits, followed by local fruit-juices and a big bowl of fatty noodle soup. You will find a couple of indoor food-courts that will serve all kind of asian foods, from thai to japanese dishes, and that was where we mostly had lunch. Foodwise, in my opinion, it was the least pleaseant food I had in all Asia, even though I can’t argue that we had good foos as well, like an amazing shrimp ramen at night, or my favorite nut-pastry in the morning. Another cool thing that we discovered in Taiwai, was the electric rental-scooter from the company “Gogo Ro”. In Keelung barely nobody would offer the usual scooters for rental. The easiest way to move around the Island, was the Gogoro electro-scooter. The bike was packed with 2 removable batteries, that lasted around 60-80 km. As soon as you reached 40% of battery-power, it was about time to open google-maps and look for the closes battery-charging-station. Some of the gas-stations were equipped with those power-stations, where you’d stop by, remove both batteries from the scooter, and put them into a big white wall. The station would “spit out” two batteries that were fully loaded. The good thing about that, you wouldn’t have to pay for gas, as the batterie-exchange came without further costs. The electro-bike was way faster than a gasoline scooter. However the unpleasant part was, that you could drive up to 90minutes - 100 minutes, and then you’d have to ride your bike towards the closest gas station. These last years we all got bombed with the most beautiful snapshots from all over the world thanks to Instagram. As a vivid IG follower I was blown away by the colors and the antique architectural beauties of Marrakech. As I was hoplessly browsing for cheap holidays I opted for Marrakech. I was highly influenced by those beautiful photos I knew from social media and I was really intrigued by the arabic cuisine, as I love cooking with their traditional spices at home. My girlfriend was traveling across Iceland that time, so I thought spending a couple of days in Morocco and planning on visiting the sahara desert would be a beautiful experience. To cut a long story short, this trip to Morocco hadn’t nearly fulfilled my expectations. The flight-ticket was a bargain, as I flew from Frankfurt-Hahn to Marrakech for less than 130 Euros (a two-way-ticket). My beautiful riad “Rodamon Riad Marrakech”cost around 100 Euro for 6 nights. Sounds like cheap but great holidays. As soon as I landed in Morocco the frustrations began at the immigration desk. It took more than an hour to get my passport stamped. Due to school holidays all over Europe, the queue lasted forever. And I guess I wasn’t the only one with a grumpy face in line. Same case with the queue at the ATM. After two everlasting hours I made it out of the airport, where the first struggles came into play. The cabs. The bandit taxi-drivers of Marrakech Just nearby the taxi area was a sign with the different taxi-rates priced in dirham (moroccan currency). The ride to the city was listed as 110 dirham which would be around 10 euro / 12 us$. I asked the first taxi driver how much it would cost to take me to the city-center “Oh you don’t know the rates? Well it costs 200 dirham (20 euro) taxes all included". Obviously I didn’t agree with the price as the big sign mentioned the 110 dirham. I asked a second driver “ohh that will be 200 dirham because of the taxes”. I went passed to a third driver. Same story…. 200 dirham. As it was my first time in Morocco I agreed to pay 200 dirham, and of course I added another 20 dirham as a tip at the final destination, just for being the gentle travel who I am. On my last day I took a taxi to make it back to the airport, asked the same question and all I got as a satisfying answer “ohhh my brother, of course same price as always, city center to the airport will be 100 dirham”. So be cautious about the cab-drivers. The lovely gentleman who drove me back explained that it would be better walking 5-10 minutes to the closest parking lot next to the departure hall, because that’s the spot where the locals hop on a cab for a much lower price. As my riad (traditional moroccan hotel) was located inside Medina, the old-town of the city, the driver dropped me at one of the closest gates nearby the riad. From that point on you gotta walk through the cute small alleys to your hotel. At first sight I loved the tiny streets that reminded me of a medieval arabic maze. I passed the security guard of my riad and went for the check-in. Actually my riad was a hostel, and I had to share the dorm-room with 5 other guests. The facilities easily looked like the one of 4 star hotel. I couldn’t wait to start discovering the neighbourhood. Either the “grande place” or the “tanneries”. After walking away from the hotel, during the first 5 minutes, the city-hawks made their “first attack”. I was asked by a local if I needed directions to the “Jemaa el-Fnaa” square. I denied the question as I wanted to stroll randomly through the streets and shoot a couple of photos. Just because the local dude seemed to be pretty nice I asked for the “tanneries”, the place where moroccans color the leathers in a traditional and natural way. Obviously one of his friends was walking towards the “tanneries” and asked me to follow him. I instantly informed him that I wasn’t looking for a guide and that I wouldn’t pay a dime for his help. "No no… free.. no money”. As soon as we made it the gate of the tanneries another local jumped in and introduced himself as the security guard who would show me around. Of course it wasn’t a security guard, just another local who was looking to make some pocket-money. The whole tour with a minimum of explainations lasted about 5 minutes. Everywhere was a sign with “no photo” on it. At the end of the mini-tour the so-called guard brought me to a leather shop very nearby and I gently refused his offer, telling him I wouldn’t be interested in buying leather products. That was the point where I got served my bill on a plate. I didn’t want to be rude and offered him 50 dirham (5 euro) . He asked for 100 dirham, so I insisted in a gentle way “50 d or nothing”. He grabbed the 50 dirham note and left. At that point the first guy jumped in, the one who walked me to the gate…and asked money as well. He wanted 100 dirham as well. Suddenly I was surrounded by 3 moroccans, all of them asking for money. I started giving them bad names and pulled out a 50 dirham bill to avoid any trouble. They weren’t happy at all, as it was far less than they demanded. I read about the same story just before leaving my riad on google reviews. And guess what, it all happened to me exact the same way. So expect to be asked every half an hour “are you looking for the grande-place or the tanneries” ? Sightseeing in Marrakech. Well on my first day I was strolling through the old town trying to get some good snaps of the locals or the buildings. After a couple of hours I noticed that there aren’t any impressive buildings in the city center. There are a handful of beautiful mosques in and around the city, however as a non-muslim visitor access will be denied. Outside of the buildings you will see signs with “non-muslims not allowed”. Bummer! The “Jemaa el-Fnaa” square looks really dull during day-time. It’s far less crowded, and packed with beggars, snake charmers, cripples who are begging for money, a bunch of syrian families sitting on the pavement with their kids and asking for money as well… The restaurants around the main square aren’t that great. I had lunch and dinner at two different restaurants and was kinda disappointed by their dishes. As I was trying to get some descente photographs of moroccan people, the locals started screaming “no photos, no photos!” and trying to hide their faces with one of their hands. It seemed to be super impolite taking photos of people. And it wasn’t about taking portraits photos, just randomly shooting. Marrakech is packed with “souks”, traditional arabic markets, which can be compared with streetmarkets in asia. The souks are packed with stalls that sell all kind of ceramics, spices, clothes and local products. The souks open early in the morning and close late at night. You can spend hours at the “souks” digging for antique collector pieces or buying “tajines” for your friends and family. On my second day I went to visit the popular “Majorelle Gardens” designed by Yves Saint Laurent. You had to pay 7 or 8 euro for the entrance to the garden. The garden was beautiful of course, however it was pretty small and paaaaaaacked with too many french people. The park was filled up with palm trees and all kinds of cacti (cactuses). There was one eye-catching blue building in the center of the park, where all the visitor were fighting each other to take a photo next to a blue wall covered with a shiny yellow window frame. After having seen too many beautiful public parks in Delhi (India) I wasn’t impressed by the “Majorelle Gardens”. It was just a tourist attraction as no local would spend time in a tiny park overcrowded with tourists. No peaceful location. Within 24 hours I discovered the souks, two different tanneries, the big main square, the Majorelle gardens, passed by the Koutoubia mosque and the beautiful Ben Youssef mosque (as non-muslims aren’t allowed inside the building… you just admire them from the outside), spent sometime near the pool of my beautiful riad. I spent money on ceramics and spices and bought myself a second-hand tajine. That’s mostly all you can do in the city center of Marrakech, the old-town of Medina. Eat, sleep, spend money, drink tea, spend money, and got to bed. Photos aren’t appreciated. Too many locals will begg for money or ripp you off when handing you back the change. I really don’t see how visitor could love this place. From 6 nights to 1 night. During my 2 days I spent in Marrakech I was so annoyed by all the local moroccans who were trying to steal my money at every occasion. As I was using my iphone (with a moroccan sim-card) with google-maps to find my way hrough the maze of Medina, I got asked too many times “hey can I help you? are you going to the grande place?”. I gently declined and told them that I was following my GPS. A common thing was that the guy was trying to keep the conversation going on with random small-talk. “Oh it’s this way”… I gently refused his help and replied that I got my gps and wouldn’t need any further assistance. However he still felt the urge to follow me. Approximately after a 100 meters, they asked for a tip “I showed you the directions you were asking for…be a gentleman..and show me some gratitude”. Of course I wouldn’t give them a cent. This happened to me at least 5 times within 24 hours. And obviously the conversation always ended with harsh arabic words I wouldn’t understand, high probably funny insults. At night, at the crazy busy “Jemaa el-Fnaa” square, where you would find endless amounts of locals dishes, the food vendors would grab you by your jacket and pull you into their restaurant. If you pushed them back, they follow you and kept asking you for your favorite food. As I was soooooo annoyed and felt more than a victim than a visitor I decided to book a flight home on my second day. I was really looking forward to discover the sand-dunes of the sahara desert, a very popular tour which was organised by my hostel. However I could imagine that these kinds of hassles would go on these upcoming days, as the desert-tour would stop at major touristic spots, so I decided to fly back home. I’ve been to many places all over the world. India and Morocco were definitely the worst destinations where locals would do anything to make it to your wallet. At least in Delhi, there so much to discover, huge amounts of temples, hundreds of parks, statues, markets, fountains and lakes. Things I really missed in Marrakech. Maybe I was just unlucky and had the worst experience someone could have in Marrakech. So after having spent 10 fabulous nights in Thailand, I had to choose my next destination for my pre-summer trip in june. I was pretty sure that it had to be Asia, as I just came back from a very satisfying visit in Bangkok & Chiangmai. It was about time to break my solo-traveling routine, because a good friend was about to join me. So after a few seconds of brain-storming we came up with Japan, Bali or Thailand. Since my plan was learning how to surf in 2018, we shared the same thought that taking a first surfing class as a 35 and a 39 year old young man, would be a pretty cool experience. Surfboards, cafe racers, beaches and jungles... we opted for Bali. And besides all that I would celebrate my 36th birthday on the island. It all sounded like a lot of fun. Sadly two weeks prior my departure my good friend had a motorbike accident and got badly injured with a broken foot. This meant that I had to travel on my own. Back then I couldn't tell why, but I really wasn't in the mood for visiting Bali all by myself. Maybe because we know Bali from dreamy photos on Instagram, where you get to see endless photos of couples, engagements, weddings, ... It all sounded like "noooooope. this is a lovers' destination". Ubud. I started my trip in Ubud. I was told that Ubud would be super touristic and packed with Yoga people. Actually I do love yoga, but I can imagine, being surrounded by gurus and spiritual nerds, that this could become pretty annoying. I booked a bed at the "Pillow Hostel", because their rooms looked pretty descent, and they offered free yoga classes in the early morning. Sounded pretty ok! However because of the daily rain showers the yoga classes didn't take place on the open-air rooftop. I knew about the rain-season before traveling to Bali. So I wasn't disappointed about the rainfall, mostly during the night, and couple of hours during daytime. Luckily there were some days without rain as well. What to do in Ubud? Well I won't list any super fancy touristic spots, that I would highly recommend, or any must-try restaurants. All I can tell, go rent a scooter! You will definitely not enjoy Ubud without a scooter, if you're not doing any yoga-esque activities. There's a daily market in the very center of Ubud. The streets are packed with shops, the restaurants are filled with tourists. You hardly won't meet any local people on a night out. I really wasn't keen about renting a scooter, in a country, where people drive on the left side of the road. I haven't been riding a motorbike for too many years. Then came the slippery roads because of the rain... So many reasons why I wouldn't rent a scooter. I overcame my doubts and went for it... I rented a scooter for a day. From that point I knew I would rent a scooter any time again. I discovered so many cool spots around Ubud and I met local people. Locals let me join a very religious ceremony in a hindu temple. They first denied when I asked if they would let me in. As I told them that would carry a long-sleeve shirt and a sarong (a traditional skirt for men) in my bag. They were so surprised about that, that they let me check out the temple. I met several groups of kids, who were trying to bring up their giant homemade-kite in the sky. They told me that this would be a balinese tradition, and later on my trip I noticed several spots where the sky was packed with colorful gigantic kites. Beautiful! I visited the holy bathing temple called "Tirta Empul". Everybody knows the temple from the photos. Before going to Bali, I knew that I would find this bathing temple on the island. However I didn't know that all the people I had seen on the photos, taking a shower under the several fountains, were tourists. If Balinese people jump into the bathing pool to get under the fountain, they do it in the early morning around 5 am (05:00). So expect to bump into a lot of tourists while visiting the temple. The "Pelingghi Meru", a pagoda-like structured temple, is another eye-catcher you will find on many photos. It took me almost 2 hours to reach the temple by scooter from Ubud. But I really wanted to visit that place. As I arrived in front of the pagoda I was surprised how small it was. It looked very tiny. And again packed with too many tourists. I always enjoyed the scooter-rides through the suburbs of Ubud. Lots of nature: rice-fields, palmtrees, lakes, beautiful sunsets. So many spots to take a lot of beautiful photos. Have a couple of stops at the coffee-shops on the side of the road and you will be surprised how many lovely conversations you will get with balinese locals. The "Tegallalang Rice Terrace" is definitely a must-see. You can easily spend 1-2 hours on the rice fields, take many beautiful photos, enjoy a coffee, and get an instragram-cliche-shot one of the many giant-swings located around the ricefields. Even though I didn't like the center of Ubud, because of the tourists, I gotta admit that Ubud was my favorite city among Uluwatu and Canggu. With a scooter you can visit endless waterfalls which are located pretty close around Ubud. There's so much to do, even though you won't get that impression of Ubud at first sight. Uluwatu. Well I decided to have a stop at Uluwatu for 2 nights because it's supposed to have the cleanest surf beaches of Bali. Uluwatu is well known for its huge waves on the shores, which brings fabulous surf spots with it. All this sounded like a cool place to hang out. Every monday night there's a huge party at "Single Fin's". It's pretty packed and a great time is almost guaranteed. However no one tells you, that Single Fin is located on a private ground, where you gotta pay a fee to drive in with a car or on a scooter. Expect, once again, only tourists among the crowd, as balinese people can hardly afford a beer in that kind of restaurant/bar. I wasn't in a party mood on that monday night, so I didn't make it to the party. I visited the restaurant on the following day, and all I found out, was that I didn't like the place. The cheapeast gin&tonic was actually pretty expensive for a longdrink in Bali. However you can enjoy a pretty descent view towards the sea and watch people surfing. If this is what's you looking for, nice view, fast food and watery drinks, go for it! I stayed in the very center of Uluwatu where there was barely nothing that would a attract a 36 year old guy on a scooter. Laid back restaurants, street food stalls, hundreds of supermarkets and clothing stores, and some surfboard-rentals. To get to the closest beach it took me about 10-15 minutes on a scooter. It was called "DREAMBEACH", and it was actually a pretty nice beach compared to the rest of the beaches that I had explored in Bali. However you had to pass two security check-points, and at the end of the ride, you had to pay parking fee to park your scooter. Uluwatu was the first place, where I booked my first surfing classes ever. In my opinion the waves seemed to be huge, and as a newbie, they seemed very scary. I only surfed for about 90 minutes instead of two hours, because my arms couldn't manage the paddling anymore against those monster waves. And I wasn't too keen about the surf trainer either. But I was glad that I took the classes, as it took some courage from my side, to get into the water for the first time with a board. In Uluwato you get the chance the visit the "Garuda Wisnu Kencana Cultural Park". It's actually very touristic but I had the possibility to witness one of the biggest statues I'd ever seen. Would I call it a must-see, definitely not, however if you gotta kill some time in Uluwato, the park is definitely worth it to spend an hour or two at. Before I forget about it... there's a popular Hindu Temple in Uluwato, everybody knows about it, everybody wants to visit it. Go for it! Canggu. Canggu is supposed to be the hipster hang-out spot of the whole Island, and it definitely was the case. "Pretty Poison" offers you crowded nights on tuesdays and thursdays, big crowds hanging around the skate-bowl and cheering up the skaters. Their menu offer 4 different descent cocktails and a couple of beer brands. Hip people, trashy rock music, skaters everywhere, pretty girls... you get the vibe, it feels like Venice Beach! The first night I went to Pretty Poison, there was a concert inside the venue. Actually it was a very sweet rock band, which I'd rather watch play, than watching topless skater dudes in the bowl. I loved the quote above the bar "Someone told me there's a girl out there with love in her eyes and flowers in her hair". Cafe-Racer fans definitely know the brand "DEUS EX". It's a pretty chill hang-out spot (bar & restaurant) where you can witness the coolest bikes and the coolest custom-made surf boards on the island. They have a "DeusEx" shop where you can spend some money on clothes and other stuff. I went there on daily basis to have lunch. The food was flawless, for a reasonable price. I loved their polenta fries and falafel salad. The music at the restaurant and the indoor design was a plus! I took another 2 surf classes in Canggu, and I had the pleasure to meet a much nicer surf trainer. The beach wasn't as nice in Canggu, as it was in Uluwatu, however I enjoy the surfing sessions a lot more, because the waves weren't as huge as in the south. Besides the hip rock bars and hip surf shops, there were so many things that bothered me in canggu. The main reason was the huge amount of tourists, australian tourists. Every bar, restaurant, club, beach spot was packed with tourists. There wasn't a place where I would bump into local people in the center of Canggu. The only locals that I met was at the local tattoo shop "Bold & Bright Tattoo", where I got tattooed. I loved the tattoo artists, they were very welcoming. And I turned back home, truely satisfied about my traditional old-school dagger tattoo. The price was totally a bargain compared to the money you gotta in Europe or the USA for a descent tattoo. To be honest, I didn't like Canggu at all ! On Instagram everything looks so hip, fancy, and photogenic, but it real life it definitely wasn't. And all those thousands of tourists killed the vibe of the city. I was actually happy to get back home, after my iphone got stole a scooter drive-by while I was walking back home on my birthday night. Happy Birthday Frank! If I ever should get back to Bali, I'd definitely spend more time in the north of the island, where you won't bump into as many tourists as in Kuta, Seminyak and Canggu. Be cautious about your belongings at night. The guys from my hostels told me that I was the 3rd victim within a month, who got robbed by dimwits on a scooter. Bold & Bright Tattoo. As I just mentioned, my iphone got stole on my birthday night, as I was walking home in a very lonsome way... drunk & texting through a shortcut that all the scooters use to get quicker around the city center. While I was busy texting with my friend, as there was no one to celebrate with, a scooter approached me and grabbed my phone out of my hand. The driver just blasted away at full speed, impossible to run after him. I felt devastated... aallll my photos from Bali were gone, my videos, my contacts, my text messages. And of course I had to spend a shitload of money to buy a new phone. Besides the stole phone, I had planned to get two tattoos at "Bold & Bright". Their prices were pretty much affordable compared to european or US tattoo rates. However knowing that I had to spend the money on a new phone once I'd be back home, I decided to cancel my appointments. Ocen, the tattoo artist, was the nicest person I crossed path with in Canggu. There was no problem with canceling the appointment, even though he told me he could lower the price if I still wanted to get tattooed. The next day after waking up I decided to call Ocen, and get one tattoo done. Despite low expectation, or maybe high expectation in some points, Bali had a kind of "wow-effect". It was the first time I ever felt the island vibe on a trip, because I was used to experience the big city life while traveling. It was the first time as well, where I jumped on a surf board, and for a long time I knew somebody would be waiting for me when I get back home. So I decided to bring a lasting souvenir back to Luxembourg. Ocen was very welcoming on the day I had my appointment. He showed a lot a patience and he asked funny questions when I told him he should add a special letter to the tattoo. We talked about tattooing & music (his favorite band was Alkaline Trio), while Matt Skiba's solo record was playing in the background. I turned back home totally satisfied with my fresh tattoo, that cost me around 200$. It took me too many years to visit beautiful Thailand. Years ago Thailand used to be one of the most popular tourist destinations. This kept me from visiting Thailand. Nowadays it's gotta be Bali... everybody wants to visit Bali. So I thought: this gotta be it! Now is the right time to give that asian country a try. All I can tell after these few lines, Thailand hit me unlike any other travel-destination. I'm already planning to get back this year, for a second time. Way too many people told me to skip or avoid the capital Bangkok. After all the photos i've checked out on google, the reviews and stories I read about Bangkok, I was so convinced that I would enjoy the busiest city of Thailand. One of the main reasons why my few days in Bangkok were worthwhile, had probably to do with the lovely human encounters I experienced. It all started with a simple thank you at the airport. This might sound pretty goofy, but I think the way thai-people are thanking you, with folding both hands together and rising them upfront to the face, is just the most sincere way for showing your gratitude. After visiting quite a few asian countries, this was the first thing that I noticed at the airport: "Khob Khun Krup" (thank you for men). My first thought "ok, cool, that's a thai-thing". Of course the taxi ride, struck my mind as well. It took me almost an hour to get to my hostel, because traffic is usually very busy in Bangkok. With a pretty good tip, the cab-ride cost me less than 10$/€. After checking in at the hostel, I noticed that all the guests had to take off their shoes, before entering the main areas of the hostels (bathroom, kitchen, garden, dorms...). It definitely felt like far away from home. I stayed 4 nights in Bangkok, and all I've seen was the main area, the pretty much touristic center surrounded by temples. Of course you do have many small alleys, where all the local people live or hang out. However I didn't manage to make it to the skyscraper area on the east side, or to the north the more rural area. Temples, temples ... and even more temples. It was obvious, like in Korea, Japan, Hong-Kong... I would do many temples, and after a while I would be bored by temples. The high & colorful "prangs" which are the most eye-catching parts of the temple, were pretty much fascinating. "WAT ARUN" and "WAT PHO" were the ones I enjoyed the most. While riding a tuc-tuc across the city, you will notice those diverse temples along the road. There are just too many temples in the city. Just a quick reminder! Taxis are way cheaper than tuc-tucs, because they're using the taxi meter. I wouldn't bargain or set a fix price, because the cabs in Bangkok are dirty cheap! Tuc-tuc driver don't even bother for the low-price rides, they'll just send you to the next driver. The Grand Palace was definitely a very beautiful tourist attraction! The colors, the architecture, too much gold glitter, walls filled with precious stones, ... it's worth the visit! However the place was so crowded that I just left my camera in my bag, you couldn't get a descent shot of the place. And it was the only temple/building where I wouldn't get in with shorts. They're renting pants or you just can a buy cute elephant pants as a souvenir. The "Golden Mountain" temple is worth checking out as well ! As you will have to climb up too many stairs, however at the end you will be rewarded with a beautiful view all over Bangkok. Is there anything to do besides temple-hopping? I was really looking forward for the floating market. The old ladies on their boats, the scents, the colors, the water... all that would have made a lovely photo shooting. However I was told that the floating market take place on weekends. The best ones would be outside of the city, approximately one hour driving. Chatuchak is the biggest weekend market in the city. I was visiting Chatuchak in the very early evening on a sunday, when some of the stalls were already closing. It's mostly about food & fashion. Sounds boring huh? Trust me it's very hip! I bought around 7 shirts & t-shirts. Most of them were around 2-7$ a piece. I really loved the design, you could sell them easily in Europe for triple the price. They had all kind of street food you could expect. I spent an hour at the market, and I enjoyed it a lot. I'd definitely go back on my next trip to Bangkok. Very nearby was the "Camp - Vintage Market". That one was the cherry on top! Such a cool and hip place right in the center of Bangkok. I'd never expected to discover London's "Camden Town" in Thailand. Old trailers as coffee-bars, vintage cars with surfboards on it, cafe-racer shops, super trendy clothing stores. There was a live band playing soul-music. It was very beautiful place, less crowded and definitely more classy then London's twin-market. Khao San Road. Hate it or love... ? Ok, nope, you won't love the place, but you will definitely enjoy the place. "Khao San Road", also know as the "backpacker street", is the main party road in Bangkok. Why "backpacker street"? Well I have no clue, but I guess, because all the people look like surfers or backpackers. No fancy clothes... flip-flops, shorts, tanktops, that's all you see on Khao-San. I visited Khao San Road on my first night. And I did expected the worst! While walking through the party-mile totally sober, my first thought was to leave that place. I reached the end of the road and fled towards the "Soi Ram Buttri", which is located only a couple of footsteps away. "Soi Ram Buttri" is the total opposite of Khao-San. It still feels backpacker-like, but it's a very quite street. The same alley will lead you to the main-road where you will find quite a few music bars. I went to "JAZZ HAPPENS". It was tiny charming jazz bar. The perfect spot to start the evening. I was the only caucasian at the bar, and I found it very welcoming that the band was switching from thai to english just because of me. Gotta love thai-people! After some greasy finger-food, and a couple of gin&tonics, I felt ready to get back to Khao-San road. I stepped inside a bar that had a japanese name. And that was the place where the madness instantly kicked in. The topless male bartender greeted me, asked my name, and gave me a free shot. The thai people next to me at the bar, didn't take long to start a conversation with me. I paid a shot, they paid a shot, the bartender gave another shot for free... After way too many drinks, I left the bar with a thai dude, and we headed to the nearest streetfood-grill. That's where I made new friends again... short after that I woke up in my hostel bed the day after. I had a hard time remembering how I got home. The next evening I walked back to Khao San Road, because it was the closest place to my hostel, where life was happening at full speed. I passed by a group of thais who started smiling at me, a couple of girls and one guy. As I felt kind of not-ready, no drinks yet, I smiled back and moved on towards the end of the street. One of the girls started running after me, and said "Hey Frank!". I asked her how she would know my name, and then she started laughing "You don't remember us ???". I gently replied with a "nooooope". I joined the group of people and got to know my thai friends for the second time within 24 hours. So if I gotta summarize my last paragraphs, give Khao San a chance. Even though you might bump into tons of rubbish people, i'm pretty sure everybody can have a blast, or at least a fun night, in that street. 3 guys & 2 girls. Canal Boat Ride. If you wanna get away from the bustling city center, you can jump on a boat and get ride through the canals and along the river. It's not gonna be a beautiful boattrip! The water is pretty dirty, you will see a lot of wooden cabins, worn down houses of the locals, too many tourist boats crossing yours, and of course the floating market rip-off. One single person on a boat, approaching you to buy a souvenir or a beer for the boat-driver, is considered a "floating market". It's definitely not a must-do attraction. However I was glad I bought a ticket for the boat tour. I had a whole boat for myself. I managed to get a couple of descent shots on my camera, and you discover Bangkok from a different angle. After all, that wasn't how I expected Bangkok. Never thought I would ride a boat through several canals for almost an hour. Obviously I was checking out Bangkok at a slower pace this time. There's still so much left to discover. All I can tell, I wasn't disappointed at all ! I got to know quite a few lovely people in Bangkok. They told me that Thai people don't eat with chopstick except for the pad-thai dish, they introduced me to sticky-rice and to laughing gas.. so many unimportant things, that I still found it very interesting. And the thai people just loved my most stupid questions about Thailand, which seemed so obvious to them. I will write a seperate post about the second city I visited in Thailand, Chiangmai! Chiangmai, was different, maybe better, but Bangkok was afterall a joy-ride. In the daily news you hear a lot about Israel, mostly about the not-so-enjoyable things that happen in their country or on the borderline with their neighbor territories. However despite the headline-stories about war scenes, rocket alerts from Gaza or the recent knife attacks from Jerusalem, I was always intrigued by Israel, even though I absolutely didn't know anything about the country. An israeli friend from Germany told me about the "Purim" holiday that takes place between the months of February and March every year. You can compare it to the carnival from Germany, where people get dressed up in costumes and go out partying in the streets. Even the religious citizen are allowed to get totally drunk during Purim. It's supposed to be the most funny and exciting holiday of the year. To me, this sounded like the perfect time to visit Israel. I do love the nightlife when traveling, and I love meeting new people who can update my knowledge about their country's culture. Just for your information, most European citizen don't need to apply for a visa. And you don't get to fill out any papers on board. Just pass the passport-control, where you will be asked a couple of questions and that's it "Welcome to Israel". I remember that the people inside the airport and at the train-station were very very welcoming, and helpful to get me on the right train. When I was about to get out at the "HaHagana" train station. I noticed the luggage scanner &metal detector at the entrance of pretty small train-station. Outside one single person was guarding the entrance, while holding an automatic rifle. I figured out that the Israelis take their daily safety-precautions seriously. Tel Aviv. Prior my trip to Israel, I decided to book 5 nights in Tel Aviv, and then moving on to Jerusalem for 2 more nights. Knowing that "Purim" was taking place, having been informed about "Shabbat" (the 7th holy day, where public transportation isn't available), I decided not to rush. However in my upcoming post about Jerusalem I will tell you, why it was a rather bad decision to spend more time in Tel Aviv than any other israeli cities. Tel Aviv is supposed to be very famous for its liberal vibe, fantastic nightlife and apparently it has a worldwide positive reputation in the gay-scene. I don't want to consider Tel Aviv straight up as an unattractive city. However in my own personal oppinion, there's not much to do in the city. As a travel-photographer I do love to take photos that shows the very unique culture of a country. I wanna take portaits of local people, of food, of eye-opening architecture. So that I can bring up the special vibe & flair of the place i'm visiting. The vibe of Tel Aviv was definitely not easy to capture on photos or videos. The shore of the city was definitely one of the attractive spots of Tel Aviv. Just along the beach-walk you would bump into all kind of people: tourists, sporty locals, fishermen, surfers & the older generation chit-chatting on a bench. Walking the beach-walk up north will lead you to a boring lighthouse. Walking south-wards will lead you to Jaffa, the muslim Oldtown of Tel Aviv. I really liked spending time in Jaffa, it's a rather small neighborhood. The Old Town definitely differs from the rest of Tel Aviv's architecture. You can notice its muslim influence. Walking away from the coast will bring you the flea-market. It's rather a mix of flea-shops and flea-stalls. Vegetarian foodporn in Israel. Just next to it, you will have an endless selection of restaurants and bars. Both really look very inviting with lots of colors. However during "Purim" only a very few ones were very busy in the evening. I can't complain about the food, every single food I had in Israel was super delicious. By the way, just in case you wouldn't know (I didn't): Israel is supposed to be the "mecca of veganism". Israel's people (the jews & muslims) do cook a lot of vegan dishes. SAROMA MARKET was one of the few fancy places I discovered in the city. The indoor-foodcourt offered every kind of food, from morrocan pitas, to sushi, to italian pasta. I loved the colors and the touch of industrial-vintage-modern design of the market. Right outside of the foodcourt is an outdoor shopping area, it's a mix of parks, playground and fashion shops. SAROMA was a pretty area compared to the worn down houses of the Florentin neighborhood that I passed through every day. BEST RAMEN OUTSIDE OF JAPAN. I love ramen, I tried so many ramen soups, when traveling I love discovering new ramen places, it's all about ramen. All I can tell is that I had a WONDERFUL ramen at the ramen-shop right next to my hotel "Hiro Ramen Bar by Aharoni". Yisrael Aharoni is an israeli celebrity chef. There are two of Aharoni's ramen restaurants in Tel Aviv. Don't miss the opportunity to get some mouth-watering japanese dishes. I tried'em all, from salads, to gyozas, to japanese-oriented cocktails. I spent 5 nights in Tel-Aviv, which means I had 5 ramen in total at Aharoni's place! Nightlife. What really surprised me, was the fact that everything is pretty expensive in Israel. Restaurants aren't cheap, booze ain't cheap at all, which means the israeli nightlife experience can have a heavy toll on your wallet. I spent my holidays in the well-known hostel "Abraham Hostel" in Tel Aviv. Even at the hostel's bar you would easily pay 7-8 €/$ for a glass of wine, Gin&Tonic were about 10 €/$ for the cheap-brand-cocktail. Despite the expensive little-pleasures-of-life the city offers a great nightlife all over the week. I can't tell if it might have been because of Purim, but any day of the week, most of the bars we visited were totally packed. I will list you a few to check-out, some that are pretty popular in Tel Aviv: KULI ALMA. Kuli alma is a very arty cafe/club, colorful walls, stickers and posters all over the place. The crowd is pretty hip, and they still offer fair prices on drinks. The music varies from electronic to hiphop. Definitely a place to stop by for a drink while doing a pub crawl with friends across the city. BUXA. Buxa a small bar/club in a basement, which got a special vibe. We had a hell of a night during Purim. The tiny size of the club makes it pretty easy to bump into people and start a chit-chat. It's right on Rothschild avenue. RADIO EPGB Radio is another basement bar. We were there for a hiphop night, great music & lovely outgoing people. I really loved the place. The dimmed lights in the club and people dancing all over the bar gave this place a really welcoming vibe. Loved it! JIMMY WHO Many israelis told me that JIMMY WHO wouldn't be a cool place at all. I was visiting JIMMY WHO on a wednesday, it was my last night in Israel. I LOVED it. Around 22:00 (10pm) they had a funky live band playing pop & soul music. After the show the DJ played some dance music... the whole bar packed with people and too many pretty women. I was doing a pub crawl with the hostel, and was disappointed that we left too early for the next bar. The only negative part were the prices, we paid almost 20$/€ for 2 shots of Vodka. Definitely not the place where you wanna get wasted. Summertime in Winter. Even though I didn't enjoy the city that much. I would give it another try though and turn back during the winter season. The weather was lovely every single day, t-shirt weather in the afternoon, sweater temperatures in the evening. The food discoveries were definitely my highlight in Tel Aviv. Go for Falafels, Tahini, Shakshuka, ... you will never get tired of the mediterranean/arabic food culture. I loved "SABICH" pitas, it's a grilled pita bread filled with eggplant, tahini, hummus, 2 hardboiled eggs and a diversity of prickles. Yum! Their pastries, a fest! I stayed at the Abraham Hostel in Tel Aviv, and the one located in Jerusalem. Abraham-hostel offers their own tour-service called "Abraham Tours", where you can book pretty interesting and affordable day trips or city-activities. One of the cool features, was the shuttle from Tel Aviv's hostel to the Jerusalem hostel. No need to get your luggage to the next bus-stop or train station. I will post a more in-depth review about the hostel and my booked Abraham-tour in a couple of days. Jerusalem was definitely on the winning side of my trip. Keep your eyes open for my next post about the capital of Israel. As I finally decided to get my shit together and finalize the booking of my Cuba trip I decided to spend a whole week only in the capital Havana. A day-trip to Vinales would have nicely fit into my schedule. However doing 3 cities within a week sounded too stressful. I haven't had a "relaxed" holiday for quite a while, so I decided to take it slowly on this trip. Too many people advised me to spend only 3 days in Havana, and then I should move on to Trinidad. Everybody was bragging about that little gem of a town. I didn't give it too much attention and stuck to my plan. Now that I got back from Havana, I'd totally advise people to stay at least 5 days in Havana. You can easily do daytrips to the beach "Playa del Este" or like previously mentioned the beautiful city of Vinales. I can't imagine that you will feel the vibe of the city within only 3 days, it takes more than that. What to do in Havana? Obviously as soon as the name Havana pops up, people do think about the colorful streets of Old-Havana. "Habana-Vieja" definitely is the prettiest neighborhood in Havana. It's clean, it's lively and easy to get around. The only thing I didn't like about Old-Havana, it didn't look authentic. "Obispo" street is the main shopping lane leading through the city-center. It's packed with shops, in which ones you won't meet a local cuban, it's just too expensive. The shops are pretty much boring, except for a couple of old bookstores selling books & collector-items of Fidel & Che Guevara. As I was spending my holidays during the cuban winter season, too many places like bars & restaurants looked deserted. It didn't feel like the partying Havana-City that we all know from the movies, it was just the total opposite. I liked walking through "calle Obispo" just for the fact, that it was packed with people. I love having a cup of coffee and watching people passing by. Vedado. I won't start listing all the places you should visit, that you might find in a tourist-guide. I really didn't focus on any of the very touristic places. I really wanted to discover it on my own. I will tell you a little more about the main neighbourhoods "Habana Vieja" and "Vedado". After the end of my trip I noticed that I couldn't have had a better experience in Cuba than this first 8 days in Havana. Too many of my friends, who returned from Cuba, agreed that it was a lovely island, however none of them wanted to get back. I gotta admit that I became quite a fan of Cuba. I'd definitely recommend to stay in a "Casa Particular". First of all it's cheap! The average rate for a room is between 20-35 € or US$ a night. So you'd only pay around 180€ a week, which would not even be enough to spend 2 nights in a hotel. Don't hesitate spending a couple of bucks on cuban people in the street. I admit that it can be very annoying being asked 20 times a day, if you want to buy cigars, or if they can show you around, bring you to a bar... it's just annoying. BUT... if you agree on spending one drink (1-3$), the cubans might bring you to a bar you'd have never discovered on your own. In bars, you will meet cuban locals, telling you about the country's history. They will introduce you to other drinks than Mojito & Cuba Libre. They will teach you some salsa dancing or tell you about the most iconic salsa-musicians of Cuba. One random cubano, who asked me for a Mojito, took me to the most simple cuban bar, where Che Guevara was hiding for 3 weeks on the rooftop of the building. Inside the bar, there was a big bell, which they used to wake up "the Che", or let him know when enemies were approaching. Places to hang-out. Old Havana is definitely the nicest spots to wander around the colorful alleys, have a peek inside the livings rooms of the different houses (cuban people always leave their front-door open). Visit different art galleries, have a drink or a coffee, enjoy the different music spots throughout the city, talk to people... It just never gets boring. THE MALECON was another highlight of the city. Everybody knows the street from the photos... fishermen sitting on the edgy walls of the Malecon waiting to catch a fish, american cars driving by, waves hitting the walls and wetting the pedestrians walking along the sidewalk. The Malecon is fascinating at any time of the day. In the early hours go for a morning run, in the afternoon go have a delicious seafood meal at the "La Abadia" restaurant, in the evening walk along the walls like the locals. "La Abadia" was my favorite restaurant in the center of the city. The prices were very descent and you had a view straight onto the ocean. I mostly paid around 10-12 CUC (8-10 €/$) for a seafood-salad, a grilled seafood skewer, and a cocktail or a softdrink. VEDADO was a more authentic neighborhood of Havana, not as a fancy as Old Havana, but you will have a fun time in that area. LA RAMPA, as they call Avenue 23 (Avenida 23) is the hotspot for nightlife. "La Zorra y el Cuervo" is a pretty nice Jazz-Club, you pay 10 CUC for the entrance and get 2 free-cocktails. The night I visited the bar, there was a local jazz band playing, that didn't blow me away. But there were a couple of special guests who made it a very pleasant show. It was funny to see that the jazzclub was packed with japanese tourists, the japanese LOVE jazz music! Just right next to the club, you will find a couple of salsa&rumba clubs. Even the gay-area is right next to the Rampa. I always started my night at the dive-bar "San Juan", where I would meet the craziest cubans on my trip. One night I met a german tourist and all he could say was "man I love this bar!". Almost every night I had dinner at the restaurant "Locos por Cuba". It was just right next to my casa. The service was flawless, the food was delicious, and again crazy cheap (and they had the prettiest waitresses in Havana!). In Vedado you're only steps away from the famous "HOTEL NACIONAL DE CUBA". Also check out the most famous ice-cream spot in Havana called "COPPELIA". Expect a waiting line of 20 minutes to get your scoop of ice-cream. CALLEJON DE HAMEL is also located in the VEDADO neighborhood. It's a block of colorful & arty murals. The Hamel street was built up by the local community to raise money for disabled children. It's a very charming place which is definitely worth a stop. They also have a signature-cocktail called "BILONGO", apparently it's the only place where you can get it. My favorite Bars in Old Havana. BAR YUMURI The bar looks like the real local thing. There's live music everyday, from midday til the early evening. The bar is located just next to the "La Rosalía De Castro" Culture Center. Almost every afternoon I had a Mojito at their place. They didn't serve the best drinks, but I did like the vibe of the bar. That's also the place where I met two of the most memorable cubanos of my trip, Mario & his son Froylan! Their "signature cocktail" (don't expect too much) is the "Compay Segundo". Try it!Location: (#3 Calle Monte between Maximo Gomes (Monte) St. & Dragone St.) LA BODEGUITA DEL MEDIO La Bodeguita del Medio might be the most popular bar in Old-Havana. It's really PACKED with tourists, but the good thing about it, is its live salsa band. Many people are dancing inside the bar. Their Mojito is pretty alright, even though it's very overrated! On a wall you see a writing of the author Ernest Hemingway "My Mojito in La Bodeguita, my daiquiri in El Floridita". Outside of the bar, the walls are filled with tags, names, signatures of people who visited the place. Just hop in grab a Mojito, enjoy the music til your glass is empty, and leave... MONSERRATE BAR Monserrate is one of the popular bars as well, which is also a recommendation of the "Havana Club Rum Museum". But it was one of the bars, which had the best live music in the evening in Old-Havana. The customers were mostly tourists but it was a calm place, and it still felt like a cuban bar and not a tourist attraction. The cocktails were 4 CUC, however almost double the size than the regular highball glasses. Creperie Oasis Nelva The name of the bar might sound odd, but they do have the BEST cocktails in Old Havana. The bar doesn't even look like a creperie (a place where they make french pancakes). I had my first Pineapple-Mojito at Oasis Nelva and it was just marvelous. The interior-design looks fancy, most of the furniture is selfmade. The cocktails are pretty cheap compared to other places in and around Habana-Vieja. The also serve a big variety of organic dishes. Try their "Cuban Lemonade"! NIGHTLIFE. I would totally stay away from Old-Havana, if you're looking for the clubbing kind of nightlife. I was pretty disappointed about the fact that Old-Havana was asleep in the evening hours of a weekend. You definitely need to jump on a cab and drive to VEDADO. Check out "PALACIO DE LA RUMBA DE LA HABANA". The palacio was the first club I discovered on my holidays. Again I invited a cubano for a drink, and after the first bar shut its door, he took me to the palacio. The club opens around midnight and is pretty dead til 01:00 am. On the first night we went around 03:00 in the morning and it was super busy. Obviously they play "rumba" music. I never heard about "rumba" til I set foot into the club. I had a lot of fun in that club and all the cubans were very welcoming. CASA DE LA MUSICA DE MIRAMAR was the second club (or rather a music venue) that I visited. Casa de la musica was more about salsa music... they host very popular bands. LOTS of dancing people, fair prices on the drinks as well. The neighborhood of Mirama is a 15-minute taxi-ride away from the center. The crowd was a little bit older, than at the palacio. Definitely something you wouldn't witness in Old Havana. ENJOY HAVANA. Well Havana isn't just about drinking and eating! Obviously Salsa is a very big thing in Cuba. Why not take salsa classes??? I took 4 hours of cuban salsa classes at the "CASA DEL SON" which is located very nearby the Parque Centrale. 2 hours of dancing classes cost 30 CUC. Most of the teacher do speak very well english. The dancing school looks very nice on the inside, and they do have a bar as well, if you need to loosen up, before the classes or during the break. My teacher Eniley showed pretty much patience for someone with 2 left feet learning how to dance. I'm not a big fan of museums, but I decided to check out the "HAVANA CLUB" museum on my last day, because after all the Mojitos I had drunk, I needed to get more informed about where it comes from and how the rum gets into the bottle. If you're a beach bum you should take a ride to the "Playa del Este". I was told by the cubans that it is a lovely beach. Sadly because of the rainy days on the last part of my trip, I decided to leave the sun-tanning aside. You should combine the beach-trip with a convertible taxi ride. I guess the convertible taxi ride inside an american old-timer is a must-do as well, while in Cuba. Sadly I skipped that part as well, because I was traveling alone and my main credit-card wasn't working in Cuba. So I tried to spend less money to avoid any bad surprises. I did visit a cigar factory though. Was it worth it ? I really can't tell. First of all, you need to get the entrance ticket in advance! I read about it, didn't believe it... and I was wrong. When I went into the lobby of the factory, the security agent told me, that I wouldn't get inside the factory without the ticket from a hotel. Because I was staying in a "casa particular" I had no clue where I should get that ticket from. A taxi-driver outside the factory told me he could take me to a tourist office, where I could buy a ticket. The ticket was 10 CUC for the guided tour through the factory. SADLY... you're not allowed to take any photographs. The different facilities of the factory look very old, traditional and photogenic. I would have loved to take some photos of the factory employees. It's interesting to see where the world-famous COHIBA cigars come from, but in my opinion the guide rushed through the factory. You can't touch anything, you observe the workers from a certain distance. But... while in Cuba... you should at least visit one factory. You won't have the chance to visit a factory in every country. There's absolutely so much to do in Havana... music is big, art is big, rum is big... You hardly ever get bored if the weather is on your side. Prior my next trip to Cuba, I really want to inform myself a lot more about the revolution, Fidel, and Che Guevara. I starting reading a book about Che on the airplaine back to Europe and I would love to visit the precise places where the revolution and its take-overs happened. Cuba always used to be one of the destinations, that was on top of my travel-bucket-list, however it took me ages to make the trip. Usually when I'm visiting a unique country or city, and just right after I fastened my seat-belt on the airplane I tell myself silently "In 10 hours you will be standing in.... (the name of the city)". If it is a long-awaited destination, I really have a hard time believing that it's finally happening. With Havana it was just the same kind of "ritual" again. I couldn't imagine what it would be like to finally set foot in Cuba and again, I couldn't really believe it, that I was sitting on the airplane. After all these joyful thoughts during the flight, I gotta admit, that my face certainly didn't look that happy, when I stepped outside of the airplane. Havana definitely has the shabbiest airport I've ever walked through. Even the ones in India looked fancier. Well it was just an airport! The customs officers were sitting behind desks that looked like zoo-type-cages all painted in red. I stepped forward and softly said "Hola!" (knowing no spanish at all)... the usual procedures with fingerprints & mugshot followed, and I got a gently "Welcome!" from the officer. The baggage-claim was crowded with too many visitors. All the travelers were waiting along one single carousel. It didn't feel like you were waiting at the international airport of the capital. At the main-hall, when leaving the airport, there are a couple of ATMs where you can withdraw money. I didn't wait too long (5-10 minutes), because I landed late in the evening around 22:00h (10pm). At the same ATM you could exchange money, but the machine asked for your passport if you were exchanging cash. The governmental taxis ask a fixed price of 30 CUC (24 € / 30 us$) to bring you to the city. The ride took 20-25 minutes to reach the "parque central" where the most popular hotels are located. I took a hotel for the first 2 nights, because I didn't feel adventurous after 10 hours of flying. After the 2 nights at the hotel, I switched to two different "casas particular" (homestay with a cuban family). More to that later. I stayed at the "HOTEL PLAZA". The lobby looked very descent, old fashioned, but just as you expected a hotel to look like in Havana. I paid 100$ a night! Which was way too much. The room was OK, but I had better hostels for 20$ a night. I wouldn't complain about the hotel if I had paid 20-40$ a night. Just as a quick reminder, I paid 35$ a night at the "casa particular", which looked nicer, smelt better, felt better and of course with a light-breakfast included. VERY IMPORTANT!! BRING CASH!! I had carried two VISA-Credit Cards to Cuba. Two different banks, same country (no U.S. bank of course). My credit-card from the international bank "ING" worked without any issues. The one from my local bank "POST" did NOT work. I contacted all the different services and always was told "your card has not been blocked, and should work just fine. We couldn't notice any denied transactions". The several phone calls cost me about 100€ (115$), and I absolutely got no further help, neither from my bank, nor from the VISA service. Always the same robotic answer. The VISA customer service told me that still some VISA cards wouldn't work in Cuba. But it didn't make sense, why the credit-card from a bank of Luxembourg, wouldn't work at all. You will feel pretty lost in Cuba, if your main-payment-source is being denied on the very first day of the trip. Scams & police intervention on the first two nights. As soon as I stepped out of the hotel on my first evening around 23:00h (11 pm) a cuban girl approached me and asked where I was from, my reason for visiting Cuba, etc. She told me that I was lucky, because on that particular weekend, there would be a "Cigar Festival" and cuban people would sell them at the local low-budget store called "cooperativa". The point of the "cooperativa" was, that only the local people would get the money of the cigars, and not the government. (of course there wasn't a national cigar festival!) I could sense the act of being tricked. However I'm always too naive and I wanted to see what the "cooperativa" looked like. I followed her through the streets of "habana nueva", while talking about Cuba & Havana. The whole neighborhood, which was badly lit at night, looked very degenerated. When we arrived at the shop, they sold me 2 cigars for 10 CUC, which was way overpriced. And of course I'm a non-smoker. After that the girl asked me, if she could show me a local bar. I accepted the invitation, because I was really looking forward for my first Mojito in the city. As soon as we walked inside the first bar, I told her that I would like to move on alone and that I wouldn't like to enter a bar with no customers inside. I told her that I noticed the scam with the cigar, and that I wouldn't bother, but I'd rather leave her alone. She denied the scam and asked for a last favor. She wanted some spare change for buying powder-milk for her little girl. I refused to give her money and walked away. On my way back to the hotel, I passed by a bar that looked pretty crowded, a cubano was waiting outside and asked me if he could show me the bar. I approved and we went inside. The chico asked me to invite him for a Mojito as well. As I was traveling alone, and all the streets looked deserted, I agreed to spend a drink for a little conversation with a local. The 2 cocktails were 16 CUC (13 € / 16 us$) in total. WAY TOO MUCH for Cuba! After we took a seat at the bar, I noticed all the women inside the bar who were approaching us like vultures. Prostitutes of course... many prostitutes! I clearly told them, that I wasn't interested, and they moved back without any discussion. After the drink I decided to get out of the bar, again I didn't like the vibe. Almost having reached the hotel, I bumped into another habanero, who started a conversation. I told him, that I was tired of bumping into people, who just wanted my money and that I don't feel like spending another 8 CUC on a cocktail. The cubano started laughing and said that I got tricked. "If you want, I take you to a place where we get a Mojito for 3 CUC if you invite me." Of course I wanted another Mojito and decided to follow the cuban guy and his girl. We went to the same place where the first lady wanted to get me in for a drink, and of course she was still sitting there. As soon as she noticed me coming in with the cuban guy, hid name was Alexis, she left the bar. But hey, the drinks were 3 CUC at this bar. Alexis was fluent in italian, which was very impressive, because he had never left Cuba in his life. He told me that he learned italian because of an italian ex-girlfriend who was living a couple of months in Havana. Alexis seemed honest in what he was talking about. He also told me about the tricks with the "powder-milk" and the "expensive-cocktails". As soon as local cubans bring tourists to a bar, the prices of the drinks go up. So for exampled they charge you 2-4 CUC more, and when the tourist leaves the place, the bartender and the "inviting friend" split the over-charged-money. It works the same with the powder-milk. Powder-milk for babies is hard to get in Cuba, and of course for locals it's very expensive. They usually ask 10-13 CUC for the milk. Tourists with a big heart, follow the women to the shop, where they buy them one or two packs of milk. As soon as the tourists move on, the "scam-artist" brings back the milk to the shop, gets back the money, and they split it with the shop-woman behind the counter. My advise: never pay more than 4 CUC for a cocktail, a glass of rum is about 1 CUC, a decent meal should never be more than 12 CUC (fist plate, main dish, 1 beverage). The 3 of us, got pretty tipsy/drunk that evening. For a first night in Cuba I couldn't complain. As I could communicate fluently with Alexis, and he never asked for money on my first night, I agreed to meet-up again on the second night. On the second night he brought me to 3 bars. As we left the 2nd bar, 4-6 undercover agents, moved towards us from all directions, some were walking, and some were on a motorbike. Even though they weren't wearing uniforms, I could tell straight away that it was the cops. And they weren't happy to see Alexis with a tourist. Even though I don't speak spanish, I could vaguely figure out what they were talking about (because of the similarity with the italian language). They were pointing towards the directions/spots where I was walking around with Alexis. They knew that I was staying in a hotel near the "parque centrale". Outside of the bar they were taking mug-shots with a mobile phone of Alexi's face. And they told him in spanish "if something happens with the tourist, you will go back to jail.". I didn't want to cause Alexis any trouble, so I told them in italian/english, that I was alright, and that he was only showing me around. Stupidly I proved them that I was a police-officer as well, and they all started laughing, showing me their hidden guns, shaking hands, and telling me to be cautious, pointing at Alexis and saying "bandito viejo" (old bandit/criminal). Before the cops showed up, Alexis already told me that he spent 2 years in prison, because he was refusing to work for a monthly salary of 40 CUC. That would be a reason enough to go to jail in Cuba. However I can't tell if that's true or not. It was a fun night though. It was a weekend, and Old-Havana, the most touristic spot in Havana was dead on a saturday night. Most of the bars/restaurants were closed after midnight. So I felt alright, having spent a night-out with a "bandito" who showed me around, than spending a lonesome night somewhere else in bar. However because I spent about 100 CUC that night on drinks, I decided to check out Havana the next day on my own. And it was time to check-out of the hotel and move on into a "casa particular". Safety in Havana. After the police-control Alexis told me that two officers already asked him outside of my hotel, why he was following me. That was during the first 24 hours. It's crazy to witness, how the Cuban government wants the tourists to be & feel safe. Besides Japan, I've never visited a country where I felt that safe as in Havana. At night I often walked by myself through the darkest and dirtiest alleys. There wasn't one single incident where I felt unsafe. Many Cubans told me that the population of Havana would be around 3 millions, and that there were 1 million police officers working in the streets of "La Habana". I can't tell if it's true. All I could notice, is that the cubanos don't like the police that much, but they show a lot of respect towards the officers as soon as they show up. Especially Old Havana and Malecon is packed with officers and patrol-cars. Even the Cubans are convinced "Cuba is the safest country in the world." After my mind-blowing trip to Lisbon in 2016 I decided to get back to Portugal for this year's summer holidays. I had no clue about the southern part of Portugal called "Algarve" therefor I randomly picked the two cities "Faro" and "Albufeira". Faro because of its international airport and Albufeira for its "busy nightlife" (forget about that part!). As closer as I got to the my departure date, I felt like canceling my whole trip. A lack of energy for traveling solo and maybe the fact that I was visiting beach-cities all by myself, were the main reasons why I thought about canceling. One week prior my departure my friend Cristine decided she would join me to Portugal. I also had mixed feelings about that, because I was used to travel alone for the last couple of years... would we get along? At least I couldn't cancel the trip anymore. FARO. My first destination was FARO. Upon my arrival I still didn't know if Faro was a busy city, and what it had to offer. Summer temperatures outside of the airport, the scent of summer in the air, that's all I needed for a peaceful welcome. I took an "UBER" at the airport to get to the hostel, which only cost me about 6-7 Euros (9 US$). The hostel "HOSTEL 1878" is located in an old traditional building with a very unique touch, lots of charming details and a welcoming staff. After my check-in, the guy at the lobby informed me about a folk concert on the rooftop. It just seemed like the perfect first night. About 25 people were watching the concert. The bar on the rooftop, offered red wine for 1.50 Euro a glass, or 3 Euro a Gin&Tonic. The neighborhood looked very traditional and I definitely felt like being on the best spot for my summer holidays. Sadly Faro didn't have much to offer. I checked out the city center considered as the "Old Town", which was packed with tourists, lots of shops, restaurants, and only a few bars. On the first night I discovered the little gem called "BISTRO 31". A local restaurant with very limited tables. Fabio the owner of the place, his girlfriend and his lovely daughter were the soul of the small business! Every dish I tried at their place was a unique experience for my palate! That's why I decided to get back to "BISTRO 31" every night during my stay in Faro. My lovely friend Cristine, who joined me in Faro on my 3rd day, joined me on our last night in Faro for an amazing dinner. I'm glad she liked the dinner as much as I did. On my second day in Faro I walked through the city center, the harbor area, and went to the fanciest shopping mall in the city. There's really nothing to do in Faro except having great food, and getting drunk on delicious cocktails, wines, or port wines. It's a quiet city, even at night, the busiest bars didn't feel like a club or a dancing place. This doesn't mean that I didn't appreciate Faro. I'd recommend it to families who don't have any bigger expectations about their summer holidays. Faro definitely is more lively at night. During my short 3-day-stay a couple of events took place: as the "seafood festival", an electronic festival called "Etcetera" or the "Baixa Street Fest" in the old town. For the hostel part, most guests only stayed for 1 night. People checked-in and left the place the following day, so it wasn't really easy to socialize with the travelers and make new friends. Another bar I'd recommend was the cocktail-bar "COLUMBUS", their staff puts a lot of effort to make great-looking cocktails. ALBUFEIRA. Cristine and I left on a sunday morning towards Albufeira by train. The train-ride took about 1 hour and the single-fare cost around 2-3 Euro. A bargain! The train-station of Albufeira is located a little bit further outside of the center, so we had to take another UBER ride. After a 12 minute ride we made it to our "Topazio Hotel". The whole neighborhood just looked like any other beach town. I can't say that I enjoyed Albufeira at first sight, but at least it seemed a little busier than Faro. We left the hotel as soon as possible and walked towards the rocky beaches of the Algarve. I can't pretend that I'm a beach-bum and I've hardly ever been to an astonishing beach. So all I can tell is, that Albufeira is probably the prettiest sandy-beach-area that I ever visited in Europe. The shores weren't too busy for the high-summer-season, the water looked very blue-ish, and the beach restaurants offered satisfying seafood dishes (and delicious sangrias!). However as I mentioned in the introduction of this blog-post, the nightlife, that everybody was bragging about, was definitely the worst I've experienced in a long time. There are just too many bars in the city center. Too many empty bars, lots of 80s music, lots of families, lots of bored people spreading their boredom all over the place. The cocktails are watered-down, the bars & restaurant's indoor designs looked pretty odd and all alike, just too many Brits in a portuguese city. I was glad that we discovered two good restaurants during our nights. I can't complain about the food; we had some great cataplanas at the "O-manjar" restaurant in Albufeira, some delicious tapas at a shisha-restaurant outside of the city center. (I can't stand shishas, but the food was alright, and so were the cocktails). We decided to move on towards Lisbon instead of extending our stay in Albufeira for one more night. My highlights of Albufeira were the organized tours. We took part on a boat-trip to witness dolphins in the sea, and to get to the Benagil Cave. The Benagil Cave is only reachable through the water, by boat or by swimming. It was a very eye-opening place, however the cave was packed with too many visitors upon our arrival. Sadly the tour-organizer didn't let us leave the boat, so we only had the chance to get some shots on board. The next day we decided to do a kayaking tour alongs the rocky edges of the shore. Kayaking along the cliffs, through the caves, in the blue water, was pretty enjoyable. The fun tour lasted about 2 hours. This was definitely my highlight of the Algarve. Each tour was about 30-35 Euro a person. I'm not a huge fan about organized activities, however I have to agree that the organizer did a flawless job. LISBON. I would be lying if i'd tell you that Lisbon had the same wow-effect as it did last year. All the neighborhoods looked pretty much familiar to me. I remembered some restaurants that left some culinary marks in my stomach and in my heart from past year. I jumped into a couple of shops which I promised myself I'd turn back next time in Lisbon. Last year I got my phone stolen, because of that I wasn't able to write a review about the "YES HOSTEL"in the capital of Portugal. It was pretty obvious that I would stay at any costs at "YES HOSTEL" again. Because we didn't plan to extend one more night in Albufeira I had to make 2 different bookings. One booking for 1 night, and the second booking which I did at home prior our departure for 4 nights. While we were checking in I noticed that I only booked one bed. Sadly "YES HOSTEL" was fully booked on the very first day and we had to change plans. We stayed one night at the "Cheese & Wine Apartments" close to Alfama. Instead of paying 50 euro a night, we had to pay 200 euro a night. But! Considering that the apartment had space for 6 people (3 beds) I can't imagine about a better apartment for a group of people, and spending only about 30 euro a person. Upon our arrival at the apartment we were offered a complimentary bottle of red wine, and portuguese cheese. The next day we checked-in at the hostel. From the outside I noticed Fabio behind the check-in desk. Fabio and I pretty much became friends during my first stay in the city. I was curious if he would still recognize me 12 months later. While he was busy doing the check-ins, we walked in and waited for our turn. Just seconds later Fabio noticed me and Cristine in the corner and we got the warmest welcome ! Fabio started talking about my recent trip to India, about another luxembourgish customer... while the other guests were impatiently waiting with open-eyes at the counter. There were two things that made my stay in Lisbon unforgettable. As you can expect, the first one was meeting Fabio for the second time, and the 2nd one was the Cabo da Roca, which is the very western point of Europe. I will come back to the Cabo da Roca later. Well I gotta admit, it was lovely to travel with a girl after all those years of solo-traveling as well. If you're a vivid Instagram-User as I am, you will find endless spots to visit in Lisbon. There are so many great looking bars and coffee-bars, but I only had to chance to visit one or two. Beside my Instagram-Check-Out list, I still needed to get to the creative-hub "LX Factory" which is located just below the big red bridge. Lx Factory is packed with lovely souvenir stores, a diversity of restaurants, designer shops, and a great shop for "cafe-racer" fans. The "Time Out Market" was on our check-list as well, however visiting it right after having had breakfast, wasn't the smartest move. The food at the different shops looked very mouth-watering. However I didn't feel like waiting another hour, that's why we went on to Alfama. On our last day we opted for Cascais and Cabo da Roca. Fabio told me that ages ago "Cabo da Roca" was supposed to be the "end" of the world. It was the spot where the earth would end, and the ocean would begin. Once we made it to the edgy cliffs of "Cabo da Roca" I totally got the vibe my friend was telling me about. I've never been to Scotland or Ireland, so I can't tell about their nature spectacles. This was my first time, where I could witness this natural beauty. ““Aqui ...onde a terra se acaba e o mar comeca”” We took a couple of photos on the edges of the cliffs. Sitting down for a couple of minutes, you could only hear the ocean breath, the waves hitting the rocks, and the neverending gaze in front of you. I would love to get back to that place on my next trip, but in the very early morning, or very late at night. There's definitely so much left to discover inside and outside of Lisbon. A short train-ride (2.5 Euro) will bring you to the nearest cities within a heartbeat. If the train-ride's too slow, grab an UBER. The cities of Cascais and Belem are definitely worth a visit. Belem is known for its delicious pasteries "Pastel de Belem" and its Belem-Tower. Cascais is the "Cote d'Azur" of Lisbon, everything just looks fancier over there (but doesn't have to better). On our way back home from the Cabo da Roca, my friend Daniel showed as another great beach spot that looked totally fabulous. It was just mind-blowing driving by the beach of "Praia do Guincho" which was crammed with kite-surfers. Next time it's gonna be on my list! In May 2017 I visited Osaka for a third time, and it definitely wasn't the last time. After visiting Tokyo twice, and Osaka twice as well (prior the recent trip), it was obvious that I was rather the Osaka-kind-of-person. This time I wasn't walking around all day with a camera in my hand. I enjoyed my little moments in the city, observing people, having coffee, eating street-food, and meeting up with old and new friends at night. My recent trip to Osaka wasn't meant to bring back home the best photos or videos, to convince my friends and blog followers how awesome the city is. People who have been following my posts on this blog or on Instagram, should know by now that I'm a big fan of Japan. After being around most corners of Osaka, there wasn't much left to discover, however I never felt bored while walking through the streets of Namba. Let's start with the coffee places. This was the first time, where I was hunting for good and hip coffee places. The best coffee bars I visited were located in Amerika-mura (american-village). As you can figure out by the name, the neighborhood is heavily influenced by the western world. It's packed with western clothing brands, american bars, but the hippest coffee spots as well. My favorite bar was "LiLo Coffee Roasters" because of it's interior design; the staff was very fluent in english, and they had too many coffee-accessories for sale. Right next to Lilo's place, was another awesome coffee bar called "Streamer Coffee Company". At first sight from the outside I thought it would be a skateshop pimped up with a coffee-corner. I gotta admit that Streamer actually had the best coffee I tried in Osaka. It's not as cozy as Lilo's corner, but it's definitely worth a try. Arashiyama What would a trip to Osaka be without witnessing the beauty of Arashiyama? Arashiyama is well known for its spectacular bamboo forest. The bamboo forest actually doesn't take that much time to visit, think about 15-25 minutes. It's always hard to get a descent photoshot of the path leading through the forest, because there are just way too many visitors, any time of the day. However Arashiyama is always on my list, when visiting the Kansei region. I just love the whole vibe of the village: mountains, rivers, cute little shops, food stalls, japanese people dressed up in kimonos. For the first time, I decided to visit the monkey forest. You gotta walk up a very steep hill for about 25 minutes, til you reach the top of the monkey place. You'll get a beautiful view all over Arashiyama and Kyoto. You'll get the chance to feed the monkeys, who'll be eating out of your hands. The coolest thing was that the visitors will walk into a cabin, that feels more like a cage, and you'll be feeding the monkey from the inside through the fences of the cabin. So it doesn't feel like a zoo, where animals are captivated for the visitor's pleasure. The monkeys are jumping and climbing freely around the cabin. Those monkey hands felt like baby hands grabbing for food, it definitely was worth the way up to the mountain. If you're looking for the "kawaii" (which means cute in japanese) side of Japan, you should stop by at the Katsuoji Temple. I heard stories about it many times, but never made it to the very north of Osaka, because it takes about 90 minutes to get there. You gotta use two different trains which will lead you to the Senri-Chuo station. Outside of Senri-Chuo station you will have to catch a 40 minute bus-ride that will drop you at the entrance of Katsuoji-Temple. However the last bus will leave the train station around 3pm or 4pm. As lucky as I usually am, I had to use a taxi (single fare was 35 euro / us$). I left the temple about 5pm, and bad luck stroke again. No buses after 5pm, no taxis around the temple. Me and a 14 year-old chinese boy walked down all the way to the city. The walk took us almost an hour. I couldn't speak chinese or japanese, and the chinese teenager couldn't communicate in english or japanese. But at the end we somehow managed to jump on a bus, that brought us back to a train station after almost 2 hours. After visiting a couple of japanese cities, you easily get fed up with temples. Katsuoji however was different, in a funny way. The whole place is packed with daruma dolls, which creates a unique atmosphere. The daruma dolls at Katsuo-ji Temple are called "Kachi-daruma" (winning daruma). The darumas are eye-less goodluck charms. People are supposed to draw an eye on the doll's face when they make a wish, and draw in the other when their wish comes true. When one's daruma-doll gets both eyes drawn in, it should be brought back to the temple. Last but not least, the Taiko Bridge of the "Sumiyoshi Taisha" shrine. Again, after having witnessed numerous temples in Japan, it gets harder with each trip to be impressed about wooden temples. I have just seen to many temples in Japan. However I haven't ever seen a round bridge like the Taiko Bridge in Osaka. The first one I have ever discovered was outside of Asia, at the Japanese Garden in San Francisco. That's why I decided to jump on a train towards the Sumiyoshi shrine. In my opinion, the shrine didn't blow me away. However the bridge sourrounded by trees and a pond was worth the shot. Nightlife in Osaka. As I mentioned in the beginning of this post, that one fact that I really enjoy about Osaka is its nightlife. I mean it's not always that easy, to get in touch with japanese people. Some of them are too busy for a conversation, some are too shy or insecure to communicate in english and some don't understand any english at all. Most of the japanese people, that I had the chance to get to know, were having a drink in a bar or they worked as bartenders. It's just the perfect place to get into a chitchat. In Osaka it's even possible to bump into the same person on the same trip, which hardly ever happen in any other big city. I wouldn't brag about Namba for being the best place to go out, because there are just too many streets or bars left to discover. Some bars or clubs will always remain undiscovered for many tourists, because they aren't barely visible from the outside. I remember a club called "Bambi", where a french expat took me to. We took an elevator to the 7th floor, and as soon as the doors of the elevator opened, we stepped out right into a club. It's very common in Japan to get on top floors for having dinner or a drink. That's why locals know the best places to check out. As far as my experience goes, I'd recommend these places while going out in Osaka. They're all reachable by foot and only a couple of minutes separated from each other. Bar Zerro {Namba} The Zerro Bar is a bar packed with locals, tourists, and expats. It's usually very busy. Most of the bar tenders are pretty fluent in english. Every time I went for a drink I met people from all over the world. It's not the coolest place, but if every other bar is empty, you'll definitely find some people at Zerro. Cinque-Cento (500) {Namba} Cinque-Cento means 500 in italian. That's where the bar got its name from, because every drink or meal on their menu costs 500 yen (4 € $). The drinks are served in average size glasses, and they don't look as fancy as in a cocktail bar. But you can get a Moscow Mule or a Maitai for a very fair price. All of the bar tenders were very friendly and easy to talk to. While drinking and talking to them, they could tell you some fascinating facts about Japan. "500" easily became my favorite bar in Osaka on my last trip. And yes, you also get some finger- & fast-food for 500 yen. Mustang-Bar {Amerika-Mura} On my recent trip I didn't make it to Mustang, because I couldn't leave "500" and because Mustang is located in Amerika-Mura, the neighbor-area of Namba. But on my two first trips I had a blast at Mustang. The main reason was most definitely because of the bar-owner Neil (or Neal), an expat from Israel. Neal is high probably the craziest dude in Osaka. He used to be very entertaining and made every customer laugh with this harsh jokes. "Mustang" is a very small bar, recognizable by its ceiling, which is covered by hundreds of hanging bras. Apparently drunk women started to undo their bras, and hang them on the ceiling. I guess it's just another prove how crazy it can get at Neil's bar. Kamasutra Karaoke Bar The last episode of my nightly adventures took place at Richard's Karaoke Bar called "Kamasutra". Richard is an expat as well. And it was damn funny coincidence that I made it to Kamazutra. Six or seven years ago work colleagues told me about their crazy night at a karaoke bar where they were introduced to the bar owner called "Richard". After a drunken night at 500, some japanese people took me to a karaoke bar. It was my first time ever at a Karaoke bar. After ordering another round or trinks and starting a chit-chat with the man behind the bar, I figured out his name was "Richard". I took out my phone, to check out if the photo of my friends at "that" Richard's place was the same one where I was sitting. Richard burst out laughing, because he was still remembering the night where my colleagues were visiting him. "Those crazy guys from Luxembourg... that was a hell of a night!". Sometimes the world just seems so small, when coincidences like this one happen. I went back to Kamasutra one more time before leaving Japan. I had a blast every night! As you might have read in my blog-posts about my India trip, I sounded pretty fascinated about this little gem of a guesthouse. I tried 'em all during my journey in India, cheap hotels, one fancy hotel, a hostel and this guest house. Maybe it was the perfect match with the city, the calm laidback athmosphere at this guesthouse & the spiritual vibe all across Varanasi. All I can tell is that, Ganpati fulfilled my expectations, and that this guesthouse made me feel, like I initially expected it to be. I remember when my friend José showed me his photos of Varanasi and a couple of images of this guesthouse. Both just matched perfectly together. When I was trying to book a room at the website "booking.com", I was told that the guesthouse was sold-out during my stay in the city. But luckily a week later, I got to manage to book the last room available. GANPATI was the second "hotel" I checked-in at in India, and without any doubt it was the place where I instantly felt at home. I got a warm welcome by the guesthouse-staff and you could really feel, that the clerk at the front-desk, made some efforts to explain me how the boat-trips work, how to get to the roof-top restaurants, how much I should pay for the different services along the ganges river. I didn't feel like a living dollar-sign at this hotel. I read some unpleasant reviews about the guesthouse, so I really didn't know what to expect. Once I figured out that I would get room number 7, right in the middle of the courtyard, I felt really happy. There are lots rooms which are facing towards the river, however the ones in the center of the building, seem more peaceful and colorful. All room-doors were locked with a golden-shiva-lock. Everything was very charming about this guesthouse, the colors, the vintage locks, the scent of the rooms... The rooms weren't fancy at all, but you aren't asking for any kind of luxury when checking-in at a guesthouse. The rooms were very clean, the bathroom as well. The bathroom lacked some space, but it didn't bother me at all. I loved staying on my bed during the day, with the yellow room-door wide open. You could hear the calming noise of the water-fountain. On the roof-top there was a restaurant, that was serving food til midnight. Their menu consisted of only vegetarian dishes. The dishes were very simple, but I couldn't complain. The waiters were extremely friendly, and the food was very cheap. During my 4 days in Varanasi, I only had food at their restaurant, because everything just seemed perfect. The food tasted fresh, and of course I didn't get sick of it. There's a main-exit that leads straight down to the ghats, right to the river's edge. On the rooftop you can enjoy your breakfast or lunch with a beautiful view all over Varanasi. What can I say? There's nothing to complain about. When I was checking out, I told the staff, that I took the room's hand printed laundry tote bag, because I wanted to keep it as a souvenir. I offered them to pay for it, but the lovely man at the desk told me I could keep it for free. As soon as I left the guesthouse, I got one last "namaste" from the door-man. Everytime I left or entered the guesthouse, a "guard" opened the door, put his both hands together close to his chest and greeted me with a "namaste". I loved GANPATI GUESTHOUSE, it was one of the few lovely experiences I brought back home from India. Varanasi is supposed to be the oldest city of India. Not only the oldest, but also the holiest. Among the 5 cities I initially planned on visiting, Varanasi was the one I was really looking forward to discover. On the airplane to India, I started reading a book about the Sadhus of India. "Sadhus" are holy men, considered as renunciants who have chosen to live their life apart from society to focus on their own spiritual practices. Some sadhus used to be wealthy and successful people, but they chose a path in their life where they would cut all familial, societal and earthly attachments. This way they could achieve their purest and highest spiritual level. Sadhus don't lead a normal life like others, they choose to live poorly and only find richness in spirit and humanity. I was told by a local in Varanasi, that they use the ashes of cremated bodies to cover their skin, because the ashes of the deceased is the last remaining of a human body on earth just before it reaches heaven & god. I found the lifestyle of the Sadhus very fascinating. Sadly while discovering my first Sadhus in Varanasi, I was told that the holy men I'd meet along the ganges river, would be fake sadhus. Those were the beggars, who'd ask you for money if you'd take a photo of them. Which was actually true, some were even begging for a photo, because all they were looking for was getting a tip. Some of the boatmen considered those "fake sadhus" as lazy people, who were getting high all day, and they were making it through life just because of their fascinating look. I even noticed myself, that those sadhus were accepting money from the very poor people. The poor people were still convinced that the beggar sadhus, could bless them, for having a better life. That's how my interest in finishing the book about the Sadhus stopped! Nevertheless I was told, that there were real sadhus out there in Varanasi, but the real holy men, wouldn't hang out along the river. They would stay away from the crowds, and they would never dare to ask for a tip, if you would shoot any photos. The topic of the Sadhus still remains fascinating. Varanasi, wasn't only about the Sadhus. On my first day, upon my arrival at the beautiful guesthouse "Ganpati", I was told that there were 3 main ghats "burning ghat", "assi ghat", and guess the next one, "main ghat". The stairs that lead down to a river are called "ghat", which are usually very big stairs, big enough to do any kind of activity like meditation, yoga, washing clothes, ... The burning ghat is a public holy place where only Hindus cremate their departed in a sacred ritual. People are allowed to watch the whole ceremony, but taking photos isn't allowed, out of respect for their family. The locals still allow tourists to take photos from a boat, considering that you won't notice an morbid or personal details on a photo shot from a further distance. There are 2 cremation spots along the ganges river. At the "burning ghat" only hindus are allowed to get cremated. The cremations take place 24 hours a day, and 7 days a week. There's no time off. At the entrance to the ghat, people can weigh the wood, which is required to cremate the body. The cremation takes about 3 hours for one single body. The family gives the dead body a last massage at home, with natural oils, to make the deceased "feel good" for one last time, before they reach heaven. At the burning ghat, they wash the body right in the ganges river. Following the cleaning, they put the wrapped up body on the cremation spot. The relatives cover the body with the woods, and spread pieces of sandalwood over the body to accelerate the ignition of the deceased. The family members aren't supposed to cry in front of the body, the mourning takes place at home. After the cremation-process, the remaining ashes are shed into the river. The relatives aren't supposed to keep the ashes, otherwise the soul of the burnt body, would find its way back home. Pregnant women, children, holy men aren't allowed to get cremated, they get all wrapped up, and the whole body is thrown into the river. So there's a chance that you could witness a dead body floating on the water. Right next to the burning ghat there were lost buildings, where people used to spend their last days or weeks. Older people would come to Varanasi, just to die in Varanasi. They believe if they get cremated in the holy city, that they will make it to heaven, and won't get reborn in another life. Burning Ghat Another interesting fact was the "eternal flame of Shiva". Right next to the cremation ceremony you could notice a fire, which they used to ignite the bodies. That's the spot where one of Shiva's girlfriends set herself on fire. For more than a couple of hundreds years, people are responsible to keep that fire burning all day. All the dead bodies are lit up by the "eternal flame". It's not allowed to use any matches or lighters. The second cremation spot down the river, would allow non-hindu people to be cremated. There were daily ceremonies, to praise the gods, at the main ghat (twice a day, at 06:30 in the morning and in the evening), and another early one at 06:00 in the morning at the assi ghat. The main ceremony at the main ghat, was interesting to watch for the first time. There were thousands of visitors every evening. I personally preferred the one in the early morning. Every morning I left my guest-house at 5:30, and walked towards the assi ghat. The walk took about 20-25 minutes. Sadly it wasn't a peaceful walk, because some boatmen were awake by then, and kept asking the early birds for boat rides. The ceremony at 06:00 am at the assi ghat, started with a fire ceremony, were they burnt cow dung, to worship god. While they were doing their thing, you could observe the most beautiful sunrise arise. It was such a serene moment. And with a little luck, if you would find a spot close enough to the ceremony, the boatmen didn't dare to bother you. After the fire ceremony, followed a concert with indian meditation music, and a free yoga session. It was interesting to see the older generation sitting down on the floor and participating at the yoga class, which mainly consisted of pranayamas (breathing exercices). I wish I had participated as well, but all the instructions were in hindi, so i didn't feel comfortable sitting down among the locals, and too many tourists around me. It was also fascinating, to see how yoga is "normal thing" for the indians. People were dressed up in their daily clothes. Some used a towel, others just a plastic bag. There weren't any yoga mats, no fancy yoga clothes, ... it didn't look like trendy thing, as we know it from the western world. Some tourist girls tried to be even more indian than the locals, and they tried really hard to be the most convincing yogi among the locals. It looked so pathetic. After the whole ceremony which lasted around 90 minutes, you could watch how the locals of Varanasi, made it the shore, to take a bath, wash their clothes. Another thing I hadn't seen before. Some of the locals were meditating towards the sunrise, others completed their yoga postures. Kids started running around. It felt very uncommon for me to see so much life in the streets at seven o'clock in the morning. Varanasi totally fulfilled my expectations, how I had imagined India. However I gotta admit, after 3 nights in Varanasi, the endless "GOD" topics and stories, got a little to much. The locals would mention Shiva, Parvati, Ganesha, in every second sentence, it was all about the holy river of ganges, shiva power (weed), shiva-city (Varanasi), holy cows, pujas (prayer ritual)... The indians would even drink the water of the ganges river, the dirtiest of the dirtiest rivers. The walks along the river and the different ghats never got boring. I totally appreciated the mix of street art, hand-painted letterings, and the very old architecture of the city. There wasn't much going on in the busy main streets of Varanasi. It just looked like any other indian city. The narrow alleys, that felt like a walk through a maze, were another charming part of the city. However the streets were most likely very dirty. Cow shit and urine all the way. Too many police officers on every corner, due to a recent threat by the pakistanis, who mentioned they would blow up the "golden temple" of Varanasi. That's why there were too many heavily armed police men, as well the military, securing the streets. Even though the boatmen could get very annoying, the boat rides were the only quiet moment you would find along the river. I took about 3 boat rides during my stay in Varanasi. I got to know a lovely man, called "Diamond" (which is the translation of his hindi name). Even though, I was just another customer, Diamond seemed to be very legit, and I had the most interesting discussion with that man on his boat. The boatman explained me that there were too many boatmen on the river, more boats than tourists, which would make it pretty hard to earn any money. Diamond allowed me to switch places, and I had a chance to get a grip on the paddles. I gotta admit that it was a pretty hard job rowing for 30-60 minutes. Diamond was half my size, and he would keep on rowing for an hour. I could feel my shoulders getting tired after 5 minutes. Despite the amounts of physical power they had to put into the rowing, the boatmen only made 5 to 10 euros/dollars an hour. Diamond proudly showed me his shiva tattoo, which he got in Goa (south of India). It was the last time Diamond had ever traveled. Because I was curious about his life, and his stories, I promised Diamond one last boat ride before I'd leave Varanasi. The next day, I took a last ride on his boat. As a gift, Diamond offered me one of his shiva-beeds necklaces. That was a lovely gift! Since the old man told me, that he couldn't afford any new clothes, I gave him two of my shirts I was carrying in my backpack. Diamond gladly accepted the shirts and thanked me with his shining eyes. Varanasi was quite an experience. Now being back home for almost a week, and writing about the city on this post, I actually realize how unique the city was. While being in a city, we're so busy soaking up all the informations around us, the noises, the smells, the views, the people... and once we get back home, our mind gets the time to process all the informations we collected, especially when we start writing about it. That's what I like about my travel blog, it doesn't just keep me busy, sharing photos, videos, and stories with people all around the world, but it helps me processing the memories I collected on my trips, and bring them to "digital paper". Update (02.04.2017). Like I mentioned above, it really does take a while til you realize what you've been through on your journey across the world. I wish I could thank the "yogi" in my video on the top of this page, for being such an inspirational person. While I was observing the early morning yoga session, this gentleman just caught my eyes, and I kept observing him for a while. It just seemed very authentic to my eyes, and I was just blown away to see how much devotion this man put in his daily practice. I guess that's why I also chose to take a couple of shots & film-footage of him. High probably I just looked like any other tourist, taking photos of the locals. I really didn't want to offend anyone, and sometimes I just wish, I could show them what the end-product looks like. Of course it's not a professional documentary and it never will, but it's going to be a souvenir for the rest of my life. My memories in motion, which I will be able to share with my family & friends, and other travelers across the world. Last friday during my first yoga class, following my trip to India, I was happy to witness that I hadn't lost any of my flexibility after a one-month-break. But the most beautiful part, was that everytime I closed my eyes during the asanas practice, Varanasi popped up in my mind. I had all these colors, the sunset, the children's choir chants, the morning yoga rituals, right in front of me. After the class I came to the conclusion that Varanasi had a bigger impact on myself, despite the numerous negative moments I went through on my India trip. Sometimes we just aren't aware of what we experienced on our holidays, til the right moment kicks in, in the near future. I'm so glad that I had the chance to visit Varanasi, and that I was able to absorb and capture the sounds, the colors, the scents of the city. India's been on my travel-list since I started with yoga practice half a year ago. To be honest, I never imagined visiting India someday, til a work-colleague amazed me with photos of his trip to India and Nepal. The city of Varanasi looked so surreal on his pictures. That's exactly how I got really curious about the huge country of India: the origins of Yoga & the holi city of Varanasi. Now after I made it back home "safely", I really can't choose if I should start with my "love" or "hate" part of my journey abroad. This is going to be quite a long blog post, because there's so much to write about. I will get into more detailed stories with upcoming blog-posts about Varanasi and the "Ganpati Guesthouse" in Varanasi. For now, I'm going to summarize my good- and not so pleasant experiences. It all started with my trip to Delhi, the capital of India. My expectations of the capital were pretty low, after I've read too many travel reviews about it, and most travelers were advising to just skip Delhi at all cost. Just for your information, ... Delhi isn't the worst. I had a typical indian welcome as soon, as I left the airplane on indian soil. The E-Visa appliers were split up into different queues. I had to wait almost 50 minutes to make it to the counter, where my fingerprints were taken, a snapshot, and I was good to leave the airport. I went to the "official" taxi booth and asked for a cab. The ride from Delhi international airport to the city center takes about 40-60 minutes. I didn't bargain on my first cab-ride, and was kindly asked to pay 800 IR (10 euros/dollars). On the way to the hotel the driver told me in a veeeerry broken english, that he didn't know where my hotel was located. So he tried to call the lobby at the hotel, but no one was taking the call (it was already 2:00 am). After several attempts of contacting the hotel, I asked the taxi driver about his plan, and he replied "you choose different hotel!". Well man, I had it all booked in advance, and I wanted to get dropped in front of THAT hotel. So after a couple of seconds of total silence, I asked him for his GPS and I entered the address. So I'm pretty sure that the good man was an illiterate. The hotel was only 3 minutes away. After I got dropped, I had to notice that, the lobby was busy with 2 hotel employees but still no one dared to pick-up the phone. "Lodi Garden in Delhi" I told the receptionist that I booked a room for 3 nights at their hotel "GRAND GODWIN". They seemed to be very welcoming at first and offered me a chai (tea) or a coffee, which I gently refused. They picked up my luggage, and told me to follow them to the building next-door. I could feel the taste of "rip-off" in the air. I told them that I certainly booked a hotel at the "GRAND GODWIN" and not at the "GODWIN DELUXE". But they were insisting that I was wrong, and that my room would be ready inside the neighbor building. I was just too tired to argue about it... But I wanted to check the room first. The whole staff, were debating in indian and I could feel that there was something wrong. After they brought me up on the 2nd floor, showed me the room, I agreed to accept it. Of course I tipped the bellboy who carried my backpack. Pretty soon I wanted to get online, but noticed that the wifi password wasn't working. I took the room-key ... Damn! They didn't gave me room key, but a paper business-card. Of course being pretty naive, I still tried it, but obviously it wouldn't open my room. I went downstairs and asked them for a proper room-key, and was told "paper card works, but we can give you plastic card instead (broken english)". By the way, later for my check-out at the hotel "Godwin Deluxe", they tried to rip me off again. On the check-out bill, they added every single payable tax twice, and charged me for a airport pick-up which I never asked for. They charged me double the price, than the one which was set during my booking at the website booking(dot)com. I hadn't visited anything in Delhi yet, but still I had to manage several issues of incompetence of the indian world. Delhi. I got up pretty early, because I couldn't wait anymore to discover India. I left the hotel around 8:00am, and walked towards the main road, which lead to a bridge. I bumped into a local, who recommended to take a rickshaw (tuc-tuc) because walking to the different tourist spots would be way to exausting. "Don't pay more than 20 IR (30 cents)", and of course the first tuc-tuc driver accepted to bring me to a tourist office for only 20 IR. I went to the first tourist office, just to get a free map of Delhi. As soon as I sat down, they were trying to sell me a bus-tour to other indian cities. I told them that I already pre-booked my trip, and that I just needed a map. I left their office as quickly as I could. On the next corner I bumped into another local, and we got into a little chit-chat. After walking a hundred meters, he told me "Hey, it's your first day in the city, I can bring you to my friend's office. If you have any questions about Delhi, they will help you." I really don't know why I even followed the stranger. It was just another tourist trap. One office, 4 guys sitting on a couch, and 1 dude sitting behind the desk. They tried to rip me off for sure... but in the end I bought a city tour by taxi for 4 hours, for only 10 euros/dollars. It actually was a bargain, because I saw most sights within those 4 hours. A cab picked me up in front of the office. While I was waiting I got introduced to every single "clerk" who was sitting on the couch. Of course they all looked like the "world's most stupid criminals". I just could tell, that this wasn't a proper tourist office. "Humayun-Mausoleum in Delhi" However I was glad that I met Prem, my taxi driver, through that office. Prem seemed to be a genuine guy, and like after half an hour, he told me that he would be working for that office, but recommended me not to trust those guys. They were just after the money, and of course with his broken english, he tried to explaine that they had no good "karma" :). After the 4 hours, I was supposed to get back to the office. Prem explained me that this was the condition of this sightseeing trip. I told Prem, that I was definitely not going back to their office, and if he wouldn't accept that, I would jump out of the car on the next crossing. Prem called the office, and explained them that I wasn't coming back. They asked for me on the phone. I told them that I wanted to get back at my hotel... but, almost like a threat, they forced me to come back with Prem. I told them to f*** o**, and hung up the call. Prem unterstood my decision and drove me to Connaught Place, a huge shopping lane, in the center of Delhi. I paid Prem another 1000 IR, because I wasn't sure if he would get this share of the "deal", since he didn't drop me at the tourist office. I was glad to be out the cab, and asked Prem for his phone number. He seemed to be a trustworthy driver, so I told him I'd be glad if he could drive me back to the airport for my trip to Varanasi. After that day, I tried to avoid any contact with locals, because I knew that a short introduction, or just any small-talk would lead me into trouble. On my second day in Delhi, I just got ripped off by some tuc-tuc drivers. Nothing too bad though, instead of paying 2 euros/dollars, I had to pay 5. Gurudwara Bangla Sahib - Sikh temple in Delhi I had a memorable experience on my second day though. Somehow I never accepted a rickshaw ride, if the divers were hunting for customers. I always picked the drivers I had a certain sympathy for. I opted for Jagdish, a punjabi tuc-tuc driver with a well groomed moustache, who was wearing a yellow turban (see the photo above). On my way back to the hotel, I asked him if he was a hindu or a muslim. He explained me that most religious people wearing that specific turban would be worshiping the religion of Sikhism (sikh). To be honest, I've never heard of the sikh relgion prior that tuc-tuc ride. Jagdish suggest, he could bring me to the biggest Sikh temple in Delhi. I gladly accepted the invitation. The visit was for free, and I was shown all of it. I had to wear a head-cover as well, as all the men did inside the temple. Drinking "holy water", tasting a sweet almond dough, and a private tour through the kitchen where they were preparing the free food for the poor people, were the more entertaining moments of this visit. I have to admit that it was a lovely temple, all white and golden. And all the "sikh" people seemed to be very welcoming, they didn't care to see me in short pants, all covered up with tattoos. After the visit Jagdish insisted for a selfie in his rickshaw, and asked me forward the photo to his son's mobile phone, that would make him happy. Well ... that's what I did! :) Varanasi. Just before taking off for Varanasi, i had to suffer another major panic attack. The ATM at the airport didn't allow me to withdraw any cash, with the reason "CARD BLOCKED". Being stuck in India for 11 more days without any money wouldn't be fun. I tried calling my bank, but their hotline wasn't reachable because of the timezone difference. After my dad helped me out, the bank told him that they blocked my card, because their security service noticed money movements inside of India, and they decided to block my card. SO! Just prior your India trip, contact your bank, and tell them that you're traveling abroad, to avoid this sort of unpleasant surprises. Varanasi struck me like a lightning. The oldest and holiest city of India was my indian destination with a "wow" effect. Once again I had a typical indian welcome. After my suicidal airport ride stopped at a big crossing (1 hour driving, for 800 IR - 10 euros/dollars), there was already a young local guy who opened the side-door, and helped me getting to the guesthouse. For once, I gotta admit, that I would have never found the guesthouse on my own. The streets were crazy busy with thousands of pedestrians and rickshaws. I followed the guide through very narrow lanes among the old colurful buildings, and after 10 minutes we finally reached my guest house, ... well after I had to tip the young man. The Ganpati Guesthouse was the loveliest place I stayed at in India. The staff was amazingly welcoming, and the whole place just felt very cosy. I was lucky to get a room without a balcony, but instead my room-door lead straight to a colorful courtyard. There was a noticeable scent of flowers, inside my room and outside, around a mandala-shaped fountain. It was my first moment of pure happiness in India. I couldn't wait to get out and have a look at the ganges river. I left the guest house, and asked the first locals I met for the right direction to reach the river. And again, the chitchat started, they advise me to visit the "Burning Ghat". The burning ghat is a public holy place where only Hindus cremate their departed in a sacred ritual. People are allowed to watch the whole ceremony, but taking photos isn't allowed, out of respect for their family. My teenage-guide showed me the three main ghats along the river. It was about time to pay a tip, and to spend even more money at his uncle's shop, where I got ripped off. I paid more like the triple for a silk scarf... but yeah, you only live once. I remember how I couldn't stop repeating "this is unbelievable. I saw all those photos of Varanasi, and now i'm standing right in the middle of it". I was so blown away by the very old temple-shaped buildings, all worn off. Many walls were covered with hand-painted letterings and signs. The whole place just looked so photogenic. Sadly after my first hours in Varanasi, with disappointment I had to notice, that all the boatmen, the locals, the fake sadhus (wanna-be-saints), wouldn't stop asking for a boatride, for prayers, for a massage... You were invited to spend money on bracelets, on floating flower pots, on colored powder. Tourists just couldn't be on their own, and enjoy the scenic views for 10 minutes. Even in the very morning, when tourists were leaving their hotels at 5:30 am to walk towards the "Assi Ghat", for an early morning ceremony, the boatmen started following you, and kept asking for a boatride. The boatrides were pretty cheap, they charged you 4 euro/dollars for a 30-40 minute boat-ride. But it was a real pain in the ass, explaining them that you weren't interested. It went on like this, for the 4 days I spent in Varanasi. I will write another more detailed blog post about Varanasi, so stay tuned for more informations. Agra. I will keep my summary very short about Agra. It's not even worth mentioning. Well ... once again... I reached Agra, leaving from Delhi, in a very typical indian way. I booked a bus-ticket the evening just prior my departure to Agra. It was a crazy cheap ticket, and the tourist-office guy told me to show up at their office around 06:00 am. That's what I did. While I was trying to wake him up after I reached his place, he instantly stood up, and pretended like he hadn't even slept. He took out his mobile and made a phone-call. When the bus-driver showed up 10 minutes later, he was kinda in a hurry, and told me to follow him. On the way to his bus he asked me in a pissed-off way "Why did you book your tickets 5 minutes ago?". I told him, that I did the booking the previous evening, and that I paid my bus-ticket in advance. "Really? Your tourist-guide contacted me 5 minutes ago, and you gotta be very lucky today, because there was only 1 seat left on the bus"!! From 06:00 to 08:00 am, the bus was picking up people all across Delhi, fueled up the bus at a gas station, and finally took off after 8 o'clock. It took us 4 hours to reach Agra (my worst bus-ride ever). After the bus had dropped us at the "Old Fort" in Agra, I had to explain them, that I wasn't interested in a tour, and that I just needed a ride to Agra. I got my back-pack and took a rickshaw to get to my hotel "Grand Imperial Hotel". This one surely was my fanciest stay for one night. The hotel had a colonial architecture flair, and it was pretty posh for India. Sadly the neighborhood outside of the hotel, was a pile of dirt. Extreme poverty, and too much filth covering the streets of Agra. After I checked in, and already had paid in advance, the receptionist brought me to my awesome room and started asking me "Excuse me sir. Due to the heavy rain yesterday, a couple of hotel rooms were flooded, and we can't host all the guests who booked a room at this hotel." I got pretty mad, because they put another colorful dot on my forehead upon my arrival, they garnished me with a flower-necklace, I got a free orange juice, I paid the room... and after all that, I was kindly asked if I would agree to spend my night at another 5-star-hotel, which wouldn't cost me a dime. I disagreed, because I was so looking forward to spend one night at their beautiful hotel. Agra... the Taj Mahal... that's it. That's all I did. There was absolutely nothing else to do, except for the Old Fort. The streets of Agra were extremly dirty, hundreds of tuctuc-drivers handing out their phone numbers. It wasn't a peaceful place, and I was happy to leave. Vrindavan. In Agra, I left in the early morning to get to the train station. I went to their ticket office, and got a train ticket to Mathura, the city just next to Vrindavan. The train ticket was 80 IR, not even 1 euro/dollar. The train station was quite an adventure. I felt completely lost, and had to asked several indians which train would leave towards Mathura. Once I stepped inside the train, I could notice the scent of poo and urine. A passenger invited me to sit right next to him. Jimmy, a university student, was one of the few indians I met, who wasn't after my money. The friendly young man, had to spend 28 hours on that train, to get back home. Honestly, I was glad, I could get out of it, after 2 hours. Outside of the train stations, the tuc-tuc drivers were flying around me like vultures. I was asked by ten men, if I needed a ride. I gently denied and picked out a driver who seemed cool. The one I chose wasn't cool though. He couldn't speak english, and didn't know the location of my hotel. On the way to Vrindavan, I gave him my phone so he could contact the hotel for precise directions. Vrindavan was just crazy. It was supposed to be the most traditional, but also the craziest, city for the "Holi Fest" in India. I gotta admit, it was just too much for my taste. On my way to the hotel, I got covered with too many colors. My black backpack was all messed up, my new shirt was all covered up with colorful sand/dust. It went on like this for the next 2 days. Myself, I barely could stay outside of the hotel for 2-3 hours. Every local felt so lucky to color my face, kids were amazed to pour endless buckets of colored water over me. They used big water guns as well, with artifical colors. Those colors wouldn't even vanish after 4 showers. After my first 3 hours among the crowds, my hotel room looked like a mess. I was glad that the room service didn't clean up my room on the next morning, because on the 13th of march, the official holi-day, got just insane. The Hindus were rushing towards the several temples in the cities, throwing all kinds of colors in the air, pushing women, and kids aside. It was a real battle making it inside the temple. I got heavily pushed back by a police officer, because I wasn't barefoot, so I decided not to follow the crowd inside the holy building. Every body aperture was filled up with colors, I had to throw away my clothes, it took an hour to clean my camera, and my go-pro. This was a next-level holi experience. The locals really didn't care, they smashed the colored powder right into the your eyes. I'd definitely recommend wearing goggles! The hotel I stayed at was total crap. They had no mini-bar, and no shop, where I could buy water or food. Outside of the hotel weren't any shops or restaurants. It almost felt like a survival training, getting plastic bottles of clean water, and killing my hunger with street food. After my lucky catch with the street-food samosas, I suffered a severe diarrhea for the next 3 days. I couldn't wait to leave Vrindavan again. Because of my bad experience in Agra, and Vrindavan, I decided to not move on towards Jaipur, the last indian city I was supposed to visit on my trip. But instead I turned back to Delhi, and booked a room for my last 4 nights at a hostel. I was looking forward to some chit-chat with travelers. I really haven't had a real discussion with people during those first 9 nights in India. I really missed the contact with people around me. So I thought that a hostel-stay would feel great. February highlights the end of carnival season in Germany, mostly in the central part of the cities. Cologne is well known for being "THE" place to celebrate "Rosenmontag" (rose monday), the last day of the carnival celebrations. Compared to the U.S. where the craziest day happens to be on a tuesday (mardi gras), for the germans it takes place on a monday, just before "mardi gras". We decided to spend 2 nights in Düsseldorf, the city neighbouring Cologne. In 2016 we celebrated in Cologne, which ended up as a kind of disappointing trip, due to the horrible weather and the lack of visitors because of the recent attacks on women during the night of new years eve. We were told to check out Düsseldorf. Without any doubt we had a blast in Düsseldorf! Not only because of the partying, the lovely people we met in Düsseldorf, but also because of the Max Brown Hotel. Our stay at this hotel definitely contributed to our excellent time in the city. The vintage design of the lobby is the first eye-catch you'll notice while checking in. The staff is welcoming you, dressed up with denim-aprons, behind a desk that reminds you of a vintage shop from the 50s. Vintage "toys" are up for sale, like retro-ish designed boomerangs, playing cards and notebooks. Our first two nights were spent in a beautifully designed smaller room, big enough for 2 people. The room was equipped with a portable vinyl player, a couple of vinyls (mostly soul&indie music), colorful hangers, vintage looking water boiler & cups. After two nights, we decided to extend our stay for another night. The hotel staff offered us a great rate, even cheaper then booking(dot)com. We spent our last night in a bigger room, which had the size of a small studio. It looked even nicer with a vintage couch in the middle of the room. The breakfast was alright, the usual continental one. Nothing fancy, but the decoration in the dining room made the breakfast so much cosier. All the people we met in Düsseldorf were super friendly. There are so many opportunities to satisfy your shopping wishes, just way to many unique shops. Düsseldorf isn't the prettiest city you'll discover in Germany, but the city as a whole, will give you a decent experience. We loved it, without any doubt! I'd choose Düsseldorf, over Cologne, in a heartbeat. I'm pretty sure that i'm returning to Düsseldorf very soon. And I'll most definitely stay at Max Brown Hotel. White Chapel is a damn fine Gin-Bar nearby Union Square and Market Street in San Francisco. I hardly ever write blog-posts about bars, however if i'm writing a review about it, it's pretty obvious that i had a splendid time and a great night at the café. The walk from Union Square towards White Chapel will lead you through sketchy corners at night, but it definitely was worth the adventure. Passing by the bar, you hardly recognize it as a gin bar from the outside. After getting the head nod from the bouncer I walked in, as soon as i passed the door I exhaled an inner-wow. The interior design was astonishing! It reminded me of the shapes and forms of a cathedral, so did the low dimmed ambient light. I took a seat on at the bar and waited for ordering my first drink. While traveling solo, the first order often gives me a weird insecure feeling, because most of the customers are in groups or couples. The bartender Keli, who considered herself as a "ginoisseur", took care of my first gin&tonic made out of "Brooklyn Gin". To make me even more insecure she asked if i ordered a "brooklyn" or "brockley"gin. Because of the ambient noise I didn't understand what she was talking about. So she showed me both bottles and I picked the right one. Instantly I was amazed by Keli's knowledge about gin. After having downed my first drink, another unknown bartender, asked me for another gin&tonic. I agreed, and he filled up a glass with a homemade g&t from the tap. Gin&Tonic from a tap? That was weird and that's how it tasted, weird. I couldn't drink it. So I called Keli and asked her for another drink. She noticed that I didn't like the tap g&t. I opted for an icelandic gin. Kelli told me it's on the house. Considering that most gin&tonics were around 10-14$ , i found it pretty nice to get a free drink. After that drink Keli taught me lots about gin, and we talked about her travels, her experiences with foreign gins, etc. It was crazy to see how the gin scene had evolved since my last visit in San Francisco. Later in the evening I got in touch with Andrew and Enoch, two damn talented bartenders, who impressed me quite a lot with their mixing skills. When Andrew added me on instagram, we found out that we had lots of common interests, coffee, music and photography. I was invited to have a coffee at Andrew's place the next day. The roller coaster ride went on and I got served more gin&tonics, port wines, and cocktails. It actually was mind blowing to see how much effort and details Andrew and Enoch put into each cocktail they were pouring out. It looked and felt very artistic. I had quite a few tastings of several gins. I left the bar pretty wasted, but i was really happy that i ran into these people. Actually it was the first time where I had fun at a bar, only because of the staff working at the bar. I wish I had met more locals like Keli and Andrew in San Francisco. Genuine people! I just came back home from my 6th trip to San Francisco, and thought I'd get bored of publishing another blog-post about one of my very favorite U.S. cities, but that ain't the case. Once again I soaked up many new impressions and travel memories in San Francisco. Just before my trip, I put a list together with all the interesting parts & sights I hadn't discovered yet. I pretty well filled up the schedule of my 6 days and planned ahead which parts I'd visit on the specific weekdays. As my trip came to an end, I sadly realized that I still missed so many things, and that I barely completed my check-list. There's still so much to discover in San Francisco, even after 6 trips to the city. This time I really put my focus on its beaches. I was browsing through a couple of photos of the golden gate bridge, which were taken from the Baker Beach angle. I kind of felt ashamed that I never made it to Baker Beach, because you definitely get the best photos from that viewpoint. The typical tourist photos you see from right in front of one of both ends of the bridge, are the least impressive in my opinion. So I was looking forward to get to Baker Beach. Baker Beach. As I don't like taking bus-rides in big cities, I decided to start my "baker beach hike" early in the morning at 6am, just before the sunrise, to get a couple of descent photos of the city, just before sun rise. I walked from the union square neighbourhood toward the ferry building very next to the bay bridge, that leads to Oakland. I haven't even been close to the ferry building, on my previous trips, and I felt like i missed a beautiful spot of the city. You can watch the sun rise on the pretty wooden pier, walking through the middle of the lamp-post lane. The cupid-arch is withing walking distance as well. Inside the ferry building you'll find lovely shops selling different kinds of crafts, "french" pastries, delicious coffee at "Blue Bottle". I tried to avoid the popular pier 39, which only has tasteless tourist-shop to offer, and almost only restaurants which serve bad and greasy food. From the ferry building, I walked up too many stairs til I reach the beautiful Coit-Tower. It became one of my favorite parts of the city, even though it attracts a lot of tourists. The altitude of the hill gives beautiful views all over the different areas of the city. I moved forward through the colorful North Beach, towards the "Ghirardelli Square" at North Point Street, where I stopped for my second coffee in the city. I was impressed how good their chocolate was. Who ever thought Americans were great at making chocolate ? ;) Outside of the Ghirardelli square, you already can witness the beauty of the famous red bridge, and it feels like it's already pretty close, but it's not! It takes another 40-50 minutes to reach it. After I made it to the bridge, I decided to move on to Baker Beach. Starting from the Golden Gate Bridge, you can choose different trails that will lead you to Baker beach. To get to the trails, you gotta follow the path below the bridge, as I can remember it's the only way to get to the other side without a car. You walk past several view points and it felt like forever to reach Baker Beach. I took my first photo shots down at Marshall Beach. There are a couple of paths that lead you down to the shore, but don't forget, that you gotta walk those paths uphill again to move on towards Baker Beach. On my way a couple of tourists asked me if I had seen restaurants nearby, but I didn't. I guess those folks, underestimated the distance of the trails, like I did. And of course, it felt like summer! The weather was just great for a november, real t-shirt and shorts weather. I caught a light sunburn, walking all day in the sun. What I learned after I had reached Baker Beach: - it's further and more exhausting than I thought it would be.- it's only a small part of the San Francisco shores.- once you've made it to the beach, you gotta get back to the city. If you don't have the exact change for the bus ride, can't get a cab in the area, "uber" doesn't work, because you don't have internet-access on your mobile phone because of roaming issues, it's gonna be a hell of walk to walk back in the city center. Ocean Beach & Sutro Beach. On my second day, I decided to get back to the beach area. Walking down Powell Street towards Market Street, I took the "#5R-Fulton Rapid" busline, which was only 2.25$ . It takes approximately 35-45 minutes to reach the last bus stop of the route. From the bus stop it only takes a short walk to reach the beach, or to get to the wind mill that is located at the "Golden Gate Park". Nearby there's a beach house, where I stopped by for coffee & breakfast. It was kind of pricey, but you could enjoy an ocean view while having breakfast. North of the beach there's the popular camera obscura and the famous "Cliffhouse Restaurant". Behind the restaurant, there were several pathes which lead to Sutro Beach, where only ruins of the once public swimming pool are left. Following the different paths will lead you northbound towards Baker Beach, but it's still quite a few miles away. Nearby Sutro Beach, there's another vista point, which will give you a lovely view onto the Golden Gate Bridge. Besides the view, there's another big circle made out of stone to discover. It's really not a must-see, but while being in the area, why not check it out. Before heading back to the busstop, to get back to the hostel, I enjoyed some time on the beach, watching the waves collapse in front of me. The weather was just outstanding for a november. There aren't many cities that would come to mind, if i had to recommend a travel destination for the last two months of the year, except for asian countries or southern american countries. San Francisco would be one of the cities I'd consider turning back to in november or december months. Ocean Beach. Hayes Street (Patricia's Green). Afer visiting an art gallery which hosted a couple of artworks of Shepard Fairey (OBEY), I was told that Fairey recently painted two new murals in San Francisco. The one I really wanted to see, was a mural of Cesar Chavez, which was located at Hayes Street, nearby the Patricia's Green square. I can't remember if i'd ever been to Hayes Street, but I was so impressed by the charm of that lovely and colorful neighborhood. The hood was packed with different coffee bars, art galleries, craft-shops... Once I'll get back to San Francisco, this is definitely gonna be the place where I'd love to hangout or even book a room at a hostel or hotel in that part of the city. White Chapel (Gin Bar). More to come about this fabulous place. I will write a separate review about my favorite bar in town. The link to the review will be added soon. Clement Street (and 5th Avenue). I had my best night at Clement Street (with 5th avenue). I met up with my friend Jessica on a Saturday at Haight Street for a coffee. She decided to take me out the same evening to a show at the venue called "Neck of the Woods". The whole alley on Clement Street was packed with different restaurants, bars, bakeries, flower shops. Somehow it felt totally different than the other areas I've been to in San Francisco. It had the vibe of a little american village. There weren't barely any tourists, and it definitely felt like a local spot. People were a lot more outgoing and easy to talk to. I realized again, that the city has so much more to offer than just the popular spots. Even after my 6th visit in the "City By The Bay" there's still so much left to discover. San Francisco remains one my favorite U.S. cities, it could even be my favorite. I felt proud again that I had the initials -SF- tattooed on my right arm. Despite the fact, that I grew up in Luxembourg around a numerous amount of portuguese people, while hearing their language on a daily basis and getting partly in touch with their culture, it still took me 34 years to discover the beauty of Portugal's capital Lisbon. For too many years, relatives and friends, were talking about traveling to Barcelona, the catalonian capital. Rarely my friends used "Lisbon" to pinpoint their next destination. So after my recent trip to Portugal, all I can tell is that "Lisbon is going to be the next Barcelona". Talking about a hip city? Lisbon is hip! Partying with a mediterranean flair? You get it in Lisbon. Delicious mediterranean cuisine and its matching wines? Lisbon, check! Traveling on budget? You won't find cheaper than Portugal. Maybe I was just lucky, for having met amazing fellow travelers in Lisbon. The weather definitely was on my side, during my 5 days in the capital of Portugal. I had the best stay, i could have ever expected, at the "YES HOSTEL" very nearby the Praca do Comercio. I don't really know what made my journey in Lisbon so special, it just must have been the whole package. Getting out of the hostel, and walking two blocks south, I met up with my best friend at the Praca do Comercio. It's a large public place, with an old historic arch leading to the main shopping street of the Baixa district. But passing the Praca do Comercio will lead you to the shore, where you can have a summerish cocktail, and enjoy the stroll towards the docks {docas}, or the famous "Ponte 25 de Abril" bridge. Almost any tiny alley that will lead you north to Bairro Alto, is packed with unique gems: bars, bakeries, tiny traditional restaurants, clubs. Just explore the whole area, and learn how to enjoy the diversity of the colorful capital. On my first days, I visited the Alfama district twice. Just after passing the busy main shopping street of Baixa, the first alleys will get very steep after a couple of hundred meters. The different paths will lead you to the top of the "Sao Jorge" castle. Sadly the entrance fee to the castle isn't cheap, so don't plan on visiting it twice. I would recommend it, for taking scenic photos of the city. If you've visited a castle before, this one won't be a lot different. But you get a bunch of impressive overlooks. The prettiest part of Alfama for me, were the different street art spots or urban art installations. Whole Alfama is packed with uban art. While looking at the colorful murals, you will hear the different trams passing by. The old tram lines definitely bring a unique charm to the capital. In my opinion it's an important part of the city's landmark, like the cabs of London. Expect at least half a day to explore the prettiest corners of Alfama. Have one or two port wines on one of the few scenic terraces or patios, have a mediterranean lunch, and listen to some Fado. You will love that district of Lisbon. From the city center of Lisbon, you can easily catch a short train ride, and visit Belem or Cascais, two beautiful gems which are definitely worth a visit. Sadly I jumped on an express train, which didn't stop at Belem, and I was just too exhausted to switch the train for a 3rd time. The same train line, takes approximately 15 minutes to Belem, and 45 minutes to Cascais. The one-way ticket to Cascais only costs 2.20 Euro (3 us$). However if you plan on visiting around mid-day expect long waiting queues in summer. A lot of tourists and locals plan on visiting the beaches around Lisbon. I waited at least 40 minutes to get a ticket, since the metro-card won't work for the train lines. After having jumped off the train in Cascais, I felt like i made it to the "Santa Barbara" of Portugal. The streets of Cascais looked fancy, lots of beautiful people on the beaches, infinite lines of white buildings and hundreds of shops. How can you not like Cascais? It surely attracts too many tourists in summer, but the views, the sun, the beaches are all worth it. A 30-40 minutes walk from the train station will lead you uphill to the "boca do inferno", an impressive shore of seaside cliffs, a total different nature-spectacle compared to the fancy beaches downtown. I can't tell anything about Belem, but all the locals told me to check out the Belem tower, and enjoy the famous "pasteis de belem", a culinary highlight. So much different parts of the city to check out during hot summer days. But what about nightlife? Except the nightlife of "Bairro Alto" I haven't seen much of the busy spots, which wasn't bad at all actually. I had an amazing time at the "YES HOSTEL". Every evening I could enjoy wine, port wine or delicious sangria for 1 Euro a cup... yep, you got it right, 1 Euro only! Around dinner time, 8pm or 9pm all the guests of the hostel came downstairs to the bar, to start the evening. Just standing at the counter and ordering a drink, made you bump into travelers and start a conversation right away. I met a lot of lovely travelers from Sweden, Canada and Germany. After having met the first time on my first night in Lisbon, we met up every other evening for a couple of drinks, and went out to different parts of the city. Some were quiet, some were busy. The Bairro Alto block, was definitely very very busy on the weekend, too many bars and too many people. Actually it was a good place to go out, but as a tourist it was hard to tell which bar to choose. The drinks weren't the best ones, but cheap. So in Bairro Alto is was quantity over quality, the perfect spot to get wasted. I would say it's the place where people go "hunting", you could smell the flirting on every corner. I did like the "House of Gin" [or the "vintage gourmet" which is the name of restaurant]. Nuno, the barman, had an impressive knowledge about gin, and easily owns over 150 different gins from all over the world. I had the chance to try a couple of gins, which I couldn't find nearby the place where i live: Brooklyn Gin (USA), Nao Gin (P), Adamus Gin (P). Of course the drinks weren't cheap, expect to pay 10-13 euro for a drink. I guess those are the prices you'll have to pay all over Europe for a fancy gin & tonic. Sadly I got my mobile phone stolen on my following trip to Barcelona, and didn't manage to back-up my photos from Portugal. I was glad I put some shots on Instagram and Facebook, which I could save at a later time, to add on this blog-post. The whole city of Lisbon is packed with architectural pearls and colorful murals. It takes you more than 5 days to discover the beauties of the capital. That's why I've decided to do a road trip across Portugal in 2017. This trip amazed me with only positive impressions, obrigado Lisboa! Useful informations You can get a cheap bus ride right outside of the airport. Check the different bus stops (with numbers on it), and look which one leads to your destination. I paid 3.50 Euro for a ticket, and the ride from the airport to the Praca Do Comercio took about 40 minutes. A taxi ride could cost you between 25 and 30 euro, and doesn't need to be faster during rush hour. After my couple of days in Lisbon, I took a train ride to Porto. The train took almost 3 hours to reach Porto. The one day ticket costs 30 Euros. During the very busy summer season, I still managed to get a train ticket on the day I left Lisbon. Trains to Porto leave every 30 to 60 minutes. I can't tell you any negative parts of my trip, or which tourist traps you should avoid. I felt safe all the time, at any hour of the day. Even the most touristic places, offer you fair prices for food and drinks. Expect to pay 6-10 Euro for lunch or dinner, and 1-2 Euro for the common drinks like soft drinks, wines or beers. Most people do speak english, french or german, even the older people. It wasn't hard to get around. Even though we met some younger folks who weren't fluent in english, somehow we managed to communicate, and it was a lot of fun, discovering the different cultural sides of the city. A lot of tourists as well, but it was so easy to make new friends in Lisbon. I will definitely add a small review of the "YES" hostel, which gave me the warmest welcome in Portugal. Sadly like previously mentioned, I got my phone stolen in Barcelona, and I forgot to back up my photos from my Iphone. I wish I could have fed you with a lot more of beautiful shots of Lisbon. After having taken place in a shuttle-bus, that brings you from the center of Hanoi to Halong-Bay, you will be explained the different schedules of the guests who booked "2 days 1 night" or "3 days 2 nights". Prior my departure to Vietnam, I opted for the package "2 days 1 night", which means you will spend 1 night on a cruiser boat, and the crew will do their best to keep you entertained for the the 2 half days on the boat, the "Halong Silversea Cruise". The journey starts right in the center of the old town of Hanoi. Most companies offer a free shuttle from any hotel in the center of Hanoi, to the docks where you get on the boat. The ride usually takes about 3 to 4 hours. After 90 minutes, all the shuttles have a break at the same tourist-trap, where you can buy local products, food, snacks, drinks for the rest of your trip, and of course there are a couple of toilets, which looked pretty clean for vietnmese restrooms. As soon as you leave the bus, the Ha Long Bay experience starts. We jumped on a smaller boat, had to put on swimming-vests, and 45seconds later, we docked on the main cruiser. Totally worth it, to put on the safety vests. On the boat, we got introduced to the boat-crew. The manager, main contact during the cruise, was the only person who was fluent in english. But it really didn't bother, most of the crew would understand all the basic words in english. After a short introduction it was time for the check-in, where all the guests got their room keys. I never expected such a nice room on a boat! Beautifully furnitured bedroom, with an even nicer looking bathroom. We barely had time for a shower, and lunch was already served. 4 to 5 differents meals were served, and all of them were crazy delicious. I really never expected that sort of quality food on a cruising ship. Can't complain about the lunch part of the first day. But after having had breakfast, a coffee break at the rest-area, most of the guests weren't really hungry around 1 pm. No time for boredom! From lunch, into the bathing suits, into the kayak. The kayaking part was my favorite part of the whole Ha Long Bay experience. I never kayaked before. So having the chance to get introduced to kayaking in the middle of nowhere, among the huge rocks, the blue-greenish water, that was absolutely surreal. And I had the chance to have met a great lady on the boat, who was my partner. So I shared the kayak together with Kieu. After 45 minutes of kayaking, some people could swim around the boat, or go on the rooftop, to enjoy the views and a couple of cocktails. One hour later, we visited a "pearl farm". Apparently, according to the guide, there are only two pearl farms in all of Vietnam, and the one we visited, was a colaboration amongs the viets and the japanese. Of course, after the tour on the pearl farm, you get invited to buy pearl earrings, collars, bracelets. But for a really affordable price, so that I felt obliged to buy earrings for my mom. After the farm, it was time for dinner. I gotta admit, there was barely no time left to enjoy yourair-conditioned room on the boat, or enjoy the roof top for a couple more hours. The dinner was by far not as classy as lunch. It was all kind of different vietnamese dishes, that you had to share with the table. During and after dinner, the manager, was trying to get the guests into the mood for karaoke. Nobody was drunk on the boat, because they didn't gave us the time to enjoy a couple of glasses. So it was disappointing, that there wasn't any partying on the cruise. The three girls on our table, and I, we spent some time on the roof top, where it was so dark, that you hardly couldn't recognize the rocks around the boat. After an hour of chatting, we all went to bed. The next morning, we all had breakfast, went to visit a cave, and after the cave, some guests were brought to a different cruiser, because they opted for the "3 days 2 nights" package. Later my kayak partner, Kieu from Austin, told me that she spent her 2nd day on a little island, where they could play beach-ball, do kayaking, or go swimming. The cabins with their bedrooms, weren't air conditioned during these very hot weeks, and of course didn't look as fancy as the rooms on our boat. So if you're asking me, which package would be the best to book. I really can't tell. I would have loved to spend more time on the boat, chilling or kayaking. But if you gotta pay double the price for another night, for sitting in the sand, and sleeping in wooden cabins with no A.C., i'm really not sure if it's worth the money. My package "2d1n" cost 150 € (170 us$). I gotta admit that the river is pretty dirty, there's a massive load of dirt floating around the rocks and the different boats. I'm glad I did the tour, but I wouldn't do it again. Maybe someday as a couple I would turn back to Ha Long Bay. In my opinion it just got that touristic vibe, with a lot of entertainment around you, but I guess that's sadly the only way to discover the bay area, on the easiest way.

Q: ATtiny85 Servo PWM angle granularity I am currently working on controlling servo motors with an ATtiny85. I have a hard time understanding how to achieve a fine granularity for the angles of the servo. I am using a similar technique as the one stated by KyranF. A servo angle is determined by the pulse width between 1-2ms of an 50Hz PWM. I am using Timer 1 with a prescaler of 1 with a 8 Mhz clock. This means a timer overflow(tick) takes (1/8MHz) * 256 = 32 microseconds. A 20ms period takes 625 overflows. This means my 1ms granularity is 625/20ms = 31,25 = ~31 ticks per ms. Because a servo angle is controlled by setting the pulse width somewhere between 1-2ms, I can only have a precision of 31/180°= ~6 degrees. Is there a way to achieve 1° precision ? A: Because a servo angle is controlled by setting the pulse width somewhere between 1-2ms, I can only have a precision of 31/180°= ~6 degrees. Is there a way to achieve 1° precision ? Most servos only move ~120º with 1-2ms. However assuming 1-2ms = 180º you need 180 counts of 5.55us per count. The Attiny85 has an 8 bit PWM generator that can do up to 256 counts, but doesn't have a prescaler division ratio that can do 5.55us steps at 8MHz. The nearest is 8us per count with a 1/64 prescale, which corresponds to 125 counts in 1ms for a resolution of 1.44º per count (if 1ms = 180º). To get this you could set up Timer0 to produce a one-shot PWM pulse of 125-250 which equals 1-2ms, and use timer1 to repeat the pulse at approximately 20ms intervals. Most servos should get close to 1º resolution with these 8us steps. If 8us is not fine enough then you will have to use a software delay. At 8Mhz 44 CPU cycles take 5.5us, which is 99% of the desired 5.55us and provides enough instructions to make an accurate variable timing loop of 1-2ms. You could try writing the code for this in C (with a few NOPs to adjust the timing) but it might be easier to do in assembler. To generate an entire frame you would first set up a timer to interrupt at ~20ms intervals. In the timer ISR you would start the servo pulse, wait for a variable 1-2ms using your software timer, then end the servo pulse. During this time the CPU can't do anything else, but you still have ~18-19ms available per 20ms frame.

Over-expression of astrocytic ET-1 attenuates neuropathic pain by inhibition of ERK1/2 and Akt(s) via activation of ETA receptor. A differential role of endothelin-1 (ET-1) in pain processing has recently been suggested. However, the function of central ET-1 in neuropathic pain (NP) has not been fully elucidated to date. We report here the action of endogenous central ET-1 in sciatic nerve ligation-induced NP (SNL-NP) in a transgenic animal model that over-expresses ET-1 in the astrocytes (GET-1 mice). We hypothesized that the over-expression of astrocytic ET-1 would exert anti-allodynic and anti-hyperalgesic effects in NP, as demonstrated by mechanical threshold and plantar withdrawal latency using the von Frey filament and heat stimuli. In our animal model, GET-1 mice showed an increase in the withdrawal threshold and latency in response to the mechanical and thermal stimuli, respectively, in pain behavior tests after SNL. ET-1 and endothelin type A receptor (ETA-R) levels were increased significantly in L4-L6 segments of the spinal cord (ipsilateral to SNL) of GET-1 mice at 7 and 21days after surgery. Moreover, intrathecal administration of a specific ETA-R antagonist, BQ-123, attenuated the anti-allodynic and anti-hyperalgesic phenotype in GET-1 mice. The effects of BQ-123 on the mRNA expression of extracellular signal-regulated protein kinase 1/2 (ERK1/2) and protein kinase B/serine protein kinase (Akt(s)) were assessed in the ipsilateral L4-L6 segments harvested 30min after BQ-123 administration on day 7 after surgery. Phosphorylation of ERK1/2 and Akt(s) in the ipsilateral spinal cord of GET-1 mice was reduced following SNL, whereas no reduction was observed after intrathecal injection of BQ-123. In conclusion, our results showed that the xover-expression of astrocytic ET-1 reduced SNL-induced allodynia and hyperalgesia by inhibiting the activation of ERK1/2 and Akt(s) via the ETA-R-mediated pathway.

A bacterial infection is one of the most common and fatal cause to the human diseases, unfortunately, an abuse of the antibiotics has caused an antibiotics resistance to bacterium. In fact, the resistance rate of bacterium to a new antibiotics is much faster than the developing rate of newly made antibiotics analogue. For example, Enterococcus faecalis, Mycobacterium tuberculosis and Pseudomonas aeruginosa, which can be threaten to a life, have grown the resistance to all antibiotics known up to the present (Stuart B. Levy, Scientific American, 46-53, 1998). The tolerance to the antibiotics is a distinguished phenomenon from the resistance to the antibiotics. The above tolerance to the antibiotics was firstly found from Pneumococcus sp in the 1970's and gave an important clue to a mechanism of action of Penicillin (Tomasz et al., Nature, 227, 138-140, 1970). The species having the tolerance to the antibiotics stop growing under the normal concentration of the antibiotics, but do not die in the event. The tolerance is caused because an activity of the autolytic enzymes, like autolysin, is not occurred when the antibiotics inhibits a cell wall's synthetase. In case of Penicillin, it may kill a bacterium by activating an endogenous hydrolytic enzymes, but in another case a bacterium may be survived at the time of antibiotics' treating by controlling an activation of the enzyme. Having the tolerance to a bacterium is clinically very important this is because if it is impossible to kill the tolerance bacterium, the effective of antibiotic's treating to a clinical infection may be decreased (Handwerger and Tomasz, Rev. Infec. Dis., 7, 368-386, 1985). In addition, the tolerance is regarded as a kind of essential prerequisite to generate the bacterium's resistance to the antibiotics as there may be certain survived strain by the antibiotic treating. The survived strain can grow continually under the existence of the antibiotics by way of obtaining a new genetic element having the resistance to the antibiotics. In fact, it is known that all the bacterium having the resistance to the antibiotics also have the tolerance to the antibiotics (Liu and Tomasz, J. Infect. Dis., 152, 365-372, 1985), thus it is necessary to develop the new antibiotics, which can kill a bacterium having the resistant to the antibiotics. The tolerance can be divided into two cases in a point of a mechanism of action, wherein the first case is a phenotypic tolerance, which is generated from all the bacterium when the growth rate is decreased (Tuomanen E., Revs. Infect. Dis., 3, S279-S291, 1986) and the second case is a genetic tolerance by a mutation, which is generated from a certain bacterium. A basic phenomenon for both cases is the regulation of decreasing the activation of autolysin enzyme. This regulation may be temporary when it is the phenotypic tolerance by an external stimulus, but the regulation may be permanent when it is the genetic tolerance causing the change of channel for regulating a hemolysis. Evidently, the simplest genetic tolerance is the one generated by the lack of autolysin enzyme. However, due to several uncertain reasons, there has been no precedent case of clinically finding the strain having the tolerance by the lack of autolysis enzyme, preferably the tolerance found clinically is made under the process of regulating the activation of autolysin enzyme (Tuomanen et al., J. infect. Dis., 158, 36-43, 1988). As examined in the above, the development of the new antibiotics is needed in order to kill the bacterium having the resistance to the antibiotics and it is necessary to develop the new antibiotics, which can act independently irrespective of the activation of the autolysin enzyme. Meanwhile, the bacterium can kill a neighboring bacterium by synthesizing peptides named as a bacteriocin or small organic molecules, wherein those bacteriocins are structurally divided into three kinds. The first kind is lantibiotics, the second kind is nonlantibiotics, and the third kind is the one secreted by a signal peptide (Cintas et al., J. Bad., 180, 1988-1994, 1998). The animal, including the insect, can also produce a peptide antibiotics by themselves (Bevins et al., Ann. Rev. Biochem., 59, 395-414, 1990), wherein there may be three divided groups according to the structure. The first group is a cysteine-rich β-sheet peptide, second group is an α-helical amphiphilic peptide molecule, and third group is a praline-rich peptide (Mayasaki et al., Int. J. Antimicrob. Agents, 9, 269-280, 1998). It is well known that these kinds of antibacterial peptides play an important role both in host defense and innate immune system (Boman, H. G., Cell, 65:205, 1991; Boman, H. G., Annu. Rev. Microbiol., 13:61, 1995). Additionally, the antibacterial peptides have various structures according to the amino acid sequence. The most common one among the structures is the structure forming an amphiphilic alpha helical structure but without cysteine residue like a cecropin, which is the antibacterial peptide, found in the insect. Although there has been a hypothesis that a peptic ulcer is caused by a stress and a product of hyperchylia, however interest is on a Helicobacter pylori bacterium after it is disclosed that the peptic ulcer is caused by the Helicobacter pylori bacterium (Blaser, M J., Trends Microbiol., 1, 255-260, 1991). The Helicobacter pylori bacterium belonging to the Gram negative bacterium is very slow in the growth rate and is anaerobic microorganism having a helical body and flagella. RPPL1 protein among the most proteins produced by the Helicobacter pylori bacterium is consisted of 230 numbers of amino acid and it is disclosed that the amino terminal of the proteins has the same structure as the cecropin's, especially eight number of amino acid. The RPL1's amino terminal of the Helicobacter pylori bacterium has a complete amphiphilic helical-shaped structure (Putsep, K. et al., Nature, 398, 671-672, 1999). There has been a report about the mechanism of action that the amphiphilic peptide destructs the lipid of the microorganism by connecting with the lipid of cell membrane of the microorganism or by changing a displacement of the lipid of cell membrane because the amphiphilic peptide is comprised of the structure similar to the lipid of cell membrane. In addition, there has been a report that the amino terminal of RPL1's protein in the Helicobacter pylori bacterium also has the antibacterial activity (Putsep K. et al., Nature, 398, 671-672, 1999). Accordingly, a lot of researches have been made, and using these researches, lots of researches to develop the antibiotics to the bacterium have also been tried. The amphiphilic peptides being reported until now are HP (2-20) peptide and melittin peptide and etc. It has been reported that HP (2-20) peptide, which has the amphiphilic activation among the parts of the amino terminal of RPL1's protein derived from the Helicobacter pylori along with having the antibiotic activation, has not a cytotoxicity but has antibacterial activation together with an antifungal effect (Biochem. Biophys. Res. Commun., 2002, 291, 1006-1013, Biochim. Biophys. Acta. 2002, 1598, 185-194). Besides, it has been reported that the melittin peptide, which occupies more than 50% of the Pan-Cake among the bee venom's ingredients, wherein a carboxy terminal has become amidation. And it has been reported that the melittin peptide can destruct the cell of the higher animal well under the low concentration due to having the high cytotoxicity to a eukaryotic cell and has the antibacterial activation to the Gram negative bacterium and Gram positive bacterium (Habermann, E., Science, 177: 314, 1972; Steiner, H., et al., Nature, 292: 246, 1981; Tosteson, M. T., et al., Biochemistry, 228: 337, 1987). What is more, the amphiphilic peptide belonging to the cecropin series HP (2-20) comprising the amino acid similar to the HP (2-20) was firstly found from a drosophila, and since then it is also found from a silk worm pupa and a small intestine of a pig. Among them, it has been reported that a cecropin A has the high antibacterial activation, but has the low antifungal and anticancer effect (Boman, H. G. and Hultmark, D., Annu. Rev. Microbiol., 41: 103, 1987). Also, in addition to the research about the activation of the above amphiphilic peptide, it is confirmed that the characteristic of sequence is closely related to the antibacterial activation when inspecting the amino acid sequence and protein structure of the amphiphilic peptide. Therefore, a conjugation peptide can be made by substituting the certain parts of the sequence with the similar amino acid using the amino acid sequence of the above amphiphilic peptide or by recombinating the certain sequences. And the production of a new synthetic peptide having the excellent antibacterial, antifungal or anticancer activation can be also made by inversing the certain parts of the function of the peptide sequence (Chan, H. C., et al., FEBS Lett., 259: 103, 1989; Wade, D., et al., Int. J. Pept. Prot. Res., 40: 429, 1992). In fact, a synthetic peptide mag A and mag G, which have the anticancer effect, were prepared by applying the amphiphilic peptide and the potency was also reported (Ohsaki, et al., Cancer Res., 52: 3534, 1992). Additionally, the synthetic peptides having the antifungal activation by mutually connecting the amino acids in the amphiphilic parts, flexibility parts and hydrophobic parts from a magainin 2 and melitin peptides have been developed, and those developed peptides was granted as a patent because of the action to bacteria and the strain in a fungus (KR Patent no. 0204501). Also, the inventors for the present invention substituted the certain amino acids of the existing HP (2-20) peptide with a tryptophan and resulted in the addition of hydrophobic (sequence no. 2) By doing so, the inventors confirmed the addition of the antibiotics effect and the present invention was granted a patent with the antibiotics peptide (KR Patent no. 0459808). Also, the present inventors synthesized the antibiotics peptide, which was only left the helical structure of the peptide but added the cation property, by amputating the relaxation structure from the antibiotic peptide comprising of the helical structure in a straight line, wherein they confirmed the high effect of the antibacterial and antifungal of the above peptide without having the cell toxicity and filed an application with the above contents (KR Patent no. 10-2007-0088127). Recently, lots of researches to develop an excellent antibiotic peptide having more antibacterial activity and less cell toxicity than the existing antibiotic peptides. Accordingly, the present inventors have tried to develop the excellent antibiotic peptide using the existing antibiotic peptide. By the process of development try, they have completed the present invention by confirming the fact that both the new peptide comprising of amino acid sequence of SEQ. ID. NO:2, which was produced by substituting both the first and the eighth position of Phenylalanine from the antibiotic peptide each alanine comprising the amino acid sequence of the existing SEQ. ID. NO:1, and the new peptide comprising the amino acid sequence of SEQ. ID. NO:3, which was produced by substituting Asparagine at the thirteenth position of the above peptide with lysine have less cell toxicity and have similar antibacterial activity or more antibacterial activity than the antibiotic peptide comprising of amino acid sequence of SEQ. ID. NO: 1

2018 International Challenger Zhangjiagang – Singles Jason Jung was the defending champion but lost in the final to Yasutaka Uchiyama. Uchiyama won the title after defeating Jung 6–2, 6–2 in the final. Seeds Draw Finals Top half Bottom half References Main Draw Qualifying Draw International Challenger Zhangjiagang - Singles 2018 Singles

Q: Table replication with extra TIMESTAMP column on slave I have a table on master and same table on slave with an extra column like InsertTime timestamp DEFAULT CURRENT_TIMESTAMP I want to keep record of time when there is update on slave. Replication is working fine, but added column InsertTime on slave DB is storing 000.000.00 00-00-00 value. It is not storing current system timestamp. When I issue separate insert statement on slave side, it is storing system time but not with replication. Can anyone suggest me how to achieve system timestamp on slave side? Other details as follows: MySQL DB: MariaDB 5.5.23 Replication Type: Row based Platform: Linux A: The behavior you are seeing is normal for row-based replication. Extra columns are valid at the right-hand "side" of the table, but row-based replication operates at a level, on the slave, where automatic timestamps aren't updated. Statement-based replication has been suggested, but it seems likely to become even more fragile than it already is. MariaDB 10.1 introduces slave triggers for row-based replication, which could accomplish the purpose, assuming the master does not already have triggers on the table. Normally, when an event is replicated in row format, triggers do not fire on the slave, because the changes made on the master by the triggers will have replicated with the row events. MariaDB 10.1 can be configured such that row events will fire on the slave, under one condition: if the event encounters a trigger on the slave, but no trigger fired on the master, because there is no trigger defined on the master, then the slave trigger will fire. Since this requires the master to include new information in the binlog (I can't think of any facet of binary loggong that captures this now) then the master would need to be running 10.1 also. This capability seems like it could accomplish what you want.

(1) Field of the Invention: This invention relates to metal vapor discharge lamps useful in photochemical reactions or for hardening paints and inks. (2) Description of the Prior Art: Ultraviolet rays are often used to induce photochemical reactions or to harden paints and inks. For these purposes, ultraviolet rays having a wavelength range of about 280-400 nm are effective. As sources for such ultraviolet rays, electrode-type high-pressure mercury vapor discharge lamps in each of which a discharge takes place between its electrodes have conventionally been used. Furthermore, electrodeless high-pressure mercury vapor lamps have also been known recently, in each of which mercury and a rare gas are filled in amounts sufficient to retain a discharge within an electrodeless light-emitting tubing, and electromagnetic waves such as high-frequency waves of several tens MHz or higher or microwaves are externally irradiated to the tubing so as to excite the internally-filled mixture and to produce a discharge as light. By the way, each of these electrode-type or electrodeless high-pressure mercury vapor lamps emits light having a line spectrum which comprises a number of peaks and extends over a considerably wide wavelength range. It is therefore inefficient to use high-pressure mercury vapor lamps for photochemical reactions or hardening of paints, which require the above-mentioned range as an effective wavelength range. Accordingly, there are often employed metal vapor discharge lamps in each of which a metal halide is filled as a light-emitting material within the light-emitting tubing so as to increase the light quantity of a specific effective wavelength range. Metal vapor discharge lamps in which iron is filled are particularly convenient for such purposes as photochemical reactions and hardening of paints, because the lights from these lamps is continuously emitted in the range of the 350-400 nm. When a metal vapor discharge lamp filled with iron in an amount of enough to provide an iron-related spectrum of sufficient intensity is lit over many hours, iron is caused to deposit on the inner wall of its light-emitting tubing so that a thin film is formed thereon. For this reason, the amount of iron which contributes to the emission of light decreases and at the same time, the thus-formed thin film prevents the transmission of ultraviolet rays, leading to a problem that the output of ultraviolet rays is reduced. With a view toward improving this problem, it has been proposed to additionally incorporate and fill lead within a metal vapor discharge lamp which contains iron therein (Japanese Utility Model Publication No. 15503/1979). Although such an addition of lead can prevent the formation of a thin iron film and can retain the output of ultraviolet rays as intended, the output of large bright lines of 302 nm, 313 nm and 365 nm from mercury is extremely weakened by the thus-added lead. It is hence not desirable to add lead. Such lead-added metal vapor discharge lamps are not suited for such purposes as photochemical reactions or hardening of paints. It has also been known to add tin. Similar to lead, tin is accompanied by a drawback that the output of the line spectrum of mercury is lowered to a significant extent.

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1. Field of the Invention The present invention relates to a communication system, a communication apparatus and method and a program, and more particularly to a communication system, a communication apparatus and method and a program capable of suppressing a communication process speed from being lowered by signal collision. 2. Description of Related Art In a conventional communication system, as signals are transmitted from a plurality of transmission apparatus at the same time to the same communication medium, a signal collision occurs so that a reception apparatus cannot receive signals correctly in some cases. Particularly in the case wherein devices respond to a request transmitted from one device through broadcasting, there is a high possibility that response timings of the devices become coincident with each other, and a probability of signal collision occurrence becomes high. For example, in a non-contact type IC card system for short distance wireless communications, when a reader/writer requests identification information from IC cards existing in a communicable range, the reader/writer transmits the request through broadcasting (transmits the request to many and unspecified IC cards). If there exist a plurality of IC cards in the range communicable with the reader/writer, each IC card responds to the request and transmits its identification information. However, since a possibility of coincident transmission timings becomes high, there is a high fear that the reader/writer cannot acquire correctly each identification information piece, because of signal collision occurrence. In this connection, for example, there is a method of avoiding a signal collision by assigning a specific code and frequency to each device. However, if the number of devices (in this case, IC cards and a reader/writer) is large such as in a non-contact type IC card system for short distance wireless communications, codes and frequencies to be assigned become insufficient. In this connection, there is a method of intentionally shifting timings of signal transmissions from devices by providing a communication process with time slots (for example, refer to Japanese Patent Application Publication No. 2003-317042). Namely, one signal transmission process is provided with a plurality of temporal transmission timings (time slots). When a signal is transmitted, each device generates a random number, and transmits the signal at the timing (time slot) corresponding to the generated random number. In this manner, it becomes possible to suppress a signal collision occurrence, because signal transmission timings are dispersed.

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Q: Threads being taken from the Asp.net Thread pool? When im running an Asp.net ( cs file) page : and creating Thread T = new Thread(...) or using BeginInvoke() Does the Thread is being taken from the Asp.net reserved Thread Pool ? edit Essentially, .NET maintains a pool of threads that can handle page requests. When a new request is received, ASP.NET grabs one of the available threads and uses it to process the entire page. That same thread instantiates the page, runs your event handling code, and returns the rendered HTML. If ASP.NET receives requests at a rapid pace—faster than it can serve them—unhandled requests will build up in a queue. If the queue fills up, ASP.NET is forced to reject additional requests with 503 “Server Unavailable” errors. I dont want to impact the Asp.net "requests threads..." A: When you use new Thread(), it actually creates a new thread that is not related to the ThreadPool. When you use Delegate.BeginInvoke(), the delegate executes on the .Net ThreadPool (there is no special ASP.NET ThreadPool). Usually, it's best if you use the ThreadPool for a short running tasks and create a thread manually if you need to run a long-running task. Another option is to use .Net 4.0 Task, which gives you a nicer, consistent API. CPU-bound Tasks usually run on the ThreaPool, but you can specify a LongRunning option, so that they create their own thread. In general, you probably don't have to worry about starving the ThreadPool, even in ASP.NET applications, because the limits are high enough (at least in .Net 4.0, they were somewhat lower in previous versions). If you do encounter these problems, you can try increasing the number of thread in the ThreadPool, or you can use a separate thread pool (which will require some code, but you should be able to find code for this on the internet). Using a custom thread pool is easier if you used Tasks, because it means just switching a TaskScheduler.

Q: Styling ordered lists with CSS I have an ordered list in HTML. I would like to add styling only to the numbers (1,2,3,...), and not to the list items themselves. Is there a way to refer to these numbers ? Thanks ! A: CSS2 provides for control over generated content, which will let you style the auto-generated content independently of the rest of the item using the :before pseudoclass. Here's a solution that meet's the OP's follow-up criteria (background color on the list enumerator but not the item). <!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd"> <html xmlns="http://www.w3.org/1999/xhtml" xml:lang="en"> <head profile="http://gmpg.org/xfn/11"> <meta http-equiv="Content-Type" content="text/html; charset=UTF-8" /> <style type="text/css"> body { margin: 0; padding: 10px; } ol { counter-reset: item; margin: 0; padding: 0; } li { display: block; padding: 10px 0; margin: 0 0 10px 0; } li:before { content: counter(item); /* To generate punctuation after the number, just precede or follow with a string: content: "Chapter " counter(item) " >> "; To make nested counters (1, 1.1, 1.1.1, etc.), use: content: counters(item, "."); */ counter-increment: item; background-color: #ddd; margin-right: 15px; padding: 10px; } ol li ol { margin-bottom: -10px; padding-top: 10px; } ol li ol li { margin: 10px 0 0 30px; } </style> </head> <body> <ol> <li>Turtles</li> <li>Lizards <ol> <li>Salamanders</li> <li>Geckos</li> </ol> </li> <li>Velociraptors</li> </ol> </body> </html> A: Yes, you simply style the ol element and then override the style on the li element. ol { color: blue; font-style: italic; } ol li p { color: black; font-style: normal; } with <ol> <li><p>Text</p></li> <li><p>Text</p></li> <li><p>Text</p></li> </ol> You can change the p tags to <divs> if you want, but if you keep them as p's you'll have to strip margins and paddings.

Madhu Koda Scandal: You know you've made your mark in Indian politics when an entire scam is named after you. Madhu Koda, ex-chief minister of Jharkhand, knows the feeling all too well post November 2009's leviathan accusations hurled his way. The charges? It seems the 'good man' had laundered money in the audacious amount of Rs. 4000 crore, not to mention shown a seriously disproportionate income. Five currency counting machines were found at his residence which he promptly used to buy hotels in Thailand, mines in Liberia, companies in Dubai and even more property in countries like Indonesia, Laos and Malaysia to name but a few! He built an empire out of this stolen money and suffice to say that as one of the formative faces in Indian politics at the time, the disgusting level of corruption caused a furore. Thankfully, in a rare show of real justice, the despicable politician has been in jail ever since post several multiple bail pleas' rejection! 2G Spectrum Scam: They've begun to refer to this one as the mother of all scams. It involved the process of allocating unified access serving licenses and the man who took center stage was of course a politician—none other than A Raja, our telecom minister at the time. According to the comptroller and auditor general of India (CAG) the man had evaded norms at every level possible to rake in moolah for himself by offering dubious 2G license awards in 2008 at throw-away prices. What makes it a true political scandal however is the CAG's argument that the Indian government had full authority to allocate these licences through a process of competitive bidding but Raja instead chose to misuse the system for personal gain. Please, somebody tell us a new story. Either way, the issue received massive media coverage, public outrage, saw hugely influential (and previous considered untouchable) businessmen and politicians locked away for their misconduct. Note For Vote Scandal: This is 'fondly' remembered as India's most ignominious political scandal ever. It took place in 2008 and has even made it to worldwide lists of the worst political scams ever. Here's what went down. Right in the middle of parliamentary discussions, MPs belonging to Samajwadi Party began to wave large bundles of money while still seated in Parliament! They claimed that Manmohan Singh's party had been trying to bribe them and disallow them from voting in favor of BJP. News channels actually had to cut off the live feed due to the despicable airing of dirty laundry in public but the damage had already been done. The entire episode led to one of the biggest rallies between political parties the country has ever seen and as such, it's entirely deserving of a place on this list. Incidentally, a tape covering the bribery was aired in August of 2008 leading to even more political upheaval in a country that could ill afford more. Political Wiretap Scandal: Reminiscent of the Murdochian privacy-invasion scam as well as Watergate, there was a revelation that government intelligence services had been monitoring the telephone communications of senior political figures. Outlook magazine reported on the same and their findings suggested that both the UPA and Congress had ordered intelligence officers to tap the telephone communications of several politicians. These included the likes of Bihar state's chief minister Nitish Kumar and Minister for agriculture Sharad Pawar. The party also used tapping techniques to investigate the conversations of opposition leaders during vital times such as 2008's no-confidence motion on the Indo-US Nuclear deal. The Telgi Scam: Introducing Abdul Karim Telgi—master forgery expert, money hungry and ruthless scamster—the man perfected the art of duplicating stamp papers and sold them to banks and other massive institutions. It dug its roots deep and before anyone knew it, the scam had penetrated over 12 states, countless government departments and was estimated to be worth over Rs. 20,000 crore making it one of the most costly scams the country has ever seen. However, more than the money lost was the strong evidence of neck-deep corruption India seemed to be swimming around in as there were obviously a lo of government departments responsible for the production and sale of high security stamps. Note For Vote Scandal: This is 'fondly' remembered as India's most ignominious political scandal ever. It took place in 2008 and has even made it to worldwide lists of the worst political scams ever. Here's what went down. Right in the middle of parliamentary discussions, MPs belonging to Samajwadi Party began to wave large bundles of money while still seated in Parliament! They claimed that Manmohan Singh's party had been trying to bribe them and disallow them from voting in favor of BJP. News channels actually had to cut off the live feed due to the despicable airing of dirty laundry in public but the damage had already been done. The entire episode led to one of the biggest rallies between political parties the country has ever seen and as such, it's entirely deserving of a place on this list. Incidentally, a tape covering the bribery was aired in August of 2008 leading to even more political upheaval in a country that could ill afford more.

Q: Call several dependant functions before render I need to fetch data before the render function is called. I do this in componentDidMount. In this I call a function which returns data which is used in another function call. How can I wait for this data? state = { myData: [] }; componentDidMount() { var result = []; getAllData().then((valuesReturnedByAPI) => { valuesReturnedByAPI.forEach(element => { getSpecificData(element.key).then((status) => { result.push({ name: element.name, status: status }); }); }); }).then(() => { // I would like to set the state only once when all data has been pushed into result this.setState({ myData: result }); }); } A: You need to use Promise.all to wait for all inner requests to complete. componentDidMount() { getAllData().then((valuesReturnedByAPI) => { return Promise.all(valuesReturnedByAPI.map(element => { return getSpecificData(element.key).then((status) => { return { name: element.name, status }; }); })); }).then((myData) => { // I would like to set the state only once when all data has been pushed into result this.setState({ myData }); }); } Formatted version w/ implicit return componentDidMount() { getAllData() .then(valuesReturnedByAPI => Promise.all( valuesReturnedByAPI.map(element => getSpecificData(element.key).then(status => ({ name: element.name, status })) ) ) ) .then(myData => this.setState({ myData })); }

Role of Ia antigen in the induction of adoptively transferred acute and chronic relapsing demyelinating disease in mice. Acute and chronic relapsing forms of experimental allergic encephalomyelitis (EAE) can be induced in SJL/J mice following transfer of myelin basic protein (MBP)-sensitized T cells which have been challenged in vitro with MBP. In this study, addition of specific anti I-A antibody during the culture blocked the antigen-specific proliferation of T cells and inhibited the transfer of both acute and relapsing EAE. Treatment of T cell recipients with anti I-As antibody daily for 10 days suppressed the induction of acute EAE. Further treatment of mice with anti I-As antibody reduced the number of relapses and improved their conditions. We conclude that MBP-sensitized T cells interact with Ia positive cells, both in vitro and in vivo, to induce acute and chronic relapsing EAE, respectively. The mechanism of this interaction and its role in the disease process are discussed.

##  :cn: [点击进入简体中文版](https://github.com/JackJiang2011/beautyeye/blob/master/README.md) :bulb: BeautyEye has migrated from [Google Code](https://code.google.com/p/beautyeye/) since 2015-01-30. BeautyEye is a cross platform Java Swing look and feel;<br> Benefit from basic GUI technology of Android, BeautyEye is so different from other look and feel.<br> BeautyEye is open source and free. ## Source code online Click here: [http://www.52im.net/thread-112-1-1.html](http://www.52im.net/thread-112-1-1.html)。 ## Latest Release #### :page_facing_up: v3.7 release note Release time: `2015-11-13 17：23`<br> 1. Resolved text components can not edit on JPopupMenu; <br> 2. Resolved issue that JFormattedTextField has not ui. <br> > BeautyEye first code since 2012-05, v3.0 released date is 2012-09-11, latest version released date is 2015-11-13. [More release notes](https://github.com/JackJiang2011/beautyeye/wiki/BeautyEye-release-notes) ## Compatibility BeautyEye can be run at java 1.5,1.6,1.7 and 1.8 or later. [See compatibility test](https://github.com/JackJiang2011/beautyeye/wiki/Compatibility_test_results). ## Feature * Cross-platform; * Main ui style; * Better compatibility. ## Demos <b>Tip:</b> Ensure has install JRE(java1.5+). * :paperclip: [Download demo jar\\(Swingsets2\\)](https://raw.githubusercontent.com/JackJiang2011/beautyeye/master/demo/excute_jar/SwingSets2\\(BeautyEyeLNFDemo\\).jar) * :paperclip: [Download demo jar\\(Swingsets3\\)](https://raw.githubusercontent.com/JackJiang2011/beautyeye/master/demo2/SwingSets3(BeautyEyeLNFDemo).jar) <font color="#FF6600"> \\[Recommend:thumbsup:\\]</font> ## Download :paperclip: .zip package：[Download now!](https://github.com/JackJiang2011/beautyeye/archive/v3.6.zip) (included demos, api docs , dist jar and so on). ## Development Guide #### :triangular_flag_on_post: First step: Import *`beautyeye_lnf.jar`* you can found dist jar *`beautyeye_lnf.jar`* at *“`/dist/`”*。 #### :triangular_flag_on_post: Second step: Code like this: ```Java public static void main(String[] args) { try { org.jb2011.lnf.beautyeye.BeautyEyeLNFHelper.launchBeautyEyeLNF(); } catch(Exception e) { //TODO exception } ..................... Your code ......................... ..................... Your code ......................... } ``` :green_book: Introduction：[BeautyEye L&F brief introduction](https://github.com/JackJiang2011/beautyeye/wiki/BeautyEye-L&F%E7%AE%80%E6%98%8E%E5%BC%80%E5%8F%91%E8%80%85%E6%8C%87%E5%8D%97). ## License Open source and free. ## Contact * Issues mail to :love_letter: `jb2011@163.com`; </li> * Welcome to Java Swing QQ:`259448663` <a target="_blank" href="http://shang.qq.com/wpa/qunwpa?idkey=9971fb1d1845edc87bdec92ad03f329c1d1f280b1cfe73b6d03c13b0f7f8aba1"><img border="0" src="http://pub.idqqimg.com/wpa/images/group.png" alt="Java Swing技术交流" title="Java Swing技术交流"></a>; * [Twitter](https://twitter.com/JackJiang2011/). ## About Author  ## Preview #### :triangular_flag_on_post: Part 1/2：[Original image](https://raw.githubusercontent.com/JackJiang2011/beautyeye/master/preview/be_lnf_preview_36.png)  #### :triangular_flag_on_post: Part 2/2：[Original image](https://raw.githubusercontent.com/JackJiang2011/beautyeye/master/preview/be_lnf_preview2_36.png)  ## More Screenshots #### :triangular_flag_on_post: Case :one:：SwingSets2 :point_right: [See more](https://github.com/JackJiang2011/beautyeye/wiki/Screenshots-all-in-one) #### :triangular_flag_on_post: Case :two:：SwingSets3  :paperclip: [download jar\\(Swingsets3\\)](https://raw.githubusercontent.com/JackJiang2011/beautyeye/master/demo2/SwingSets3(BeautyEyeLNFDemo).jar) #### :triangular_flag_on_post: Case :three:：DriodUIBuilder  :point_right: DroidUIBuilder: [see more](https://github.com/JackJiang2011/DroidUIBuilder) #### :triangular_flag_on_post: Sace :four:：Draw9patch   ## Wiki :notebook_with_decorative_cover: [See more](https://github.com/JackJiang2011/beautyeye/wiki) ## Other projects * **DroidUIBuilder**：一款开源Android GUI设计工具（已于2012年底停止开发），[:octocat: see more](https://github.com/JackJiang2011/DroidUIBuilder)。<br> * **Swing9patch**：一组很酷的Java Swing可重用组件或UI效果，[:octocat: see more](https://github.com/JackJiang2011/Swing9patch)。<br>

Reaching for the Moon (2013 film) Reaching for the Moon (, "Rare Flowers") is a 2013 Brazilian biographical drama film directed by Bruno Barreto. The film is based on the book Flores Raras e Banalíssimas (in English, Rare and Commonplace Flowers), by Carmem Lucia de Oliveira. The film dramatizes the love story of the American poet Elizabeth Bishop and the Brazilian architect Lota de Macedo Soares. Set largely in Petrópolis between the years 1951 and 1967, the film tells the story of Bishop’s passionate and often tumultuous life with Soares in Brazil. Cast Glória Pires as Lota de Macedo Soares Miranda Otto as Elizabeth Bishop Tracy Middendorf as Mary Morse Treat Williams as Robert Lowell Marcello Airoldi as Carlos Lacerda Lola Kirke as Margaret Luciana Souza as Joana Tânia Costa as Dindinha Marianna Mac Nieven as Malu Release Reaching for the Moon had its world premiere at the Berlin Film Festival, before screening at Tribeca Film Festival and opening the 2014 Mardi Gras Film Festival. Following the sold-out screenings at Mardi Gras Film Festival, distributor Leap Frog Films announced it was planning a limited release across Australia in 2014. International distribution The International distribution rights are being licensed by Cinema Management Group. References External links Category:2013 films Category:2010s biographical drama films Category:2010s LGBT-related films Category:Biographical films about writers Category:Brazilian biographical films Category:Brazilian drama films Category:Brazilian films Category:Brazilian LGBT-related films Category:Films scored by Marcelo Zarvos Category:Films about architecture Category:Films based on biographies Category:Films based on Brazilian novels Category:Films directed by Bruno Barreto Category:Films set in the 1950s Category:Films set in the 1960s Category:Films set in Brazil Category:Films set in Rio de Janeiro (city) Category:Films shot in Rio de Janeiro (city) Category:Lesbian-related films

Controller/Purchasing Agent Under the direction of the Finance Director, this position assists in the directing, planning, coordination and administration of the financial affairs of the city. Oversee the daily operations of the municipal business offices, including accounting, finance, fixed assets payroll and purchasing. Administer all state and federal grants. Responsible for the management of state, federal, enterprise and other funds. DUTIES & RESPONSIBILITIES: Subject to the provisions of the city charter and ordinances, duties include but shall not be limited to: Responsibility for the day to day running of all accounting systems including reporting, budgeting, forecasting, cash flow, invoicing, accounts payable, accounts receivable, purchasing, payroll, bank reconciliations, fixed assets, Federal and State reports, data surveys, and auditing; Oversee the disbursement of all monies and exercising control over all expenditures to ensure that budget appropriations are not exceeded; Having custody of all public funds belonging to or under the control of the city; Having custody of all public funds and the investment of idle funds for the city, or in their possession in a fiduciary capacity; having the safekeeping of all bonds and notes of the city; Responsibility and administration of all financial aspects of grant preparation, maintenance and reporting; Responsible for the operation and the administration of the Purchasing Division within guidelines established by the City Charter, the Purchasing Ordinance and RI General Laws. Solicits all bids for formal purchases as required or desired. Opens, tabulates and evaluates all bids Oversee the general accounting systems for the city and each of their respective offices, departments and agencies; Supervise the finance department personnel; Performing all such other duties as reasonably necessary or assigned by the Finance Director. DESIRED KNOWLEDGE, SKILLS AND ABILITIES: Thorough knowledge of the principles of governmental accounting and finance; proficiency with computerized financial systems; ability to write instructions, procedures, policies, and opinions; ability to make oral presentations; considerable knowledge of modern methods and practices of public administration with special reference to budgetary and financial administration; and ability to multi-task while juggling multiple priorities, reach consensus, and create culture of collaboration and accountability. EDUCATION & EXPERIENCE REQUIRED: Minimum education and experience requirements include a Bachelor’s Degree from an accredited learning institution; and five (5) or more years of hands-on accounting managerial experience involving full responsibility for the supervision of budget development, accounting, purchasing, investment and collection operations for a governmental organization, or comparable experience in private industry or equivalent work experience. Or any equivalent combination of education and experience which provides the desired knowledge, skill and ability. Please submit an application and resume to the City of East Providence Human Resources Department, 145 Taunton Avenue, room 201, East Providence, RI, 02914 or email to hr@cityofeastprov.com. No phone calls, please. Application and resume must be submitted no later than Friday, April 14, 2017, by 4:00 PM. The City of East Providence does not discriminate on the basis of race, color, national origin, sex, religion, age or disability in employment or the provision of services.

<group name="ha_sles" version="10" release="215" pattern:ordernumber="1050" pattern:category="Base Technologies" pattern:summary="High Availability" pattern:description="Provide tools to ensure a high degree of operational continuity and reduce the downtimes of your system." pattern:visible="true" > <pattern name="basesystem" relationship="required" /> <group relationship="required"> <package name="drbd" /> <package name="heartbeat" /> <package name="heartbeat-ldirectord" /> <package name="ocfs2console" /> <package name="ocfs2-tools" /> </group> </group>

Q: All data (key-value pairs) was erased from a child when i tried to save data by passing "" for key and value I am using Firebase. My declaration, initialisation and impletementation was as below: FirebaseDatabase firebaseDatabase; DatabaseReference schoolNamesDatabaseReference; firebaseDatabase = FirebaseDatabase.getInstance(); schoolNamesDatabaseReference = firebaseDatabase.getReference().child("schoolNames"); AutoCompleteTextView schoolNameET = (AutoCompleteTextView) findViewById(R.id.view); String schoolName = schoolNameET.getText().toString; //schoolNameEt can be empty. if (!MainMenuActivity.schoolsList.contains(schoolName)){ // schoolName is a string and can be "" String schoolNameString = schoolName; //Removing '.' , '#' , etc. from schoolName schoolName = schoolName.replace(".",""); schoolName = schoolName.replace("#",""); schoolName = schoolName.replace("$",""); schoolName = schoolName.replace("[",""); schoolName = schoolName.replace("]",""); //Using schoolName as a key (or say child) and schoolNameString as its value. schoolNamesDatabaseReference.child(schoolName).setValue(schoolNameString); } My initial database structure was as below: "root-node" : { "schoolNames" : { "key1":"value1", "key2":"value2", // and more... } } When I tried to save data to my Firebase Realtime Database, when AutoCopleteTextView is empty(means setting schoolNames as "" and callingschoolNamesDatabaseReference.child(schoolName).setValue(schoolNameString);) my database structure becomes as follow: "root-node" : { "schoolNames" : "" } Means all the previous data was erased from the "schoolNames". Why is it happening? Note: There is no error when there is some string in schoolName variable. A: This is happening because you are using setValue() method instead of updateChildren() method. Firebase database is structured as a pair of key and value, so in case of Map, it replaces the old value with the new one. So to solve this, use DatabaseReference's updateChildren() method and your problem will be solved.

Myths and Facts About Connecticut's Marriage Decision The Connecticut Supreme Court today ruled that the State Constitution requires the state to allow same sex couples to obtain civil marriage licenses. "This is a proud day for the people of Connecticut, and a good day for the principle of equality," said Kathryn Kolbert, president of People For the American Way Foundation. "The Supreme Court's decision was grounded in constitutional principles and core American values. Discrimination is wrong. Unequal treatment under the law is wrong. Everyone deserves to be treated equally." People For Foundation has long been an advocate for full equality for LGBT Americans, including marriage equality. In addition, People For the American Way Foundation has long challenged the lies and distortions used by opponents of LGBT rights to try to diminish support for marriage equality. People For the American Way Foundation also released a guide to myths and facts about the impact of the decision. MYTH #1: Churches in Connecticut will be forced to perform same-sex marriages, even if they don't want to. FACT: No church will ever have to perform any marriage it disapproves of. That's protected in the First Amendment of the US Constitution and will never change. MYTH #2: This isn't an issue that courts should get involved in. FACT: The state Constitution requires equality under the law for all Connecticut residents, and the justices on the Court had an obligation to stand up for that principle, just like courts stood up for rights for women or the legality of interracial marriage. Throughout American history, courts have stood up for those whose rights are being violated. Those decisions were often unpopular, but now we look back on them proudly. MYTH #3: This is bad for marriage. FACT: This is great for marriage! When two people love each other and want to make a lifelong commitment to care for and be responsible for each other, they should be able to get married. Starting today, marriage will be stronger, not weaker. Stopping some people from getting married doesn't help anyone's marriage — it only hurts those who are discriminated against and their families. You can read more about People For's work promoting equal rights for all Americans here[1].

# Copyright 2013 the V8 project authors. All rights reserved. # Copyright (C) 2005, 2006, 2007, 2008, 2009 Apple Inc. All rights reserved. # # Redistribution and use in source and binary forms, with or without # modification, are permitted provided that the following conditions # are met: # 1. Redistributions of source code must retain the above copyright # notice, this list of conditions and the following disclaimer. # 2. Redistributions in binary form must reproduce the above copyright # notice, this list of conditions and the following disclaimer in the # documentation and/or other materials provided with the distribution. # # THIS SOFTWARE IS PROVIDED BY APPLE INC. AND ITS CONTRIBUTORS ``AS IS'' AND ANY # EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED # WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE # DISCLAIMED. IN NO EVENT SHALL APPLE INC. OR ITS CONTRIBUTORS BE LIABLE FOR ANY # DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES # (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; # LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON # ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT # (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS # SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. Tests that ToString on a possible-non-cell value works. On success, you will see a series of "PASS" messages, followed by "TEST COMPLETE". PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,42" PASS "" + foo("foo", i % 2 ? "hello" : 42) is "foo,hello" PASS successfullyParsed is true TEST COMPLETE

{#sp1 .451}

--- abstract: 'Cyclic codes are an important class of linear codes, whose weight distribution have been extensively studied. So far, most of previous results obtained were for cyclic codes with no more than three zeros. Recently, [@Y-X-D12] constructed a class of cyclic codes with arbitrary number of zeros, and computed the weight distributions for several cases. In this paper, we determine the weight distribution for a new family of such codes. This is achieved by certain new methods, such as the theory of Jacobi sums over finite fields and subtle treatment of some complicated combinatorial identities.' author: - 'Jing Yang,[^1] Lingli Xia, [^2] Maosheng Xiong [^3]' title: Weight Distributions of a Class of Cyclic Codes with Arbitrary Number of Zeros II --- Cyclic codes, weight distribution, Gaussian periods, Jacobi sums. Introduction {#sec-into} ============ A linear code $\\mathcal{C}$ over the finite field $\\mathbb{F}_q$ of length $n$ is a subspace of $\\mathbb{F}_{q}^n$. It is called *cyclic* if it also satisfies that any $(c_0,c_1,\\cdots ,c_{n-1})\\in \\mathcal{C}$ implies $(c_{n-1},c_0,\\cdots,c_{n-2})\\in \\mathcal{C}$. By the one-to-one correspondence $$\\begin{array}{cccl} \\sigma:& \\mathcal{C}&\\rightarrow &R:=\\mathbb{F}_{q}[x]/(x^n-1)\\\\ &(c_0,c_1,\\cdots ,c_{n-1})&\\mapsto&c_0+c_1x+\\cdots +c_{n-1}x^{n-1}, \\end{array}$$ each cyclic code $\\mathcal{C}$ is equivalent to an ideal of $R$. Since $R$ is a principal ideal ring, there exists a unique monic polynomial $g(x)$ with least degree such that $\\sigma(\\mathcal{C})=g(x)R$ and $g(x)\\mid (x^n-1)$. The $g(x)$ is called the *generator polynomial* of $\\mathcal{C}$ and $h(x):=(x^n-1)/g(x)$ is called the *parity-check polynomial* of $\\mathcal{C}$. The cyclic code $\\mathcal{C}$ is called irreducible (resp. reducible) if $h(x)$ is irreducible (resp. reducible) over $\\mathbb{F}_q$. For $\\mathcal{C}$ reducible, we say that $\\mathcal{C}$ *has $t$ ($\\ge 2)$ zeros* if $h(x)$ has $t$ irreducible factors over $\\mathbb{F}_{q}$. (In the literature some authors call $\\mathcal{C}$ as “the dual of a cyclic code with $t$ zeros” instead.) Denote by $A_i$ the number of codewords of $\\mathcal{C}$ with Hamming weight $i$. The [*weight enumerator*]{} of $\\mathcal{C}$ with length $n$ is a polynomial in $\\mathbb{Z}[Y]$ defined by $$A_0+A_1Y+A_2Y^2+ \\cdots + A_nY^n.$$ The sequence $(A_0,A_1,\\cdots ,A_n)$ is called the *weight distribution* of $\\mathcal{C}$. The study of weight distribution of a linear code is important in both theory and application, since the weight distribution of a code gives the minimum distance and thus the error correcting capability of the code, and the weight distribution of a code allows the computation of the probability of error detection and correction with respect to some algorithms [@Klov]. Moreover, the weight distribution is always related to interesting and challenging problems in number theory ([@cal; @Schroof]). For irreducible cyclic codes, an identity due to McEliece [@McE74] shows that the weights of the codes can be expressed via Gauss sums. Because Gauss sums in general are extremely difficult to evaluate, the weight distribution of irreducible cyclic codes is still quite difficult to obtain, however, extensive studies have been carried out with much success by various number theoretic techniques ([@AL06; @BM72; @BM73; @fit; @McE74; @McE72; @Rao10; @van; @wol]). In particular nice characterizations were given in [@D-Y12; @Vega1; @Vega2] for irreducible cyclic codes with exactly one nonzero weight; necessary and sufficient conditions were provided and conjectures were also raised by Schmidt and White [@schmidt] for irreducible cyclic codes with at most two nonzero weights. Interested readers may consult the survey paper [@D-Y12] for more updated information on the weight distribution of irreducible cyclic codes. For reducible cyclic codes, it has been known that the determination of weight distribution involves the evaluation of exponential sums. This may be even more difficult in general. For many special families of reducible cyclic codes where neat expressions are available, various delicate techniques from number theory and algebraic combinatorics have been developed and utilized, and for some of such families, the weight distribution can been obtained (see for example [@Ding2; @FL08; @Feng12; @F-M12; @holl; @luo2; @luo3; @luo4; @Ding1; @M09; @Mois09; @Vega12; @Tang12; @Xiong1; @Xiong2; @Xiong3; @zeng]). However, to our best knowledge, most of these literature works focus on reducible cyclic codes with two or three zeros. The exponential sums which have been explicitly evaluated seem to share a common feature that they attain only a few distinct values. For reducible cyclic codes with more than three zeros, not much is known. In a beautiful work [@gegeng], the authors obtained the weight distribution of a class of cyclic codes with arbitrary number of zeros. Their work built upon an unexpected connection between the corresponding exponential sums and the spectra of Hermitian forms graphs which were known in the literature. In another recent work [@Y-X-D12] a general family of reducible cyclic codes with arbitrary number of zeros were constructed and under certain conditions the weight distribution was also obtained. The purpose of this paper is to explore the construction of [@Y-X-D12] much further and to determine the weight distribution for another new family of reducible cyclic codes with arbitrary number of zeros. Compared with [@Y-X-D12], we achieve our goal by more advanced theory of Jacobi sums and by more subtle treatment of some complicated combinatorial identities. The rest of the paper is organized as follows. The codes we consider will be introduced in Section \\[sec-II\\], so are the main results (Theorems 1, 2 and 3). Section \\[sec-pre\\] introduces some mathematical tools such as cyclotomy, Gaussian periods and general Jacobi sums that will be needed later. In Sections \\[sec-main\\] and \\[sec-mainII\\] we prove our main theorems. To streamline the proofs of Theorems \\[thm-e1\\], \\[thm-e2\\] and \\[thm-e3\\] we have left out the proof of a complicated combinatorial identity to Section \\[sec-app\\]. Section \\[sec-conclusion\\] concludes this paper. Weight Distribution of Code $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ {#sec-II} ============================================================ We first fix some notation. Let $p$ be a prime, $q=p^s$, $r=q^m$ for some integers $s,m\\geqslant 1$. Let $\\mathbb{F}_r$ be a finite field of order $r$ and $\\gamma$ be a generator of the multiplicative group $\\mathbb{F}_{r}^*:=\\mathbb{F}_r \\setminus \\{0\\}$. For any $t \\ge 2$, the family of reducible cyclic codes $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ with $t$ zeros were introduced in [@Y-X-D12] as follows. *For any $e \\geqslant t \\geqslant 2$, assume that* - *$a \\not \\equiv 0 \\pmod{r-1} \\mbox{ and } e|(r-1)$;* - *$a_i \\equiv a+\\frac{r-1}{e}\\Delta_i \\pmod{r-1},\\, 1\\leqslant i \\leqslant t$, where $\\Delta_i \\not \\equiv \\Delta_j \\pmod{e}$ for any $ i \\ne j$ and\\ $\\gcd(\\Delta_2-\\Delta_1,\\ldots,\\Delta_t-\\Delta_1,e)=1$;* - *$ \\deg h_{a_1}(x)=\\cdots=\\deg h_{a_t}(x)=m, \\mbox{ and } h_{a_i}(x) \\neq h_{a_j}(x)$ for any $1\\leqslant i\\neq j\\leqslant t$, where $h_{a_i}(x)$ is the minimal polynomial of $\\gamma^{-a_i}$ over $\\mathbb{F}_q$*; - *$N=\\gcd \\left(\\frac{r-1}{q-1},a e\\right)$*; - *$\\delta=\\gcd(r-1,a_1,a_2,\\cdots ,a_{t}),\\ n=\\frac{r-1}{\\delta}$*. *The cyclic code $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ with $t$ zeros $\\gamma^{-a_1},\\cdots,\\gamma^{-a_t}$ is given by* $$\\label{def} \\begin{array}{l} \\mathcal{C}_{(a_1,\\cdots,a_t)}=\\left\\{ c(x_1,x_2,\\cdots,x_{t})=\\left({{\\mathrm{Tr}}}_{r/q}\\left(\\sum_{j=1}^t x_j \\gamma^{a_ji} \\right)\\right)_{i=0}^{n-1}~:~\\forall \\, x_1,\\cdots,x_{t}\\in\\mathbb{F}_{r} \\right\\}, \\end{array}$$ *where ${{\\mathrm{Tr}}}_{r/q}$ denotes the trace map from $\\mathbb{F}_{r}$ to $\\mathbb{F}_{q}$.* It shall be noted that Condition iii) can be easily verified, for example, it holds if $\\frac{r-1}{q^\\ell - 1}\\nmid N$ for any proper factor $\\ell$ of $m$ (i.e. $\\ell \\mid m$ and $\\ell<m$, see [@Y-X-D12 Lemma 6]). In particular this is always the case if $N=2$, which is our interest in the paper. Delsarte’s Theorem [@Delsarte] states that $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ is an $[n,tm]$ cyclic code over $\\mathbb{F}_{q}$ with parity-check polynomial $h(x)=h_{a_1}(x)\\cdots h_{a_{t}}(x)$. This class of codes $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ contain many interesting cyclic codes as special cases which have been extensively studied in the literature ([@Ding1; @Ding2; @F-M12; @Tang12; @Xiong1; @Xiong2; @Xiong3]), all of which focus on the case $t=2$. For any $t \\ge 3$, in [@Y-X-D12] we obtain the weight distribution of $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ under either of the following conditions: - for any $t,e \\ge 2$ when $N=1$; or - for any $t=e \\ge 2$ with $N=1,2,3$; or with $N=(p^j+1)/k$ for some positive integers $j,k$; or with $N$ being a prime number such that $N \\equiv 3\\pmod{4},{\\left(\\frac{p}{N}\\right)}=1$ (here ${\\left(\\frac{*}{*}\\right)}$ denotes the Legendre symbol). In this paper we obtain the weight distribution of $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ for any $t \\ge 2$ such that $t=e-1$ and $N=2$. Note that under these conditions, it is necessary that $q$ is odd, $m$ is even and $2|ae$. Our main results are stated as follows. \\[thm-e1\\] For $N=2$ and any $t=e-1 \\geqslant 2$, we further assume that $$\\begin{aligned} \\label{1:assumption} e|(q^{m/2}-1) \\, \\mbox{ \\emph{and} } \\, 2|a.\\end{aligned}$$ Then $\\mathcal{C}_{(a_1,\\ldots,a_t)}$ is an $[n,tm]$ cyclic code over ${{\\mathbb F}}_q$ with the minimal Hamming distance $d=\\frac{2(q-1)(r-\\sqrt{r})}{(t+1)q\\delta}$. It has (at most) $\\frac{1}{2}(t^2+5t-2)$ nonzero distinct weights. - If $q \\equiv 1 \\pmod{4}$, then the weight distribution is listed in Table \\[Table1\\]. - If $q \\equiv 3 \\pmod{4}$, then the weight distribution is listed in Table \\[Table2\\]. ------------------------------------------------------------------------------------------------------------------------------------------------------------------- Weight Frequency $\\quad (\\forall \\, 1 \\leqslant k \\leqslant t, 0 \\leqslant u\\leqslant k+1)$ ------------------------------------------------------------------------- ----------------------------------------------------------------------------------------- $0$ once $\\frac{q-1}{(t+1) q \\delta}\\cdot \\bigg\\{(k+1)r-(k+1-2u)\\sqrt{r}\\bigg\\}$ $\\frac{(r-1)}{r 2^{k+2}}\\cdot \\binom{t+1}{k+1}\\binom{k+1}{u}\\cdot \\bigg\\{2(r-1)^k-$ $(-1)^k\\left\\{ (1+\\sqrt{r})^u(1-\\sqrt{r})^{k+1-u}+(1-\\sqrt{r})^u(1+\\sqrt{r})^{k+1-u}\\right\\}\\bigg\\}$ ------------------------------------------------------------------------------------------------------------------------------------------------------------------- : The weight distribution of $\\mathcal{C}$ when $N=2$ and $t=e-1\\geqslant 2$: Case (i).[]{data-label="Table1"} ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- Weight Frequency $\\quad (\\forall \\, 1 \\leqslant k \\leqslant t, 0 \\leqslant u\\leqslant k+1)$ ----------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------- $0$ once $\\frac{q-1}{(t+1) q \\delta}\\cdot \\bigg\\{(k+1)r-(-1)^{m/2}(k+1-2u)\\sqrt{r}\\bigg\\}$ $\\frac{(r-1)}{r 2^{k+2}}\\cdot \\binom{t+1}{k+1}\\binom{k+1}{u}\\cdot \\bigg\\{2(r-1)^k-$ $(-1)^k\\left\\{ (1+\\sqrt{r})^u(1-\\sqrt{r})^{k+1-u}+(1-\\sqrt{r})^u(1+\\sqrt{r})^{k+1-u}\\right\\}\\bigg\\}$ ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- : The weight distribution of $\\mathcal{C}$ when $N=2$ and $t=e-1\\geqslant 2$: Case (ii).[]{data-label="Table2"} We remark that if $N=2$ and $t=e-1$ is even, then the condition (\\[1:assumption\\]) will always be satisfied, so this settles the case completely. In particular the special case $N=2,e=3,t=2$ was already studied in [@Tang12]. When $N=2$ and $t=e-1$ is odd, there are two cases: if the condition (\\[1:assumption\\]) is satisfied, this is again settled by Theorem \\[thm-e1\\]; on the other hand, if the condition (\\[1:assumption\\]) is not satisfied, in principle the weight distribution can still be obtained. However, the formulas become quite complicated. To illustrate that, we first present the weight distribution for the simple case $t=3$ in Theorem \\[thm-e2\\], and then give a computational formula for the general case in Theorem \\[thm-e3\\]. \\[thm-e2\\] For $N=2$ and $t=e-1 =3$. Then $\\mathcal{C}_{(a_1,a_2,a_3)}$ is an $[n,3m]$ cyclic code over ${{\\mathbb F}}_q$ with the minimal Hamming distance $d=\\frac{(q-1)(r-\\sqrt{r})}{2q\\delta}$. It has (at most) $12$ nonzero weights. - If $2|a$, then its weight distribution is listed in Table \\[Table3\\] (or Table \\[Table1\\] with $t=3$). - If $2 \\nmid a$, then its weight distribution is listed in Table \\[Table4\\]. Weight Frequency ---------------------------------------- ---------------------------- 0 once $\\frac{q-1}{2\\delta q}(r+\\sqrt{r})$ $3(r-1)$ times $\\frac{q-1}{2\\delta q}(r-\\sqrt{r})$ $3(r-1)$ times $\\frac{3(q-1)}{4\\delta q}(r+\\sqrt{r})$ $(r-1)(r-5)/2$ times $\\frac{3(q-1)}{4\\delta q}(r-\\sqrt{r})$ $(r-1)(r-5)/2$ times $\\frac{(q-1)}{4\\delta q}(3r+\\sqrt{r})$ $3(r-1)^2/2$ times $\\frac{(q-1)}{4\\delta q}(3r-\\sqrt{r})$ $3(r-1)^2/2$ times $\\frac{(q-1)}{\\delta q}(r+\\sqrt{r})$ $(r-1)(r^2-2r+9)/16$ times $\\frac{(q-1)}{\\delta q}(r-\\sqrt{r})$ $(r-1)(r^2-2r+9)/16$ times $\\frac{(q-1)}{2\\delta q}(2r+\\sqrt{r})$ $(r-1)(r^2-4r+3)/4$ times $\\frac{(q-1)}{2\\delta q}(2r-\\sqrt{r})$ $(r-1)(r^2-4r+3)/4$ times $\\frac{(q-1)}{\\delta q}r$ $3(r-1)^3/8$ times : The weight distribution of $\\mathcal{C}_{(a_1,a_2,a_3)}$ when $t=e-1=3,N=2$ and $2\\mid a$.[]{data-label="Table3"} Weight Frequency ---------------------------------------- ----------------------------- 0 once $\\frac{q-1}{2\\delta q}(r+\\sqrt{r})$ $(r-1)$ times $\\frac{q-1}{2\\delta q}(r-\\sqrt{r})$ $(r-1)$ times $\\frac{q-1}{2\\delta q}r$ $4(r-1)$ times $\\frac{3(q-1)}{4\\delta q}(r+\\sqrt{r})$ $(r-1)^2/2$ times $\\frac{3(q-1)}{4\\delta q}(r-\\sqrt{r})$ $(r-1)^2/2$ times $\\frac{(q-1)}{4\\delta q}(3r+\\sqrt{r})$ $(r-1)(3r-7)/2$ times $\\frac{(q-1)}{4\\delta q}(3r-\\sqrt{r})$ $(r-1)(3r-7)/2$ times $\\frac{(q-1)}{\\delta q}(r+\\sqrt{r})$ $(r-1)^3/16$ times $\\frac{(q-1)}{\\delta q}(r-\\sqrt{r})$ $(r-1)^3/16$ times $\\frac{(q-1)}{2\\delta q}(2r+\\sqrt{r})$ $(r-1)(r^2-4r+3)/4$ times $\\frac{(q-1)}{2\\delta q}(2r-\\sqrt{r})$ $(r-1)(r^2-4r+3)/4$ times $\\frac{(q-1)}{\\delta q}r$ $(r-1)(3r^2-6r+11)/8$ times : The weight distribution of $\\mathcal{C}_{(a_1,a_2,a_3)}$ when $t=e-1=3,N=2$ and $2\\nmid a$.[]{data-label="Table4"} We now consider the general case for $N=2$ and $t=e-1$. Denote $g:=\\gamma^a$ and $\\beta:=\\gamma^{(r-1)/e}$. And let $A$ be the Vandermonde matrix of size $(t+1)\\times (t+1)$, given by $$\\label{matrix}A:=\\left( \\begin{array}{llll} 1&1&\\cdots&1 \\\\ 1&\\beta&\\cdots&\\beta^{e-1} \\\\ 1&\\beta^2&\\cdots&\\beta^{2(e-1)} \\\\ \\vdots &\\vdots &&\\vdots\\\\ 1&\\beta^{e-1}&\\cdots&\\beta^{(e-1)^2} \\end{array} \\right),$$ Take $B$ be the $(t+1) \\times t$-matrix whose columns consist of the $\\{\\triangle_1+1,\\ldots,\\triangle_t+1\\} \\pmod{e}$ columns of $A$, where $\\triangle_i$ are the basic parameters of $\\mathcal{C}_{(a_1,\\cdots,a_t)}$. Let $$\\label{equ-xtoy} (y_0,\\cdots ,y_{t})^T=B(x_1,\\cdots ,x_t)^T.$$ Since rank$B=t$ (see also [@Y-X-D12 Lemma 18]), this gives a one-to-one correspondence between $(y_1,\\ldots,y_t)$ and $(x_1,\\ldots,x_t)$, and there exist some $0 \\ne \\lambda_i \\in \\mathbb{F}_{q}$ for $1\\leqslant i\\leqslant t$ such that $$\\label{equ-y0} y_0+\\sum\\limits_{i=1}^t \\lambda_iy_i=0$$ We note that $\\{\\lambda_i\\}_{i=1}^t$ depend only on the parameters $\\{\\triangle_i \\pmod{e}\\}_{i=1}^t$ and $\\beta$. We further define $$\\label{equ-l1l2} \\begin{array}{l} l_0=\\#\\{i\\mid\\lambda_ig^i \\mbox{ is a square in } \\mathbb{F}_r,1\\leqslant i\\leqslant t\\};\\\\ l_1=\\#\\{i\\mid\\lambda_ig^i \\mbox{ is a nonsquare in } \\mathbb{F}_r,1\\leqslant i\\leqslant t\\}. \\end{array}$$ Next, we extend the definition of binomial coefficient to all integers such that $$\\binom{n}{i}=0,\\ \\mbox{for $i<0$ and $i>n$}.$$ With such preparations, we give our main result for the general case as follows. \\[thm-e3\\] In the case of $N=2$ and $t=e-1\\geqslant 2$, the $\\mathcal{C}_{(a_1,\\ldots,a_t)}$ is an $[n,tm]$ cyclic code over ${{\\mathbb F}}_q$ with the minimal Hamming distance $d=\\frac{2(q-1)(r-\\sqrt{r})}{(t+1)q\\delta}$, and the Hamming weight of its codewords takes the value 0 once and the value $$\\begin{aligned} \\frac{(q-1)}{(t+1)q \\delta}\\left[k(r-1)-2u\\eta_0^{(2,r)}-2(k-u)\\eta_1^{(2,r)}\\right], \\end{aligned}$$ for any $2 \\le k \\le t+1$ and $0 \\leqslant u \\le k$, with the frequency $$\\begin{aligned} \\sum_{k_0=0}^k\\sum_{u_0=0}^u\\binom{l_0+1}{k_0}\\binom{l_1}{k-k_0} \\binom{k_0}{u_0}\\binom{k-k_0}{u-u_0}\\Omega_{{\\scriptsize \\underbrace{0 \\cdots 0}_{2u_0+k-k_0-u,} \\underbrace{1\\cdots 1}_{k_0+u-2u_0}}}. \\end{aligned}$$ where $\\eta_0^{(2,r)},\\eta_1^{(2,r)}$ are given by Lemma \\[lem-degree2\\], $\\Omega_{{\\scriptsize \\underbrace{0 \\cdots 0}_{u} \\underbrace{1\\cdots 1}_{v}}}$ is determined by Lemma \\[thm-NNN3\\] and $l_0,l_1$ are defined by (\\[equ-l1l2\\]). We remark that Theorem \\[thm-e3\\] is a general computational formula for the weight distribution of $\\mathcal{C}_{(a_1,\\cdots,a_t)}$, and the results of Theorem \\[thm-e1\\] and Theorem \\[thm-e2\\] can be viewed as its corollaries. However, the frequency formula in Theorem \\[thm-e3\\] is complicated since it depends on the choice of $\\triangle_1,\\cdots,\\triangle_t$, and there seems no easy way to write them down in a simple closed form as Theorem \\[thm-e1\\]. In the end of this section, we give serval numerical examples to illustrate the our main theorems. Let $(q, m, e, t)=(5,2,4,3)$. Then $\\frac{r-1}{3}=\\frac{5^2-1}{4}=6$. Let $\\gamma$ be the generator of ${{\\mathbb F}}_{25}^*$ with characteristic polynomial $\\gamma^2 + 4\\gamma + 2=0$. Let $(\\triangle_1,\\triangle_2,\\triangle_3)=(1,2,3)$. - For $a=2$ we have $(a_1,a_2,a_3)=(8,14,20)$, $(\\delta,n)=(2,12)$ and $$h_{a_1}(x)=x^2 + x + 1, \\, h_{a_2}(x)= x^2 + 3x + 4, \\, h_{a_3}(x)= x^2 + 4x + 1.$$ The parity-check polynomial of $\\mathcal{C}$ is then $ h(x)=x^6 + 3x^5 + 3 x^3+3x+4. $ The code $\\mathcal{C}$ is a $[12,6,4]$-cyclic code over ${{\\mathbb F}}_5$ with weight enumerator given by $$1+72Y^4+312 Y^{6}+864 Y^{7}+1740 Y^{8}+3408 Y^{9}+5184 Y^{10}+3168 z^{11}+876 Y^{12}.$$ This also follows from Table III. There are 8 distinct non-zero weights because some of the weights in Table III turn out the same. More precisely, $$\\begin{aligned} \\label{1:eqns} \\begin{array}{ccc} \\frac{(q-1)}{2 \\delta q}(r+\\sqrt{r}) =\\frac{3(q-1)}{4 \\delta q}(r-\\sqrt{r}), \\\\ \\frac{(q-1)}{4 \\delta q}(3r+\\sqrt{r})=\\frac{(q-1)}{\\delta q}(r-\\sqrt{r}),\\\\ \\frac{3(q-1)}{4 \\delta q}(r+\\sqrt{r})=\\frac{(q-1)}{2 \\delta q}(2r-\\sqrt{r}).\\end{array}\\end{aligned}$$ - For $a=1$ we have $(a_1,a_2,a_3)=(7,13,19)$, $(\\delta,n)=(1,24)$ and $$h_{a_1}(x)=x^2 + x + 2, \\, h_{a_2}(x)= x^2 + 2x + 1, \\, h_{a_3}(x)= x^2 + 4x + 2.$$ The parity-check polynomial of $\\mathcal{C}$ is then $ h(x)=x^6 + 2x^5 + 4x^4 + x^3+2x^2+3x+4. $ The code $\\mathcal{C}$ is a $[24,6,8]$-cyclic code over ${{\\mathbb F}}_5$ with weight enumerator given by $$1+24Y^8+96 Y^{10}+312 Y^{12}+816 Y^{14}+1680 Y^{16}+3456 Y^{18}+5208 z^{20}+3168 Y^{22}+ 864 Y^{24}.$$ This also follows from Table IV. There are 9 distinct non-zero weights because some of the weights in Table IV turn out the same. More precisely, the equations (\\[1:eqns\\]) still hold true. Cyclotomy, Gaussian periods and Jacobi sums {#sec-pre} =========================================== An [*additive character*]{} of $\\mathbb{F}_{r}$ is a nonzero function $\\phi$ from $\\mathbb{F}_{r}$ to the set of complex numbers such that $\\phi(x+y)=\\phi(x) \\phi(y)$ for any pair $(x, y) \\in \\mathbb{F}_{r}^2$. Let ${{\\mathrm{Tr}}}_{r/p}$ denote the trace function from $\\mathbb{F}_{r}$ to $\\mathbb{F}_{p}$ and $\\zeta_p=e^{2\\pi \\sqrt{-1}/p}$ be the primitive $p$-th complex root of unit. The additive character $\\psi$ given by $$\\begin{aligned} \\label{dfn-add} \\psi(c)=\\zeta_p^{{{\\mathrm{Tr}}}_{r/p}(c)} \\ \\ \\mbox{ for any } c\\in\\mathbb{F}_{r}\\end{aligned}$$ is called the [*canonical additive character*]{} of $\\mathbb{F}_{r}$. For any $x\\in \\mathbb{F}_{r}$, one can easily check the orthogonal property $$\\label{add-orth} \\frac{1}{r}\\sum\\limits_{x\\in \\mathbb{F}_{r}}\\psi(ax)=\\left\\{ \\begin{array}{ll} 1, & \\hbox{if $a=0$;} \\\\ 0, & \\hbox{if $a\\in \\mathbb{F}^*_{r}$.} \\end{array} \\right.$$ Let $r-1=l L$ for two positive integers $l, L\\geqslant 1$, and let $\\gamma$ be a fixed primitive element of $\\mathbb{F}_{r}$. Define $C_{i}^{(L,r)}=\\gamma^i \\langle \\gamma^{L} \\rangle$ for $i=0,1,...,L-1$, where $\\langle \\gamma^{L} \\rangle$ denotes the subgroup of $\\mathbb{F}_{r}^*$ generated by $\\gamma^{L}$. The $C_{i}^{(L,r)}$ are called the [*cyclotomic classes*]{} of order $L$ in $\\mathbb{F}_{r}$. The [*Gaussian periods*]{} of order $L$ are defined by $$\\eta_i^{(L,r)} =\\sum_{x \\in C_i^{(L,r)}} \\psi(x), \\quad i=0,1,..., L-1.$$ The values of Gaussian periods are difficult to compute in general. However, they are known in a few cases. We will need the following whose proofs can be found in [@B-E-W] and [@Myer]. \\[lem-degree2\\] When $L=2$, the Gaussian periods are given by $$\\begin{aligned} \\eta_0^{(2,r)}= \\left\\{ \\begin{array}{ll} \\frac{-1+(-1)^{s\\cdot m-1}r^{1/2}}{2}, & \\mbox{if $p\\equiv 1 \\pmod{4}$} \\\\ \\frac{-1+(-1)^{s\\cdot m-1}(\\sqrt{-1})^{s\\cdot m} r^{1/2}}{2}, & \\mbox{if $p\\equiv 3 \\pmod{4}$} \\end{array} \\right.\\end{aligned}$$ and $\\eta_1^{(2,r)} = -1 - \\eta_0^{(2,r)}.$ A [*multiplicative character*]{} of ${{\\mathbb F}}_r$ is a nonzero function $\\chi$ from ${{\\mathbb F}}_r^*$ to the set of complex numbers such that $\\chi(xy)=\\chi(x)\\chi(y)$ for all the pairs $(x, y) \\in {{\\mathbb F}}_r^* \\times {{\\mathbb F}}_r^*$. For $j=1,2,\\ldots,r-1$, one can easily check that the functions $\\chi^{(j)}$ with $$\\begin{aligned} \\label{dfn-mul} \\chi^{(j)}(\\gamma^k)=\\zeta_{r-1}^{jk} \\ \\ \\mbox{for } k=0,1,\\ldots,r-2 \\nonumber\\end{aligned}$$ give all the multiplicative character of order dividing $r-1$, here $\\zeta_{r-1}$ denotes the primitive complex $(r-1)$-th root of unit. When $j=r-1$, $\\varepsilon(c):=\\chi^{(r-1)}(c)=1 \\mbox{ for all } c\\in{{\\mathbb F}}_r^*,$ which is called the [*trivial multiplicative character*]{} of ${{\\mathbb F}}_r$. One can check the following orthogonal property of multiplicative characters $$\\label{equ-orthogonal1} \\frac{1}{r-1}\\sum\\limits_{x\\in \\mathbb{F}_{r}^*}\\chi(x)= \\left\\{ \\begin{array}{ll} 1, & \\hbox{if\\ }\\chi=\\varepsilon; \\\\ 0, & \\hbox{otherwise.} \\end{array} \\right.$$ Furthermore, we may extend the definition of any multiplicative character $\\chi$ to $\\mathbb{F}_{r}$ as follows, $$\\label{equ-chi(0)} \\chi(0)=\\left\\{ \\begin{array}{ll} 0, & \\hbox{if }\\chi\\neq \\varepsilon; \\\\ 1, & \\hbox{if }\\chi=\\varepsilon. \\end{array} \\right.\\nonumber$$ Let $k\\geqslant 2$ and $\\chi_1,\\cdots ,\\chi_k$ be multiplicative characters of $\\mathbb{F}_{r}$. The *Jacobi sum* related with $\\chi_1,\\cdots ,\\chi_k$ over $\\mathbb{F}_{r}$ is defined by $$J(\\chi_1,\\cdots ,\\chi_k):=\\sum\\limits_{z_1,\\cdots z_k\\in \\mathbb{F}_{r}\\atop z_1+\\cdots +z_k=1}\\chi_1(z_1) \\chi_2(z_2)\\cdots \\chi_k(z_k).$$ The following ([@B-E-W]) are elementary properties of Jacobi sums. \\[lem\\_J\\] (a). $J(\\underbrace{\\varepsilon,\\cdots ,\\varepsilon}_k)=q^{k-1}$. (b). $J(\\chi_1,\\cdots,\\chi_k)=0$ if some but not all of $\\chi_1,\\cdots ,\\chi_k$ are trivial. (c). When $r$ is odd, let $\\rho$ be the quadratic multiplicative character of $\\mathbb{F}_{r}$, then $$J(\\underbrace{\\rho,\\cdots,\\rho}_k)= \\left\\{ \\begin{array}{ll} -\\rho(-1)^{\\frac{k}{2}}r^{\\frac{k-2}{2}}, & \\hbox{if $k$ is even;} \\\\ \\rho(-1)^{\\frac{k-1}{2}}r^{\\frac{k-1}{2}}, & \\hbox{if $k$ is odd.} \\end{array} \\right.$$ We now define the *reduced Jacobi sums* below, which is needed in the next section. $$\\label{equ-J*} J^*(\\chi_1,\\cdots ,\\chi_k):=\\sum\\limits_{z_1,\\cdots z_k\\in \\mathbb{F}^*_{r}\\atop z_1+\\cdots +z_k=1}\\chi_1(z_1) \\chi_2(z_2)\\cdots \\chi_k(z_k).$$ Notice that $J^*(\\chi_1,\\cdots ,\\chi_k)=J(\\chi_1,\\cdots ,\\chi_k)$ if all of $\\chi_1,\\cdots ,\\chi_k$ are non-trivial. The following results give the evaluation of $J^*(\\chi_1,\\cdots ,\\chi_k)$ if some of $\\chi_1,\\cdots ,\\chi_k$ are trivial. The next result is not difficult but may be of independent interest. It is essential in Section \\[sec-app\\] to establish a complicated combinatorial identity, which is needed in the proofs of Theorems \\[thm-e1\\] and \\[thm-e2\\]. \\[lem-J\\*\\] (a). $J^*(\\varepsilon,\\cdots ,\\varepsilon)=\\left\\{(r-1)^k-(-1)^k\\right\\}/r$. (b). Define $J(\\chi):=1$ for any multiplicative character $\\chi$. Let $u$ be an integer such that $0\\leqslant u\\leqslant k-1$. If $\\chi_1,\\cdots ,\\chi_{k-u}$ are all nontrivial multiplicative characters, then $$J^*(\\chi_1,\\cdots ,\\chi_{k-u},\\underbrace{\\varepsilon,\\cdots ,\\varepsilon}_{u})=(-1)^uJ(\\chi_1,\\cdots ,\\chi_{k-u}).$$ By definition, we have $$J^*(\\varepsilon,\\cdots ,\\varepsilon)=J(\\varepsilon,\\cdots ,\\varepsilon)-\\sum\\limits_{\\mathcal{I}} \\sum\\limits_{\\sum\\limits_{i\\in \\mathcal{I}} z_i=1}\\varepsilon(\\prod\\limits_{i\\in \\mathcal{I}} z_i),$$ where the subscript $\\mathcal{I}$ under the $\\sum$ symbol means to sum over all subsets $\\mathcal{I}$ such that $\\mathcal{I}\\subsetneqq\\{1,2,\\cdots ,k\\}$. Using the Inclusion-exclusion principle, Part (a) of Lemma \\[lem-J\\*\\] can be easily proved. Now for Part (b), we have $\\mathcal{I}'\\subsetneqq\\{k-u+1,\\cdots ,k\\}$, then $$\\begin{array}{l}J^*(\\chi_1,\\cdots ,\\chi_{k-u},\\underbrace{\\varepsilon,\\cdots ,\\varepsilon}_{u})\\\\ \\ =J(\\chi_1,\\cdots ,\\chi_{k-u},\\underbrace{\\varepsilon,\\cdots ,\\varepsilon}_{u})-\\sum\\limits_{\\mathcal{I}'}\\sum\\limits_{\\sum_{j=1}^{k-u} z_j+\\sum\\limits_{i\\in\\mathcal{I}'}z_i=1}\\chi_1(z_1)\\chi_2(z_2)\\cdots\\chi_k(z_{k-u})\\varepsilon(\\prod\\limits_{i\\in \\mathcal{I}'}z_i)\\\\ \\ =0-\\binom{u}{1}J^*(\\chi_1,\\cdots ,\\chi_{k-u},\\underbrace{\\varepsilon,\\cdots ,\\varepsilon}_{u-1})- \\binom{u}{2}J^*(\\chi_1,\\cdots ,\\chi_{k-u},\\underbrace{\\varepsilon,\\cdots ,\\varepsilon}_{u-2})-\\cdots - \\binom{u}{u}J^*(\\chi_1,\\cdots ,\\chi_{k-u}). \\end{array}$$ By induction, Part (b) can be also verified. Proof of Theorem \\[thm-e1\\] {#sec-main} =========================== The weight distribution of $\\mathcal{C}_{(a_1,\\cdots ,a_t)}$ and Summation of Gaussian periods {#sec-Weight of C} ---------------------------------------------------------------------------------------------- We now consider the weight distribution of the cyclic code $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ given in (\\[def\\]). Using the orthogonal relation (\\[add-orth\\]) and some computational techniques, in [@Y-X-D12] we haved expressed the Hamming weight of the codeword $c(x_1,\\cdots,x_{t})$ by $$\\begin{aligned} \\label{equ-Weight of C} w_H(c(x_1,\\cdots,x_{t})) =\\frac{(r-1)(q-1)}{q \\delta}-\\frac{N(q-1)}{ eq \\delta}\\sum\\limits_{h=0}^{e-1} \\bar\\eta^{(N,r)}_{g^{h}\\cdot\\sum\\limits_{\\tau=1}^{t} x_\\tau \\beta_\\tau^{h}},\\end{aligned}$$ where $g=\\gamma^a$, $\\beta_\\tau=\\gamma^{\\frac{r-1}{e}\\Delta_\\tau}$ for $1\\leqslant \\tau\\leqslant t$ and $\\bar\\eta^{(N,r)}_{v}=\\sum\\limits_{z\\in C_{0}^{(N,r)}}\\psi(vz)$ for any $v\\in\\mathbb{F}_{r}$. These $\\bar\\eta^{(N,r)}_v$ are called the *modified Gaussian periods*, given by $$\\left\\{ \\begin{array}{l} \\bar\\eta^{(N,r)}_0=\\frac{r-1}{N}\\\\ \\bar\\eta^{(N,r)}_{\\gamma^{i}}=\\eta_i^{(N,r)}\\quad \\hbox{ for $0\\leqslant i\\leqslant N-1$,} \\end{array} \\right.$$ where these $\\eta_i^{(N,r)}$ are the ordinary Gaussian periods. Thus, to compute the weight distribution of cyclic code $\\mathcal{C}_{(a_1,\\cdots,a_t)}$, it suffices to compute the value distribution of the sum $$\\label{equ-Tx} T(x_1,\\cdots ,x_{t}):=\\sum\\limits_{h=0}^{e-1}\\bar\\eta^{(N,r)}_{g^{h} \\cdot\\sum_{\\tau=1}^{t} x_\\tau \\beta_\\tau^{h}},\\quad (\\forall x_1,\\cdots ,x_t\\in \\mathbb{F}_{r}).$$ Now we deal with it under the assumption of $N=2$ and $t=e-1 \\ge 2$. $N=2$ and $t=e-1 \\ge 2$ ----------------------- Since $N=2$, it is easy to see that $q$ is odd, $m$ is even and $-1=\\gamma^{\\frac{q^m-1}{2}}$ is a square. For simplicity, let us write $$\\bar\\eta_x:=\\bar\\eta^{(2,r)}_x, \\quad \\forall x \\in {{\\mathbb F}}_r.$$ Make a change of variables $$y_h=\\sum_{\\tau=1}^{t} x_\\tau \\beta_\\tau^{h}, \\quad 0 \\le h \\le t=e-1,$$ which can be written as $$\\label{equ-xtoy} (y_0,\\cdots ,y_{t})^T=B(x_1,\\cdots ,x_t)^T$$ for some $(t+1) \\times t$ matrix $B$. Recall that $\\beta=\\gamma^{(r-1)/e}$ is an $e$-th root of unity in $\\mathbb{F}_{r}$. Since $\\beta_{\\tau}=\\beta^{\\triangle_{\\tau}}$, the matrix $B$ consists of $t$ columns of the Vandermonde matrix $A$, defined by (\\[matrix\\]). By [@Y-X-D12 Lemma 18], any $t$ rows of $B$ are linearly independent over ${{\\mathbb F}}_q$. This gives a one-to-one correspondence between $(y_1,\\ldots,y_t)$ and $(x_1,\\ldots,x_t)$ and a relation $$\\begin{aligned} \\label{3:xiong} y_0+ \\sum_{h=1}^t\\lambda_hy_h=0, \\quad \\mbox{ for some } 0 \\ne \\lambda_h \\in {{\\mathbb F}}_{q^{m}} \\, \\forall h. \\end{aligned}$$ We define $\\tilde{\\lambda}_h\\ (1\\leqslant h\\leqslant t)$ as $$\\label{equ-lambda} \\tilde{\\lambda}_h=\\left\\{\\begin{array}{ll}1,&\\mbox{if $\\lambda_hg^h$ is a square in $\\mathbb{F}_{r}$;}\\\\ \\gamma,&\\mbox{if $\\lambda_hg^h$ is a nonsquare in $\\mathbb{F}_{r}$,}\\end{array}\\right.$$ and we change variables again $\\lambda_hy_h \\to y_h$, then we see that to compute the weight distribution of the cyclic code $\\mathcal{C}_{(a_1,\\cdots,a_t)}$, it suffices to compute the value distribution of the sum $$\\label{equ-Ty} \\widetilde{T}(y_0,\\cdots ,y_{t}):=\\bar\\eta_{y_0}+\\sum\\limits_{h=1}^{t}\\bar\\eta_{\\tilde{\\lambda}_hy_h},\\quad \\forall \\, (y_1,\\cdots ,y_t)\\in \\mathbb{F}_{r}^t,$$ where $y_0:=y_0(y_1,\\ldots,y_t)$ satisfies $$\\label{eqn-y0} y_0+\\sum\\limits_{h=1}^t y_h=0$$ Proof of Theorem \\[thm-e1\\]. {#sec-sub_e4t3} ---------------------------- When $2|a$, then $g=\\gamma^a$ is a square. Moreover, $e|(q^{m/2}-1)$ means that $\\beta=\\gamma^{(q^{m/2}+1)(q^{m/2}-1)/{e}} \\in {{\\mathbb F}}_{q^{m/2}}$, hence the matrix $A$ is defined over ${{\\mathbb F}}_{q^{m/2}}$, so are all the $\\lambda_h$ in (\\[3:xiong\\]), thus $\\lambda_h$ are all squares in ${{\\mathbb F}}_{q^m}$, that is, $\\tilde{\\lambda}_h=1\\ (\\forall h)$. To study the value distribution of $\\widetilde{T}:=\\widetilde{T}(y_0,\\ldots,y_t)$, we will divide the space of $(y_1,\\ldots,y_t) \\in {{\\mathbb F}}_r^t$ according to $s$, which counts the number of $i$’s ($0 \\le i \\le t$) such that $y_i=0$. Obviously $0 \\le s \\le t+1$. If $s \\ge t$, i.e., at least $t$ terms of $y_0,y_1,\\ldots,y_t$ equal to 0, then all of them equal to 0, $\\widetilde{T}=(t+1)\\bar\\eta_0$ and the frequency is 1. If $s=t-1$, i.e., exactly $(t-1)$ terms of $y_0,y_1,\\ldots,y_t$ equal to 0, say for example the two terms which are not 0 are $y_i,y_j$ for some $0 \\le i < j \\le t$, the number of choices of such $i,j$ is $\\binom{t+1}{2}$, and the constraint (\\[eqn-y0\\]) becomes $y_i+y_j=0$, or $y_i=-y_j$. Hence for this $i,j$ we find that $$\\widetilde{T}=(t-1)\\bar\\eta_0+\\bar\\eta_{y_j}+\\bar\\eta_{-y_j}=(t-1)\\bar\\eta_0+2\\bar\\eta_{y_j}.$$ So the value distribution of $\\widetilde{T}$ for $s=t-1$ is as follows: $$\\left. \\begin{array}{ll} \\mbox{Value} \\, \\, \\widetilde{T} & \\hbox{Frequency} \\\\ (t-1)\\bar\\eta_0+2\\eta_0, & \\frac{r-1}{2} \\cdot \\binom{t+1}{2} \\\\[2mm] (t-1)\\bar\\eta_0+2\\eta_1, & \\frac{r-1}{2} \\cdot \\binom{t+1}{2} \\\\ \\end{array} \\right.$$ Now suppose in general $s=t-k$ for some $k$ with $1 \\le k \\le t$. Say the $(k+1)$ terms which are not 0 are $y_{i_0},y_{i_1}, \\ldots,y_{i_k}$ for some $0 \\le i_0< i_1 < \\cdots <i_k \\le t$. The number of ways to choose such $i_j$’s is $\\binom{t+1}{k+1}$, and for such $i_j$’s, the constraint (\\[eqn-y0\\]) becomes $$y_{i_0}+y_{i_1}+\\cdots+y_{i_k}=0,$$ and we find that $$\\widetilde{T}=(t-k)\\bar\\eta_0+\\bar\\eta_{y_{i_0}}+\\bar\\eta_{y_{i_1}}+\\cdots+\\bar\\eta_{y_{i_k}}.$$ In order to compute the value distribution of $\\widetilde{T}$ for these cases, it suffices to compute for any positive integer $u$ and any sequence $i_1,\\cdots,i_{u},i_{u+1}\\in\\{0,1\\}$ the value $\\Omega_{i_1\\cdots i_ui_{u+1}}$ given by $$\\label{equ-NNN} \\Omega_{i_1\\cdots i_ui_{u+1}}:=\\#\\left\\{(x_1,\\cdots ,x_u)\\in (\\mathbb{F}_{r}^*)^u\\ \\left|\\ x_1\\in C_{i_1}^{(2,r)},\\cdots, x_u\\in C_{i_u}^{(2,r)}, \\sum\\limits_{j=1}^ux_j\\in C_{i_{u+1}}^{(2,r)}\\right\\}\\right..$$ We will prove in Section \\[sec-app\\] that the value $\\Omega_{i_1\\cdots i_ui_{u+1}}$ depends only on the number of $0$’s and $1$’s in the sequence $i_1,\\ldots,i_{u+1}$. More precisely for any $u+v \\ge 1$ we have (see Lemma \\[thm-NNN3\\] in Section \\[sec-app\\]) $$\\Omega_{{\\scriptsize \\underbrace{0 \\cdots 0}_u \\underbrace{1\\cdots 1}_v}}=\\frac{r-1}{r 2^{u+v+1}}\\bigg\\{2(r-1)^{u+v-1}+(-1)^{u+v} \\left\\{(1+\\sqrt{r})^u(1-\\sqrt{r})^v+(1-\\sqrt{r})^u(1+\\sqrt{r})^v\\right\\}\\bigg\\}.$$ Note that the number of ways to choose a fixed $u \\ge 0$ is $\\binom{k+1}{u}$. So, for the case that $s=t-k$, $1 \\le k \\le t$, the value distribution of $\\widetilde{T}$ is given as follows $$\\left. \\begin{array}{ll} \\mbox{Value} \\,\\, \\widetilde{T} & \\hbox{Frequency} \\, (\\forall u,v \\ge 0, u+v=k+1)\\\\ (t-k)\\bar\\eta_0+u\\eta_0+v \\eta_1, & \\binom{t+1}{k+1}\\binom{k+1}{u} \\Omega_{{\\scriptsize \\underbrace{0 \\cdots 0}_u \\underbrace{1\\cdots 1}_v}} \\\\ \\end{array} \\right.$$ As for the values $\\bar\\eta_0,\\eta_0,\\eta_1$, we have $\\bar\\eta_0=\\frac{r-1}{2}$ and from Lemma \\[lem-degree2\\] $$\\begin{aligned} \\left\\{ \\begin{array}{lll} \\eta_0=\\frac{-1-\\sqrt{r}}{2}, & \\eta_1=\\frac{-1+\\sqrt{r}}{2}, & \\mbox{if $q\\equiv 1 \\pmod{4}$}, \\\\ \\eta_0=\\frac{-1-(-1)^{ms/2}\\sqrt{r}}{2}, & \\eta_1=\\frac{-1+(-1)^{ms/2}\\sqrt{r}}{2}, & \\mbox{if $q\\equiv 3 \\pmod{4}$}. \\\\ \\end{array} \\right.\\end{aligned}$$ Now we have obtained the value distribution of $\\widetilde{T}$. Returning to (\\[equ-Tx\\]) and (\\[equ-Weight of C\\]) gives us the weight distribution of the cyclic code $\\mathcal{C}_{(a_1,\\cdots,a_t)}$, which is summarized in Tables \\[Table1\\] and \\[Table2\\] in Theorem \\[thm-e1\\]. This completes the proof of Theorem \\[thm-e1\\]. Proof of Theorem \\[thm-e2\\] and Theorem \\[thm-e3\\] {#sec-mainII} ================================================== Proof of Theorem \\[thm-e3\\] {#sec-main3} --------------------------- Recall from (\\[equ-Ty\\]) and (\\[eqn-y0\\]) that to compute the weight distribution of the cyclic code $\\mathcal{C}_{(a_1,\\cdots,a_t)}$, it suffices to compute the value distribution of the sum $$\\label{equ-Ty2} \\widetilde{T}(y_0,y_1,\\cdots,y_{l_0},\\gamma z_1,\\cdots ,\\gamma z_{l_1}):=\\sum\\limits_{h=0}^{l_0}\\bar\\eta_{y_h}+ \\sum\\limits_{h=1}^{l_1}\\bar\\eta_{\\gamma z_h},\\quad \\forall \\, (y_1,\\cdots,y_{l_0},z_1,\\ldots,z_{l_1})\\in \\mathbb{F}_{r}^{l_0+l_1},$$ where $l_0,l_1$ are defined by (\\[equ-l1l2\\]) so that $l_0+l_1=t$ and $y_0:=y_0(y_1,\\ldots,y_{l_0},z_1,\\ldots,z_{l_1})$ satisfies $$\\begin{aligned} \\label{eqn-y02} y_0+y_1+\\cdots+y_{l_0}+ z_1+\\cdots+ z_{l_1}=0.\\end{aligned}$$ To study the value distribution of $\\widetilde{T}$ in (\\[equ-Ty2\\]), we consider the different subcases according to different $(k_0,k_1)$, where $k_0,k_1$ are defined by $$\\begin{array}{l} k_0:=\\#\\{i \\mid 0\\leqslant i\\leqslant l_0, y_i\\neq 0\\}; \\\\ k_1:=\\#\\{i \\mid 1\\leqslant i\\leqslant l_1, z_i\\neq 0\\}. \\end{array}$$ If $k_0+k_1 \\le 1$, by (\\[eqn-y02\\]), all of $y_0,y_1,\\ldots,y_{l_0},z_1,\\ldots,z_{l_1}$ are 0, the frequency is 1 and $\\widetilde{T}=(t+1) \\bar\\eta_0$. If $k_0+k_1 \\ge 2$, the number of ways to choose exactly $k_0$ non-zero terms in $y_0,\\ldots,y_{l_0}$ and exactly $k_1$ non-zero terms in $z_1,\\ldots,z_{l_1}$ is $\\binom{l_0+1}{k_0}\\binom{l_1}{k_1}$. Once they are chosen, without loss of generality we may assume that they are $y_1,\\ldots,y_{k_0}$ and $z_1,\\ldots,z_{k_1}$. Then in this case we have $$\\widetilde{T}=(t+1-k_0-k_1) \\bar\\eta_0+\\sum_{i=1}^{k_0}\\bar\\eta_{y_i}+ \\sum_{i=1}^{k_1}\\bar\\eta_{\\gamma z_i},$$ and the constraint (\\[eqn-y02\\]) becomes $$y_1+\\cdots+y_{k_0}+z_1+\\cdots+z_{k_1}=0.$$ In order to compute the value distribution of $\\widetilde{T}$ for these cases, let us consider for any $i_1,\\ldots,i_{k_0},j_1,\\ldots,j_{k_1} \\in \\{0,1\\}$ the value $\\Omega_{i_1\\cdots i_{k_0};j_{1}\\cdots j_{k_1}}^{'}$, given by $$\\label{equ-NNN2} \\Omega_{i_1\\cdots i_{k_0};j_{1}\\cdots j_{k_1}}^{'}:=\\#\\left\\{(y_1,\\cdots ,y_{k_0};z_1,\\cdots ,z_{k_1})\\in (\\mathbb{F}_{r}^*)^{k_0+k_1}\\ \\left|\\ {y_{u}\\in C_{i_{u}}^{(2,r)}, \\gamma z_{v} \\in C_{j_v}^{(2,r)}, 1 \\le u \\le k_0,1 \\le v \\le k_1}\\atop {y_1+\\cdots+y_{k_0}+z_1+\\cdots+z_{k_1}=0}\\right\\}\\right..$$ For any $ i \\in \\{0,1\\}$, define $\\bar{i} \\in \\{0,1\\}$ by $\\bar{i} \\equiv i+1 \\pmod{2}$. Clearly $$\\Omega_{i_1\\cdots i_{k_0};j_{1}\\cdots j_{k_1}}^{'}=\\Omega_{i_1\\cdots i_{k_0}\\bar{j}_{1}\\cdots \\bar{j}_{k_1}},$$ which is defined in (\\[equ-NNN\\]) and is evaluated in Section \\[sec-app\\]. In $\\{i_1,\\ldots,i_{k_0}\\}$, let $u_0$ be the number of $0$’s and $u_1$ be the number of $1$’s; similarly, in $\\{j_1,\\ldots,j_{k_1}\\}$, let $v_0$ be the number of $0$’s and $v_1$ be the number of $1$’s. Given such $u_0,u_1,v_0,v_1$, we have $$\\widetilde{T}=(t+1-k_0-k_1) \\bar\\eta_0+(u_0+v_0) \\eta_0+(u_1+v_1)\\eta_1,$$ and the frequency is $$\\binom{l_0+1}{k_0}\\binom{l_1}{k_1}\\binom{k_0}{u_0}\\binom{k_1}{v_0}\\Omega_{{\\scriptsize \\underbrace{0 \\cdots 0}_{u_0+v_1} \\underbrace{1\\cdots 1}_{u_1+v_0}}}.$$ Now let $k$ and $u$ be fixed such that $k_0+k_1=k$ and $u_0+v_0=u$, where $0 \\le u \\le k_0+k_1=k$ and $2 \\le k \\le l_0+l_1+1=t+1$, we conclude that $\\widetilde{T}$ takes the value $$\\begin{aligned} \\label{4:t} \\widetilde{T}=(t+1-k) \\bar\\eta_0+u \\eta_0+(k-u)\\eta_1, \\end{aligned}$$ and the frequency is $$\\begin{aligned} \\label{4:fre} \\sum_{k_0=0}^k\\sum_{u_0=0}^u\\binom{l_0+1}{k_0}\\binom{l_1}{k-k_0} \\binom{k_0}{u_0}\\binom{k-k_0}{u-u_0}\\Omega_{{\\scriptsize \\underbrace{0 \\cdots 0}_{2u_0+k-k_0-u,} \\underbrace{1\\cdots 1}_{k_0+u-2u_0}}}. \\end{aligned}$$ This, after returning to (\\[equ-Weight of C\\]), provides the weight distribution of the cyclic code $\\mathcal{C}_{(a_1,\\ldots,a_t)}$ for the general case $N=2,t=e-1\\geqslant 2$. Proof of Theorem \\[thm-e2\\] {#sec-main2} --------------------------- From $N=2=\\gcd\\left((q^m-1)/(q-1),4a\\right)$ and $t=e-1=3$, it is easy to see that $q \\equiv 1 \\pmod{4}$, $m \\equiv 2 \\pmod{4}$ and $e=4\\mid(q^{m/2}-1)$. If $2|a$, the weight distribution has been obtained from (i) of Theorem \\[thm-e1\\] with $t=3$, this is Table \\[Table3\\] in Theorem \\[thm-e2\\]. If $2 \\nmid a$, we use Theorem \\[thm-e3\\] to calculate the weight distribution. In this case $l_0=1,l_1=2$, from (\\[4:t\\]) and (\\[4:fre\\]), for any $k,u$ with $2 \\le k \\le 4,\\, 0 \\le u \\le k$, the sum $\\widetilde{T}$ takes the value $$\\widetilde{T}=(4-k) \\bar\\eta_0+u \\eta_0+(k-u)\\eta_1,$$ with frequency $$\\sum_{k_0=0 }^k\\sum_{u_0=0}^u\\binom{2}{k_0}\\binom{2}{k-k_0} \\binom{k_0}{u_0}\\binom{k-k_0}{u-u_0}\\Omega_{{\\scriptsize \\underbrace{0 \\cdots 0}_{2u_0+k-k_0-u,} \\underbrace{1\\cdots 1}_{k_0+u-2u_0}}}.$$ Using the values $$\\left\\{\\begin{array}{l} \\Omega_{00}=\\Omega_{11}=\\frac{r-1}{2}; \\quad \\Omega_{01}=0;\\\\ \\Omega_{000}=\\Omega_{111}=\\frac{r-1}{8}(r-5);\\\\ \\Omega_{001}=\\Omega_{011}=\\frac{(r-1)^2}{8};\\\\ \\Omega_{0000}=\\Omega_{1111}=\\frac{r-1}{16}(r^2-2r+9);\\\\ \\Omega_{0001}=\\Omega_{0111} =\\frac{r-1}{16}(r^2-4r+3);\\\\ \\Omega_{0011}=\\frac{(r-1)^3}{16}, \\end{array}\\right.$$ which we can obtain from Lemma \\[thm-NNN3\\] in Section \\[sec-app\\], we find that for $k=2$, $$\\left. \\begin{array}{ll} \\mbox{Value} & \\hbox{Frequency} \\\\ 2\\bar\\eta_0+2\\eta_0, & \\Omega_{00}+4\\Omega_{01}+\\Omega_{11}=r-1 \\\\[2mm] 2\\bar\\eta_0+2\\eta_1, & \\Omega_{00}+4\\Omega_{01}+\\Omega_{11} =r-1 \\\\[2mm] 2\\bar\\eta_0+\\eta_0+\\eta_{1}, & 4\\Omega_{00}+4\\Omega_{01}+4\\Omega_{11} =4(r-1)\\\\[2mm] \\end{array} \\right.$$ and for $k=3$, $$\\left. \\begin{array}{ll} \\mbox{Value} & \\hbox{Frequency} \\\\ \\bar\\eta_0+3\\eta_0, & 2\\Omega_{001}+2\\Omega_{011}=\\frac{(r-1)^2}{2} \\\\[2mm] \\bar\\eta_0+3\\eta_1, & 2\\Omega_{001}+2\\Omega_{011}=\\frac{(r-1)^2}{2}\\\\[2mm] \\bar\\eta_0+2\\eta_0+\\eta_{1},&4\\Omega_{011}+2\\Omega_{000}+2\\Omega_{111}+4\\Omega_{001}\\\\ &\\quad =\\frac{(r-1)}{2}(3r-7)\\\\[2mm] \\bar\\eta_0+\\eta_0+2\\eta_{1},&4\\Omega_{011}+2\\Omega_{000}+2\\Omega_{111}+4\\Omega_{001}\\\\ &\\quad =\\frac{(r-1)}{2}(3r-7) \\end{array} \\right.$$ and for $k=4$, $$\\left. \\begin{array}{ll} \\mbox{Value} & \\hbox{Frequency} \\\\ 4\\eta_0, & \\Omega_{0011}=\\frac{(r-1)^3}{16} \\\\[2mm] 4\\eta_1, & \\Omega_{0011}=\\frac{(r-1)^3}{16} \\\\[2mm] 3\\eta_0+\\eta_1, & 2\\Omega_{0111}+2\\Omega_{0001}=\\frac{(r-1)}{4}(r^2-4r+3) \\\\[2mm] \\eta_0+3\\eta_1, & 2\\Omega_{0111}+2\\Omega_{0001}=\\frac{(r-1)}{4}(r^2-4r+3) \\\\[2mm] 2(\\eta_0+\\eta_{1}),&\\Omega_{1111}+4\\Omega_{0011}+\\Omega_{0000}=\\frac{(r-1)}{8}(3r^2-6r+11). \\end{array} \\right.$$ Now we have obtained the value distribution of $\\widetilde{T}$. Returning to (\\[equ-Tx\\]) and (\\[equ-Weight of C\\]) gives us the weight distribution of the cyclic code $\\mathcal{C}_{(a_1,a_2,a_3)}$ with $2 \\nmid a$, which is summarized in Table \\[Table4\\] in Theorem \\[thm-e2\\]. This completes the proof of Theorem \\[thm-e2\\]. Appendix: Calculation of $\\Omega_{i_1\\cdots i_u i_{u+1}}$ {#sec-app} ========================================================= Recall that for positive integer $u$ and any sequence $i_1,\\cdots,i_{u},i_{u+1}\\in\\{0,1\\}$, the value $\\Omega_{i_1\\cdots i_ui_{u+1}}$ is defined by $$\\Omega_{i_1\\cdots i_ui_{u+1}}:=\\#\\left\\{(x_1,\\cdots ,x_u)\\in (\\mathbb{F}_{r}^*)^u\\ \\left|\\ x_1\\in C_{i_1}^{(2,r)},\\cdots, x_u\\in C_{i_u}^{(2,r)}, \\sum\\limits_{j=1}^ux_j\\in C_{i_{u+1}}^{(2,r)}\\right\\}\\right..$$ We first prove that the value of $\\Omega_{i_1\\cdots i_ti_{u+1}}$ is related to reduced quadratic Jacobi sums which were introduced in Section \\[sec-pre\\] before. \\[thm-NNN\\] The number $\\Omega_{i_1\\cdots i_ui_{u+1}}$ defined above equals to $$\\frac{r-1}{2^{u+1}}\\sum\\limits_{0 \\le v_2,\\cdots,v_{u+1} \\le 1} (-1)^{\\sum\\limits_{j=2}^{u+1}(i_1+i_j)v_j} \\rho\\left((-1)^{\\sum\\limits_{j=2}^{u}v_j}\\right) J^*(\\rho^{v_2},\\cdots,\\rho^{v_{u+1}}),$$ where $\\rho$ is the quadratic multiplicative character of $\\mathbb{F}_{r}$. For $x\\in \\mathbb{F}_{r}^*$, let $\\chi$ denote a multiplicative character of $\\mathbb{F}_{r}$. It is easy to check that $$\\label{equ-orthogonal2} \\frac{1}{2}\\sum\\limits_{\\chi^2=\\varepsilon}\\chi(x \\gamma^i)= \\left\\{ \\begin{array}{ll} 1, & \\hbox{if\\ }x\\in C_i^{(L,r)}; \\\\ 0, & \\hbox{otherwise.} \\end{array} \\right.$$ Suppose $\\chi_1,\\chi_2,\\cdots ,\\chi_{u+1}$ denote multiplicative characters of $\\mathbb{F}_{r}$. By the relation (\\[equ-orthogonal2\\]), we have $$\\begin{array}{l} \\Omega_{i_1\\cdots i_ui_{u+1}}\\\\ =\\sum\\limits_{x_1,\\cdots x_{u}\\in\\mathbb{F}_{r}^*}\\left[\\frac{1}{2}\\sum\\limits_{\\chi_1^2=\\varepsilon}\\chi_1(x_1 \\gamma^{i_1})\\right] \\cdots \\left[\\frac{1}{2}\\sum\\limits_{\\chi_u^2=\\varepsilon}\\chi_u(x_u \\gamma^{i_u})\\right] \\left[\\frac{1}{2}\\sum\\limits_{\\chi_{u+1}^2=\\varepsilon}\\chi_{u+1}(\\gamma^{i_{u+1}}\\sum\\limits_{j=1}^{u}x_j)\\right]. \\end{array}$$ Expanding the right hand side and changing the order of summation we obtain $$\\begin{array}{l} \\frac{1}{2^{u+1}}\\sum\\limits_{\\chi_j^2=\\varepsilon\\atop j=1,\\cdots,u+1}\\chi_1(\\gamma^{i_1})\\cdots\\chi_{u}(\\gamma^{i_{u}})\\chi_{u+1}(\\gamma^{i_{u+1}}) \\\\ \\qquad \\cdot\\sum\\limits_{x_1, \\ldots,x_u\\in \\mathbb{F}_{r}^*}\\chi_1(x_1)\\cdots\\chi_{u}(x_u) \\chi_{u+1}(x_1+x_2+\\cdots+x_u), \\end{array}$$ which gives $$\\begin{array}{l} \\frac{1}{2^{u+1}}\\sum\\limits_{\\chi_j^2=\\varepsilon\\atop j=1,\\cdots,u+1}\\chi_1(\\gamma^{i_1})\\chi_2(-\\gamma^{i_2})\\cdots\\chi_{u}(-\\gamma^{i_{u}})\\chi_{u+1}(\\gamma^{i_{u+1}}) \\\\ \\qquad \\cdot\\sum\\limits_{x_1, \\ldots,x_u\\in \\mathbb{F}_{r}^*}\\chi_1\\chi_2 \\cdots \\chi_{u+1}(x_1) \\chi_2(x_2)\\cdots\\chi_{u}(x_u) \\chi_{u+1}(1-x_2-\\cdots-x_u). \\end{array}$$ This is $$\\begin{array}{l} \\frac{r-1}{2^{u+1}}\\sum\\limits_{\\chi_j^2=\\varepsilon\\atop j=2,\\cdots,u+1}\\chi_2(-\\gamma^{i_1+i_2})\\cdots\\chi_u(-\\gamma^{i_1+i_u}) \\chi_{u+1}(\\gamma^{i_1+i_{u+1}})\\\\ \\qquad \\cdot\\sum\\limits_{x_2,\\cdots,x_{u}\\in \\mathbb{F}_{r}^*}\\chi_2(x_2)\\cdots\\chi_u(x_u)\\chi_{u+1}(1-x_1-\\cdots-x_u).\\end{array}$$ So we obtain $$\\begin{array}{l} \\Omega_{i_1\\cdots i_ui_{u+1}}=\\frac{r-1}{2^{u+1}}\\sum\\limits_{0 \\le v_2,\\cdots,v_{u+1} \\le 1}(-1)^{\\sum\\limits_{j=2}^{u}(i_1+i_j)v_j} \\rho\\left((-1)^{\\sum\\limits_{j=2}^{u}v_j}\\right)J^*(\\rho^{v_2},\\cdots,\\rho^{v_{u+1}}). \\end{array}$$ This completes the proof of Lemma \\[thm-NNN\\]. \\[thm-NNN2\\] Suppose that $-1$ is a square in ${{\\mathbb F}}_r$, then $$\\Omega_{i_1\\cdots i_ui_{u+1}}=\\frac{r-1}{2^{u+1}}\\left\\{\\frac{1}{r}\\bigg((r-1)^u-(-1)^u\\bigg)-(-1)^u \\sum_{1 \\le l \\le \\frac{u+1}{2} }r^{l-1}\\sum_{1 \\le j_1 <j_2<\\cdots<j_{2l} \\le u+1} (-1)^{\\sum\\limits_{k=1}^{2l}i_{j_k}} \\right\\} .$$ Since $N=\\gcd(\\frac{q^m-1}{q-1},ea)=2$ implies $2|m$, then $-1=\\gamma^{\\frac{q^m-1}{2}}$ is always a square in this paper, from Lemma \\[thm-NNN\\] we have $$\\begin{array}{l} \\Omega_{i_1\\cdots i_ui_{u+1}}=\\frac{r-1}{2^{u+1}}\\sum\\limits_{0 \\le v_2,\\cdots,v_{u+1} \\le 1}(-1)^{\\sum\\limits_{j=2}^{u}(i_1+i_j)v_j} J^*(\\rho^{v_2},\\cdots,\\rho^{v_{u+1}}). \\end{array}$$ Note that $J^*(\\rho_1,,\\cdots,\\rho_u)$ does not depend on the order of the characters $\\rho_1,\\ldots,\\rho_u$, so we have $$\\begin{array}{l} \\Omega_{i_1\\cdots i_ui_{u+1}}=\\frac{r-1}{2^{u+1}}\\sum\\limits_{I \\subset \\{2,\\ldots,u+1\\}}(-1)^{\\sum\\limits_{j \\in I}(i_1+i_j)} J^*(\\underbrace{\\varepsilon,\\ldots,\\varepsilon}_{u-\\#I},\\underbrace{\\rho,\\cdots,\\rho}_{\\#I}). \\end{array}$$ Separating the cases that $I =\\emptyset$, $\\#I>0$ is even and $\\#I$ is odd and applying Lemmas \\[lem\\_J\\] and \\[lem-J\\*\\], we can obtain $$\\begin{array}{l} \\Omega_{i_1\\cdots i_ui_{u+1}}=\\frac{r-1}{2^{u+1}} \\left\\{A+B+C\\right\\}, \\end{array}$$ where $$A=J^*(\\underbrace{\\varepsilon,\\cdots,\\varepsilon}_{u})=\\frac{1}{r}\\bigg((r-1)^u-(-1)^u\\bigg),$$ $$B=(-1)^{u+1}\\sum\\limits_{\\substack{\\emptyset \\ne I \\subset \\{2,\\ldots,u+1\\}\\\\ \\#I \\mbox{\\small \\, is even}}}(-1)^{\\sum\\limits_{j \\in I}i_j}r^{(\\#I-2)/2},$$ and $$C=(-1)^{u+1}\\sum\\limits_{\\substack{I \\subset \\{2,\\ldots,u+1\\}\\\\ \\#I \\mbox{\\small \\, is odd}}}(-1)^{i_1+\\sum\\limits_{j \\in I}i_j}r^{(\\#I-1)/2}.$$ Setting $\\#I=2l$ if $\\#$ is even and $\\#I=2l-1$ is $\\#I$ is odd completes the proof of Lemma \\[thm-NNN2\\]. It is easy to see from Lemma \\[thm-NNN2\\] that the value $\\Omega_{i_1\\cdots i_ui_{u+1}}$ does not depend on the order of the sequence $i_1,\\ldots,i_u,i_{u+1}$. Now we can prove \\[thm-NNN3\\] Suppose that $-1$ is a square in ${{\\mathbb F}}_r$, then $$\\Omega_{{\\scriptsize \\underbrace{0 \\cdots 0}_u \\underbrace{1\\cdots 1}_v}}=\\frac{r-1}{r 2^{u+v+1}}\\bigg\\{2(r-1)^{u+v-1}+(-1)^{u+v} \\left\\{(1+\\sqrt{r})^u(1-\\sqrt{r})^v+(1-\\sqrt{r})^u(1+\\sqrt{r})^v\\right\\}\\bigg\\}.$$ From Lemma \\[thm-NNN2\\], it suffices to compute $$P=\\sum_{1 \\le l \\le \\frac{u+v}{2} }r^{l-1}\\sum_{1 \\le j_1 <j_2<\\cdots<j_{2l} \\le u+v} (-1)^{\\sum\\limits_{k=1}^{2l}i_{j_k}}.$$ Since $i_j=0$ for $1 \\le j \\le u$ and $i_k=1$ for $u+1 \\le j \\le u+v$, we have $$\\sum_{1 \\le j_1 <j_2<\\cdots<j_{2l} \\le u+v} (-1)^{\\sum\\limits_{k=1}^{2l}i_{j_k}}= \\sum_{s=0}^{2l}\\binom{u}{2l-s} \\binom{v}{s} (-1)^s,$$ and the right hand side is the coefficient of $x^{2l}$ in the expansion of the polynomial $f(x):=(1+x)^u(1-x)^v$. Hence letting $$f(x)=1+\\sum_{n=1}^{u+v}a_nx^n,\\quad a_n \\in \\mathbb{R},$$ then $$P=\\frac{1}{r}\\sum_{1 \\le l \\le \\frac{u+v}{2}} a_{2l} (\\sqrt{r})^{2l}.$$ Clearly the right hand side is $$\\frac{1}{r} \\left\\{\\frac{f(\\sqrt{r})+f(-\\sqrt{r})}{2}-1\\right\\}.$$ This completes the proof of Lemma \\[thm-NNN3\\]. Conclusions {#sec-conclusion} =========== In this paper, we determine the weight distributions of a new family of cyclic codes with arbitrary number of zeros, more precisely the cyclic codes $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ given by (\\[def\\]) with any $t \\ge 2$ zeros under the conditions that $t=e-1$ and $N=2$. Our main results are as follows: - For $N=2$, $t=e-1 \\geqslant 2$, $2|a$ and $e|(q^{m/2}-1)$, we obtain the weight distribution of $\\mathcal{C}_{(a_1,\\cdots,a_t)}$. - For $N=2$ and $t=e-1=3$, we obtain the weight distribution of $\\mathcal{C}_{(a_1,\\cdots,a_t)}$. - For the general case of $N=2$ and $t=e-1\\geqslant 2$, we present a computational formula to determine the weight distribution of $\\mathcal{C}_{(a_1,\\cdots,a_t)}$. Except for these cases (in [@Y-X-D12] and this paper), the weight distribution of the code $\\mathcal{C}_{(a_1,\\cdots,a_t)}$ is open in most cases when $t < e$. It would be good if some of these open cases can be settled. Acknowledgments {#acknowledgments .unnumbered} --------------- Maosheng Xiong’s research is supported by the Hong Kong Research Grants Council under Grant Nos. 609513 and 606211. Jing Yang’s research is partly supported by the National Natural Science Foundation of China (No. 11371011). 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Q: Trigonometric identity involving sum of "Dirichlet kernel like" fractions Computing the eigenvalues of a matrix related to fast Fourier transform, we stumbled upon the following identities. Let $k$ and $N$ be natural numbers with $k<N$, then: $$\\sum\\limits_{j=1}^N (-1)^{j+1}\\frac {\\sin \\left( \\frac{2\\pi j k}{2N+1}\\right)} {\\sin\\left( \\frac{\\pi j}{2N+1}\\right)}=k$$ and $$\\sum \\limits_{j=1}^{N}(-1)^{j+1} \\sin \\left( \\frac{\\pi j k}{N}\\right) \\cot \\left( \\frac{\\pi j}{2N} \\right)=k.$$ How can these be proven? (This is not a homework question. I have seen lots of similar formulae but not exactly these ones. These can be reformulated in various ways, e.g., the first is simultaneously an identity for Chebyshev polynomials of second kind.) A: $\\square$ Let us denote $$S_k=\\sum_{j=1}^N(-1)^{j+1}\\frac{\\sin \\frac{2\\pi j k}{2N+1}}{\\sin \\frac{\\pi j}{2N+1}},$$ and observe that for $k=0,\\ldots,N-1$ one has \\begin{align}S_{k+1}-S_k&=\\sum_{j=1}^N(-1)^{j+1} \\frac{\\sin \\frac{2\\pi j (k+1)}{2N+1}-\\sin \\frac{2\\pi j k}{2N+1}}{\\sin \\frac{\\pi j}{2N+1}}=\\\\ &=2\\sum_{j=1}^N(-1)^{j+1}\\cos \\frac{\\pi j (2k+1)}{2N+1}=\\\\ &=\\sum_{j=1}^N(-1)^{j+1}e^{\\frac{\\pi i (2k+1) j}{2N+1}}+\\sum_{j=1}^N(-1)^{j+1}e^{-\\frac{\\pi i (2k+1) j}{2N+1}}=\\\\ &=e^{\\frac{\\pi i (2k+1)}{2N+1}}\\frac{1-(-1)^Ne^{\\frac{\\pi i (2k+1)N}{2N+1}}}{1+e^{\\frac{\\pi i (2k+1)}{2N+1}}}+e^{-\\frac{\\pi i (2k+1)}{2N+1}}\\frac{1-(-1)^Ne^{\\frac{-\\pi i (2k+1)N}{2N+1}}}{1+e^{-\\frac{\\pi i (2k+1)}{2N+1}}}=\\\\& =1+(-1)^{N+1}\\frac{e^{\\frac{\\pi i (2k+1)(2N+1-N)}{2N+1}}+e^{\\frac{-\\pi i (2k+1)N}{2N+1}}}{1+e^{\\frac{\\pi i (2k+1)}{2N+1}}}=\\\\ &=1.\\tag{$\\heartsuit$}\\end{align} Here at the first step we use that $\\sin a -\\sin b=2\\sin\\frac{a-b}{2}\\cos\\frac{a+b}{2}$ and the third is obtained by summing finite geometric series. Obviously, $S_0=0$, and therefore the first identity (written as $S_k=k$) easily follows from ($\\heartsuit$) by induction. $\\blacksquare$ The second identity can be proved in a completely analogous fashion - that is, by considering the difference of the left sides for two consecutive $k$, summing up the resulting finite geometric series and induction with a trivial base case. P.S. As pointed out by Grigory M, one does not even need to sum up geometric series: the same result ($\\heartsuit$) can be achieved with simpler manipulations.

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Welcome to our Community BEST PART OF MY TRIP TO SCOTLAND Posted By Christine Delia on 25/03/2018 Tour: Isle of Skye 3 Day Tour I just did the 3 day tour of the Isle of Skye. Our tour guide was Mac. We were so lucky that our first day was beautiful. I got the most amazing pictures!! Mac is unbelievable. His storytelling is so entertaining! His knowledge and love of Scotland are tremendous. I loved all the music he played along the way plus at every single stop, he gets out to pick up trash that others leave behind. Heart of Gold! Skye is gorgeous. The town of Portree so quant. Loved this. I would do it again.

--- abstract: 'Event-triggered and self-triggered control have been proposed in recent years as promising control strategies to reduce communication resources in Networked Control Systems (NCSs). Based on the notion of set-invariance theory, this note presents new self-triggered control strategies for linear discrete-time systems subject to input and state constraints. The proposed schemes not only achieve communication reduction for NCSs, but also ensure both asymptotic stability of the origin and constraint satisfactions. A numerical simulation example validates the effectiveness of the proposed approaches.' author: - 'Kazumune Hashimoto, , Shuichi Adachi,  and Dimos V. Dimarogonas,  [^1] [^2]' title: 'Aperiodic Sampled-Data Control via Explicit Transmission Mapping: A Set Invariance Approach' --- Event-triggered and self-triggered control, Constrained control, Set-invariance theory. Introduction ============ Efficient network utilization and energy-aware communication protocols between sensors, actuators and controllers have been recent challenges in the community of Networked Control Systems (NCSs). To tackle such challenges, event and self-triggered control schemes have been proposed as alternative approaches to the typical time-triggered controllers, see e.g., [@dimos2010a; @heemels2011a; @tabuada2010a]. In contrast to the time-triggered case where the control signals are executed periodically, event and self-triggered strategies trigger the executions based on the violation of prescribed control performances, such as Input-to-State Stability (ISS) [@dimos2010a] and ${\\cal L}_\\infty$ gain stability [@heemels2011a]. In particular, we are interested in designing self-triggered strategies for *constrained* control systems, where certain constraints such as physical limitations and actuator saturations need to be explicitly taken into account. One of the most popular control schemes to deal with such constraints is Model Predictive Control (MPC) [@Mayne2000a]. In the MPC strategy, the current control action is determined by solving a constrained optimal control problem online, based on the knowledge of current state information and dynamics of the plant. Moreover, applications of the event and self-triggered control to MPC have been recently proposed to reduce the frequency of solving optimal control problems, see e.g., [@evmpc_linear6; @evmpc_linear9; @evmpc_linear10; @hashimoto2015c; @hashimoto2017a; @hashimoto2017c]. The main contribution of this note is to provide novel self-triggered strategies for constrained systems from an alternative perspective to the afore-cited papers, namely, a perspective from *set-invariance theory* [@blanchini1999a]. Set invariance theory has been extensively studied for the past two decades [@blanchini1994a; @bitsoris1988a; @gilbert1991a], and it provides a fundamental tool to design controllers for constrained control systems. Two established concepts are those of a *controlled invariant set* and $\\lambda$-*contractive set*. While a controlled invariant set implies that the state stays inside the set for all time, a $\\lambda$-contractive set guarantees the more restrictive condition that the state is asymptotically stabilized to the origin. In this note, two different types of set-invariance based self-triggered strategies are presented. In the first approach, we formulate an optimal control problem such that the controller obtains stabilizing control inputs under *multiple candidates* of transmission time intervals. Among the multiple solutions, the controller selects a suitable one such that both control performance and communication load are taken into account. Asymptotic stability of the origin is ensured by using Lyapunov techniques, where the Lyapunov function is induced by a $\\lambda$-contractive set obtained offline. Although the first approach guarantees asymptotic stability, it may lead to a high computation load as it requires to solve multiple optimization problems online. Therefore, we secondly propose an alternative strategy that aims to overcome the computational drawback of the first proposal. Similarly to the concept of explicit MPC [@bemporad2002b], we provide an *offline*, explicit mapping that sends the state information to the desired transmission time interval. As we will see in later sections, the state-space is decomposed into a finite number of subsets, to which appropriate transmission time intervals are assigned. The rest of the paper is organized as follows. In Section II, the system description and some preliminaries of invariant set theory are given. In Section III, we propose the first approach of the self-triggered strategy. In Section IV, the second approach of the self-triggerd strategy is presented. In Section V, a illustrative simulation example is given. We finally conclude in Section VI.\\ *(Nomenclature)*: Let $\\mathbb{R}$, $\\mathbb{R}_+$, $\\mathbb{N}$, $\\mathbb{N}_+$ be the *non-negative reals, positive reals, non-negative* and *positive integers*, respectively. The *interior* of the set ${\\cal S} \\subset \\mathbb{R}^n$ is denoted as ${\\rm int} \\{ {\\cal S} \\}$. A set ${\\cal S} \\subset \\mathbb{R}^n$ is called *${\\cal C}$-set* if it is compact, convex, and $0 \\in {\\rm int} \\{{\\cal S}\\}$. For vectors $v_1, \\ldots, v_N$, ${\\rm co} \\{ v_1, \\ldots, v_N \\}$ denotes their *convex hull*. A set of vectors $\\{v_1, \\ldots, v_N \\}$ whose convex hull gives a set ${\\cal P}$ (i.e., ${\\cal P} = {\\rm co} \\{ v_1, \\ldots, v_N \\}$), and each $v_n$, $n\\in \\{1, 2, \\ldots, N\\}$ is not contained in the convex hull of $v_1, \\ldots, v_{n-1}, v_{n+1}, \\ldots, v_{N}$ is called a set of *vertices* of ${\\cal P}$. Given a ${\\cal C}$-set ${\\cal S} \\subset \\mathbb{R}^n $, denote by $\\partial {\\cal S} \\subset \\mathbb{R}^n$ the boundary of ${\\cal S}$. For a given $\\lambda \\in \\mathbb{R}$ and a ${\\cal C}$-set ${\\cal S}\\subset \\mathbb{R}^n$, denote $\\lambda {\\cal S}$ as $\\lambda {\\cal S} = \\{ \\lambda x \\in \\mathbb{R}^n : x \\in {\\cal S}\\}$. Given a set ${\\cal S} \\subset \\mathbb{R}^n$, the function $\\Psi_{\\cal S} : \\mathbb{R}^n \\rightarrow \\mathbb{R}_+$ with $\\Psi_{{\\cal S}}(x) = {\\rm inf} \\{\\mu : x \\in \\mu {\\cal S}, \\mu \\geq 0 \\}$ is called a *gauge function*. For given two sets ${\\cal S}_1, {\\cal S}_2 \\subset \\mathbb{R}^n$, define ${\\cal S}_1 \\backslash {\\cal S}_2$ as ${\\cal S}_1 \\backslash {\\cal S}_2 = \\{ x\\in \\mathbb{R}^n : x \\in {\\cal S}_1, x \\notin {\\cal S}_2 \\}$. Problem formulation and some preliminaries {#strategy_sec} ========================================== In this section, the system description and some established results of set-invariance theory are provided. System description and control strategy {#sys_desc_sec} --------------------------------------- Consider a networked control system illustrated in [Fig.\\[network\\]]{}. We assume that the dynamics of the plant are given by $$\\label{sys} x ({k+1}) = A x (k) + Bu (k)$$ for $k\\in \\mathbb{N}$, where $x (k) \\in \\mathbb{R}^{n}$ is the state and $u (k) \\in \\mathbb{R}^m$ is the control variable. The state and control input are assumed to be constrained as $x(k) \\in {\\cal X},\\ u(k) \\in {\\cal U}$, $\\forall k \\in \\mathbb{N}$, where ${\\cal X} \\subset \\mathbb{R}^n, \\ {\\cal U} \\subset \\mathbb{R}^m$ are both polyhedral ${\\cal C}$-sets described as $$\\label{constraint} \\begin{array}{lll} {\\cal X} = \\{x\\in \\mathbb{R}^n: H_x x\\leq h_x \\}, \\\\ {\\cal U} = \\{u \\in \\mathbb{R}^m :H_u u\\leq h_u \\}, \\end{array}$$ where $H_x \\in \\mathbb{R}^{n_x \\times n}$, $H_u \\in \\mathbb{R}^{n_u \\times m}$ and $h_x$, $h_u$ are appropriately sized vectors having positive components. The control objective is to steer the state to the origin, i.e., $x(k) \\rightarrow 0$ as $k\\rightarrow \\infty$. Let $k_m$, $m\\in\\mathbb{N}$ with $k_0 = 0$ be the transmission time instants when the plant transmits the state information $x(k_m)$ to the controller and updates the control input. In the self-triggered strategy, the transmission times are determined as $$\\label{transmission_times} k_{m +1} = k_m + \\Gamma (x(k_m)), \\ \\ m \\in \\mathbb{N},$$ where $\\Gamma : {\\cal X} \\rightarrow \\{ 1, 2, \\ldots, j_{\\max} \\}$ denotes a mapping that sends the state information to the corresponding transmission time interval. Here, a maximal transmission time interval $j _{\\max} \\in \\mathbb{N}_+$ is set apriori in order to formulate the self-triggered strategy. Due to the limited nature of communication bandwidth, we assume that only one control sample (not a sequence of control samples) is allowed to be transmitted at each transmission time. Namely, the control input is constant between two consecutive inter-transmission times, i.e., $$\\label{controller} u (k) = \\kappa (x(k_m)) \\in {\\cal U}, \\ \\ k \\in [k_m , k_{m+1} ),$$ where $\\kappa : {\\cal X} \\rightarrow {\\cal U}$ denotes the state-feedback control law. The following assumptions are made throughout the paper (see e.g., [@blanchini1994a]): The pair $(A, B)$ is controllable. [The matrix $B$ has full column rank.]{} ![Networked Control System[]{data-label="network"}](networksystem-eps-converted-to.pdf){width="7cm"} Set-invariance theory {#set_invariance_sec} --------------------- In the following, we define the standard notions of *controlled invariant set* and $\\lambda$*-contractive set* [@blanchini1994a], which are important concepts to characterize invariance and convergence properties for constrained control systems. \\[lambda\\_contractive\\] For a given ${\\cal C}$-set ${\\cal S} \\subseteq {\\cal X}$, ${\\cal S}$ is said to be a controlled invariant set in ${\\cal X}$, if and only if there exists a control law $g(x)\\in {\\cal U}$ such that $Ax + Bg(x) \\in {\\cal S}$ for all $x\\in {\\cal S}$. \\[lambda\\_contractive\\] For a given ${\\cal C}$-set ${\\cal S} \\subseteq {\\cal X}$, ${\\cal S}$ is said to be a $\\lambda$-contractive set in ${\\cal X}$ for $\\lambda\\in [0, 1] $, if and only if there exists a control law $g(x)\\in {\\cal U}$ such that $A x + B g(x) \\in \\lambda {\\cal S}$ for all $x\\in {\\cal S}$. Roughly speaking, a set ${\\cal S}$ is called $\\lambda$-contractive set if all states in ${\\cal S}$ can be driven into a tighter (or equivalent) region $\\lambda {\\cal S}$ by applying a one-step control input. From the definition, a controlled invariant set implies a $\\lambda$-contractive set with $\\lambda = 1$. We review several established results for obtaining a contractive set and the corresponding properties. For given $\\lambda \\in [0, 1)$ and ${\\cal C}$-set ${\\cal X}\\subset \\mathbb{R}^n$, there are several ways to efficiently construct a $\\lambda$-contractive set in ${\\cal X}$. For a given ${\\cal C}$-set ${\\cal D} \\subset \\mathbb{R}^n$, let ${\\cal Q}_{\\lambda}: \\mathbb{R}^n \\rightarrow \\mathbb{R}^n$ be the mapping $$\\label{kstep_contrl} {\\cal Q}_{\\lambda} ({\\cal D}) = \\{ x\\in {\\cal X} : \\exists u \\in {\\cal U},\\ A x + B u \\in \\lambda {\\cal D} \\}.$$ A simple algorithm to obtain a $\\lambda$-contractive set in ${\\cal X}$ is to compute $\\Omega_{j} \\subset \\mathbb{R}^n$, $j \\in \\mathbb{N}$ as $$\\label{iterative_procedure} \\Omega_{0} = {\\cal X}, \\quad \\Omega_{j+1} = {\\cal Q} _{\\lambda } (\\Omega_{j} ) \\cap {\\cal X},$$ and then it holds that the set ${\\cal S} = \\lim_{j\\rightarrow \\infty} \\Omega_j $ is $\\lambda$-contractive, see e.g., [@blanchini1994a]. If $\\Omega_{j+1} =\\Omega_j$ for some $j$, the $\\lambda$-contractive set is obtained as ${\\cal S} = \\Omega_j $, which requires only a finite number of iterations. Although such condition does not hold in general, it is still shown, under Assumptions 1 and 2, that the algorithm converges in the sense that for every $\\lambda < \\bar{\\lambda} <1$, there exists a finite $j \\in \\mathbb{N}_+$ such that the set $\\Omega_j $ is $\\bar{\\lambda}$-contractive (see *Theorem 3.2* in [@blanchini1994a]). Several other algorithms have been recently proposed, see e.g., [@hovd2014a; @hovd2016a] and see also [@darup2017a] for a detailed convergence analysis. The following lemma illustrates the existence of a (non-quadratic) Lyapunov function in a given $\\lambda$-contractive set: \\[stability\\_lem\\][[@blanchini1994a]:]{} Let ${\\cal S} \\subset {\\cal X}$ be a $\\lambda$-contractive ${\\cal C}$-set with $\\lambda \\in [0, 1]$ and the associated gauge function $\\Psi_{\\cal S} : {\\cal S} \\rightarrow \\mathbb{R}_+$. Then, there exists a control law $g : {\\cal X} \\rightarrow {\\cal U}$ such that $$\\label{set_induced_lyapunov} \\Psi_{\\cal S} ( Ax + B g (x)) \\leq \\lambda \\Psi_{\\cal S} ( x),$$ for all $x \\in {\\cal S}$. [Lemma\\[stability\\_lem\\]]{} follows immediately from [Definition\\[lambda\\_contractive\\]]{}. If $\\lambda < 1$, implies the existence of a stabilizing controller in ${\\cal S}$ in the sense that the output of the gauge function $\\Psi_{\\cal S} (\\cdot)$ is guaranteed to decrease. The gauge function $\\Psi_{\\cal S} (\\cdot)$ defined in ${\\cal S}$ is known as *set-induced Lyapunov function* in the literature; for a detailed discussion, see e.g., [@blanchini1994a]. Self-triggered strategy ======================= As described in the introduction, we propose two different types of self-triggered controllers; in this section, the first approach is presented. Designing a stabilizing controller {#stabilize_control_sec} ---------------------------------- For a given $\\lambda \\in [0, 1)$, let us first construct a $\\lambda$-contractive set ${\\cal S}$ in ${\\cal X}$. Note that since ${\\cal X}$ is a polyhedral ${\\cal C}$-set, one can efficiently compute the $\\lambda$-contractive set through polyhedral operations according to [^3]. The obtained $\\lambda$-contractive set ${\\cal S}$ can be denoted as $$\\label{setS} {\\cal S} = {\\rm co} \\{v_1, v_2, \\ldots, v_N \\} \\subseteq {\\cal X},$$ where $v_n, n\\in \\{1, 2, \\ldots, N \\}$ represent the vertices of ${\\cal S}$, and $N$ represents the number of them. \\[initial\\_cond\\] The initial state is inside ${\\cal S}$, i.e., $x(k_0) \\in {\\cal S}$. Based on [Assumption\\[initial\\_cond\\]]{}, we will design the self-triggered strategy such that the state remains in ${\\cal S}$ for each transmission time instant. Suppose that at a certain transmission time $k_m$, $m \\in \\mathbb{N}$, the plant transmits the state information $x(k_m)$ to the controller. Based on $x(k_m)$, the controller needs to compute both a suitable controller to be applied and a transmission time interval, such that the state is stabilized to the origin. To this end, we first propose an approach to obtain stabilizing controllers under *multiple candidates* of transmission time intervals. More specifically, we obtain different control actions under different transmission time intervals, and the controller selects a suitable one among them. To obtain the stabilizing controllers, we formulate the following optimal control problem for each $j\\in \\{1, \\ldots, j_{\\max} \\}$: \\[control\\_problem\\] For given $x(k_m)$, $j \\in \\{1, \\ldots, j_{\\max} \\}$ and the $\\lambda$-contractive set ${\\cal S}$, find $u \\in {\\cal U}$ and $\\varepsilon \\in \\mathbb{R}$ by solving the following problem:\\ $$\\label{cost_epsilon} \\underset{u \\in {\\cal U}} {\\min}\\ \\ \\varepsilon,$$ subject to $\\varepsilon \\in [0, \\lambda]$, and 1. $A^{j'} x(k_m) + \\sum^{j'} _{i=1} A^{i-1} B u \\in {\\cal X}$, $\\forall j' \\in \\{ 1, \\ldots, j \\}$; 2. $A^j x(k_m) + \\sum^{j} _{i=1} A^{i-1} B u \\in \\varepsilon \\varepsilon_{x} {\\cal S}$; where $\\varepsilon_x = \\Psi_{\\cal S}(x(k_m))$. [$\\Box$]{} In (C.2), $A^j x(k_m) + \\sum^{j} _{i=1} A^{i-1} B u$ represents a state by applying the control input $u \\in {\\cal U}$ *constantly* for $j$ time steps. Moreover, from the definition of the gauge function $\\Psi_{\\cal S}(\\cdot)$ we have $x(k_m) \\in \\varepsilon_{x} {\\cal S}$. Thus, [Problem\\[control\\_problem\\]]{} aims to find the smallest possible scaled set $\\varepsilon \\varepsilon_{x} {\\cal S}$, such that the state enters $\\varepsilon \\varepsilon_{x} {\\cal S}$ (from $\\varepsilon_x {\\cal S}$) by applying a $j$-step constant control input. This means that a stabilizing controller is found under the transmission time interval $j$. The constraint in (C.1) implies that the state must remain inside ${\\cal X}$ while applying a $j$-step constant controller, which is imposed to guarantee the constraint satisfaction. Note that [Problem\\[control\\_problem\\]]{} is a linear program, since all constraints imposed in (C.1), (C.2), as well as the cost in are all linear. For given $x(k_m)$ and $j$, let $(u^* _j, \\varepsilon^* _j )$ be a pair of optimal solutions obtained by solving [Problem\\[control\\_problem\\]]{}. From (C.2), the state enters $\\varepsilon^* _j \\varepsilon_x {\\cal S}$ if $u^* _j$ is applied constantly for $j$ steps, i.e., $A^j x(k_m) + \\sum^{j} _{i=1} A^{i-1} B u^* _j \\in \\varepsilon^* _j \\varepsilon _{x} {\\cal S}$, which means that we have $\\Psi_{\\cal S} (A^j x(k_m) + \\sum^{j} _{i=1} A^{i-1} B u^* _j ) \\leq \\varepsilon^* _j \\Psi_{\\cal S} (x(k_m))$, or $$\\label{lyapunov2} \\begin{aligned} \\Psi_{\\cal S} (A^j x(k_m) + & \\sum^{j} _{i=1} A^{i-1} B u^* _j ) -\\Psi_{\\cal S} (x(k_m)) \\\\ & \\leq - (1-\\varepsilon^* _j) \\Psi_{\\cal S} (x(k_m)) \\end{aligned}$$ with $0 \\leq \\varepsilon^* _j \\leq \\lambda < 1$. Thus, $1-\\varepsilon^* _j$ represents how much the output of the gauge function (as a Lyapunov function candidate) decreases by applying the optimal controller $u^* _j$ constantly for $j$ steps. That is, if $1-\\varepsilon^* _j$ becomes larger (i.e., $\\varepsilon^* _j$ becomes smaller), then the state will be closer to the origin and a better control performance is achieved. Now, consider solving [Problem\\[control\\_problem\\]]{} for all $j \\in \\{1, \\ldots, j_{\\max} \\}$, which provides different solutions under different transmission time intervals. In the following, let ${\\cal J} (x(k_m))$ be the set of indices (transmission time intervals) where [Problem\\[control\\_problem\\]]{} provides a feasible solution. That is, $$\\label{calJ} \\begin{aligned} {\\cal J} (x(k_m)) = \\{j \\in & \\{1, \\ldots, \\ j_{\\max}\\} : \\\\ & {\\rm {Problem\\,\\ref{control_problem}}\\ is\\ feasible\\ for\\ } j \\}. \\end{aligned}$$ \\[feasibility\\_problem\\] If $x(k_m) \\in {\\cal S}$, there always exists $u \\in {\\cal U}$ such that $A x(k_m) + B u \\in \\lambda \\varepsilon_x {\\cal S} \\subseteq {\\cal X}$ holds from the properties of the $\\lambda$-contractive set (see [@blanchini1994a]). Thus, [Problem\\[control\\_problem\\]]{} has a solution with $j=1$ for any $x(k_m) \\in {\\cal S}$, and hence, ${\\cal J} (x(k_m))$ is non-empty for any $x(k_m) \\in {\\cal S}$. [$\\Box$]{} An overall algorithm {#transmission_sec} -------------------- In this subsection an overall self-triggered algorithm is presented. After solving [Problem\\[control\\_problem\\]]{} for all $j \\in \\{1,\\ldots, j_{\\max} \\}$, which provides the optimal (feasible) sets of solutions $(u^* _j, \\varepsilon^* _j )$ for all $j \\in {\\cal J} (x(k_m))$, the controller selects a suitable transmission time interval among them. The transmission time interval is selected such that both control performance and the communication load are taken into account. A more specific way to achieve this is given in the following overall strategy:\\ *[Algorithm 1]{}* (Self-triggered strategy): For any transmission time $k_m$, $m \\in \\mathbb{N}$, do the following: 1. The plant transmits the current state information $x(k_m)$ to the controller. 2. Based on $x(k_m)$, the controller solves Problem 1 for all $j \\in \\{1, \\ldots, j_{\\max} \\}$, which provides the optimal (feasible) solutions $(\\varepsilon^* _j, u^* _j)$ for all $j \\in {\\cal J} (x(k_m))$. 3. The controller picks up an optimal index $j_m \\in {\\cal J} (x(k_m))$ by solving the following problem: $$\\label{cost_func} j_m = \\underset{j \\in {\\cal J}(x(k_m))}{\\rm argmax}\\ w_1 (1-\\varepsilon^* _j)/j + w_2 j ,$$ where $w_1, w_2 \\geq 0$ represent given tuning weight parameters. Then, set $k_{m+1} = k_m + j_m$ and $u^* (k_m) = u^* _{j_m}$, and the controller transmits $u^* (k_m)$ and $k_{m+1}$ to the plant. 4. The plant applies $u^* (k_m)$ for all $k \\in [k_m, k_{m+1})$. Set $m \\leftarrow m+1$, and then go back to step (1). [$\\Box$]{} As shown in Algorithm 1, for each $k_m$ we select the transmission time interval $j_m$ according to . As described in the previous subsection, the term $(1-\\varepsilon^* _j)$ represents how much the output of the gauge function decreases by applying the optimal controller $u^* _j$ constantly for $j$ steps. Thus, the first term $(1-\\varepsilon^* _j)/j$ represents a *reward* due to the rate of decrease of the gauge function per [one time step]{}, and a better control performance can be achieved when this term becomes larger. On the other hand, from a self-triggered control viewpoint, less control updates will be obtained when control inputs can be applied constantly longer (i.e., when $j$ becomes larger). Thus, the second part in involves $j$ to represent some [reward]{} for alleviating the communication load; as $j$ gets larger, then we obtain less communication load and a larger reward is obtained. Some remarks are in order regarding Algorithm 1: The proposed algorithm is related to *move-blocking MPC*[@move_blocking], in the sense that the optimal control inputs are restricted to be constant for some time period. Note that move-blocking MPC aims at reducing the computational complexity by decreasing the degrees of freedom of the optimal control problem[@move_blocking]; the proposed approach, on the other hand, aims at reducing the *communication load* through the move-blocking technique, and the reduction of computation load is not a primary objective here. [$\\Box$]{} In Algorithm 1, the controller solves [Problem\\[control\\_problem\\]]{} for all $j \\in \\{ 1, \\ldots, j_{\\max} \\}$ for each transmission time instant. While we can potentially achieve longer transmission intervals if $j_{\\max}$ is selected larger, the computation load of solving [Problem\\[control\\_problem\\]]{} becomes heavier. Thus, in practical implementation, the user may carefully select a suitable $j_{\\max}$ by considering the trade-off between the communication load and the calculation time of solving the optimal control problem. [$\\Box$]{} \\[stability1\\] Suppose that Assumption 3 holds, and Algorithm 1 is implemented. Then, it holds that $x (k) \\rightarrow 0$ as $k \\rightarrow \\infty$. [$\\Box$]{} We first show that is always feasible (i.e., we can always pick up a transmission time interval according to ), by proving that ${\\cal J} (x(k_m))$ is non-empty for all $m\\in \\mathbb{N}$. By [Assumption\\[initial\\_cond\\]]{} we obtain $x(k_0) \\in {\\cal S}$ and thus ${\\cal J} (x(k_0))$ is non-empty (see [Remark\\[feasibility\\_problem\\]]{}). Since $j_0$ is obtained from , we have $j_0 \\in {\\cal J} (x(k_0))$ which means that [Problem\\[control\\_problem\\]]{} has a feasible solution for $j = j_0$. Thus, from the constraint (C.2) in [Problem\\[control\\_problem\\]]{}, we obtain $x (k_1) = A^{j_0} x(k_0) + \\sum^{j_0} _{i=1} A^{i-1} B u^* (k_0) \\in {\\cal S}$, which means that ${\\cal J} (x(k_1))$ is non-empty. By recursively following this argument, it is shown that $x (k_m) \\in {\\cal S}$ for all $m\\in \\mathbb{N}$, which follows that ${\\cal J} (x(k_m))$ is non-empty for all $m\\in \\mathbb{N}$. Now, it is shown that $x (k) \\rightarrow 0$ as $k \\rightarrow \\infty$. Since $j_m \\in {\\cal J} (x_m)$, $\\forall m\\in \\mathbb{N}$, it holds from (C.2) in [Problem\\[control\\_problem\\]]{} that: $$\\label{gauge_decrease} \\begin{aligned} \\Psi_{\\cal S} (x(k_{m+1}) ) & \\leq \\varepsilon^* _{j_m} \\Psi_{\\cal S} (x(k_m)) \\\\ & \\leq \\lambda \\ \\Psi_{\\cal S} (x(k_m)). \\end{aligned}$$ with $\\lambda < 1$. Therefore, by regarding $\\Psi_{\\cal S} (\\cdot)$ as a set-induced Lyapunov function candidate (see [Lemma\\[stability\\_lem\\]]{}), the Lyapunov function is strictly decreasing and the state trajectory is asymptotically stabilized to the origin. This completes the proof. Although Theorem 1 states only asymptotic stability of the origin, exponential stability can be achieved by imposing an additional constraint when evaluating the reward function in . Specifically, let $j_\\ell$ be chosen according to , subject to the constraint $\\varepsilon^* _{j} \\leq \\lambda^{j}$. Indeed, imposing this constraint yields that $\\Psi_{\\cal S} (x(k_{m+1}) ) \\leq \\lambda^{j_{m}} \\Psi_{\\cal S} (x(k_{m}))$, $\\forall m \\in \\mathbb{N}$ (instead of $\\Psi_{\\cal S} (x(k_{m+1}) ) \\leq \\lambda \\Psi_{\\cal S} (x(k_{m}))$ as in ). Thus, we obtain $$\\label{exponential_stability} \\Psi_{\\cal S} (x(k_{m}) ) \\leq \\lambda^{j_{m-1}} \\Psi_{\\cal S} (x(k_{m-1})) \\leq \\cdots \\leq \\lambda^{k_m} \\Psi_{\\cal S} (x(0)),$$ which implies that exponential stability is guaranteed (see e.g., [@blanchini1994a]). [$\\Box$]{} Self-triggered control via explicit mapping $\\Gamma$ ==================================================== In the previous section, the self-triggered strategy has been presented by solving [Problem\\[control\\_problem\\]]{} for all $j \\in \\{ 1, \\ldots, j_{\\max} \\}$. However, solving [Problem\\[control\\_problem\\]]{} for all candidates of transmission time intervals may lead to a high computation load, which may induce computational delays to transmit control samples to the plant. A more preferred approach may be that the transmission mapping $\\Gamma: {\\cal X} \\rightarrow \\{1, \\ldots, j_{\\max}\\}$ given in , which sends the state to the desired transmission time interval, is obtained *offline*. That is, with the mapping $\\Gamma$ provided explicitly offline, the next transmission time can be directly determined from the (current) state information, without having to solve Problem 1 for all $j \\in \\{ 1, \\ldots, j_{\\max} \\}$. The approach presented in this section is related to explicit MPC framework [@bemporad2002b], in which an offline characterization of the control strategy (but here, the transmission time intervals) is given via state-space decomposition. A more specific formulation is given below. Construction of $\\Gamma$ via state-space decomposition ------------------------------------------------------ In order to create the explicit mapping of $\\Gamma$, we first *decompose* the contractive set ${\\cal S}$ into a finite number of disjoint subsets ${\\cal S}_1, \\ldots, {\\cal S}_L \\subset {\\cal S}$, i.e., $$\\label{decomposition_subsets} {\\cal S} = \\bigcup^{L} _{\\ell =1} {\\cal S}_\\ell,$$ where it holds that ${\\cal S}_\\ell \\cap {\\cal S}_{\\ell'} = \\emptyset$ for all $(\\ell, \\ell') \\in \\{1, \\ldots, L\\} \\times \\{1, \\ldots, L\\}$ $(\\ell \\neq \\ell')$. Based on the decomposition, we will then assign a specific transmission time interval to each ${\\cal S}_\\ell$, $\\ell \\in \\{1, \\ldots, L \\}$, so that the controller directly determines the next transmission time. Intuitively, if the state is located far from the origin we would like to assign a short transmission time interval to achieve stability of the origin (or achieve good control performance). In particular, in the case of un-stable systems, applying a constant control signal may lead to a divergence of states, especially if the state is far from the origin. On the other hand, if the state is close to the origin, a small control effort may be sufficient to stabilize the system. That is, assigning a long transmission time interval may be allowable to achieve both stability and communication reduction. Motivated by the above intuition, we decompose the contractive set as follows. First, for a given $L \\in \\mathbb{N}_+$, define a set of scalars $\\rho_1, \\ldots \\rho_L \\in (0, 1]$, with $$0 < \\rho_1 < \\rho_2 < \\cdots < \\rho_{L-1} < \\rho_{L} = 1.$$ Then, consider the following sequence of $L$ sets ${\\cal S}_1, {\\cal S}_2, \\ldots , {\\cal S}_{L} \\subset {\\cal S}$: $$\\label{set_sequence} \\begin{aligned} {\\cal S}_1 &= \\rho_1 {\\cal S}, \\\\ {\\cal S}_\\ell & = \\rho_\\ell {\\cal S} \\backslash {\\cal S}_{\\ell-1},\\ \\ \\forall \\ell \\in \\{2, \\ldots, L\\}. \\end{aligned}$$ ![Illustration of the decomposed subsets ${\\cal S}_\\ell$, $\\ell \\in \\{1, \\ldots, L\\}$ (for the case $L=4$) according to . In the figure, the pentagon represents the contractive set ${\\cal S}$ and the subsets ${\\cal S}_1, \\ldots, {\\cal S}_4$ are illustrated with different shades of blue. []{data-label="decomposition"}](decomposition-eps-converted-to.pdf){width="5cm"} The illustration of the sequence of sets is depicted in [Fig.\\[decomposition\\]]{}. It can be easily shown that the set sequence defined in yields a [decomposition]{} as in , which satisfies the disjoint property as described above. Now, ${\\cal S}$ has been decomposed into a finite number of $L$ sets ${\\cal S}_1, \\ldots, {\\cal S}_L$, to which we next assign suitable transmission time intervals. To this end, we formulate the following optimal control problem for each pair $(\\ell, j) \\in \\{1, \\ldots, L \\} \\times \\{1, \\ldots, j_{\\max}\\}$: \\[control\\_problem2\\] For a given pair $(\\ell, j) \\in \\{1, \\ldots, L\\}\\times \\{1, \\ldots, j_{\\max} \\}$, find $u_{1}, \\ldots, u_{N} \\in {\\cal U}$ and $\\varepsilon \\in \\mathbb{R}$ by solving the following problem:\\ $$\\underset{u_1, \\ldots, u_{N} \\in {\\cal U}} {\\min}\\ \\ \\varepsilon,$$ subject to $\\varepsilon \\in [0, \\lambda]$, and 1. For all $n \\in \\{ 1, \\ldots, N \\}$, $j' \\in \\{ 1, \\ldots, j \\}$, $$\\begin{aligned} \\label{state_constraint} A^{j'} v_{\\ell, n} + \\sum^{j'} _{i=1} A^{i-1} B u_n \\in {\\cal X}, \\end{aligned}$$ where $v_{\\ell, n} = \\rho_\\ell v_{n}$, $n \\in \\{ 1, \\ldots, N \\}$, $j' \\in \\{ 1, \\ldots, j \\}$. 2. For all $n \\in \\{ 1, \\ldots, N \\}$, $$\\label{stability_constraint} \\begin{aligned} & A^j v_{\\ell, n} + \\sum^{j} _{i=1} A^{i-1} B u_n \\in \\varepsilon \\rho_\\ell {\\cal S}. \\end{aligned}$$ [$\\Box$]{} Recall that $v_n$, $n \\in \\{1, \\ldots, N\\}$ represent the vertices of ${\\cal S}$ (see ). Thus, $v_{\\ell, n} = \\rho_\\ell v_n$, $n \\in \\{1, \\ldots, N\\}$ represent the extreme points on the outer boundary of ${\\cal S}_\\ell$ (see the illustration in [Fig.\\[decomposition\\]]{}). [Problem\\[control\\_problem2\\]]{} for $(\\ell, j)$ aims at finding a set of controllers $u_1, \\ldots, u_{N}$ and a scalar $\\varepsilon$, such that all the extreme points $v_{\\ell, n}$, $n \\in \\{1, \\ldots, N\\}$ can be driven into $\\varepsilon \\rho_\\ell {\\cal S}$ under the $j$-step constant control inputs. Note that [Problem\\[control\\_problem2\\]]{} is solved [offline]{} for all $\\ell \\in \\{1,\\ldots, L\\}$, $j\\in \\{1, \\ldots, j_{\\max} \\}$, since it can be solved by evaluating the extreme points $v_{\\ell, n}$, $n \\in \\{1, \\ldots, N\\}$ that are given offline. Now, suppose that [Problem\\[control\\_problem2\\]]{} has a solution for $(\\ell, j)$, which provides optimal control inputs and a scalar denoted as $u^* _{\\ell, j}(1), u^* _{\\ell, j}(2), \\ldots, u^* _{\\ell, j} (N) \\in {\\cal U}$, $\\varepsilon^* _{\\ell, j} \\in [0, \\lambda]$, respectively. The following lemma describes that the feasibility of [Problem\\[control\\_problem2\\]]{} for $(\\ell, j)$ implies the existence of a stabilizing controller for all $x \\in {\\cal S}_{\\ell}$: \\[stabilize\\_controller\\] Suppose that [Problem\\[control\\_problem2\\]]{} finds a solution for $(\\ell, j)$. Then, for every $x \\in {\\cal S}_\\ell$, there exists $u \\in {\\cal U}$ such that: (i) $A^{j'} x + \\sum^{j'} _{i=1} A^{i-1} B u \\in {\\cal X}$ for all $j' \\in \\{ 1, \\ldots, j \\}$; (ii) $A^j x + \\sum^{j} _{i=1} A^{i-1} B u \\in \\varepsilon^* _{\\ell, j} \\varepsilon_x \\ {\\cal S}$ with $\\varepsilon_x = \\Psi_{\\cal S} (x)$. [$\\Box$]{} Since [Problem\\[control\\_problem2\\]]{} has a solution for $(\\ell, j)$, from and we obtain $A^{j'} v_{\\ell, n} + \\sum^{j'} _{i=1} A^{i-1} B u^* _{\\ell, j} (n) \\in {\\cal X}$ for all $n \\in \\{ 1, \\ldots, N \\}$, $j' \\in \\{ 1, \\ldots, j \\}$, and $A^j v_{\\ell, n} + \\sum^{j} _{i=1} A^{i-1} B u^* _{\\ell, j} (n) \\in \\varepsilon^* _{\\ell, j} \\rho_\\ell {\\cal S}$ for all $n \\in \\{1, \\ldots, N \\}$. Suppose $x \\in {\\cal S}_\\ell$ and let $\\varepsilon_x = \\Psi_{{\\cal S}} (x) \\in [0, 1]$. Since $x \\in {\\cal S}_\\ell \\subseteq \\rho_\\ell {\\cal S}$, we have $\\varepsilon_x \\leq \\rho_\\ell$. Moreover, since $x \\in \\varepsilon_x {\\cal S}$, there exist $\\lambda_n \\in [0, 1]$, $n\\in \\{1, \\ldots, N \\}$ such that $x = \\varepsilon_x \\sum^{N} _{n=1} \\lambda_n v_{n} = (\\varepsilon_x/\\rho_\\ell) \\sum^{N} _{n=1} \\lambda_n v_{\\ell, n}$, $\\sum^{N} _{n=1} \\lambda_n = 1$, where we have used $v_{\\ell, n} = \\rho_\\ell v_n$. Let $u \\in \\mathbb{R}^m$ be given by $$\\label{feasible_input} u = \\frac{\\varepsilon_x}{\\rho_\\ell} \\sum^{N} _{n=1} \\lambda_n u^* _{\\ell, j} (n) \\in {\\cal U}.$$ Then, for all $j' \\in \\{1, \\ldots, j \\}$, we obtain $$\\begin{aligned} & A^{j'} x + \\sum^{j'} _{i=1} A^{i-1} B u \\\\ &= \\frac{\\varepsilon_x}{\\rho_\\ell} \\sum^{N} _{n=1} \\lambda_n ( A^{j'} v_{\\ell, n} + \\sum^{j'} _{i=1} A^{i-1} B u^* _{\\ell, j} (n)) \\in \\frac{\\varepsilon_x}{\\rho_\\ell} {\\cal X} \\subseteq {\\cal X}, \\end{aligned}$$ where the first inclusion holds since $A^{j'} v_{\\ell, n} + \\sum^{j'} _{i=1} A^{i-1} B u^* _{\\ell, j} (n) \\in {\\cal X}$ for all $n \\in \\{ 1, \\ldots, N \\}$, $j' \\in \\{ 1, \\ldots, j \\}$, and the last inclusion holds since $\\varepsilon_x \\leq \\rho_\\ell$. Moreover, we have $$\\begin{aligned} & A^j x + \\sum^j _{i=1} A^{i-1} B u \\\\ &= \\frac{\\varepsilon_x}{\\rho_\\ell} \\sum^{N} _{n=1} \\lambda_n ( A^j v_{\\ell, n} + \\sum^j _{i=1} A^{i-1} B u^* _{\\ell, j} (n)) \\\\ & \\in \\frac{\\varepsilon_x}{\\rho_\\ell}\\ \\rho_\\ell \\ \\varepsilon^* _{\\ell, j} {\\cal S} =\\varepsilon^* _{\\ell, j} \\varepsilon_x {\\cal S}, \\end{aligned}$$ where the inclusion holds since $A^j v_{\\ell, n} + \\sum^{j} _{i=1} A^{i-1} B u^* _{\\ell, j} (n) \\in \\rho_\\ell \\varepsilon^* _{\\ell, j} {\\cal S}$ for all $n \\in \\{1, \\ldots, N \\}$. Hence, we obtain $A^j x + \\sum^{j} _{i=1} A^{i-1} B u \\in \\varepsilon^* _{\\ell, j} \\varepsilon_x \\ {\\cal S}$. This completes the proof. [Lemma\\[stabilize\\_controller\\]]{} implies that for every $x \\in {\\cal S}_\\ell$ there exists $u\\in{\\cal U}$ such that $\\Psi_{\\cal S} (A^j x + \\sum^j _{i=1} A^{i-1} B u) \\leq \\varepsilon^* _{\\ell, j} \\Psi_{\\cal S} (x)$ holds. Thus, this means that if $x \\in {\\cal S}_\\ell$, then there exists a $j$-step stabilizing controller such that the output of the gauge function decreases. As mentioned previously in [Section\\[stabilize\\_control\\_sec\\]]{}, $(1-\\varepsilon^* _{\\ell, j})$ represents the decreasing rate of the gauge function. Thus, we can evaluate the control performance by $\\varepsilon^* _{\\ell, j}$ similarly to the self-triggered strategy presented in the previous section. Now, suppose that for each $\\ell$ we solve [Problem\\[control\\_problem2\\]]{} for all $j \\in \\{1, \\ldots, j_{\\max} \\}$. Let ${\\cal J}_{\\ell}$ be a set of indices (transmission time intervals) where [Problem\\[control\\_problem2\\]]{} has a feasible solution for $\\ell$, i.e., $$\\label{calJ2} \\begin{aligned} {\\cal J}_{\\ell} = \\{j \\in & \\{1, \\ldots, \\ j_{\\max}\\} : \\\\ & {\\rm {Problem\\,\\ref{control_problem2}}\\ is\\ feasible\\ for\\ } (\\ell, \\ j) \\}. \\end{aligned}$$ Regarding the feasible set ${\\cal J}_\\ell$, we obtain the following: \\[feasible\\_lem2\\] ${\\cal J}_{\\ell}$ is non-empty for all $\\ell \\in \\{ 1, \\ldots, L \\}$. The proof immediately follows from [Definition\\[lambda\\_contractive\\]]{} and is given in the Appendix. By evaluating the feasible solutions obtained above, we now assign to each ${\\cal S}_\\ell$ a suitable transmission time interval. In Algorithm 1, we presented the self-triggered strategy by determining the transmission interval according to the reward function in . Motivated by this, we similarly now consider the following assignment of the transmission time interval to ${\\cal S}_\\ell$, by taking both control performance and communication load into account: $$\\label{cost_func2} j^* _{\\ell} = \\underset{j \\in {\\cal J}_{\\ell} }{\\rm argmax}\\ w_1 (1-\\varepsilon^* _{\\ell, j})/j + w_2 j,$$ where $w_1, w_2 \\geq 0$ denote the given tuning weights associated to each part of the reward similarly to . Note that in contrast to the previous self-triggered strategy where a suitable transmission time interval is obtained online, is now given in an offline fashion. Suppose that we compute $j^* _\\ell$ according to for all $\\ell \\in \\{1, \\ldots, L \\}$. Then, each $j^* _{\\ell}$ is assigned to ${\\cal S}_{\\ell}$ as the suitable transmission time interval. That is, if $x(k_m) \\in {\\cal S}_{\\ell}$ for a certain transmission time $k_m$, the controller directly sets the next transmission time as $k_{m+1} = k_m + j^* _{\\ell}$. Let ${\\cal T} : {\\cal S} \\rightarrow \\{1, \\ldots, j_{\\max} \\}$ be a mapping from ${\\cal S}_\\ell$ to the assigned transmission time interval, i.e., $ j^* _\\ell = {\\cal T} ({\\cal S}_\\ell )$. Moreover, let ${\\cal R}: {\\cal X} \\rightarrow {\\cal S}$ be a mapping from $x$ to the corresponding subset that $x$ belongs to, i.e., ${\\cal R} (x) = {\\cal S}_\\ell, \\ \\ {\\rm iff} \\ x\\in {\\cal S}_\\ell,\\ \\ell \\in \\{1, \\ldots, L\\}. $ Then, the overall transmission mapping $\\Gamma: {\\cal X} \\rightarrow \\{1, \\ldots, j_{\\max} \\}$ is given by $$\\label{gamma} \\Gamma (x) = ({\\cal T} \\circ {\\cal R}) (x).$$ An overall algorithm {#an-overall-algorithm} -------------------- Given the explicit transmission mapping obtained in , the overall self-triggered algorithm is now provided below:\\ *Algorithm 2 (Self-triggered strategy via explicit mapping $\\Gamma$)*: Given the explicit mapping $\\Gamma$ obtained by and for any transmission time $k_m$, $m \\in \\mathbb{N}$, do the following: 1. The plant transmits the current state information $x(k_m)$ to the controller. 2. Based on $x(k_m)$, the controller sets the transmission time interval as $j_m =\\Gamma (x(k_m))$. Then, set the next trasmission time as $k_{m+1} = k_m + j_m$. 3. Suppose that $x(k_m) \\in {\\cal S}_{\\ell_m}$ for some $\\ell_m \\in \\{1, \\ldots, L \\}$. For a given $j_m$ obtained in step 2), the controller sets $u^* (k_m) = (\\varepsilon_x / \\rho_{\\ell_m}) \\sum^{N} _{n=1} \\lambda_n u^* _{\\ell_m, j_m} (n) \\in {\\cal U}$, where $\\varepsilon_x = \\Psi_{\\cal S}(x(k_m))$ and $u^* _{\\ell_m, j_m} (1), \\ldots, u^* _{\\ell_m, j_m} (N) \\in {\\cal U}$ are the solution to [Problem\\[control\\_problem2\\]]{} for $(\\ell_m, j_m)$. Then, the controller transmits $u^* (k_m)$ and $k_{m+1}$ to the plant. 4. The plant applies $u^* (k_m)$ for all $k \\in [k_m, k_{m+1})$. Set $m \\leftarrow m+1$ and then go back to step 1). [$\\Box$]{} As shown in Algorithm 2, in contrast to the first approach the controller only needs to compute the control input for a given transmission time interval from the explicit mapping $\\Gamma$. For each transmission time $k_m$, the controller needs to find a suitable subset ${\\cal S}_\\ell$ such that $x(k_m)\\in {\\cal S}_\\ell$ holds to determine the assigned transmission time interval according to . This problem, which we call *the point location problem*, can be easily solved by using the following property: we have $x(k_m) \\in {\\cal S}_1 \\Leftrightarrow x(k_m) \\in \\rho_1 {\\cal S}$, and for all $\\ell \\in \\{2, \\ldots, L\\}$, $$x(k_m) \\in {\\cal S}_\\ell\\ \\Leftrightarrow\\ x(k_m) \\notin \\rho_{\\ell-1} {\\cal S},\\ x(k_m) \\in \\rho_{\\ell} {\\cal S}.$$ Hence, the point location problem can be solved by checking if $x(k_m) \\in \\rho_\\ell {\\cal S}$, $\\ell \\in \\{1, \\ldots, L\\}$ sequentially in that order, and takes the first index $\\ell$ such that $x (k_m) \\in \\rho_\\ell {\\cal S}$ holds. [$\\Box$]{} Suppose that Assumptions 3 holds, and Algorithm 2 is implemented. Then, it holds that $x (k) \\rightarrow 0$ as $k \\rightarrow \\infty$. [$\\Box$]{} We first show that selecting $j_m$ as $j_m = \\Gamma (x (k_m) )$ is always feasible by proving that $x(k_m) \\in {\\cal S}$ for all $m \\in \\mathbb{N}$ (if $x(k_m) \\notin {\\cal S}$, the controller cannot determine $j_m$ since the mapping is not defined). By [Assumption\\[initial\\_cond\\]]{}, we obtain $x(k_0) \\in {\\cal S}$. To prove by induction, assume $x(k_m) \\in {\\cal S}$ for some $m\\in \\mathbb{N}_+$, and we will show $x(k_{m+1}) \\in {\\cal S}$. Suppose that $x(k_m) \\in {\\cal S}_{\\ell_m} \\subseteq {\\cal S}$ for some $\\ell_m \\in \\{ 1,\\ldots, L\\}$, which means from that $j_m = j^* _\\ell = \\Gamma (x (k_m))$ with $\\ell = \\ell_m$. Since $j_m = j^* _\\ell \\in {\\cal J}_\\ell$ with $\\ell = \\ell_m$, [Problem\\[control\\_problem2\\]]{} has a solution for the pair $(\\ell_m, j_m)$. Let $\\varepsilon^* _{\\ell_m, j_m} \\in [0, \\lambda]$ be the optimal $\\varepsilon$ as a solution to [Problem\\[control\\_problem2\\]]{} for $(\\ell_m, j_m)$. Then, from the proof of [Lemma\\[stabilize\\_controller\\]]{}, setting $u^*(k_m) = (\\varepsilon_x /\\rho_{\\ell_m}) \\sum^{N} _{n=1} \\lambda_n u^* _{\\ell_m, j_m} (n)$ yields that $x(k_{m+1}) = A^{j_m} x(k_m) + \\sum^{j_m} _{i=1} A^{i-1} B u^* (k_m) \\in \\varepsilon_x \\varepsilon^* _{\\ell_m, j_m} {\\cal S} \\subseteq {\\cal S}$. Therefore, we have $x(k_m) \\in {\\cal S}$ for all $m\\in \\mathbb{N}$. Now, it is shown that $x (k) \\rightarrow 0$ as $k \\rightarrow \\infty$. Since $x(k_m) \\in {\\cal S}$ for all $m\\in \\mathbb{N}$, we obtain from [Lemma\\[stabilize\\_controller\\]]{} that $$\\begin{aligned} \\Psi_{\\cal S} (x(k_{m+1}) ) & \\leq \\varepsilon^* _{\\ell_m, j_m} \\Psi_{\\cal S} (x(k_m)) \\\\ & \\leq \\lambda \\ \\Psi_{\\cal S} (x(k_m)), \\end{aligned}$$ with $\\lambda < 1$. Therefore, by considering $\\Psi_{\\cal S}(\\cdot)$ as a set-induced Lyapunov function candidate, the state trajectory is asymptotically stabilized to the origin. This completes the proof. Comparisons between first and second approach {#discuss_alg2_sec} --------------------------------------------- In this subsection we discuss both advantages and drawbacks of the second approach (Algorithm 2), by making some comparisons with the first one (Algorithm 1). As stated previously, the second approach is advantageous over the first one in terms of the computation load, since the transmission mapping $\\Gamma$ is given offline according to the procedure presented in the previous subsection. Note, however, that in the second approach, each $j^* _\\ell$ is computed by solving [Problem\\[control\\_problem2\\]]{} that evaluates *the extreme points* of ${\\cal S}_\\ell$ (i.e., $v_{\\ell, n}$, $n \\in \\{1, \\ldots, N\\}$). This means that, while $x(k_m)$ is in the *interior* of ${\\cal S}_\\ell$, which is not on some extreme point of ${\\cal S}_\\ell$, there may exist some $j \\in {\\cal J}_\\ell \\ (j\\neq j^* _\\ell)$, such that applying $u^* (k_m) = (\\varepsilon_x/\\rho_\\ell) \\sum^{N} _{n=1} \\lambda_n u^* _{\\ell, j} (n) \\in {\\cal U}$ [could]{} yield a *larger* reward in than the one obtained with $\\varepsilon^* _{\\ell, j^* _\\ell}$. In this sense, the second approach yields a suboptimal (or conservative) solution compared with Algorithm 1 on the selection of transmission time intervals. This observation is also illustrated in the simulation example, where it is shown that Algorithm 1 achieves less communication load than Algorithm 2 for the case $w_1 = 0$ (for details, see Section V). Simulation results ================== In this section we provide an illustrative example to validate our control schemes. The simulation was conducted on Matlab 2016a under Windows 10, Intel(R) Core(TM) 2.40 GHz, 8 GB RAM, using Multi-Parametric Toolbox (MPT3) to compute the $\\lambda$-contractive set. We consider a control problem of a *batch reactor system*, which is often utilized as a benchmark in the NCSs community (see, e.g., [@heemels2012a]). The linearized model is given in the continuous-time domain as $\\dot{x} (t) = A_c x(t) + B_c u(t)$, where $A_c, B_c$ are given by $${\\small \\begin{aligned} A_c & = \\left [ \\begin{array}{cccc} 1.380 & -0.208 & 6.715 & -5.676 \\\\ -0.581 & -4.290 & 0 & 0.675 \\\\ 1.067 & 4.273 & -6.654 & 5.893 \\\\ 0.048 & 4.273 & 1.343 & -2.104 \\\\ \\end{array} \\right ] \\\\ B_c & = \\left [ \\begin{array}{cc} 0 & 0 \\\\ 5.679 & 0 \\\\ 1.136 & -3.146 \\\\ 1.136 & 0 \\end{array} \\right ]. \\end{aligned} }$$ The system is unstable having unstable poles $1.9911, 0.0633$. We assume ${\\cal X} = \\{ x\\in \\mathbb{R}^4 : ||x||_\\infty \\leq 2 \\}$, ${\\cal U} = \\{ u \\in \\mathbb{R}^2 : ||u||_{\\infty} \\leq 5 \\}$ and $j_{\\max} = 30$. We obtain the corresponding discrete-time system under a zero-order-hold controller with a sampling time interval $0.1$, and the $\\lambda$-contractive set ${\\cal S}$ is obtained with $\\lambda=0.99$ according to the procedure presented in Section II. [Fig.\\[state\\_trajectory\\]]{} illustrates the resulting state trajectories and the corresponding control inputs by implementing Algorithm 1, starting from the initial state $x(k_0) = [1;\\ 2;\\ 2;\\ 0.5]$ and the weights $(w_1, w_2) = (50, 1)$. The figure shows that the resulting state trajectories are asymptotically stabilized to the origin, and control inputs are updated only when necessary. To analyse the effect of weights, we again simulate Algorithm 1 with $x(k_0) = [1;\\ 2;\\ 2;\\ 0.5]$ under different selection of weights $(w_1, w_2) =(0, 1), (50,1), (100, 1)$. We then compute the convergence time steps when the state enters the small region around the origin (the region satisfying $||x|| \\leq 0.001$), and the total number of transmission instances during the time period $k \\in [0, 100]$. The results are shown in [Table\\[result\\_alg1\\]]{}. From the table, $(w_1, w_2) = (100, 1)$ achieves the fastest speed of convergence. This is due to the fact that by selecting $w_1$ larger, the reward for the control performance (i.e., the first term in ) is emphasized to be obtained. On the other hand, the number of transmission instances is the smallest for the case $(w_1, w_2) =(0, 1)$, which means that the smallest communication load is obtained. Therefore, it is shown that there exists a trade-off between control performance and communication load, and such trade-off can be regulated by tuning the weights $(w_1, w_2)$. ($w_1, w_2$) (0,1) $(50,1)$ $(100, 1)$ ------------------------ ------- ---------- ------------ Convergence (steps) 141 93 69 Transmission instances 5 6 10 : Convergence time and number of transmission instances[]{data-label="result_alg1"} ![Simulation results of state trajectories (upper) and the control inputs (lower) by applying Algorithm 1.[]{data-label="state_trajectory"}](state_input_ver2-eps-converted-to.pdf){width="7.8cm"} ![$j^* _\\ell$ as a function of $\\ell$ with $(w_1, w_2) = (0, 1), (400, 1), (600,1)$. []{data-label="jmax"}](jmaxmapping4-eps-converted-to.pdf){width="7.8cm"} To implement the second proposal, we decompose ${\\cal S}$ into $L=10$ subsets with $\\rho_\\ell = 0.1 \\ell$, $ \\ell \\in \\{1, \\ldots, 10 \\}$ and the mapping $\\Gamma$ is constructed according to Section IV. The selected transmission time intervals $j^* _\\ell$ as a function of $\\ell$ are illustrated in [Fig.\\[jmax\\]]{} under different selections of the weights $(w_1, w_2) = (0, 1), (400, 1), (600,1)$. The figure shows that the transmission time interval tends to be smaller as the weight $w_1$ increases. This means that attaining control performance is emphasized more than attaining communication reduction, if the weight for achieving the control performance $w_1$ is selected larger. In [Fig.\\[jmax\\]]{}, we also illustrate the selected transmission time intervals for $(w_1, w_2) = ( 0 , 1 )$ (i.e., the blue dashed line). Since $w_1 = 0$, each $j^* _\\ell$ corresponds to the *largest* transmission time interval such that [Problem\\[control\\_problem2\\]]{} becomes feasible for $\\ell$ (i.e., the maximal index in the feasible set ${\\cal J}_\\ell$). As shown in the figure, the feasible transmission time interval gets smaller as $\\ell$ increases. Intuitively, this is due to that for unstable systems, applying a constant control input leads to a divergence of states, especially if the extreme points to solve [Problem\\[control\\_problem2\\]]{} are located far from the origin. To illustrate the calculation time and the optimality of Algorithm 1 and 2 as discussed in [Section\\[discuss\\_alg2\\_sec\\]]{}, we again simulate the two algorithms with $(w_1, w_2) = (0, 1)$ and the initial state $x(k_0) = [1;\\ 2;\\ 2;\\ 0.5]$. As previously described, setting $w_1 = 0$ corresponds to selecting the largest index in ${\\cal J}_\\ell$. [Table\\[result\\_tab\\]]{} illustrates the total number of transmission instances and the average calculation time to compute the control input for each transmission instance (i.e., the calculation time from step 2) to step 3) in Algorithms 1, 2). Here, both the total number of transmission instances and the average calculation time are computed over the time period $k \\in [0, 100 ]$. From the table, Algorithm 1 achieves less communication load than Algorithm 2. As already discussed in [Section\\[discuss\\_alg2\\_sec\\]]{}, this is because of the sub-optimality of Algorithm 2; while Algorithm 1 solves [Problem\\[control\\_problem\\]]{} based on the current state information online, [Problem\\[control\\_problem2\\]]{} is solved offline by evaluating the extreme points of the subsets. On the other hand, Algorithm 2 achieves less calculation time than Algorithm 1, as the transmission mapping $\\Gamma$ is explicitly given offline. Algorithm 1 Algorithm 2 ------------------------ ------------- ------------- Transmission instances 5 7 Calculation time (sec) 2.98 0.83 : Number of transmission instances and average calculation time with $(w_1, w_2) = (0, 1)$. []{data-label="result_tab"} Conclusion ========== In this note, we present two different types of self-triggered strategies based on the notion of set-invariance theory. 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Johansson, and P. Tabuada, “An introduction to event-triggered and self-triggered control,” in *Proceedings of the 51st IEEE Conference on Decision and Control (IEEE CDC)*, 2012, pp. 3270–3285. *(Proof of [Lemma\\[feasible\\_lem2\\]]{}) :* We show that ${\\cal J}_\\ell$ is non-empty for all $\\ell \\in \\{1, \\ldots, L \\}$, by proving that [Problem\\[control\\_problem2\\]]{} is feasible for $(\\ell, 1)$. Since $v_{\\ell, 1}, \\cdots, v_{\\ell, N} \\in \\rho_\\ell {\\cal S}$, it holds that there exist a set of controllers $\\tilde{u}_{\\ell, 1}, \\cdots, \\tilde{u}_{\\ell, N}\\in {\\cal U}$, such that $A v_{\\ell, n} + B \\tilde{u}_{\\ell, n} \\in \\lambda \\rho_\\ell {\\cal S} \\subseteq {\\cal X}$, $\\forall n \\in \\{1, \\ldots, N \\}$ from the properties of the $\\lambda$-contractive set. Thus, this directly means from , that [Problem\\[control\\_problem2\\]]{} has a feasible solution for $(\\ell, 1)$, with $\\varepsilon = \\lambda$ and $u_{\\ell, n} = \\tilde{u}_{\\ell, n}$, $\\forall n \\in \\{1, \\ldots, N \\}$. This completes the proof. [$\\Box$]{} [^1]: Kazumune Hashimoto and Shuichi Adachi are with Department of Applied Physics and Physico-Informatics, Keio University, Japan. Hashimoto’s work is supported by Grant-in-Aid for JSPS Research Fellow (DC2). [^2]: Dimos V. Dimarogonas is with the department of Electrical Engineering, KTH Royal Institute of Technology, Sweden. His work was supported by the Swedish Research Council (VR), the Swedish Foundation for Strategic Research (SSF), ERC Starting Grant BUCOPHSYS, and Knut och Alice Wallenberg foundation (KAW). [^3]: If the iterative procedure in does not converge in finite time, one can stop the procedure to obtain a $\\bar{\\lambda}$-contractive set ($\\lambda < \\bar{\\lambda} <1$) in a finite number of iterations. In such case, we use $\\bar{\\lambda}$ (instead of $\\lambda$) as the parameter to design the self-triggered strategies provided throughout the paper.

Rowing at the 1992 Summer Olympics – Women's single sculls The women's single sculls competition at the 1992 Summer Olympics took place at took place at Lake of Banyoles, Spain. Results The following rowers took part: References Category:Rowing at the 1992 Summer Olympics

/* SPDX-License-Identifier: GPL-2.0 */ /****************************************************************************** * * Copyright(c) 2007 - 2017 Realtek Corporation. * * This program is free software; you can redistribute it and/or modify it * under the terms of version 2 of the GNU General Public License as * published by the Free Software Foundation. * * This program is distributed in the hope that it will be useful, but WITHOUT * ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or * FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for * more details. * *****************************************************************************/ #define _RTW_IOCTL_SET_C_ #include <drv_types.h> #include <hal_data.h> extern void indicate_wx_scan_complete_event(_adapter *padapter); #define IS_MAC_ADDRESS_BROADCAST(addr) \\ (\\ ((addr[0] == 0xff) && (addr[1] == 0xff) && \\ (addr[2] == 0xff) && (addr[3] == 0xff) && \\ (addr[4] == 0xff) && (addr[5] == 0xff)) ? _TRUE : _FALSE \\ ) u8 rtw_validate_bssid(u8 *bssid) { u8 ret = _TRUE; if (is_zero_mac_addr(bssid) || is_broadcast_mac_addr(bssid) || is_multicast_mac_addr(bssid) ) ret = _FALSE; return ret; } u8 rtw_validate_ssid(NDIS_802_11_SSID *ssid) { #ifdef CONFIG_VALIDATE_SSID u8 i; #endif u8 ret = _TRUE; if (ssid->SsidLength > 32) { ret = _FALSE; goto exit; } #ifdef CONFIG_VALIDATE_SSID for (i = 0; i < ssid->SsidLength; i++) { /* wifi, printable ascii code must be supported */ if (!((ssid->Ssid[i] >= 0x20) && (ssid->Ssid[i] <= 0x7e))) { ret = _FALSE; break; } } #endif /* CONFIG_VALIDATE_SSID */ exit: return ret; } u8 rtw_do_join(_adapter *padapter); u8 rtw_do_join(_adapter *padapter) { _irqL irqL; _list *plist, *phead; u8 *pibss = NULL; struct mlme_priv *pmlmepriv = &(padapter->mlmepriv); struct sitesurvey_parm parm; _queue *queue = &(pmlmepriv->scanned_queue); u8 ret = _SUCCESS; _enter_critical_bh(&(pmlmepriv->scanned_queue.lock), &irqL); phead = get_list_head(queue); plist = get_next(phead); pmlmepriv->cur_network.join_res = -2; set_fwstate(pmlmepriv, _FW_UNDER_LINKING); pmlmepriv->pscanned = plist; pmlmepriv->to_join = _TRUE; rtw_init_sitesurvey_parm(padapter, &parm); _rtw_memcpy(&parm.ssid[0], &pmlmepriv->assoc_ssid, sizeof(NDIS_802_11_SSID)); parm.ssid_num = 1; if (_rtw_queue_empty(queue) == _TRUE) { _exit_critical_bh(&(pmlmepriv->scanned_queue.lock), &irqL); _clr_fwstate_(pmlmepriv, _FW_UNDER_LINKING); /* when set_ssid/set_bssid for rtw_do_join(), but scanning queue is empty */ /* we try to issue sitesurvey firstly */ if (pmlmepriv->LinkDetectInfo.bBusyTraffic == _FALSE || rtw_to_roam(padapter) > 0 ) { u8 ssc_chk = rtw_sitesurvey_condition_check(padapter, _FALSE); if ((ssc_chk == SS_ALLOW) || (ssc_chk == SS_DENY_BUSY_TRAFFIC) ){ /* submit site_survey_cmd */ ret = rtw_sitesurvey_cmd(padapter, &parm); if (_SUCCESS != ret) pmlmepriv->to_join = _FALSE; } else { /*if (ssc_chk == SS_DENY_BUDDY_UNDER_SURVEY)*/ pmlmepriv->to_join = _FALSE; ret = _FAIL; } } else { pmlmepriv->to_join = _FALSE; ret = _FAIL; } goto exit; } else { int select_ret; _exit_critical_bh(&(pmlmepriv->scanned_queue.lock), &irqL); select_ret = rtw_select_and_join_from_scanned_queue(pmlmepriv); if (select_ret == _SUCCESS) { pmlmepriv->to_join = _FALSE; _set_timer(&pmlmepriv->assoc_timer, MAX_JOIN_TIMEOUT); } else { if (check_fwstate(pmlmepriv, WIFI_ADHOC_STATE) == _TRUE) { /* submit createbss_cmd to change to a ADHOC_MASTER */ /* pmlmepriv->lock has been acquired by caller... */ WLAN_BSSID_EX *pdev_network = &(padapter->registrypriv.dev_network); /*pmlmepriv->fw_state = WIFI_ADHOC_MASTER_STATE;*/ init_fwstate(pmlmepriv, WIFI_ADHOC_MASTER_STATE); pibss = padapter->registrypriv.dev_network.MacAddress; _rtw_memset(&pdev_network->Ssid, 0, sizeof(NDIS_802_11_SSID)); _rtw_memcpy(&pdev_network->Ssid, &pmlmepriv->assoc_ssid, sizeof(NDIS_802_11_SSID)); rtw_update_registrypriv_dev_network(padapter); rtw_generate_random_ibss(pibss); if (rtw_create_ibss_cmd(padapter, 0) != _SUCCESS) { ret = _FALSE; goto exit; } pmlmepriv->to_join = _FALSE; } else { /* can't associate ; reset under-linking */ _clr_fwstate_(pmlmepriv, _FW_UNDER_LINKING); /* when set_ssid/set_bssid for rtw_do_join(), but there are no desired bss in scanning queue */ /* we try to issue sitesurvey firstly */ if (pmlmepriv->LinkDetectInfo.bBusyTraffic == _FALSE || rtw_to_roam(padapter) > 0 ) { u8 ssc_chk = rtw_sitesurvey_condition_check(padapter, _FALSE); if ((ssc_chk == SS_ALLOW) || (ssc_chk == SS_DENY_BUSY_TRAFFIC)){ /* RTW_INFO(("rtw_do_join() when no desired bss in scanning queue\\n"); */ ret = rtw_sitesurvey_cmd(padapter, &parm); if (_SUCCESS != ret) pmlmepriv->to_join = _FALSE; } else { /*if (ssc_chk == SS_DENY_BUDDY_UNDER_SURVEY) { } else {*/ ret = _FAIL; pmlmepriv->to_join = _FALSE; } } else { ret = _FAIL; pmlmepriv->to_join = _FALSE; } } } } exit: return ret; } u8 rtw_set_802_11_bssid(_adapter *padapter, u8 *bssid) { _irqL irqL; u8 status = _SUCCESS; struct mlme_priv *pmlmepriv = &padapter->mlmepriv; RTW_PRINT("set bssid:%pM\\n", bssid); if ((bssid[0] == 0x00 && bssid[1] == 0x00 && bssid[2] == 0x00 && bssid[3] == 0x00 && bssid[4] == 0x00 && bssid[5] == 0x00) || (bssid[0] == 0xFF && bssid[1] == 0xFF && bssid[2] == 0xFF && bssid[3] == 0xFF && bssid[4] == 0xFF && bssid[5] == 0xFF)) { status = _FAIL; goto exit; } _enter_critical_bh(&pmlmepriv->lock, &irqL); RTW_INFO("Set BSSID under fw_state=0x%08x\\n", get_fwstate(pmlmepriv)); if (check_fwstate(pmlmepriv, _FW_UNDER_SURVEY) == _TRUE) goto handle_tkip_countermeasure; else if (check_fwstate(pmlmepriv, _FW_UNDER_LINKING) == _TRUE) goto release_mlme_lock; if (check_fwstate(pmlmepriv, _FW_LINKED | WIFI_ADHOC_MASTER_STATE) == _TRUE) { if (_rtw_memcmp(&pmlmepriv->cur_network.network.MacAddress, bssid, ETH_ALEN) == _TRUE) { if (check_fwstate(pmlmepriv, WIFI_STATION_STATE) == _FALSE) goto release_mlme_lock;/* it means driver is in WIFI_ADHOC_MASTER_STATE, we needn't create bss again. */ } else { rtw_disassoc_cmd(padapter, 0, 0); if (check_fwstate(pmlmepriv, _FW_LINKED) == _TRUE) rtw_indicate_disconnect(padapter, 0, _FALSE); rtw_free_assoc_resources_cmd(padapter, _TRUE, 0); if ((check_fwstate(pmlmepriv, WIFI_ADHOC_MASTER_STATE) == _TRUE)) { _clr_fwstate_(pmlmepriv, WIFI_ADHOC_MASTER_STATE); set_fwstate(pmlmepriv, WIFI_ADHOC_STATE); } } } handle_tkip_countermeasure: if (rtw_handle_tkip_countermeasure(padapter, __func__) == _FAIL) { status = _FAIL; goto release_mlme_lock; } _rtw_memset(&pmlmepriv->assoc_ssid, 0, sizeof(NDIS_802_11_SSID)); _rtw_memcpy(&pmlmepriv->assoc_bssid, bssid, ETH_ALEN); pmlmepriv->assoc_by_bssid = _TRUE; if (check_fwstate(pmlmepriv, _FW_UNDER_SURVEY) == _TRUE) pmlmepriv->to_join = _TRUE; else status = rtw_do_join(padapter); release_mlme_lock: _exit_critical_bh(&pmlmepriv->lock, &irqL); exit: return status; } u8 rtw_set_802_11_ssid(_adapter *padapter, NDIS_802_11_SSID *ssid) { _irqL irqL; u8 status = _SUCCESS; struct mlme_priv *pmlmepriv = &padapter->mlmepriv; struct wlan_network *pnetwork = &pmlmepriv->cur_network; RTW_PRINT("set ssid [%s] fw_state=0x%08x\\n", ssid->Ssid, get_fwstate(pmlmepriv)); if (!rtw_is_hw_init_completed(padapter)) { status = _FAIL; goto exit; } _enter_critical_bh(&pmlmepriv->lock, &irqL); RTW_INFO("Set SSID under fw_state=0x%08x\\n", get_fwstate(pmlmepriv)); if (check_fwstate(pmlmepriv, _FW_UNDER_SURVEY) == _TRUE) goto handle_tkip_countermeasure; else if (check_fwstate(pmlmepriv, _FW_UNDER_LINKING) == _TRUE) goto release_mlme_lock; if (check_fwstate(pmlmepriv, _FW_LINKED | WIFI_ADHOC_MASTER_STATE) == _TRUE) { if ((pmlmepriv->assoc_ssid.SsidLength == ssid->SsidLength) && (_rtw_memcmp(&pmlmepriv->assoc_ssid.Ssid, ssid->Ssid, ssid->SsidLength) == _TRUE)) { if ((check_fwstate(pmlmepriv, WIFI_STATION_STATE) == _FALSE)) { if (rtw_is_same_ibss(padapter, pnetwork) == _FALSE) { /* if in WIFI_ADHOC_MASTER_STATE | WIFI_ADHOC_STATE, create bss or rejoin again */ rtw_disassoc_cmd(padapter, 0, 0); if (check_fwstate(pmlmepriv, _FW_LINKED) == _TRUE) rtw_indicate_disconnect(padapter, 0, _FALSE); rtw_free_assoc_resources_cmd(padapter, _TRUE, 0); if (check_fwstate(pmlmepriv, WIFI_ADHOC_MASTER_STATE) == _TRUE) { _clr_fwstate_(pmlmepriv, WIFI_ADHOC_MASTER_STATE); set_fwstate(pmlmepriv, WIFI_ADHOC_STATE); } } else { goto release_mlme_lock;/* it means driver is in WIFI_ADHOC_MASTER_STATE, we needn't create bss again. */ } } #ifdef CONFIG_LPS else rtw_lps_ctrl_wk_cmd(padapter, LPS_CTRL_JOINBSS, 0); #endif } else { rtw_disassoc_cmd(padapter, 0, 0); if (check_fwstate(pmlmepriv, _FW_LINKED) == _TRUE) rtw_indicate_disconnect(padapter, 0, _FALSE); rtw_free_assoc_resources_cmd(padapter, _TRUE, 0); if (check_fwstate(pmlmepriv, WIFI_ADHOC_MASTER_STATE) == _TRUE) { _clr_fwstate_(pmlmepriv, WIFI_ADHOC_MASTER_STATE); set_fwstate(pmlmepriv, WIFI_ADHOC_STATE); } } } handle_tkip_countermeasure: if (rtw_handle_tkip_countermeasure(padapter, __func__) == _FAIL) { status = _FAIL; goto release_mlme_lock; } if (rtw_validate_ssid(ssid) == _FALSE) { status = _FAIL; goto release_mlme_lock; } _rtw_memcpy(&pmlmepriv->assoc_ssid, ssid, sizeof(NDIS_802_11_SSID)); pmlmepriv->assoc_by_bssid = _FALSE; if (check_fwstate(pmlmepriv, _FW_UNDER_SURVEY) == _TRUE) pmlmepriv->to_join = _TRUE; else status = rtw_do_join(padapter); release_mlme_lock: _exit_critical_bh(&pmlmepriv->lock, &irqL); exit: return status; } u8 rtw_set_802_11_connect(_adapter *padapter, u8 *bssid, NDIS_802_11_SSID *ssid) { _irqL irqL; u8 status = _SUCCESS; bool bssid_valid = _TRUE; bool ssid_valid = _TRUE; struct mlme_priv *pmlmepriv = &padapter->mlmepriv; if (!ssid || rtw_validate_ssid(ssid) == _FALSE) ssid_valid = _FALSE; if (!bssid || rtw_validate_bssid(bssid) == _FALSE) bssid_valid = _FALSE; if (ssid_valid == _FALSE && bssid_valid == _FALSE) { RTW_INFO(FUNC_ADPT_FMT" ssid:%p, ssid_valid:%d, bssid:%p, bssid_valid:%d\\n", FUNC_ADPT_ARG(padapter), ssid, ssid_valid, bssid, bssid_valid); status = _FAIL; goto exit; } if (!rtw_is_hw_init_completed(padapter)) { status = _FAIL; goto exit; } _enter_critical_bh(&pmlmepriv->lock, &irqL); RTW_PRINT(FUNC_ADPT_FMT" fw_state=0x%08x\\n", FUNC_ADPT_ARG(padapter), get_fwstate(pmlmepriv)); if (check_fwstate(pmlmepriv, _FW_UNDER_SURVEY) == _TRUE) goto handle_tkip_countermeasure; else if (check_fwstate(pmlmepriv, _FW_UNDER_LINKING) == _TRUE) goto release_mlme_lock; handle_tkip_countermeasure: if (rtw_handle_tkip_countermeasure(padapter, __func__) == _FAIL) { status = _FAIL; goto release_mlme_lock; } if (ssid && ssid_valid) _rtw_memcpy(&pmlmepriv->assoc_ssid, ssid, sizeof(NDIS_802_11_SSID)); else _rtw_memset(&pmlmepriv->assoc_ssid, 0, sizeof(NDIS_802_11_SSID)); if (bssid && bssid_valid) { _rtw_memcpy(&pmlmepriv->assoc_bssid, bssid, ETH_ALEN); pmlmepriv->assoc_by_bssid = _TRUE; } else pmlmepriv->assoc_by_bssid = _FALSE; if (check_fwstate(pmlmepriv, _FW_UNDER_SURVEY) == _TRUE) pmlmepriv->to_join = _TRUE; else status = rtw_do_join(padapter); release_mlme_lock: _exit_critical_bh(&pmlmepriv->lock, &irqL); exit: return status; } u8 rtw_set_802_11_infrastructure_mode(_adapter *padapter, NDIS_802_11_NETWORK_INFRASTRUCTURE networktype, u8 flags) { _irqL irqL; struct mlme_priv *pmlmepriv = &padapter->mlmepriv; struct wlan_network *cur_network = &pmlmepriv->cur_network; NDIS_802_11_NETWORK_INFRASTRUCTURE *pold_state = &(cur_network->network.InfrastructureMode); u8 ap2sta_mode = _FALSE; u8 ret = _TRUE; u8 is_linked = _FALSE, is_adhoc_master = _FALSE; if (*pold_state != networktype) { /* RTW_INFO("change mode, old_mode=%d, new_mode=%d, fw_state=0x%x\\n", *pold_state, networktype, get_fwstate(pmlmepriv)); */ if (*pold_state == Ndis802_11APMode || *pold_state == Ndis802_11_mesh ) { /* change to other mode from Ndis802_11APMode/Ndis802_11_mesh */ cur_network->join_res = -1; ap2sta_mode = _TRUE; #ifdef CONFIG_NATIVEAP_MLME stop_ap_mode(padapter); #endif } _enter_critical_bh(&pmlmepriv->lock, &irqL); is_linked = check_fwstate(pmlmepriv, _FW_LINKED); is_adhoc_master = check_fwstate(pmlmepriv, WIFI_ADHOC_MASTER_STATE); /* flags = 0, means enqueue cmd and no wait */ if (flags != 0) _exit_critical_bh(&pmlmepriv->lock, &irqL); if ((is_linked == _TRUE) || (*pold_state == Ndis802_11IBSS)) rtw_disassoc_cmd(padapter, 0, flags); if ((is_linked == _TRUE) || (is_adhoc_master == _TRUE)) rtw_free_assoc_resources_cmd(padapter, _TRUE, flags); if ((*pold_state == Ndis802_11Infrastructure) || (*pold_state == Ndis802_11IBSS)) { if (is_linked == _TRUE) { rtw_indicate_disconnect(padapter, 0, _FALSE); /*will clr Linked_state; before this function, we must have checked whether issue dis-assoc_cmd or not*/ } } /* flags = 0, means enqueue cmd and no wait */ if (flags != 0) _enter_critical_bh(&pmlmepriv->lock, &irqL); *pold_state = networktype; _clr_fwstate_(pmlmepriv, ~WIFI_NULL_STATE); switch (networktype) { case Ndis802_11IBSS: set_fwstate(pmlmepriv, WIFI_ADHOC_STATE); break; case Ndis802_11Infrastructure: set_fwstate(pmlmepriv, WIFI_STATION_STATE); if (ap2sta_mode) rtw_init_bcmc_stainfo(padapter); break; case Ndis802_11APMode: set_fwstate(pmlmepriv, WIFI_AP_STATE); #ifdef CONFIG_NATIVEAP_MLME start_ap_mode(padapter); /* rtw_indicate_connect(padapter); */ #endif break; #ifdef CONFIG_RTW_MESH case Ndis802_11_mesh: set_fwstate(pmlmepriv, WIFI_MESH_STATE); start_ap_mode(padapter); break; #endif case Ndis802_11AutoUnknown: case Ndis802_11InfrastructureMax: break; case Ndis802_11Monitor: set_fwstate(pmlmepriv, WIFI_MONITOR_STATE); break; default: ret = _FALSE; rtw_warn_on(1); } /* SecClearAllKeys(adapter); */ _exit_critical_bh(&pmlmepriv->lock, &irqL); } return ret; } u8 rtw_set_802_11_disassociate(_adapter *padapter) { _irqL irqL; struct mlme_priv *pmlmepriv = &padapter->mlmepriv; _enter_critical_bh(&pmlmepriv->lock, &irqL); if (check_fwstate(pmlmepriv, _FW_LINKED) == _TRUE) { rtw_disassoc_cmd(padapter, 0, 0); rtw_indicate_disconnect(padapter, 0, _FALSE); /* modify for CONFIG_IEEE80211W, none 11w can use it */ rtw_free_assoc_resources_cmd(padapter, _TRUE, 0); if (_FAIL == rtw_pwr_wakeup(padapter)) RTW_INFO("%s(): rtw_pwr_wakeup fail !!!\\n", __FUNCTION__); } _exit_critical_bh(&pmlmepriv->lock, &irqL); return _TRUE; } #if 1 u8 rtw_set_802_11_bssid_list_scan(_adapter *padapter, struct sitesurvey_parm *pparm) { _irqL irqL; struct mlme_priv *pmlmepriv = &padapter->mlmepriv; u8 res = _TRUE; _enter_critical_bh(&pmlmepriv->lock, &irqL); res = rtw_sitesurvey_cmd(padapter, pparm); _exit_critical_bh(&pmlmepriv->lock, &irqL); return res; } #else u8 rtw_set_802_11_bssid_list_scan(_adapter *padapter, struct sitesurvey_parm *pparm) { _irqL irqL; struct mlme_priv *pmlmepriv = &padapter->mlmepriv; u8 res = _TRUE; if (padapter == NULL) { res = _FALSE; goto exit; } if (!rtw_is_hw_init_completed(padapter)) { res = _FALSE; goto exit; } if ((check_fwstate(pmlmepriv, _FW_UNDER_SURVEY | _FW_UNDER_LINKING) == _TRUE) || (pmlmepriv->LinkDetectInfo.bBusyTraffic == _TRUE)) { /* Scan or linking is in progress, do nothing. */ res = _TRUE; } else { if (rtw_is_scan_deny(padapter)) { RTW_INFO(FUNC_ADPT_FMT": scan deny\\n", FUNC_ADPT_ARG(padapter)); indicate_wx_scan_complete_event(padapter); return _SUCCESS; } _enter_critical_bh(&pmlmepriv->lock, &irqL); res = rtw_sitesurvey_cmd(padapter, pparm); _exit_critical_bh(&pmlmepriv->lock, &irqL); } exit: return res; } #endif #ifdef CONFIG_RTW_ACS u8 rtw_set_acs_sitesurvey(_adapter *adapter) { struct rf_ctl_t *rfctl = adapter_to_rfctl(adapter); struct sitesurvey_parm parm; u8 uch; u8 ch_num = 0; int i; BAND_TYPE band; u8 (*center_chs_num)(u8) = NULL; u8 (*center_chs)(u8, u8) = NULL; u8 ret = _FAIL; if (!rtw_mi_get_ch_setting_union(adapter, &uch, NULL, NULL)) goto exit; _rtw_memset(&parm, 0, sizeof(struct sitesurvey_parm)); parm.scan_mode = SCAN_PASSIVE; parm.bw = CHANNEL_WIDTH_20; parm.acs = 1; for (band = BAND_ON_2_4G; band < BAND_MAX; band++) { if (band == BAND_ON_2_4G) { center_chs_num = center_chs_2g_num; center_chs = center_chs_2g; } else #ifdef CONFIG_IEEE80211_BAND_5GHZ if (band == BAND_ON_5G) { center_chs_num = center_chs_5g_num; center_chs = center_chs_5g; } else #endif { center_chs_num = NULL; center_chs = NULL; } if (!center_chs_num || !center_chs) continue; if (rfctl->ch_sel_within_same_band) { if (rtw_is_2g_ch(uch) && band != BAND_ON_2_4G) continue; #ifdef CONFIG_IEEE80211_BAND_5GHZ if (rtw_is_5g_ch(uch) && band != BAND_ON_5G) continue; #endif } ch_num = center_chs_num(CHANNEL_WIDTH_20); for (i = 0; i < ch_num && parm.ch_num < RTW_CHANNEL_SCAN_AMOUNT; i++) { parm.ch[parm.ch_num].hw_value = center_chs(CHANNEL_WIDTH_20, i); parm.ch[parm.ch_num].flags = RTW_IEEE80211_CHAN_PASSIVE_SCAN; parm.ch_num++; } } ret = rtw_set_802_11_bssid_list_scan(adapter, &parm); exit: return ret; } #endif /* CONFIG_RTW_ACS */ u8 rtw_set_802_11_authentication_mode(_adapter *padapter, NDIS_802_11_AUTHENTICATION_MODE authmode) { struct security_priv *psecuritypriv = &padapter->securitypriv; int res; u8 ret; psecuritypriv->ndisauthtype = authmode; if (psecuritypriv->ndisauthtype > 3) psecuritypriv->dot11AuthAlgrthm = dot11AuthAlgrthm_8021X; #ifdef CONFIG_WAPI_SUPPORT if (psecuritypriv->ndisauthtype == 6) psecuritypriv->dot11AuthAlgrthm = dot11AuthAlgrthm_WAPI; #endif res = rtw_set_auth(padapter, psecuritypriv); if (res == _SUCCESS) ret = _TRUE; else ret = _FALSE; return ret; } u8 rtw_set_802_11_add_wep(_adapter *padapter, NDIS_802_11_WEP *wep) { u8 bdefaultkey; u8 btransmitkey; sint keyid, res; struct security_priv *psecuritypriv = &(padapter->securitypriv); u8 ret = _SUCCESS; bdefaultkey = (wep->KeyIndex & 0x40000000) > 0 ? _FALSE : _TRUE; /* for ??? */ btransmitkey = (wep->KeyIndex & 0x80000000) > 0 ? _TRUE : _FALSE; /* for ??? */ keyid = wep->KeyIndex & 0x3fffffff; if (keyid >= 4) { ret = _FALSE; goto exit; } switch (wep->KeyLength) { case 5: psecuritypriv->dot11PrivacyAlgrthm = _WEP40_; break; case 13: psecuritypriv->dot11PrivacyAlgrthm = _WEP104_; break; default: psecuritypriv->dot11PrivacyAlgrthm = _NO_PRIVACY_; break; } _rtw_memcpy(&(psecuritypriv->dot11DefKey[keyid].skey[0]), &(wep->KeyMaterial), wep->KeyLength); psecuritypriv->dot11DefKeylen[keyid] = wep->KeyLength; psecuritypriv->dot11PrivacyKeyIndex = keyid; res = rtw_set_key(padapter, psecuritypriv, keyid, 1, _TRUE); if (res == _FAIL) ret = _FALSE; exit: return ret; } /* * rtw_get_cur_max_rate - * @adapter: pointer to _adapter structure * * Return 0 or 100Kbps */ u16 rtw_get_cur_max_rate(_adapter *adapter) { int j; int i = 0; u16 rate = 0, max_rate = 0; struct mlme_priv *pmlmepriv = &adapter->mlmepriv; WLAN_BSSID_EX *pcur_bss = &pmlmepriv->cur_network.network; int sta_bssrate_len = 0; unsigned char sta_bssrate[NumRates]; struct sta_info *psta = NULL; u8 short_GI = 0; #ifdef CONFIG_80211N_HT u8 rf_type = 0; #endif #ifdef CONFIG_MP_INCLUDED if (adapter->registrypriv.mp_mode == 1) { if (check_fwstate(pmlmepriv, WIFI_MP_STATE) == _TRUE) return 0; } #endif if ((check_fwstate(pmlmepriv, _FW_LINKED) != _TRUE) && (check_fwstate(pmlmepriv, WIFI_ADHOC_MASTER_STATE) != _TRUE)) return 0; psta = rtw_get_stainfo(&adapter->stapriv, get_bssid(pmlmepriv)); if (psta == NULL) return 0; short_GI = query_ra_short_GI(psta, rtw_get_tx_bw_mode(adapter, psta)); #ifdef CONFIG_80211N_HT if (is_supported_ht(psta->wireless_mode)) { rtw_hal_get_hwreg(adapter, HW_VAR_RF_TYPE, (u8 *)(&rf_type)); max_rate = rtw_mcs_rate(rf_type , (psta->cmn.bw_mode == CHANNEL_WIDTH_40) ? 1 : 0 , short_GI , psta->htpriv.ht_cap.supp_mcs_set ); } #ifdef CONFIG_80211AC_VHT else if (is_supported_vht(psta->wireless_mode)) max_rate = ((rtw_vht_mcs_to_data_rate(psta->cmn.bw_mode, short_GI, pmlmepriv->vhtpriv.vht_highest_rate) + 1) >> 1) * 10; #endif /* CONFIG_80211AC_VHT */ else #endif /* CONFIG_80211N_HT */ { /*station mode show :station && ap support rate; softap :show ap support rate*/ if (check_fwstate(pmlmepriv, WIFI_STATION_STATE) == _TRUE) get_rate_set(adapter, sta_bssrate, &sta_bssrate_len);/*get sta rate and length*/ while ((pcur_bss->SupportedRates[i] != 0) && (pcur_bss->SupportedRates[i] != 0xFF)) { rate = pcur_bss->SupportedRates[i] & 0x7F;/*AP support rates*/ /*RTW_INFO("%s rate=%02X \\n", __func__, rate);*/ /*check STA support rate or not */ if (check_fwstate(pmlmepriv, WIFI_STATION_STATE) == _TRUE) { for (j = 0; j < sta_bssrate_len; j++) { /* Avoid the proprietary data rate (22Mbps) of Handlink WSG-4000 AP */ if ((rate | IEEE80211_BASIC_RATE_MASK) == (sta_bssrate[j] | IEEE80211_BASIC_RATE_MASK)) { if (rate > max_rate) { max_rate = rate; } break; } } } else { if (rate > max_rate) max_rate = rate; } i++; } max_rate = max_rate * 10 / 2; } return max_rate; } /* * rtw_set_scan_mode - * @adapter: pointer to _adapter structure * @scan_mode: * * Return _SUCCESS or _FAIL */ int rtw_set_scan_mode(_adapter *adapter, RT_SCAN_TYPE scan_mode) { if (scan_mode != SCAN_ACTIVE && scan_mode != SCAN_PASSIVE) return _FAIL; adapter->mlmepriv.scan_mode = scan_mode; return _SUCCESS; } /* * rtw_set_channel_plan - * @adapter: pointer to _adapter structure * @channel_plan: * * Return _SUCCESS or _FAIL */ int rtw_set_channel_plan(_adapter *adapter, u8 channel_plan) { /* handle by cmd_thread to sync with scan operation */ return rtw_set_chplan_cmd(adapter, RTW_CMDF_WAIT_ACK, channel_plan, 1); } /* * rtw_set_country - * @adapter: pointer to _adapter structure * @country_code: string of country code * * Return _SUCCESS or _FAIL */ int rtw_set_country(_adapter *adapter, const char *country_code) { #ifdef CONFIG_RTW_IOCTL_SET_COUNTRY return rtw_set_country_cmd(adapter, RTW_CMDF_WAIT_ACK, country_code, 1); #else RTW_INFO("%s(): not applied\\n", __func__); return _SUCCESS; #endif } /* * rtw_set_band - * @adapter: pointer to _adapter structure * @band: band to set * * Return _SUCCESS or _FAIL */ int rtw_set_band(_adapter *adapter, u8 band) { if (rtw_band_valid(band)) { RTW_INFO(FUNC_ADPT_FMT" band:%d\\n", FUNC_ADPT_ARG(adapter), band); adapter->setband = band; return _SUCCESS; } RTW_PRINT(FUNC_ADPT_FMT" band:%d fail\\n", FUNC_ADPT_ARG(adapter), band); return _FAIL; }

249 F.3d 592 (7th Cir. 2001) COMMODITY FUTURES TRADING COMMISSION, Plaintiff-Appellee,v.CARMEN FIELD, individually and d/b/a HFI, MONA SMITH, individually and d/b/a HFI, Defendants-Appellants. No. 00-1764 In the United States Court of Appeals For the Seventh Circuit Argued September 28, 2000Decided April 24, 2001 Appeal from the United States District Court for the Northern District of Indiana, South Bend Division. No. 98 C 281--Allen Sharp, Judge. Before MANION, ROVNER, and DIANE P. WOOD, Circuit Judges. ROVNER, Circuit Judge. 1 The Commodity Futures Trading Commission (the "Commission") filed a civil complaint against appellants and other defendants, alleging that they defrauded participants in two commodity pools by misappropriating participants' funds, misrepresenting material facts while soliciting participants, and issuing false statements to the pool participants. The parties engaged in settlement discussions, which form the basis of this appeal. Field and Smith contend that a binding oral agreement resulted from those discussions, and the Commission disputes that assertion. The district court sided with the Commission, and after a bench trial, found Field and Smith in violation of antifraud and registration provisions of the Commodity Exchange Act including 7 U.S.C. sec.sec. 1a(4), 6o(1), 6b(a)(i), and 6b(a)(ii), and its regulation 17 C.F.R. sec.4.20. The district court ordered permanent injunctive relief, enjoining Field and Smith from further violations, and inter alia, from directly or indirectly soliciting or accepting funds in connection with the sale of a commodity futures contract, trading commodity futures or commodity options for their own accounts or on their behalf, or controlling or directing commodity futures trading. They were further ordered to disgorge their ill-gotten gains in the amount of $880,811, and Smith was additionally ordered to disgorge the sum of $146,154. The court also ordered Field and Smith to pay restitution totaling $1,026,965.15 to certain investors, and Field was ordered to make further restitution of $234,561.52 to other investors. The appellants moved for a new trial, asserting that the district court erred in ruling that there was no settlement agreement, and in failing to at least grant an evidentiary hearing on the issue. The court denied the motion, and they now raise those same issues on appeal. 2 Appellants maintain that an oral settlement agreement was reached with the Commission as a result of a settlement conference on June 9, 1999 with Magistrate Judge Pierce, approximately a month before his untimely death. We need not explore the contours of that alleged agreement, however, because it is clear that the attorneys representing the Commission at that conference were without authority to enter into any binding settlement agreement, and therefore no enforceable agreement could have resulted from that conference. The sequence of events makes that crystal clear. 3 In the order scheduling the settlement conference, the magistrate judge required that, unless excused by the court in advance, persons possessing final decision-making authority with respect to settlement had to attend the settlement conference. In response to that order, the attorneys for the Commission sent a letter to the magistrate judge requesting an exception to that requirement. The letter explained that the Commission prosecutes actions through its Division of Enforcement (the "Division"), but that the Division does not possess independent settlement authority. Instead, the Division "presents executed offers of settlement to the Commission with specific recommendations that any such offer be accepted or declined, and in the case of federal litigation, to grant the Division authority to enter into the proposed settlement." CFTC requested that it be allowed to work within that framework, and specifically requested that it "be allowed to participate in the settlement conference with a Division attorney possessing authority to negotiate the terms of a settlement that the Division will affirmatively recommend the Commission accept." The magistrate judge granted that request to modify the usual requirement that someone with final authority to settle be present, and issued an order tracking the language requested by the Commission allowing participation by persons with authority to negotiate terms that would be recommended to the Commission. 4 It is well settled that a settlement on behalf of the United States may be enforced only if the person who entered into the settlement had actual authority to settle the litigation. United States v. LaCroix, 166 F.3d 921, 923 (7th Cir. 1999); Urso v. United States, 72 F.3d 59, 60 (7th Cir. 1995). That stands in contrast to settlement of cases by private parties, where apparent authority may be sufficient to bind a litigant. See Pohl v. United Airlines, Inc., 213 F.3d 336 (7th Cir. 2000). The sequence of events recited above leaves no doubt that the attorneys who engaged in the settlement discussion on behalf of the Commission lacked the actual authority to bind the government, a fact that should have been clear to appellants as well given the letter from the Commission and the magistrate judge's subsequent order allowing the participation of the Division attorneys even though they lacked final authority to settle. The appellants seem to misread the Commission's statement that the attorneys would have the authority to negotiate, as somehow implying that they had authority to finally settle the case. That reading defies the plain language of the letter and the magistrate judge's order. Because the Division attorneys lacked the actual authority to settle the case, no agreement reached with them at the settlement conference is binding on the government. We note in passing that even if they had the authority to settle, it is fairly clear from the record that no settlement was actually reached at that conference, but that step we need not take given their lack of authority to enter into a binding settlement agreement in the first place. For the above reasons, the decision of the district court is AFFIRMED.

These days travelling with technology can really make the whole experience so much easier. However, you still need to keep your digital security in mind. We can go through a checklist together and I can personalise your technology for your travel needs.

Post a Message Magician Rich Ferguson, AKA "The Ice Breaker", calls the central coast of California home. He works all over the globe demonstrating unusual magic and mentalism at parties, corporate events and VIP gala's. Rich is also a celebrity in the world of poker and magic as a well known creator and host of numerous DVDs and books on the subject. In recent years, he's been called "The Idea Man" as a creative consultant to entertainers and businesses alike with the creation of effects, strategies, marketing ideas and inventions. For more information or for booking Rich for a private party or for creative consultation, please visit his official site at http://www.RichFerguson.com

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(i) Field of the Invention The present invention relates to a method for preparing amines, and more specifically, it relates to a method for preparing methylamines from methanol and ammonia in which monomethylamine and dimethylamine are obtained in larger amounts, while the production of trimethylamine is inhibited to a sufficiently low level. The methylamines obtained by the method of the present invention are useful as raw materials for the manufacture of solvents and various intermediates of organic synthesis. (ii) Description of the Prior Art Methylamines, i.e., monomethylamine, dimethylamine and trimethylamine have been prepared by a method in which methanol or a mixture of methanol and dimethyl ether is reacted with ammonia, a method in which prussic acid is subjected to catalytic reduction, or the like. These methylamines are produced as a mixture of monomethylamine, dimethylamine and trimethylamine, and they have independent applications, respectively. On the other hand, the demand of these methylamines is localized on dimethylamine and monomethylamine, and so trimethylamine is nowadays in little demand. The methylamines obtained by the reaction of methanol and ammonia in the presence of a conventional amorphous silica-alumina catalyst contain trimethylamine as a main component, and the process using this catalyst has the drawback that the production of dimethylamine which is in great demand is insufficient. In order to overcome this drawback, U.S. Pat. No. 3,384,667 has suggested a technique in which a dehydrated crystalline aluminosilicate (a zeolite) having a pore diameter of 5-10 .ANG. is used as a catalyst in the reaction of an alcohol having 1 to 18 carbon atoms with ammonia to predominantly produce monoamine and diamine over triamine. Furthermore, as zeolites suitable for the above-mentioned reaction, natural zeolites and synthetic zeolites are recited. That is, this U.S. patent discloses that examples of the desirable natural zeolites include faujasite, analcite, clinoptilolite, ferrierite, chabazite, gmelinite, levynite, erionite and mordenite. It is also disclosed that examples of the desirable synthetic zeolites include X type, Y type and A type zeolites. There are known a method which comprises mixing methanol with ammonia in a specific ratio, and then carrying out the reaction in the presence of a catalyst such as mordenite to form monomethylamine in a surprisingly large amount (Japanese Patent Application Laid-open No. 113747/1981), and a method which comprises disproportionating monomethylamine on a crystalline aluminosilicate selected from Na mordenites to prepare dimethylamine with a high selectivity (Japanese Patent Application Laid-open No. 46846/1981). In addition, there are also known a method in which a natural mineral is used as a mordenite in the same manner as in the above-mentioned U.S. Pat. No. 3,384,667 (Japanese Patent Application Laid-open No. 169444/1982), a method in which a mordenite ion-exchanged with lanthanum ions is used as the catalyst (Japanese Patent Application Laid-open No. 49340/1983), a method in which a mordenite containing an ion-exchanged alkaline metal in a specifically limited amount range is used as the catalyst (Japanese Patent Application Laid-open No. 210050/1984), a method in which a steam-treated mordenite is used as the catalyst (Japanese Patent Application Laid-open No. 227841/1984), a method in which an A type zeolite having a low binder content is used as the catalyst (Japanese Patent Application Laid-open No. 69846/1983), and a method in which a Rho type (ZK-5) zeolite is used as the catalyst. When the zeolite catalyst is used by any of the above-mentioned methods, the production of trimethylamine can be inhibited, but for the purpose of inhibiting the production of trimethylamine to zero or substantially zero, some methods are also known in which a mordenite having pores treated by CVD (chemical vapor deposition) of silicon tetrachloride is used as the catalyst (Japanese Patent Application Laid-open No. 262540/1991; J. Catal., Vol. 131, pp. 482 (1991); and U.S. Pat. No. 5,137,854). Another method is also present in which chabazite, erionite, ZK-5 or a Rho type zeolite deposited or modified with compounds of silicon, aluminum, phosphorus or boron is used as the catalyst to restrict the production of trimethylamine (Japanese Patent Application Laid-open No. 254256/1986, and U.S. Pat. No. 4,683,334). Moreover, there is also known a method which comprises reacting an alcohol with ammonia by the use of SAPO of a non-zeolite molecular sieve as the catalyst to obtain alkylamines (Japanese Patent Application Laid-open No. 734/1990). As described above, the production of trimethylamine which is in little demand can be inhibited to a low level by using any of the various already disclosed zeolite-based catalysts in the reaction of methanol and ammonia, so that the production of dimethylamine which is in great demand can be increased. However, even if the zeolite-based compound is used as the catalyst, the production ratio of trimethylamine can be merely restricted to usually 10%, or at most about 5%. If the production of trimethylamine can be inhibited to about 1 to 3%, it is not necessary to recycle trimethylamine which is in little demand to the reaction system for disproportionation, and as a result, a manufacturing process can be simplified and utilities, steam or the like, to be used can be decreased. As a method for decreasing the production of trimethylamine to several percent, there is the above-mentioned method disclosed in Japanese Patent Application Laid-open No. 262540/1991 (U.S. Pat. No. 5,137,854) in which a mordenite deposited with silicon tetrachloride by a CVD treatment is used as the catalyst. However, this method can be easily carried out on a laboratory scale, but it is difficult to industrially manufacture a large amount of the catalyst for use in preparing methylamines. In the above-mentioned method in which ZK-5 or a Rho type zeolite treated with silicon, aluminum, phosphorus or a boron compound is used to inhibit the production of trimethylamine to several percent (U.S. Pat. No. 4,683,334), there is the drawback that a specific synthetic zeolite such as ZK-5 or Rho is required to be used.

Q: Convert C# generic into Java generic How can I convert the following C# code to Java? private T GenericMethod<T>(String value) { return (T)Enum.Parse(typeof(T), value , true); } A: Wherever you call your method: // C# MyEnum value = TemplateMethod<MyEnum>("AnEnumValue"); In Java you can do it like this: // Java MyEnum value = MyEnum.valueOf("AN_ENUM_VALUE"); If you're worried about case, and if you follow Java conventions of using upper case enum values, then you can just do this: MyEnum value = MyEnum.valueOf(anEnumValue.toUpperCase()); To encapsulate it in a method: static <E extends Enum<E>> E parse(Class<E> enumType, String value) { return (E)Enum.valueOf(enumType, value.toUpperCase()); } Call it like this: MyEnum value = parse(MyEnum.class, anEnumValue);

Cucuruzzu Cuccuruzzu is an archaeological site in Corsica. It is located in the commune of Levie. History of Development of the site After the interest in Cucuruzzu in 1959 by Roger Grosjean, archaeologist known for having studied Filitosa, and the excavations which he instigated in 1963 and 1964, the site was acquired in 1975 by the state and declared an historical monument in 1982. It is now owned by the Territorial Collectivity of Corsica. Restored in 1991, stripping the vegetation which invaded it, its development provides public access while limiting its degradation. Category:Archaeological sites in Corsica

Q: Apply a javaScript function to 1 div when there are more divs with the same class I'm trying to make a simple timeline that informs users. When they click on a date, there should be some sort of "accordion" system that drops down and give more information. When they click on it again, the "accordion" closes again. I've included some pictures to make it somewhat more clear: And: The first image shows what the user is seeing when he gets onto the page, the second picture shows what he sees when he clicks on 1 of the elements. The problem ive at the moment is when he clicks on 1 day, all the information is shown. I dont know how i can get some sort of index so only that particular day shows its hidden information. At the moment I've the following code: JavaScript $counter=1; $(document).ready(function(){ $(".tijdlineElement").click(function(){ $(".tijdlineElementHidden").slideToggle("slow"); if($counter == 1){ getElementsByClassName("tijdlineElementHidden").style.display = "block"; $counter = 2 } else{ getElementByClass("tijdlineElementHidden").style.display = "none"; $counter =1 } }); }); and the PHP to make 1 Day: echo "<div class='tijdlineElement'>"; echo "<div class='tijdlineP2Element' >" . $topic['Uur']."<br /><br />" . $topic['Beschrijving'] . "</div>"; echo "<div class='tijdlinePElement'>". $newDate . '<br />'. $newDate1 . ' '. $newDate1a . '<br />' . $newDate2 ."</div>"; echo "<img src='images/meerFase1.png'/>"; echo "</div>"; echo "<div class='tijdlineElementHidden' style='display:none;'>"; echo "<div class='tijdlineP2Element'>" . $topic['LangeBeschrijving'] . "</div>"; echo "<div class='tijdlinePElement'></div>"; echo "</div><br />"; The issue is, when a user clicks on 1 date, all the information from the other days get revealed aswell. So my question is: How can i get access to that particular div, so only the information from the selected(the div that was clicked on) div is shown? A: With your current code by using $(".tijdlineElement").click(function(){ } You are triggering the click event on all elements with that class. What you could do is use something like .each() and $(this) to scope it to your currently clicked element. $(".tijdlineElement").each(function(){ $(this).on({ click:function() { $(this).slideToggle("slow"); // other click function stuff } }); }); Quick Demo: http://jsfiddle.net/9v2D5/ Updated Demo: http://jsfiddle.net/9v2D5/25/

Thrombotic thrombocytopenic purpura (TTP) leading to pseudotumour's autoimmune pancreatitis (AIP): a case report. Autoimmune pancreatitis is an idiopathic inflammatory disease that produces pancreatic masses and ductal strictures. This benign disease can be associated with extrapancreatic manifestations including cholangitis, sialadenitis, inflammatory bowel disease or retroperitoneal fibrosis, mediastinal adenopathy, interstitial nephritis mainly due to immunoglobulin G4 (Ig G4), and occasional association with other auto-immune diseases. We report a 57-year-old woman who developed thrombotic thrombocytopenic purpura (TTP) and pseudo-tumour's seronegative autoimmune pancreatitis (AIP) type 1. The patient was initially treated with pulse corticosteroids and plasmapheresis; afterwards two cures of i.v. Vincristin with inadequate response and subsequently with four weekly pulses dose of i.v. Rituximab, leading to full remission. This case represents the first report of TTP associated to pseudo-tumour's seronegative AIP type 1 successfully treat by Rituximab.

Q: Is there a command that makes food restore health I want to create an adventure map, with healing items, but potions aren't stackable, what isn't very good. So, is there a command in 1.13/1.14 that makes food heal the player? A: I assume you want players to get an effect when eating foods. If you want one kind of food in general to heal, then that's easy. First, create a scoreboard that tracks players who eat the kind of food you want to heal (in this case, a cookie): /scoreboard objectives add heal minecraft.used:minecraft.cookie Then run these commands in a repeating chain: effect give @a[scores={heal=1..}] instant_health scoreboard players reset @a heal This will give players who have used a cookie instant health, and then immediately resets their score so they can do it again. If you want named foods to give health, you'll need to add some more commands. Put this in a repeating chain instead: effect give @a[tag=heal,scores={heal=1..}] instant_health scoreboard players reset @a heal tag @a remove heal tag @a[nbt={SelectedItem:{id:"minecraft:cookie",tag:{display:{Name:"\\"Health Biscuit\\""}}}}] add heal This tags players who are holding a cookie named "Health Biscuit" with a "heal" tag, then the same thing is done in the first example. The reason why I put the tag commands below the effect and scoreboard commands is because once you have used the cookie, it would no longer be in your hand, so it would be impossible to tag the player. Putting the tag commands on the bottom will tag the player, then in the next tick, when they have eaten the cookie, will heal the player because he already has that tag. To change what you want your food to be, just change the objective to minecraft.used:minecraft.foodnamehere. This is where to change what you want the food's name to be in the tag command: tag @a[nbt={SelectedItem:{id:"minecraft:cookie",tag:{display:{Name:"\\"HERE IS WHERE TO EDIT YOUR FOOD NAME\\""}}}}] add heal

1. Field of the Invention The invention relates generally to a parts cleaning apparatus and more specifically, but not exclusively, to a centrifugal parts cleaning apparatus for cleaning parts covered with a fluid. 2. Description of the Related Art During the process of machining, it is common to use fluids to lubricate parts in order to reduce wear on equipment and to facilitate the machining process. However, fluid residue left on parts after the machining process is generally unwanted and often removed. One common way to remove the fluid from parts is to wash the parts with a solvent capable of removing or dissolving the fluid. One drawback of such a process, however, is that the fluid removed from the parts cannot be reclaimed without an expensive secondary process. Moreover the solvent itself is often expensive. It is also known to remove fluid from parts using centrifugal force. Parts are placed in a centrifuge and spun until the fluid is removed from the parts. Such a process however, imparts a great deal of force on the parts and has the capability to dislodge parts, causing damage and lost parts.

package com.argusapm.android.debug.tasks; import com.argusapm.android.api.ApmTask; import com.argusapm.android.core.IInfo; import com.argusapm.android.core.job.activity.ActivityInfo; import com.argusapm.android.debug.config.DebugConfig; import com.argusapm.android.debug.output.OutputProxy; import com.argusapm.android.debug.utils.DebugFloatWindowUtls; import org.json.JSONException; import org.json.JSONObject; /** * Debug模块 Activity分析类 * * @author ArgusAPM Team */ public class ActivityParseTask implements IParser { /** * 生命周期所用时间 * * @param info */ @Override public boolean parse(IInfo info) { if (info instanceof ActivityInfo) { ActivityInfo aInfo = (ActivityInfo) info; if (aInfo == null) { return false; } if (aInfo.lifeCycle == ActivityInfo.TYPE_FIRST_FRAME) { saveWarningInfo(aInfo, DebugConfig.WARN_ACTIVITY_FRAME_VALUE); DebugFloatWindowUtls.sendBroadcast(aInfo); } else if (aInfo.lifeCycle == ActivityInfo.TYPE_CREATE) { saveWarningInfo(aInfo, DebugConfig.WARN_ACTIVITY_CREATE_VALUE); DebugFloatWindowUtls.sendBroadcast(aInfo); } else if (aInfo.lifeCycle == ActivityInfo.TYPE_RESUME) { saveWarningInfo(aInfo, DebugConfig.WARN_ACTIVITY_CREATE_VALUE); DebugFloatWindowUtls.sendBroadcast(aInfo); } else { saveWarningInfo(aInfo, DebugConfig.WARN_ACTIVITY_CREATE_VALUE); } } return true; } private void saveWarningInfo(ActivityInfo aInfo, int warningTime) { if (aInfo.time < warningTime) { return; } try { JSONObject obj = aInfo.toJson(); obj.put("taskName", ApmTask.TASK_ACTIVITY); OutputProxy.output("LifeCycle:" + aInfo.getLifeCycleString() + ",cost time:" + aInfo.time, obj.toString()); } catch (JSONException e) { e.printStackTrace(); } } }

Crocodylus Park Crocodylus Park is a zoo situated in Berrimah, Northern Territory, Australia. It specialises in the conservation of saltwater and freshwater crocodiles and features a comprehensive crocodile museum. The park also has big cats, monkeys, birds, turtles and snakes. References External links Category:Zoos in the Northern Territory Category:Tourist attractions in the Northern Territory Category:1994 establishments in Australia

Q: Adding tables to dashboard pages programmatically? I think that is not possible with some actions or filters, I know that I can do it just with html and using right css styles, and of course php to achieve what I need, or to write some minde actions. Is there already some predefined functions for this or not? Thanks. A: Well in that case take a look at this tutorial on how to use the native WP_List_Table

Join Our Epee and Sabre Classes Welcome to Dream Fencing Club Whether you think fencing may be your thing, or you just want to try something new, Dream Fencing is for you. Sign up to try fencing at one of our Beginners’ Courses! ...and bring your parents too! There is no upper age limit. We look forward to welcoming you and your children soon. Try fencing ~ change your life! This is a sport that can last a lifetime with competitions from age under 9 to Veterans from 40+ up to 70+ Dream Fencing International Summer Camp 2019 Fencers from Russia, Italy, France, Spain, Denmark and United Kingdom are already signed up for the fencing camp..Looking forward to see you all in July --D--- More information and online registration here: dreamfencing.co.uk/events-calenda… Well done to Jasper who won Silver at Camden sabre intermediate! National Finals U12 boys Congratulations to Aleksey Choi for his silver medal.

In this list, we’ve assembled 8 of the finest CBD oil tinctures on the market complete with all the information you need to know about each offering, and we also answer your most pressing CBD questions at the end. Overall 95% 95% Flavor Options - 94% 94% Activation Time - 90% 90% Effect - 98% 98% Lifetime - 98% 98% Pros Effects from sublingually consuming CBD last on average between 4-8 hours Easy to consume exact dosage Options Cons Flavor daily Takes longer than vape or smoke to activate Doing your research is all-important when you want to select the right CBD products. In this list, we’ve assembled 10 of the finest CBD oil tinctures on the market complete with all the information you need to know about each offering, and we also answer your most pressing CBD questions at the end. Buckle up, and dive into tons of product information, lab testing, and studies on hemp, CBD, and even CBG! Pros 2. 600mg of CBD with less than 0.03% THC – Guaranteed (you can buy 100mg, 300mg, and 600mg tinctures) 3. 90-day money-back guarantee 4. You get a huge discount if you buy in 6-month bulk, good for a daily consumer Cons 1. The highest concentration is 600mg Key Features CBDPure prides itself on only using natural, organic non-GMO ingredients. The oil has a very light earthy flavor, the activation time is about 15 to 20 minutes. Over a 30-day period, the oil lasted on average 4-6 hours per day. During that time period, I felt more relaxed, less anxious during my workday. At night, 2 hours before bed I would take 1 more full dropper. If you struggle with falling asleep or staying asleep, I strongly recommend you learn more about CBDPure to see if the oil is right for you. Recommended Dosage As with most CBD tinctures, try taking between half a dropper and a full dropper to fully gauge the effects. The dropper is very easy to use, you’ll have no problem measuring out the amount you need. About The Brand Here is a message from the CBDPure team: “CBDPure follows strict cGMP manufacturing guidelines as well as stringent quality control protocols necessary to provide the highest quality CBD product available on the market. From soil to oil, we control and test every link in the chain to make sure every drop of CBDPure is the best, most natural source of CBD available to our customers. The certified lab tests and reports for each lot number and batch are available upon request. You deserve the best for your health and CBDPure ensures our product meets the purity standards and quality our customers demand.” Cons 2. Chlorophyll is not dangerous, but it can make the taste of CBD oil more intense Key Features With a focus on organic, natural products, NuLeaf Naturals offers a lineup of tinctures with nothing in them to cause concern. From natural hemp oil to CO2-extracted CBD, NuLeaf Naturals has you covered. Recommended Dosage NuLeaf Naturals CBD oil is more concentrated than tinctures from other brands that you might have tried, so take things easy at first. Coupon Code 3. CBDfx 1500mg Tincture Pros 1. One of the overall best CBD tinctures on the market in terms of potency, ingredients, pricing, and other factors 2. Features non-GMO, organic CBD oil 3. Only contains CBD oil and MCT oil, which is a carrier oil that has its own impressive health benefits 4. CBDfx is one of the most integral, honest, and transparent CBD companies on the market Cons 1. Like most things cannabidiol, CBDfx tinctures are somewhat pricey 2. You might want to try one of CBDfx’s new flavored tinctures if you aren’t a fan of hemp oil’s unique taste Key Features If you’re looking for the strongest CBD tincture on the market, this might be it. While other tinctures may contain more cannabidiol molecules, CBDfx carries the most weight when it comes to product quality and customer service. Recommended Dosage Whether you’re looking for 500mg, 1000mg, or 1500mg of CBD oil in your tincture, CBDfx has you covered. This ultra-strength 1500mg option contains around 25-35mg of CBD per dropper, so start with just a few drops under your tongue to determine the effects before you try a higher dosage. Coupon Code Pros 1. Instead of affecting the 5-HT1A and TRPV1 receptors like CBD, cannabigerol appears to boost levels of anandamide and GABA 2. Anandamide is known as the “bliss molecule,” and GABA prevents fear and anxiety 3. Steve’s CBG oil is widely regarded as the most reliable source of cannabigerol products Cons 1. CBG oil is not the same thing as CBD oil – don’t get them mixed up! 2. Unfortunately, it takes a ton of hemp biomass to make pure CBG isolate since most cannabis strains only contain 1% CBG or less Key Features Looking for Steve’s CBG Oil review? You’ve come to the right place. Steve is one of the only guys in the industry offering CBG products, which makes his company a pioneer that will be remembered in cannabinoid history books. Recommended Dosage If you’re on the hunt for a Steve’s CBG oil coupon you can use to save, check the sidebar on this page, or scroll down to the bottom to find the coupon codes for the products we’ve listed. There’s no established dosage for CBG yet, but we’ll keep you in the know. Pros Cons 1. Organic CBD commands a high price Key Features No brand cares more about the beneficial effects of hemp on human mass consciousness and society than Hemplucid. This company encourages you to get the most out of life, and your very own whole-plant Hemplucid tincture is a great place to start. You have tons of dosage options to choose from with your Hemplucid tincture, so whether you’re new to CBD oil and or you know you want the highest dosage possible right from the get-go, you’ll love the flexibility that Hemplucid provides. Recommended Dosage Depending on the strength of the tincture you chose, it might make sense to use a greater or lesser amount at first. If you’re already used to taking CBD tinctures and want to switch to another brand, go ahead and take a full dropper at once. Pros Cons 1. 250mg is a relatively low dosage for people with serious conditions Key Features JustCBD’s website is easy to navigate, and this brand even offers financing options. We like the addition of honey to this CBD tincture; according to various ancient traditions, honey has incredible health benefits, so pairing it with CBD simply makes sense. Recommended Dosage Whether you’re trying CBD oil for cancer or any other condition, you’ll need to consult with your doctor to dial in on the right CBD dosage for your needs. With this JustCBD tincture, you shouldn’t have any problem with trying a dropper under your tongue and waiting a few minutes to gauge the effects. Pros 1. Delicious vanilla flavor for those who don’t like the taste of hemp 2. Great bundle deals that help you save 3. Finance options offered Cons 1. Some brands focus a little bit more on natural ingredients Key Features This is the tincture for you if you want to indulge your sweet tooth while you soak up the relaxing effects of CBD. Sugar & Kush takes a unique approach to CBD tinctures, and by making their products as sweet as they are effective, this brand captures the need to be pampered that we all feel inside. Recommended Dosage You have 500mg and 1000mg options to choose from, so indulge in whichever concentration helps you enjoy CBD the best. Pros 2. One of the biggest brands in the industry, which provides reliability Cons 1. This brand focuses heavily on CBD isolate, so be prepared to go elsewhere for your broad-spectrum or full-spectrum CBD oil needs Key Features CBDistillery became famous as one of the first brands offering isolate CBD shatter, but now, this brand provides a little bit of everything. This isolate CBD tincture is perfect if you’ve been looking for a reliable way to enjoy the benefits of isolated cannabidiol molecules with no THC. Recommended Dosage Wondering how to use CBDistillery tinctures? This THC-free tincture offers 33mg CBD per serving, so simply calibrate how much of your dropper you want to squirt under your tongue at a time for the best effects. 17 Popular CBD FAQs Answered By A Cannabis Expert: 1. Why is CBD oil so expensive? In most cases, because it is so expensive to produce. Generations of a worldwide stance against marijuana have resulted in a global economy that isn’t equipped to handle the recent interest in hemp-derived CBD. As regulations and laws around the world inevitably align with the values of the people, the CBD industry will continue to go mainstream. As a result, costs will go down. Some unethical companies may still charge more than they should; rely on Best Dosage for the information you need to separate the wheat from the chaff. 2. Where to buy CBD oil near me? You can purchase any of the fine cbd products in this list by clicking the product name listed above in each section. Doing so will route you to a secure webpage where you can purchase the tincture you want immediately or select from among your chosen cbd brand’s entire catalog. 3. How long does it take for CBD oil to work? The time it takes to feel the effects of CBD varies depending on how you use this substance. Inhaling CBD vapor, for instance, might provide almost instantaneous effects. When you take a CBD capsule or chew up some CBD gummies, however, it might take 40-60 minutes to notice the effects. Topical and sublingual CBD products usually have very fast activation times as well. 4. How long does CBD oil stay in your system? CBD and other cannabinoids are fat-soluble, which means that they build up in your tissues and remain in your body for around 30 days. Since no modern drug tests are calibrated to detect the presence of CBD, however, there’s no reason to be concerned about cannabidiol building up in your body. 5. How long does CBD oil last? The duration of the effects of CBD varies depending on how you ingest this cannabinoid. If you vape your CBD, for instance, the effects you feel may only last for an hour or less. The effects of orally administered CBD, however, last the entire time it takes for cannabidiol to pass through your digestive tract, which is generally 5-8 hours. Oral ingestion isn’t without its drawbacks, however; some estimates put the bioavailability of orally ingested CBD at around 20%, which means that a lot of the CBD you eat or drink isn’t used efficiently. 6. What does CBD oil feel like? CBD appears to affect all members of the mammal sub-group essentially the same way. Every mammal has an endocannabinoid system (many other animals have them too), which is a term that scientists have given to a loose complex of biochemical mechanisms that are affected by cannabis constituents or naturally-produced compounds that mimic phytocannabinoids. The most commonly reported and recorded feelings associated with CBD usage are relaxation, mental clarity, reduction of pain, and an overall sense of comfort and well-being. 7. What does CBD oil taste like? CBD-rich hemp oil often has a very plant-like taste like tree leaves. Some people find this taste unpleasant, so they use isolate CBD instead. This type of CBD extract consists of only cannabidiol molecules, which removes all the plant matter and other substances from the equation. Some CBD companies may use extraction processes that do not entirely remove chlorophyll from their hemp oil. Try a different brand before you throw your full-spectrum or broad-spectrum CBD away due to the taste. 8. What is the difference between hemp oil and CBD oil? “Hemp oil” usually refers to an extract of the seeds of the hemp plant that contains lots of fatty acids and essential nutrients but no cannabinoids. “CBD oil” is a flower extract of a Cannabis sativa strain that has been bred to be high in CBD but low in THC. 9. How much THC is in CBD oil? CBD oil must contain less than 0.03% THC. Broad-spectrum and isolate CBD products contain untraceable levels of THC, but the THC concentration in full-spectrum CBD oil may be as high as 0.03%. 10. How to consume CBD oil? If you’re wondering how to take THC-free CBD oil for pain or you’re on the hunt for the best way to ingest as many beneficial terpenes as possible, you’ll need to know that you can take CBD orally, inhale it, or apply it to your skin. Each administration method has its benefits, so you should try them all. 11. How does CBD oil make you feel? Most people who try CBD oil report that this natural substance has a calming and relaxing effect. Scientists have determined that cannabidiol is a potent antioxidant and anti-inflammatory substance, which means that it removes irritation in your hormonal, neurochemical, or intracellular systems to promote overall happiness and well-being. 12. What is MCT oil? Medium-chain triglyceride (MCT) oil is a distillation of coconut oil that incorporates only the most beneficial parts of this natural lipid. Often used as a base for tinctures in the natural health industry, MCT oil appears to improve your energy, help you lose weight, and lower your blood sugar. 14. What does CBG help with? Among other things, CBG is an antibacterial and neuroprotectant substance. It may help improve your overall well-being or assist in the treatment of psychiatric disorders such as depression, but we still don’t know a lot about the effects of cannabigerol. On the subject of CBD and depression, however, we have a lot of data to go on. Various clinical trials have shown that CBD can help with depression, and it appears that this cannabinoid’s interaction with the brain’s 5-HT1A receptors may be to blame. 15. What is CBG oil good for? Cannabigerol appears to help with depression, anxiety, and other forms of mental illness. This cannabinoid may also be effective against infections, inflammation, and oxidative stress. 16. Is CBD or CBG better? CBG shows just as much promise as CBD but in different categories. Both of these cannabinoids appear to help with psychiatric disorders, pain, and inflammation, but CBG is more targeted toward destroying invaders while CBD is more focused on regulating your body’s internal mechanisms. 17. Does CBG help anxiety? Some preliminary research shows that CBG may have promise as an anxiolytic agent, but we’ll need to study this subject in more detail before we can be sure. Check out this scientific paper for some more information on CBG, cannabinoids, and psychological health: Conclusion You’ll note that we’ve left plenty of links throughout this article. We encourage you to check out our sources for yourself if you still have any lingering questions about the CBD tinctures in this list. Doing your own research is always best, and we think you’ll find that cannabidiol is a fascinating subject that only becomes more rewarding the more you learn. Here are a few informative CBD studies if you’re looking for somewhere to start: As CBD gains popularity around the world, scientific research is staying apace and providing the answers we need to navigate the Cannabis sativa plant with the utmost accuracy and efficiency. We still are little more than bumbling children when it comes to our understanding of cannabinoids, but everyone has to start somewhere. Even in a future where we’ve unlocked the mysteries of CBD, CBG, CBN, and the other cannabinoids, we hope you’ll continue to rely on Best Dosage for the highest-quality CBD information on the planet. No matter how the hemp industry changes, you’ll still need to educate yourself thoroughly to protect your health and get the best deals. Check out our guides or read some in-depth reviews to deepen your cannabinoid knowledge. You may also like About the author Chad W The cannabis industry is an analytical chemist's dream. Hi, my name is Chad, and I'm the head chemist at bestdosage.com. My job here is to determine if CBD brands are honest. My recommendations sitewide are based on data. A brand must have visible lab reports, trusted customer reviews, and quality ingredients. Over the past 3 years, my team and I tested over 150 CBD brands. Explore bestdosage.com to find the handful we recommend.

Randa Jarrar Randa Jarrar (born 1978) is an American writer and translator. Her first novel, the coming-of-age story A Map of Home (2008), won her the Hopwood Award, and an Arab-American Book Award. Since then she has published short stories, essays, and the collection, Him, Me, Muhammad Ali (2016). She teaches creative writing in an MFA program at California State University at Fresno. In 2018, Jarrar was the subject of news coverage when she tweeted her opinion of Barbara Bush on social media following Bush's death. Biography Randa Jarrar was born in 1978 in Chicago to an Egyptian mother and a Palestinian father. She grew up in Kuwait and Egypt. After the Gulf War in 1991, she and her family returned to the United States, living in the New York area. Jarrar studied creative writing at Sarah Lawrence College, receiving an MA in Middle Eastern Studies from the University of Texas at Austin, and an MFA in Creative Writing from the University of Michigan. She is a creative writing professor at California State University. Of her writing, author and critic Mat Johnson has said “Randa Jarrar’s prose is bold and luscious and makes the darkly comic seem light." Writings Jarrar has written nonfiction and fiction, publishing her first short story in the prestigious Ploughshares literary journal in Fall 2004. Her short story, "You Are a 14-Year-Old Arab Chick Who First Moved to Texas" was the winner of the first Million Writers Award for online fiction. She has published two Lives columns in The New York Times Magazine, exploring her past as a single mother. Her first novel came out to critical acclaim in 2008. The Christian Science Monitor wrote: “Randa Jarrar takes all the sappy, beloved clichés about “where you hang your hat” and blows them to smithereens in her energizing, caustically comic debut novel, A Map of Home.” Her second book, a collection of stories, won A PEN Oakland Award, A Story Prize Spotlight Award, and an American Book Award. Of her stories, critic Lorraine Ali wrote "Jarrar is hardly the romantic. Love between couples here is often no more than sex, casual and flippant in the new world, or the unwanted consequence of an arranged marriage in the old world. When her characters are in relationships, it's often in the context of a parent or family they never really had a strong bond with in the first place. It might be the resentment-filled space between mothers and daughters, or the disappointment of fathers who are just far enough out of touch to remain a mystery. But when Jarrar's sense of humor tangles with her character's feelings of estrangement, the results are often charming and funny — in a bittersweet sort of way." Jarrar wrote an opinion piece called "Why I Can't Stand White Belly-Dancers", published in Salon in 2014. In this piece, Jarrar said she felt that white women who take part in the art of bellydance are engaging in cultural appropriation and "brown face." Her commentary was widely criticized; UCLA law professor Eugene Volokh stated, "Maybe telling people that they can’t work in some field because they have the wrong color or ancestry would be ... rats, I don’t know what to call it. If only there were an adjective that could be used to mean 'telling people that they mustn’t do something, because of their race or ethnic origin'". Atlantic writer Conor Friedersdorf offered: "[W]ith regional variations, something like Raqs Sharqi seems to have been known throughout the Mediterranean and certainly flourished in Egypt and the Eastern Mediterranean before the arrival of the Arabs in the 7th century". Novelist and comics writer G. Willow Wilson wrote in defense of Jarrar, "When you shimmy around a stage in a hip band and call yourself Aliya Selim and receive praise and encouragement, while the real Aliya Selims are shortening their names to Ally and wondering if their accent is too strong to land that job interview, if the boss will look askance at their headscarf, if the kids at school are going to make fun of their children, guess what: you are exercising considerable privilege." In response to these criticisms, Jarrar wrote a follow-up to her piece, titled "I Still Can't Stand White Bellydancers". Free Speech and First Amendment Activism On April 17, 2018, following the death of former first lady Barbara Bush, Jarrar described the former first lady as "a generous and smart and amazing racist who, along with her husband, raised a war criminal. Fuck outta here with your nice words", referring to Bush's son, former President George W. Bush. She said she felt compelled to speak “because I want people to remember history. I want people to know that our country’s actions don’t just disappear; they have real, negative consequences,” she said in an email. “If we want a better future, we have to confront our past.” Jarrar elaborated on her criticism of the former First Lady, citing the Bush family legacy in Iraq and Barbara's comments about Anita Hill (whose claims she doubted) and Katrina victims (she once said evacuees were “underprivileged anyway” and better off in the Astrodome). “The Bush family — including Barbara Bush — supported policies that harmed and destroyed the lives of millions,” she said. Jarrar was sharply criticized for her remarks, and demands were made that she be terminated from her job. In response to this, she tweeted that she will "never be fired" for her words, because she has tenure at California State University at Fresno. The ACLU of Northern California, PEN America, The Thomas Jefferson Center for Freedom of Expression, The Electronic Frontier Foundation, and others sent letters in support of Jarrar. Suicide prevention hotline Jarrar provided a telephone number on her Twitter account as if it was her own contact number, stating "If you really wanna reach me, here's my number ok?" The phone number that she provided was that of an emergency suicide/crisis hotline at Arizona State University. ASU said that they did not believe anyone who needed to get through was unable to. California State University at Fresno administration response California State University at Fresno president Joseph Castro responded to widespread public outrage, saying "Professor Jarrar’s expressed personal views and commentary are obviously contrary to the core values of our University, which include respect and empathy for individuals with divergent points of view". Fresno State confirmed that she was on leave from the university at the time the controversial comments were made. At a news conference, university provost Lynnette Zelezny confirmed that Jarrar's tenure would not protect her from termination, but did not specify whether termination was appropriate at the time. On April 25, 2018 News Metropolis reported that a Change.org petition to remove Jarrar from her position at Fresno State University had received over 90,000 signatures. Further Activism On July 27, 2018, Jarrar tweeted, "At some point, all of us in the literary community must DEMAND that white editors resign. It’s time to STEP DOWN and hand over the positions of power. We don’t have to wait for them to fuck up. The fact that they hold these positions is fuck up enough." This was in response to the publication in The Nation of a poem that made what some commentators perceived as racist attempts at black vernacular, which sparked a backlash, and which the editors later apologized for publishing. Personal life Jarrar has written about her experiences with domestic violence and reproductive coercion. She is openly queer. Awards 2004 Million Writers Award for best short story online 2007 Hopwood Award for Best Novel 2009 Arab American Book Award 2016 Story Prize Spotlight Award 2017 American Book Award 2017 PEN Oakland Josephine Miles Award Bibliography A Map of Home: A Novel Hardcover: Other Press 2008. . A Map of Home: A Novel Paperback: Penguin 2009. . Him, Me, Muhammad Ali Paperback: Sarabande Books 2016. Anthologies Words Without Borders: The World Through the Eyes of Writers, Alane Salierno Mason, Dedi Felman, Samantha Schnee (eds), Anchor Books, March 2007, Beirut39 Bloomsbury 2010 Watchlist: 32 short stories by persons of interest O/R Books 2016 Translation The Year Of The Revolutionary New Bread-making Machine by Hassan Daoud, 2007. , Published by Telegram, Paperback References External links Author's website Category:1978 births Category:Living people Category:21st-century American novelists Category:21st-century American short story writers Category:21st-century American women writers Category:21st-century translators Category:American Book Award winners Category:American people of Egyptian descent Category:American people of Palestinian descent Category:American translators Category:American women novelists Category:American women short story writers Category:American writers of Palestinian descent Category:Novelists from Illinois Category:Sarah Lawrence College alumni Category:University of Michigan alumni Category:Writers from Chicago Category:Queer writers Category:LGBT writers from the United States

Dr. Welch has served as a public health director in Virginia since 1976. Currently, she is the Director of the Chesapeake Health Department and the Interim Director of Western Tidewater Health District. Her major professional focus is utilizing data analysis as a persuasive motivator for individuals and communities to actively engage in healthier lifestyle habits. She received her B.S. at Lynchburg College, Degree in Medicine at Duke University and M.B.A. at Old Dominion University. Her Pediatric Residency and Masters of Health Administration were at the University of Colorado. She is board certified in both Pediatrics and Public Health/ Preventive Medicine; Dr. Welch is also a Retired Colonel in the U.S. Army Reserve. She serves on a variety of boards and committees developing community programs that enhance the health status and quality of life for our citizens. She has received numerous awards of distinction, such as the Lynchburg College Distinguished Alumni Award and Richard A. Thornton Award for Excellence. She is a member of the Delta Omega Society, Alpha Kappa Chapter (honor society for public health) and the Delta Kappa Gamma, Omega Chapter (key women educators). She received the Hampton Roads YWCA Women of Distinction Award for Medicine in 2012 and the Hampton Roads Chamber of Commerce Marian P. Whitehurst Women in Leadership Award in 2013. She was conferred the Honorary Degree of Doctorate in Science from Lynchburg College in 2014.

Standing at the Crossroads of Life’s Transitions It was 2am. After hours of packing and cleaning, my wife and I sat alone on the floor of our oldest daughter’s nursery, exhausted from a long day, preceded by an even longer week, and something happened that had rarely occurred in our 4-year old marriage – I began to weep. As I sat in the house we planned and had built, the room we lovingly painted and furnished just over a year prior and considered all that had occurred in three years in our West Virginia home, the excitement of a move to St. Louis was overshadowed by the strange grief of change. What had at one time been only an unknown future hope was now a package of past memories tenuously stored in our minds and hearts, as we set off on our next adventure. Three states and six homes later, I’m increasingly aware of the simultaneous grief and joy that lie in the crossroads of life’s many transitions. Share this: 5 Years – 5 Prayers of Thanksgiving for Calvary PCA When I first stepped into the pulpit at Calvary five-years ago this week, I could not possibly have imagined the joys, sorrows, challenges and triumphs that lie ahead. I could not have known that my family would live in three homes, that one of my children would be enrolled in three schools in as many years, or the extent to which we would be loved by a congregation seeking and praying for God’s renewing grace in their midst. I could not have known the names or faces that would come and go, making an indelible mark on our family and church by bringing joy through friendship and sorrow through loss. I could not have known who would make a midnight phone call, seeking comfort in the midst of crisis, or who would pull me aside after church to express their delight at the news of a new job, new life, new relationship, or new opportunity. I knew that pastoral ministry was a beautiful, difficult calling, but the details of what we would face together in the coming years were a mystery, just as what lies ahead for us in the future is unknown to all but God. Moving from the Buffet Line to the King’s Table: Savoring Mercy Where do you want to go to eat? This question in my home typically elicits one of three answers. If it’s not my children’s favorite fast food joint or a place serving breakfast all day, it’s almost always their favorite buffet – known affectionately in our home as the hog trough. Why? Because buffets are full of choices – unending choices, sure to please the pickiest eater. Of course, the enticing, all-you-can-eat dessert station, complete with cotton candy, might have something to do with their palate’s restaurant of choice. Our lives are often a lot like that buffet. Every week includes a series of choices – some that fill us well and others that feel good for a moment, but leave us empty, like the cotton candy in the dessert line. But in any case, we make the choice – from the places we shop, to the sports we play, to the videos we stream on the device we choose to carry into the restaurant we choose to patron, to the church activities in which we engage. Life’s options often feel like a line at the local buffet. In fact, for many of us, the Christian life has become a series of trips to the buffet line. Share this: Hurry Up and Wait! Nearly every morning, one of my children waits by the door. Backpack slung around their shoulders, left hand on the doorknob and eager anticipation written on their face. “Dad, can I go yet? I don’t want to miss the bus!” “Not yet,” is often my reply 5-10 minutes before it’s time to leave. “Isn’t there something you can do while you wait? This familiar exchange reminds me that unlike their father, this young child has mastered the art of being early, which means the opportunity to learn the art of “hurry up and wait!” Life, in many ways, is a series of waitings – filled with regular opportunities to hurry up and wait. We wait to graduate from school. We wait to hear back from a prospective employer about a new job. We wait for the day we can finally afford that house, that car, that vacation. We wait to meet the love of our life. We wait for the birth of a child. We wait by the bed of a sick or dying loved one. We wait for that diagnosis to discover the cause of our symptoms. We wait for reconciliation. We wait by the phone for a call that may never come. The question for us is not will we have to wait, but instead, what will we do in our waiting? Share this: What is the purpose of a gift? In recent days, I have been thinking about this question, as my children excitedly complete their Amazon wish lists with a number of items they hope to receive as gifts this year. As I scroll through their list, I’m not sure there is enough hours in a year to play all the video games they’ve saved, enough space to fit all the stuffed animals my daughter has marked, or enough bins to hold the variety of Legos they want to add to their collection. As I look around our home, interspersed with long-neglected toys, clothes that still include the tags, and books collecting dust, I cannot help but wonder – how long it will take for this year’s gifts to join them in the dustbin of obsolescence. Both giving and receiving gifts is a special experience, but the reality is, once the initial excitement wears off, gifts often fail to live up to the purpose for which they were given in the first place. This is a picture of what can happen in the local church. Share this: From Danger to Praise! “Warning! Serious Injuries and deaths have occurred beyond this point.” These are the “welcome” signs that awaited Bethany and me this week, as we hiked at Hanging Rock State Park together in celebration of 14 years of marriage. I both chuckled and cringed at these signs of warning, knowing they portend real potential danger, illustrated in the stories of real lives lost and real lives changed by a false step, or simply an unforeseen disaster. Yet, we forged ahead, along with countless other men, women and children, because at the peak of hanging rock is a glorious view that with sure footing leads to praise! “You’re almost there,” people would say to us on their way down. “It’s beautiful and amazing and so worth it!” They were right. As we stood at the peak of Hanging Rock, I thought, “I can’t imagine what would have been lost if I’d turned back at those signs.” Many of us, including myself, often view the journey of the Christian life as a hike to the top of Hanging Rock, particularly when it comes to the call in the life of every believer to evangelism, or sharing one’s faith. The journey is one full of signs that scream, “Warning! Serious injury and deaths have occurred beyond this point.” Sharing our faith can be quite an adventure, but we are often afraid of the dangers, the consequences of saying the wrong thing or of being rejected by our families, our neighbors, our friends, and that can feel like death. However, when we have seen a greater glory, we cannot help but respond in a praise that extends beyond ourselves and to those around us who are hiking the truly dangerous journey of life – one without God. In Psalm 40:2-3, the Psalmist testifies to what God has done for him, saying, “He drew me up from the pit of destruction, out of the miry bog and set my feet upon a rock, making my steps secure” (vs. 2). When Jesus saves, he does so out of our real danger and sets our feet upon the One who is our solid rock, enabling us to behold a greater glory. The response? Praise that extends to a world in danger. He continues, “He put a new song in my mouth, a song of praise to our God. Many will see and fear, and put their trust in the Lord” (vs. 3). Has the Lord Jesus taken you out of the pit of destruction, the miry bog and set your feet upon the rock? Has he put a new song of praise in your mouth? If so, may He enable your praise to extend beyond yourself to your family, your neighbors, your friends and co-workers, who are in need of the same. This Sunday at Calvary, is Neighbor Sunday, and we will be sharing the Good News of how Jesus has come to seek and save the lost, those who are truly in danger, that they might see a greater glory. Use this opportunity to invite your friends to join us, that they, too, might “put their trust in the Lord.” Share this: Whom Should I Invite? Whom should I invite? This was the question my wife Bethany had to answer leading into her 10th-birthday sleepover some years ago. As she pondered this question, she couldn’t fathom leaving any of the girls from her 4th-grade class out of the opportunity to gather for her party, so her parents graciously let her invite every girl from her class. I’m not sure they ever did that again, but Bethany had a great time, and all of the girls felt welcomed! We extend invitations for events that we think are important and to people whom we care about. In Luke 14:15-24, Jesus tells a parable about a man who sent out invitations for a great party. Invitations were extended to close friends, but they made excuses. They had better things to do and other commitments in their life. So, the servants were sent to the alley-ways and the overpasses of the city to extend invitations to the homeless, the blind, the crippled, and the lame. When that didn’t fill his party, he sent his servants to extend invitations to people outside the city – the highways and the hedges. Why? It was to be a great party, and a great party needs guests eager to dine at the table of the host. Do you believe that that the people you know and meet need to be invited to the great party to dine at the table of the great host, Jesus? When was the last time you invited someone to church? When was the last time you invited someone to meet your church family, or more importantly, to meet Jesus? After all, there is no greater party than the ones thrown by Jesus. On Sunday, August 6, Calvary will be hosting “Neighbor Sunday”, complete with a community party. This is a unique opportunity to invite our family members, co-workers, neighbors, and friends to dine at the table of the great host, Jesus, whose parties outshine all the rest. We will have great food, games, and bounce house and slides for the kids. This is not a gimmick, but an opportunity. It’s not a guilt trip but an invitation. It’s not high-pressure, but a friendly welcome to all who would come to meet Jesus and meet your church family. Let’s consider together whom we might invite, because we aren’t simply extending an invitation to a fun afternoon on a hot summer day, we’re inviting those we care about to come and dine at the table of King Jesus. Share this: Welcome to Calvary Thank you for visiting our website. We are a Gospel-centered community, seeking to lift high the name of Jesus, fall more in love with our Savior, and love our neighbors for His sake. We are a broken people being made whole by the love and grace of Jesus. We are excited that you have chosen to check out our website, and we would love the opportunity to get to know you.

IL-13 promotes the proliferation of rat pancreatic stellate cells through the suppression of NF-kappaB/TGF-beta1 pathway. In chronic pancreatitis, pancreatic stellate cells (PSCs) play a central role in tissue fibrogenesis. Transforming growth factor beta(1) (TGF-beta(1)) and the Th2 lymphokines such as interleukin (IL)-13 are major profibrogenic cytokines in many organs. Activated PSCs produce various inflammatory cytokines including TGF-beta(1). In this study, we investigated whether IL-13 affects pancreatic fibrogenesis by modulating the functions of PSCs. IL-13 promoted PSCs proliferation without activation through the suppression of autocrine TGF-beta(1). IL-13 enhanced Stat6 phosphorylation in PSCs but Stat6 was not involved in the suppression of TGF-beta(1). IL-13 inhibited the transcriptional activity of NF-kappaB, and the expression of mutant I-kappaB reproduced the suppression of autocrine TGF-beta(1) and promoted PSCs proliferation. Taken together, we demonstrated that IL-13 promotes PSCs proliferation through the suppression of the transcriptional activity of NF-kappaB, resulting in the decrease of autocrine TGF-beta(1). This finding provides an unequivocal evidence of IL-13 participation in pancreatic fibrosis, illustrating a new strategy for chronic pancreatitis.

UFC 239’s Thiago Santos Not Giving Away Game Plan, But Predicts He Will Be Champ July 6 UFC Light heavyweight title challenger Thiago Santos, scheduled to face Jon Jones at UFC 239 on July 6, is sounding confident ahead of the biggest fight of his career. Los Angeles, CA — Ahead of UFC 239, the key players throwing down at International Fight Week were out making the media rounds. That, of course, included light heavyweight title challenger Thiago Santos. The Brazilian has been on an impressive run since moving to 205lbs from middleweight — coincidentally the path the last title challenger, Anthony Smith, took. Smith, of course, lost to champ Jon Jones at UFC 235. Santos (21–6), who is currently on a four-fight win streak with three straight finishes, will look to avoid a similar fate to Smith, a man he beat back in his middleweight days. As to how he plans to do it, Santos told Cageside Press via translator on Monday that “July 6, we will see. I will do it. I will be champion.” Not giving away his game plan, then. As he enters the biggest fight of his career, Santos will ride in on a wave of newfound popularity. His aggressive style has caught on with fans, who are behind him more than ever before. “I love this,” he said of the situation. “I love to fight. The fight is my life. I want to do my best July 6, and give another show for the people, the public.” As for his aggressive style, it’s always been there. “I fight this kind [of fight]. Aggressive. I love it, to fight this kind [of fight].” And while Jon Jones has a tendency to shut down opponent’s game plans and beat them at their own style, expect Santos to be his usual, hard-hitting self. Asked if he’s been able to appreciate the scope of UFC 239, Santos said that there’s been “just a little stress.” “But I understand,” he added. “This [is] part of the show. I like it just fight [without distractions].” Santos is one of the few fighters remaining at 205lbs not already vanquished by champion Jones. Another is fellow Brazilian Johnny Walker. Asked about a match-up with the rising prospect, Thiago Santos said it’s a fight he would take. “It is a possibility. For me, no problem.” “Thank you so much for all, I would like that you show me [support on] July 6. I will [try] to do my best, and I will be champion July 6,” he said in a final message to fans.

Ask HN: In what ways do non-developers waste money not knowing how to code? - castig ====== mrfusion There are probably a lot of use cases for version control in the non programming world where people could benefit. I'm guessing people waste time copying and versioning files, and emailing updates back and forth, losing old changes, etc. ------ lsiebert Taking data in one system or format that is already in a computer, and manually performing one of, or a combination ofm transformations, filtering, aggregating, moving to another system, etc. Like I have gone through voter mailing data for a political candidate and filtered it, removed individuals who's addresses were outside the area or who hadn't voted in the last election, combined individuals with the same last name and the same address, then transformed it into a format suitable for address printing. All that is pretty easy to do with code. If you wanted to go through several thousand by hand though in an unsorted list, that would be a pain. Businesses will have similar requirements... like taking sales data that is already entered and formatting it for a report. Where non developers waste money is doing a repetitive time consuming rules based task on a computer without automating it. Ancedotally, non developers also tend to undervalue their and their employee's time. If you are paying an employee to do a task, if it's not absolutely essential or doesn't have a ROI that's higher then money you are paying the employee per hour to handle it, it's time to consider how important that task is. Finally, again ancedotally, non developers often won't invest in maintenance costs, and instead end up paying for time sensitive repairs or fixes, because they are easier to reason about. A coder is more likely to expect things to break, code to rot, etc. This can be in objects, services or in underpaying trained individuals so that their is a high turn over rate, where better pay might reduce that. Costco for example makes money despite it's higher pay because they have to train employees less. I think high pay also tends to reduce employee pilferage. ~~~ allendoerfer I would second that and add, that there are two groups of people: Members of the first group, generally a bit older and less tech savvy, see these problems as actual skilled work, which needs explanation. "Then you got to move your mouse over here and click, when this pops up you need to …" People from the second group realize, that they are doing dumb work and either do not care or realize, that a computer should do this. If they have seen a solution in the past, they use it. For example using Doodle instead of e-mail to schedule an event or using Dropbox or Google Docs to collaborate. They might even come up with a process, which removes the need for the manual work, for example by putting the data in the right format in the first place. What they often can not see is, that you could hire somebody to connect the systems let alone use some Unix piping magic on their own. Also they do not consider the implications of using a consumer solution in a business setting like security concerns, fragmentation etc. ------ mrfusion How about knowing what things are easy or hard [1]. I'm guessing a lot of business owners might dismiss good ideas as being too difficult/expensive when they're actually easy to program. [1] [http://xkcd.com/1425/](http://xkcd.com/1425/) ~~~ LarryMade2 I think the other bit is not realizing what is possible. Many non-developers only see as far as what paper accomplishments they have already created with their projects. Programmers, on the other hand, see further possibilities in data entry, management, and reporting, also methods to reduce the amount of work that could be done. Sometimes that also leads to that XKCD cartoon, where non-programmers think the computers can do anything, or think that an automated X is the way to go. Seasoned developers can offer valuable insight on what might or might not be a good idea and provide wisdom on why. ------ castig My first suggestion here is: having to pay your developer to make even the smallest changes (like a spelling mistake between a <h1> that if you knew the tiniest bit of code you could potentially fix by yourself).

https://zoeandmorgan.com/uk/kun-green-tourmaline/4145Kun Ring / Green Tourmalinehttps://zoeandmorgan.com/media/catalog/product/k/u/kun_ring_green_tourmaline-hero.jpg440GBPInStock/Shop/Shop/Fine Jewellery/Shop/Fine Jewellery/New In/Shop/Fine Jewellery/Rings/Shop/Fine Jewellery/Shop All/Shop/Rings/New In/Shop/Rings/Fine Rings/Shop/Rings/Shop All/You are the Sky/Shop/Gemstones PP<p>18k yellow gold set with crystal cut Green Tourmaline.</p> <p>Measurements: Length: 0.5cm, Width: 0.4 cm</p> </p></p> <p>These bespoke hand cut stones make each ring truly unique, with their own subtle shade of colour and naturally occurring inclusions.</p> <p></p> </p>If not in stock, the Kun ring will be specially made for you in 4-8 weeks. We can also make any size or gold colour on request</p> <p>The Kun ring features a Green Tourmaline crystal cut set horizontally in an 18k gold frame to perfectly compliment the charm of its geometrical shape. The pointed edge of the stone perfectly transitions into the sword edge band. </p> <p>This collection draws from the infinite power of mountains, that have existed since the beginning of time and undoubtedly will last forever. This inspired our own unique cut named 'Crystal'. This cut symbolises symmetrical peaks of the Himalayan mountains that, like the stones we use, have formed freely over thousands of years.</p>440https://zoeandmorgan.com/media/catalog/product/k/u/kun_-_pink_tourmaline_-_hover-1_1_1.jpghttps://zoeandmorgan.com/media/catalog/product/k/u/kun_ring_green_tourmaline-angle-2.jpghttps://zoeandmorgan.com/media/catalog/product/k/u/kun_ring_green_tourmaline-angle_copy.jpghttps://zoeandmorgan.com/media/catalog/product/k/u/kun_ring_green_tourmaline-profile.jpghttps://zoeandmorgan.com/media/catalog/product/k/u/kun_-_pink_tourmaline_-_story-1_1_1.jpg These bespoke hand cut stones make each ring truly unique, with their own subtle shade of colour and naturally occurring inclusions. If not in stock, the Kun ring will be specially made for you in 4-8 weeks. We can also make any size or gold colour on request Story The Kun ring features a Green Tourmaline crystal cut set horizontally in an 18k gold frame to perfectly compliment the charm of its geometrical shape. The pointed edge of the stone perfectly transitions into the sword edge band. This collection draws from the infinite power of mountains, that have existed since the beginning of time and undoubtedly will last forever. This inspired our own unique cut named 'Crystal'. This cut symbolises symmetrical peaks of the Himalayan mountains that, like the stones we use, have formed freely over thousands of years. Shipping Info FREE Standard Shipping on all UK Orders over £100, Worldwide over £150 Hints & tips Product care Zoe and Morgan jewellery is handmade with care and we know you’re going to want to keep it looking great. So here are some tips to help you do just that. Using your handbag as storage? Storing your jewellery properly is important too. To avoid damage, store your jewellery separate from each other to minimise scratching and tangling. All of our Zoe and Morgan pieces come in their own beautiful packaging so you can keep them safe in that. This site uses cookies and other tracking technologies to assist with navigation and your ability to provide feedback, analyse your use of our products and services, assist with our promotional and marketing efforts, and provide content from third parties. Read our Cookie Policy here

Malechówko Malechówko is a village in the administrative district of Gmina Malechowo, within Sławno County, West Pomeranian Voivodeship, in north-western Poland. It lies approximately east of Malechowo, south-west of Sławno, and north-east of the regional capital Szczecin. Before 1945 the area was part of Germany. For the history of the region, see History of Pomerania. The village has a population of 180. References Category:Villages in Sławno County

Incontinence associated with sexual activity encompasses several forms, including orgasm-associated incontinence and climacturia, and can involve incontinence at different points along the sexual spectrum, for example, at penetration, during intercourse, or at climax. The condition can be associated with disorders including overactive bladder (OAB) and neurogenic detrusor overactivity (NDO), and has received increasing attention in the medical literature. Additionally, it can significantly impact sexual satisfaction among both sufferers (both men and women) and their partners. Some male sufferers develop incontinence associated with sexual activity following prostate surgery such as radical prostatectomy (RP; removal of the prostate) or brachytherapy. Prostate cancer is the second most commonly diagnosed cancer in males in the United States, accounting for approximately 33% of new cancer cases, and is the third leading cause of cancer-related death in men. Several surgery-related complications are associated with RP, including urinary incontinence and sexual dysfunction. The nature and degree of sexual dysfunction can vary widely following RP, including erectile dysfunction, loss of libido, orgasm alterations (anorgasmia, decreased orgasmic intensity, dysorgasmia and orgasm-associated incontinence) and decreased sexual satisfaction. Abouassaly and coworkers (Abouassaly R, Lane B. Lakin M, Klein E, Gill I. Ejaculatory incontinence after radical prostatectomy: a review of 26 cases. Program and abstracts of the Sexual Medicine Society of North America Fall Meeting; Nov. 17-20, 2005; New York, N.Y. Abstract 1) reported their findings with men who had climacturia after having undergone radical prostatectomy. Of an estimated 220 patients evaluated, 26 men experienced urine leak almost exclusively at the time of orgasm. The average age of the patients was 62 years. Patients experienced anywhere from 3 to 120 mL of urine leak (by patient self-report) at the time of orgasm. The authors felt that the occurrence of ejaculatory incontinence is high enough to be considered as part of the routine post-prostatectomy evaluation. In a 2006 study of 42 men, two years following RP, 68% reported experiencing climacturia. Forty-eight percent felt that it was a significant bother to them. In a 2007 study of 475 patients, 20% reported incontinence associated with sexual activity following radical pelvic surgery. Men were more likely to experience it in the first twelve months following surgery than later. Common methods of dealing with incontinence associated with sexual activity include emptying the bladder before sex and wearing a condom during sex. Thus, improved treatment methods are sought. Men can also display a form of stress incontinence after RP wherein incontinence can occur during intercourse and continue through climax. In women, incontinence associated with sexual activity may be associated with detrusor overactivity linked to overactive bladder (OAB), or to neurogenic detrusor overactivity (NDO)—one study has found that orgasm can produce an uninhibited detrusor contraction. It has also been associated with female ejaculation in the absence of OAB (Cartwright, 2007) or other urodynamic abnormality. Additionally, some researchers speculate that incontinence associated with sexual activity can be linked with stress or sphincter incontinence. This incontinence can, as in the case with males, occur at any point from before penetration to after climax. Coital Incontinence (CI) is urinary leakage that occurs during either penetration or orgasm and can occur with a sexual partner or with masturbation. It has been reported to occur in 10% to 24% of sexually active women with pelvic floor disorders, yet CI may still be an underreported problem since sexual or urinary dysfunction may not be often or readily discussed due to patient or physician embarrassment. Unfortunately, CI can have a disturbing impact on Quality of Life (QoL) and sexuality. Women rarely refer to it spontaneously, with only 3% of women self-reporting sexual disorders including CI; even with direct questioning, only 20% will admit to it. The impact on QoL from CI is significant. Sexually active women with CI reported a worse QoL than those without it. Coital incontinence is divided into 2 subtypes based on when urinary leakage occurs: incontinence with penetration and incontinence with orgasm. Each has different pathophysiologic causes. In the original series of 79 patients with CI, two-thirds experienced CI with penetration, while one-third did so with orgasm. After uro-dynamic testing, CI with penetration was strongly correlated to stress urinary incontinence, while CI from orgasm was strongly correlated with detrusor overactivity. A larger, more recent series of 132 women confirms the findings that the majority of women, 63%, experience CI from penetration, while 37% do so from orgasm. Botulinum toxin type A is the most lethal natural biological agent known to man. About 50 picograms of botulinum toxin type A (available from Allergan, Inc., of Irvine, Calif. under the tradename BOTOX®) is an LD50 in mice. One unit (U) of botulinum toxin is defined as the LD50 upon intraperitoneal injection into female Swiss Webster mice weighing 18-20 grams each. Seven immunologically distinct botulinum neurotoxins have been characterized, these being respectively botulinum neurotoxin serotypes A, B, C1, D, E, F and G, each of which is distinguished by neutralization with type-specific antibodies. The different serotypes of botulinum toxin vary in the animal species that they affect and in the severity and duration of the paralysis they evoke. The botulinum toxins apparently bind with high affinity to cholinergic motor neurons, are translocated into the neuron and block the release of acetylcholine. Botulinum toxins have been used in clinical settings for the treatment of neuromuscular disorders characterized by hyperactive skeletal muscles. Botulinum toxin type A has been approved by the U.S. Food and Drug Administration for the treatment of blepharospasm, strabismus, hemifacial spasm, cervical dystonia, and migraine headaches. Botulinum toxin type B has also been approved by the FDA for the treatment of cervical dystonia. Clinical effects of peripheral intramuscular botulinum toxin type A are usually seen within one week of injection. The typical duration of symptomatic relief from a single intramuscular injection of botulinum toxin type A averages about three months. It has been reported that botulinum toxin type A has been used in clinical settings as follows: about 75-125 U (U) of BOTOX® per intramuscular injection (multiple muscles) to treat cervical dystonia; 5-10 U of BOTOX® per intramuscular injection to treat glabellar lines (brow furrows) (5 U injected intramuscularly into the procerus muscle and 10 U injected intramuscularly into each corrugator supercilii muscle); about 30-80 U of BOTOX® to treat constipation by intrasphincter injection of the puborectalis muscle; about 1-5 U per muscle of intramuscularly injected BOTOX® to treat blepharospasm by injecting the lateral pre-tarsal orbicularis oculi muscle of the upper lid and the lateral pre-tarsal orbicularis oculi of the lower lid. to treat strabismus, extraocular muscles have been injected intramuscularly with between about 1-5 U of BOTOX®, the amount injected varying based upon both the size of the muscle to be injected and the extent of muscle paralysis desired (i.e. the amount of diopter correction desired). to treat upper limb spasticity following stroke by intramuscular injections of BOTOX® into five different upper limb flexor muscles, as follows: (a) flexor digitorum profundus: 7.5 U to 30 U (b) flexor digitorum sublimis: 7.5 U to 30 U (c) flexor carpi ulnaris: 10 U to 40 U (d) flexor carpi radialis: 15 U to 60 U (e) biceps brachii: 50 U to 200 U. Each of the five indicated muscles has been injected at the same treatment session, so that the patient receives from 90 U to 360 U of upper limb flexor muscle BOTOX® by intramuscular injection at each treatment session. To treat migraine, pericranial (symmetrically into glabellar, frontalis and temporalis muscles) injection of BOTOX® has showed significant benefit as a prophylactic treatment compared to vehicle as measured by decreased measures of migraine frequency, maximal severity, associated vomiting and acute medication use over the three month period following the 25 U injection. Additionally, intramuscular botulinum toxin has been used in the treatment of tremor in patients with Parkinson's disease, although it has been reported that results have not been impressive. Marjama-Jyons, J., et al., Tremor-Predominant Parkinson's Disease, Drugs & Aging 16(4); 273-278:2000. In addition to having pharmacologic actions at the peripheral location, botulinum toxins may also have inhibitory effects in the central nervous system. Work by Weigand et al., Naunyn-Schmiedeberg's Arch. Pharmacol. 1976; 292, 161-165, and Habermann, Naunyn-Schmiedeberg's Arch. Pharmacol. 1974; 281, 47-56 showed that botulinum toxin is able to ascend to the spinal area by retrograde transport. A Botulinum toxin has also been proposed for the treatment of rhinorrhea, hyperhidrosis and other disorders mediated by the autonomic nervous system (U.S. Pat. No. 5,766,605), tension headache, (U.S. Pat. No. 6,458,365), migraine headache (U.S. Pat. No. 5,714,468), post-operative pain and visceral pain (U.S. Pat. No. 6,464,986), pain treatment by intraspinal toxin administration (U.S. Pat. No. 6,113,915), Parkinson's disease and other diseases with a motor disorder component, by intracranial toxin administration (U.S. Pat. No. 6,306,403), hair growth and hair retention (U.S. Pat. No. 6,299,893), psoriasis and dermatitis (U.S. Pat. No. 5,670,484), injured muscles (U.S. Pat. No. 6,423,319, various cancers (U.S. Pat. No. 6,139,845), pancreatic disorders (U.S. Pat. No. 6,143,306), smooth muscle disorders (U.S. Pat. No. 5,437,291, including injection of a botulinum toxin into the upper and lower esophageal, pyloric and anal sphincters)), prostate disorders (U.S. Pat. No. 6,365,164), inflammation, arthritis and gout (U.S. Pat. No. 6,063,768), juvenile cerebral palsy (U.S. Pat. No. 6,395,277), inner ear disorders (U.S. Pat. No. 6,265,379), thyroid disorders (U.S. Pat. No. 6,358,513), parathyroid disorders (U.S. Pat. No. 6,328,977). Additionally, controlled release toxin implants are known (see e.g. U.S. Pat. Nos. 6,306,423 and 6,312,708). Adrenergic nerves release norepinephrine as the neurotransmitter for the sympathetic nervous system. The sympathetic system activates and prepares the body for vigorous muscular activity, stress, and emergencies. Adrenergic drugs stimulate the adrenergic nerves directly by mimicking the action of norepinephrine or indirectly by stimulating the release of norepinephrine. An adrenergic agent is a drug, or other substance, which has effects similar to, or the same as, epinephrine (adrenaline). Thus, it is a kind of sympathomimetic agent. Alternatively, it may refer to something which is susceptible to epinephrine, or similar substances, such as a biological receptor (specifically, the adrenergic receptors). Adrenergic agonists stimulate a response from the adrenergic receptors. The five categories of adrenergic receptors are: α1, α2, β1, β2, and β3, and agonists vary in specificity between these receptors, and may be classified respectively. However, there are also other mechanisms of adrenergic agonism. Epinephrine and norepinephrine are endogenous and broad-spectrum. More selective agonists are more useful in pharmacology. A great number of drugs are available which can affect adrenergic receptors. Each drug has its own receptor specificity giving it a unique pharmacological effect. Other drugs affect the uptake and storage mechanisms of adrenergic catecholamines, prolonging their action. Agents that work with and activate the adrenergic receptors include alpha- and beta-adrenergic agonists. Agents that increase neurotransmission in endogenous chemicals such as epinephrine and norepinephrine include amphetamines, cocaine, methylenedioxymethamphetamine (MDMA), tyramine, nicotine, caffeine, and methylphenidate. Agents that exhibit aspects of both of these modes include ephedrine and pseudoephedrine. Adequate treatments for incontinence associated with sexual activity are currently lacking, therefore long-lasting, minimally invasive methods of treatment are desirable.

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1101110101001010 In base 15, what is 7b77 - -8? 7b80 In base 16, what is -101 - -8a? -77 In base 14, what is -394cc + -20? -3950c In base 16, what is efd46 + 2? efd48 In base 2, what is -100001 + 10001000010110101? 10001000010010100 In base 5, what is 10 + 100423011? 100423021 In base 13, what is -4974 - -60? -4914 In base 7, what is -30004 + -5? -30012 In base 4, what is -11 - -3120112? 3120101 In base 6, what is -2 + -25454404? -25454410 In base 6, what is -1543 - -4232? 2245 In base 7, what is -342 + -13013? -13355 In base 6, what is 2 - 304? -302 In base 6, what is 1310410 + -2? 1310404 In base 5, what is 32441 - 414? 32022 In base 7, what is -25464 + -1262? -30056 In base 7, what is 10 - 5454? -5444 In base 10, what is -5 - -54? 49 In base 5, what is 101244412 + -2? 101244410 In base 6, what is 11020 - 1221? 5355 In base 8, what is 1 + -1012024? -1012023 In base 11, what is 79a7 + -21? 7986 In base 5, what is 1332130 - 10? 1332120 In base 2, what is 10000 + -1011001101? -1010111101 In base 7, what is 3140 + -210? 2630 In base 9, what is -63 - -165? 102 In base 10, what is 0 - 124077? -124077 In base 12, what is 803 - -33? 836 In base 2, what is -1 - -1010100100000110? 1010100100000101 In base 16, what is 58 - 77? -1f In base 7, what is 3541 - -13003? 16544 In base 16, what is -218 - 84? -29c In base 10, what is -134 + 249? 115 In base 9, what is -2200 + 2825? 625 In base 11, what is -42 - a15? -a57 In base 3, what is -22 + 2020020020? 2020012221 In base 12, what is -8a48 - -4? -8a44 In base 3, what is 11100011 + 10220? 11111001 In base 11, what is -433 - -630? 1a8 In base 5, what is -140432 + 21? -140411 In base 12, what is -29780 - 6? -29786 In base 16, what is 56a + a3? 60d In base 4, what is -2130013 + -2? -2130021 In base 14, what is 3 + -85b8? -85b5 In base 2, what is 11100 - 100110010000001? -100110001100101 In base 10, what is -5 + 16870? 16865 In base 13, what is -a11 + -77? -a88 In base 8, what is 5 + -504556? -504551 In base 5, what is -11 + 1310321? 1310310 In base 7, what is 1 + 1013355? 1013356 In base 15, what is -c63 + -1e1? -e54 In base 8, what is 1125 + -1264? -137 In base 15, what is -9 - 58c? -596 In base 6, what is -14150 - -551? -13155 In base 3, what is 1101000012 + 0? 1101000012 In base 15, what is a10 - -38b? d9b In base 9, what is 7720 + -2? 7717 In base 3, what is 202 + 12210110? 12211012 In base 8, what is -216 + 2000? 1562 In base 2, what is 111110110 + 10110010? 1010101000 In base 6, what is -2352 - -25? -2323 In base 8, what is -317755 + -5? -317762 In base 15, what is -12 + 2735? 2723 In base 14, what is -5 + -156467? -15646c In base 6, what is 11134544 + 4? 11134552 In base 8, what is -5 - 54105? -54112 In base 10, what is 92771 + 10? 92781 In base 8, what is 1006565 + -3? 1006562 In base 11, what is -3 + -5493? -5496 In base 14, what is 605 - -46? 64b In base 12, what is -3283 + -3? -3286 In base 4, what is 20 - -12232002? 12232022 In base 12, what is -173 + 53? -120 In base 13, what is -4576 - 3? -4579 In base 5, what is -12 - -231412? 231400 In base 11, what is -4 - -588a9? 588a5 In base 2, what is -1100001010010 - 0? -1100001010010 In base 16, what is 5 + -57d? -578 In base 4, what is -120010 - -12? -113332 In base 10, what is 747 + -28? 719 In base 5, what is -3022 - 2230? -10302 In base 12, what is -131a55b - -3? -131a558 In base 6, what is 4 - 222552? -222544 In base 8, what is 616516 + -12? 616504 In base 9, what is 16 - 276611? -276584 In base 7, what is -5 - 56150? -56155 In base 7, what is 6 - -33632? 33641 In base 7, what is 25332 - -1? 25333 In base 13, what is a753 + 4? a757 In base 5, what is -10 - 22014002? -22014012 In base 9, what is -5 + 3152? 3146 In base 5, what is -10 - -114130433? 114130423 In base 11, what is -10 - -312574? 312564 In base 14, what is -277 + -26d? -506 In base 15, what is -c5 + -118? -1dd In base 4, what is -2 - 1020030031? -1020030033 In base 3, what is -11 + 10001? 2220 In base 14, what is -5 - 284b? -2852 In base 9, what is 2012 - 7? 2004 In base 16, what is -d1 - 729? -7fa In base 2, what is 11101101110100000000001 - 100? 11101101110011111111101 In base 10, what is -1220 + 23? -1197 In base 9, what is -3051 + 2281? -660 In base 15, what is 3 + -1a741? -1a73d In base 8, what is 17 + -263115? -263076 In base 5, what is 1243 + 40204? 42002 In base 14, what is 8cc + 34? 922 In base 10, what is -5 - -12255? 12250 In base 14, what is 18a - 31? 159 In base 4, what is 1111023231 + -1? 1111023230 In base 2, what is 101011001101010 - 110? 101011001100100 In base 12, what is -8a0 + -3? -8a3 In base 2, what is 111 - -1111011011000? 1111011011111 In base 11, what is 3 - -8a462? 8a465 In base 13, what is -4 + c317? c313 In base 16, what is -43 + 3188? 3145 In base 16, what is -1165c + -1? -1165d In base 13, what is -c0256a - -2? -c02568 In base 2, what is -11011111011111 - -1000? -11011111010111 In base 16, what is 12 - d3a? -d28 In base 9, what is 1244 - -13? 1257 In base 8, what is 16 - -3044? 3062 In base 9, what is 3418068 + -5? 3418063 In base 5, what is -10 - 1201012? -1201022 In base 10, what is 8923497 + 1? 8923498 In base 16, what is 18 - -13c? 154 In base 5, what is 13120233 + -1? 13120232 In base 2, what is 1111101111111100100 + 11? 1111101111111100111 In base 7, what is 5 - -124633? 124641 In base 11, what is -53a - 24? -563 In base 10, what is 103780 + -1? 103779 In base 14, what is -5 + -79658? -7965d In base 5, what is 11442 + 13004? 30001 In base 6, what is -2523040 - -1? -2523035 In base 9, what is 2 + 13050? 13052 In base 8, what is -3 + 272750? 272745 In base 4, what is -1330 + -2132? -10122 In base 16, what is -33 + -1515? -1548 In base 4, what is 10 + -12220? -12210 In base 3, what is -1 + 22201020? 22201012 In base 4, what is 223 + 210330100? 210330323 In base 8, what is -4 + 2147403? 2147377 In base 16, what is 10b9 + -8f? 102a In base 13, what is a35 + -2b? a07 In base 12, what is 53940 - 31? 5390b In base 6, what is -5 - -10204? 10155 In base 8, what is -42331 + 6? -42323 In base 13, what is 101c1 + -4? 101ba In base 10, what is 7 + 366378? 366385 In base 16, what is 0 - e01f? -e01f In base 12, what is -3 + -2b507? -2b50a In base 14, what is -23644d + 1? -23644c In base 3, what is -1 + 1221202110200? 1221202110122 In base 2, what is -11 + 10011001111111111? 10011001111111100 In base 4, what is 22120210 + 23? 22120233 In base 14, what is 3d + -35? 8 In base 3, what is -2111201120 + 101? -2111201012 In base 2, what is 1 - -10001110011001? 10001110011010 In base 14, what is 2b0 - -144? 414 In base 7, what is 0 - 2650215? -2650215 In base 16, what is 40e4 + -4? 40e0 In base 4, what is -2102 - -103312? 101210 In base 13, what is -478a - 1? -478b In base 7, what is 545 - 662? -114 In base 11, what is 4a9a + a6? 5095 In base 13, what is -5 + -1069? -1071 In base 15, what is 3 + -6e48? -6e45 In base 14, what is 5c01 + -155? 5a8a In base 16, what is 7 + 24e40? 24e47 In base 16, what is 13e + -a3d? -8ff In base 11, what is 0 + -13a65? -13a65 In base 7, what is -2 + 2655435? 2655433 In base 15, what is 16 + 1b7a? 1b91 In base 3, what is 112101112021 - 0? 112101112021 In base 10, what is -6089 - -2? -6087 In base 10, what is -552 + 103? -449 In base 13, what is -284

Filed 11/19/15; pub. order 12/18/15 (see end of opn.) IN THE COURT OF APPEAL OF THE STATE OF CALIFORNIA SIXTH APPELLATE DISTRICT JONNIE ROE, a Minor, etc., et al., H042060 (San Benito County Petitioners, Super. Ct. No. CU-14-00017) v. SUPERIOR COURT OF SAN BENITO COUNTY, Respondent; HOLLISTER SCHOOL DISTRICT et al., Real Parties in Interest. Petitioners Jonnie Roe, a minor, (Jonnie), Jane Roe (Jane), and John Roe (John) assert, among other claims, that the superior court had no authority to order interviews of Jane and John, Jonnie’s parents, collateral to the mental examination of Jonnie and, in issuing such an order, the court exceeded its authority under Code of Civil Procedure section 2032.020.1 As explained below, we agree. I Background Real parties in interest (defendants) are the named defendants in the underlying civil action for damages (CU-14-00017) brought by Jonnie (by and through his guardian 1 All further statutory references are to the Code of Civil Procedure unless otherwise specified. ad litem, John) and Jane. The complaint alleges that Jonnie, while a kindergartner at an elementary school in the Hollister School District, was sexually molested at school by another male kindergartener on two occasions.2 The named defendants are Hollister School District (School District) and Bill Sauchau, who is alleged to be the elementary school’s principal; Kathy Hudson, who is alleged to be a teacher at the school; and a person with the surname of Zamora (first name unknown), who is alleged to be, “a playground monitor and/or yard supervisor” at the school. School District brought a motion in respondent San Benito County Superior Court (superior court) for an order compelling Jonnie to submit to an independent mental examination, which would include personal interviews of Jonnie and his parents by Dr. Anlee Kuo, a psychiatrist, and psychological testing of Jonnie by Dr. Sarah Hall, a psychologist. The superior court granted the motion on March 2, 2015. Petitioners sought a writ of mandate “compelling the respondent court to vacate its order of March 2, 2015 insofar as it compels John and Jane Roe to submit to interviews by the defense forensic psychiatrist, refuses to permit John, as guardian, to attend Jonnie’s interview, and refuses to order defendants to deliver the written tests administered to Jonnie and their results and to enter a new order without requiring such interviews and requiring defendants to deliver the tests and the results . . . .” On March 12, 2015, we issued a limited order staying the superior court’s March 2, 2015 order only insofar as it compels the interview of Jonnie’s parents, until further order of this court. We subsequently ordered the respondent superior court “to 2 The first cause of action for negligence, the second cause of action for negligence per se-failure to report known and/or suspected child abuse, and the third cause of action for negligent supervision were asserted by only Jonnie (by and through his guardian ad litem); the fourth cause of action for intentional infliction of emotional distress and the fifth cause of action for negligent infliction of emotional distress were asserted by both Jonnie (by and through his guardian ad litem) and his mother, Jane; and the sixth cause of action for concealment was asserted by only Jane. 2 show cause . . . why a peremptory writ should not issue as requested in the petition for writ of mandate.” II Discussion A. Parental Interviews Collateral to Mental Examination of Minor 1. Facts The superior court’s March 2, 2015 order sets forth the scope and length of the mental examination of Jonnie by Drs. Kuo and Hall. The order authorizes Dr. Hall to administer four specific psychological tests to Jonnie. It prohibits third-party observers during those examinations but requires the examinations to be audiotaped. The March 2, 2015 order further compels Jonnie’s parents to submit to “collateral interviews” as part of the mental examination of their son. The order limits the scope of those interviews to parental “observations about the mental physical symptoms that Jonnie Roe has expressly put into controversy . . . .” It also places the following limitations on those interviews: “Any questioning must be directly relevant, and a nexus must exist to the information sought and the claimed symptoms so as to protect Jonnie Roe’s, Jane Roe’s, and John Roe’s privacy. Dr. Kuo may not inquire about Jane Roe’s or John Roe’s mental state. [¶] Dr. Kuo’s interview shall not be unnecessarily repetitive of questions asked in deposition proceedings and other written discovery to date.” 2. Section 2032.020 Section 2032.020, subdivision (a), sets forth the three categories of persons subject to mental examinations: “Any party may obtain discovery, subject to the restrictions set forth in Chapter 5 (commencing with Section 2019.010), by means of a physical or mental examination of (1) a party to the action, (2) an agent of any party, or (3) a natural person in the custody or under the legal control of a party, in any action in which the mental or physical condition (including the blood group) of that party or other person is in controversy in the action.” There is no dispute that Jonnie’s mental state is in 3 controversy. (See Vinson v. Superior Court (1987) 43 Cal.3d 833, 839 [“a party who chooses to allege that he has mental and emotional difficulties can hardly deny his mental state is in controversy”].) The mental examination must be “performed only by a licensed physician, or by a licensed clinical psychologist who holds a doctoral degree in psychology and has had at least five years of postgraduate experience in the diagnosis of emotional and mental disorders.” (§ 2032.020, subd. (c).) Defendants argue that a collateral interview of a minor’s parents is permissible as part of an independent mental examination of the minor and is required by the professional standard of care in psychiatry. They suggest that, since the examiner must be a licensed physician or psychologist, the California Legislature “must expect a minimum level of competence from the physician or psychologist and similarly must require the physician or psychologist to practice within the standard of care applicable to their [sic] licensure or specialty.” They assert that “[a] collateral interview is therefore at least implicitly authorized by the Code of Civil Procedure.” This case presents a straightforward question of statutory interpretation. “ ‘As in any case involving statutory interpretation, our fundamental task here is to determine the Legislature’s intent so as to effectuate the law’s purpose.’ [Citation.] ‘We begin with the plain language of the statute, affording the words of the provision their ordinary and usual meaning and viewing them in their statutory context, because the language employed in the Legislature’s enactment generally is the most reliable indicator of legislative intent.’ [Citations.] The plain meaning controls if there is no ambiguity in the statutory language. [Citation.]” (People v. Cornett (2012) 53 Cal.4th 1261, 1265.) “A statutory provision is ambiguous if it is susceptible of two reasonable interpretations. (Hoechst Celanese Corp. v. Franchise Tax Bd. (2001) 25 Cal.4th 508, 519.)” (People v. Dieck (2009) 46 Cal.4th 934, 940.) “[I]f the language allows more than one reasonable construction, we may look to such aids as the legislative history of the measure and maxims of statutory construction. In cases of uncertain meaning, we 4 may also consider the consequences of a particular interpretation, including its impact on public policy. [Citations.]” (Wells v. One2One Learning Foundation (2006) 39 Cal.4th 1164, 1190.) “Only when the language of a statute is susceptible [of] more than one reasonable construction is it appropriate to turn to extrinsic aids, including the legislative history of the measure, to ascertain its meaning. [Citation.]” (Diamond Multimedia Systems, Inc. v. Superior Court (1999) 19 Cal.4th 1036, 1055.) “When statutory language is clear and unambiguous, there is no need for construction and courts should not indulge in it. [Citations.]” (People v. Overstreet (1986) 42 Cal.3d 891, 895.) “ ‘[A]n intention to legislate by implication is not to be presumed.’ [Citations.]” (In re Christian S. (1994) 7 Cal.4th 768, 776.) “A court may not, ‘under the guise of construction, rewrite the law or give the words an effect different from the plain and direct import of the terms used.’ (California Fed. Savings & Loan Assn. v. City of Los Angeles (1995) 11 Cal.4th 342, 349.)” (DiCampli-Mintz v. County of Santa Clara (2012) 55 Cal.4th 983, 992.) “ ‘Where the words of the statute are clear, we may not add to or alter them to accomplish a purpose that does not appear on the face of the statute or from its legislative history.’ [Citation.]” (In re Jennings (2004) 34 Cal.4th 254, 265.) “[W]e are mindful of this court’s limited role in the process of interpreting enactments from the political branches of our state government. In interpreting statutes, we follow the Legislature’s intent, as exhibited by the plain meaning of the actual words of the law, ‘ “ ‘whatever may be thought of the wisdom, expediency, or policy of the act.’ ” ’ [Citation.] ‘[A]s [the Supreme Court] has often recognized, the judicial role in a democratic society is fundamentally to interpret laws, not to write them. The latter power belongs primarily to the people and the political branches of government . . . .’ (Kopp v. Fair Pol. Practices Com. (1995) 11 Cal.4th 607, 675 (conc. opn. by Werdegar, J.).) It cannot be too often repeated that due respect for the political branches of our government requires us to interpret the laws in accordance with the expressed intention of the Legislature. ‘This court has no power to rewrite the statute so as to make it conform to a 5 presumed intention which is not expressed.’ [Citations.]” (California Teachers Assn. v. Governing Bd. of Rialto Unified School Dist. (1997) 14 Cal.4th 627, 632-633.) Section 2032.020 establishes only three categories of persons subject to mental examination. “The three statutory categories of persons who may be examined are exclusive because, after the adoption of the 1957 statutes dealing with civil discovery, our courts lack the power to order discovery beyond that permitted by the statutes. [Citations.]” (Cruz v. Superior Court (2004) 121 Cal.App.4th 646, 650 (Cruz) [former § 2032, subd. (a) (now § 2032.020, subd. (a))]; see Reuter v. Superior Court (1979) 93 Cal.App.3d 332, 343 (Reuter) [stating with respect to former § 2032, “[t]he persons covered by the statute are clearly specified”].) While Jane is a plaintiff in the underlying action, the motion sought to compel a mental examination of only Jonnie. Jane was not a “party” for purposes of that motion. John is not a “party” for the purposes of that motion either; he is not even a “party” to the underlying action. The “guardian ad litem is not a party to the action; instead, he or she is a representative of record of a party who lacks capacity to sue. (J.W. v. Superior Court (1993) 17 Cal.App.4th 958, 964.)” (Safai v. Safai (2008) 164 Cal.App.4th 233, 245; see § 372.) There is no argument that either parent is an agent of Jonnie or in the custody or under the legal control of Jonnie within the meaning of section 2030.020, subdivision (a). Nothing in section 2032.020 contemplates a “collateral interview” of a minor’s parents as part of a mental examination of a party who is a minor. In Reuter, a mother and her son were plaintiffs in a lawsuit that arose “from an automobile accident in which the son was injured and his father killed.” (Reuter, supra, 93 Cal.App.3d at pp. 334-335.) The appellate court held that former section 2032 did not authorize psychological testing of plaintiff mother collateral to the psychiatric examination of her son where mother’s mental condition was not in controversy even though the psychiatrist stated that testing of the mother was necessary to complete his examination of the son. (Reuter, supra, at pp. 340-345.) The court stated: “[M]any different parties may be the main influence in 6 any particular persons’ [sic] mental state—his parent, his priest, his teacher, his [L]ittle [L]eague coach. [Former] Section 2032 does not create a power broad enough to allow the court to order all these parties to submit to a battery of tests to determine the extent of their influence on a child’s mental state merely on a psychiatrist’s declaration that he needs them.” (Id. at p. 342.) While interviewing the parents of a child to gain background and information about that child may be a sound professional practice from a psychiatrist’s viewpoint, section 2030.020’s plain language does not empower a trial court to make a discovery order requiring such parental interview as part of a mental examination of a party who is a minor.3 Such authority must come from the Legislature. B. Mental Examination of Jonnie Ordered for March 16, 2015 The plaintiffs in the underlying action requested that John, as Jonnie’s guardian ad litem, be permitted to observe Dr. Kuo’s interview of Jonnie. The March 2, 2015 order set Dr. Kuo’s mental examination of Jonnie for March 16, 2015 (unless the parties agreed to an alternative date) and, as indicated, it prohibited third-party observers during the examination. Petitioners have informed this court that this examination has been completed and any issue concerning the presence of an observer or attorney during that examination is moot. We agree that issue has been rendered moot since there is no effectual relief that may be granted, and we do not address it. (See Consol. etc. Corp. v. United A. etc. Workers (1946) 27 Cal.2d 859, 862-863.) 3 Our conclusion renders moot the questions (1) whether collateral interviews of Jane and John, as an adjunct to the mental examination of Jonnie, would violate their constitutional rights to privacy or their rights to confidential marital communications and (2) whether the order’s language setting forth the scope of the collateral parental interviews is impermissibly vague. 7 C. Written Testing Materials and Jonnie’s Answers Section 2032.610, subdivision (a), provides in pertinent part: “If a party submits to . . . a physical or mental examination in compliance with . . . an order of court under Article 3 (commencing with Section 2032.310) . . . , that party has the option of making a written demand that the party at whose instance the examination was made deliver . . . the following to the demanding party: [¶] (1) A copy of a detailed written report setting out the history, examinations, findings, including the results of all tests made, diagnoses, prognoses, and conclusions of the examiner.” If the party submitting to an examination exercises the option of making such a demand, a copy of the requested reports must “be delivered within 30 days after service of the demand, or within 15 days of trial, whichever is earlier.” (§ 2032.610, subd. (b).) In their opposition to the motion to compel the mental examination of Jonnie, plaintiffs requested an order compelling defendants to produce all reports required by section 2032.610. They additionally stated that they should be provided with copies of the written test questions and Jonnie’s responses. In its reply to that opposition, School District responded that Dr. Hall objected to production of testing materials because they were subject to copyright law, and it sought a protective order in the event the superior court ordered disclosure of those materials. It agreed to provide a written report pursuant to section 2032.610, subdivision (a). During the hearings on the motion, the superior court told the parties: “I’m going to order that [Dr. Hall] comply with the Code of Civil Procedure [section 2032.610]. I’m not going to start defining the elements. We’ll wait and see how she complies, and if you believe she has failed to comply, then you can deal with that with a motion to compel.” It agreed that the phrase “the results of all tests” did not mean the written testing materials but rather the findings made. The superior court indicated that it would order compliance in the statutory language of section 2032.610. 8  As part of the March 2, 2015 order, the superior court ordered both examiners to provide plaintiffs with the reports statutorily required by section 2032.610. Without specifying any legal basis, the superior court specified that plaintiffs were not entitled to the written testing materials used by Dr. Hall and Jonnie’s answers thereto without further order of the court. Petitioners seek a writ of mandate compelling defendants in the underlying case to deliver the written tests administered to Jonnie and the test results, impliedly including Jonnie’s test answers. Petitioners argue that copyright law is not a valid reason for the court to refuse to compel the examiner to deliver the tests and test results. The petition does not, however, allege that the superior court’s refusal was based on copyright law and support that allegation by citation to the record. (See Cal. Rules of Court, rules 8.204(a)(1)(C), 8.485(a), and 8.486(b).) The superior court’s ultimate order did not contain any mention of copyright law. We will not issue an advisory opinion on an abstract question of law. In their argument, petitioners imply that section 2032.610, subdivision (a)(1), requires the production of the written testing materials and Jonnie’s answers by analogy to Penal Code section 1054.3, subdivision (a)(1), a criminal discovery provision that specifies the disclosure that the defense must make to the prosecution regarding witnesses whom the defense intends to call at trial.4 They offer a brief quote from People v. Hajek and Vo (2014) 58 Cal.4th 1144 (Hajek), which considered Penal Code section 1054.3, subdivision (a)(1): “This provision includes the raw results of standardized 4 Penal Code section 1054.3, subdivision (a), provides in pertinent part: “The defendant and his or her attorney shall disclose to the prosecuting attorney: [¶] (1) The names and addresses of persons, other than the defendant, he or she intends to call as witnesses at trial, together with any relevant written or recorded statements of those persons, or reports of the statements of those persons, including any reports or statements of experts made in connection with the case, and including the results of physical or mental examinations, scientific tests, experiments, or comparisons which the defendant intends to offer in evidence at the trial.” 9 psychological and intelligence tests administered by a defense expert upon which the expert intends to rely. (Woods v. Superior Court (1994) 25 Cal.App.4th 178, 184-185.)” (Hajek, supra, at p. 1233.) Without providing any legislative history relevant to statutory interpretation, petitioners argue that the phrase “the results of all tests made” (§ 2032.610, subd. (a)(1)) and the phrase “the results of physical or mental examinations” (Pen. Code, § 1054.3) both encompass raw test data. They attempt to invoke the principle that courts presume that the Legislature intended similar statutory language covering similar subjects to be similarly construed. We first observe that “maxims of statutory construction are not immutable principles that dictate how a statute is to be interpreted. (See In re Joseph B. (1983) 34 Cal.3d 952, 957.)” (Bisno v. Kahn (2014) 225 Cal.App.4th 1087, 1104.) Second, it is a principle of statutory construction that “[w]here . . . legislation has been judicially construed and a subsequent statute on the same or an analogous subject uses identical or substantially similar language, we may presume that the Legislature intended the same construction, unless a contrary intent clearly appears. [Citations.]” (Estate of Griswold (2001) 25 Cal.4th 904, 915-916.) This principle does not support petitioners’ argument. The first sentence of former section 2032, subdivision (h), which was substantively continued in section 2032.610, subdivision (a),5 predates the 1994 judicial construction of Penal Code section 1054.3, subdivision (a)(1), in Woods v. Superior Court, supra, 25 Cal.App.4th at pp. 184-185 (Woods), which was cited by Hajak. The Legislature could not have been aware of Woods’ construction when it earlier enacted or amended former section 2032. (See fn. 5, ante.) Furthermore, Penal Code section 1054.3, subdivision (a)(1), concerns “the results of physical or mental 5 “Subdivision (a) of Section 2032.610 continues the first sentence of former Section 2032(h) without substantive change.” (Cal. Law Revision Com. com., 21A West’s Ann. Code of Civ. Proc. (2007 ed.) foll. § 2032.610, p. 436; see e.g. Stats.1993, ch. 219, § 71, p. 1591; Stats. 1986, ch. 1336, § 1, p. 4751.) 10 examinations . . . which the defendant intends to offer in evidence at the trial.” (Italics added.) In this respect, section 2032.610, subdivision (a), and Penal Code section 1054.3, subdivision (a)(1), appear dissimilar. (Cf. Woods, supra, at pp. 184-185 [“Requiring pretrial disclosure of the raw results of standardized psychological and intelligence tests administered and relied upon by an expert the defense intends to call at trial allows access to information necessary to prepare the case, reduces the chance of surprise at trial, furthers the attainment of truth and lessens the risk of a judgment based on incomplete testimony”].) Petitioners have not shown that the Legislature’s intent and purpose with regard to section 2032.610, subdivision (a), support their argument. Petitioners also assert that section 2032.610’s phrase “results of all tests made” constitutes “plain language” that requires Jonnie’s answers to be provided to him, but they offer absolutely no support for that assertion.6 Petitioners’ undeveloped analyses fail to establish that section 2032.610 requires defendants to deliver the written testing materials and Jonnie’s raw answers to the plaintiffs. Consequently, they have not demonstrated in this writ proceeding that the superior court was under a legal duty to order, or that its discretion could be legally exercised only by ordering, such delivery. (See § 1085 [“A writ of mandate may be issued by any court to any inferior tribunal . . . to compel the performance of an act which the law specially enjoins . . . .”]; Babb v. Superior Court (1971) 3 Cal.3d 841, 851 [A writ of mandate will lie where, under the facts, discretion can be exercised in only one way].) 6 “When attempting to ascertain the ordinary, usual meaning of a word, courts appropriately refer to the dictionary definition of that word. [Citations.]” (Wasatch Property Management v. Degrate (2005) 35 Cal.4th 1111, 1121-1122.) The word “result” generally refers to the consequence or outcome of something. (See <http://www.oxforddictionaries.com/us/definition/american_english/result>[as of Nov. 19, 2015]; Webster’s New World College Dictionary (4th ed. 2008) p. 1223.) The plain language of the statute does not resolve whether test “results” encompasses the examinee’s raw responses. 11  Moreover, petitioners have not demonstrated there is no “plain, speedy, and adequate remedy, in the ordinary course of the law” available to them (§ 1086). Petitioners bear the burden of showing that they lack such a remedy. (Phelan v. Superior Court in of San Francisco (1950) 35 Cal.2d 363, 366.) The March 2, 2015 order suggests that plaintiffs may request a further order of the court as to the written testing materials used by Dr. Hall and Jonnie’s answers thereto. If plaintiffs did not receive reports satisfying section 2032.610, subdivision (a), pursuant to the court’s March 2, 2015 order, there is a statutory right to bring a motion for an order compelling delivery of reports demanded under Section 2032.610.7 (§ 2032.620, subd. (a) [“If the party at whose instance an examination was made fails to make a timely delivery of the reports demanded under Section 2032.610, the demanding party may move for an order compelling their delivery”].) Finally, there is a right of appeal from a final judgment. No writ relief is warranted concerning the written testing materials used by Dr. Hall and Jonnie’s answers thereto. DISPOSITION Let a peremptory writ of mandate issue, commanding respondent court to vacate its March 2, 2015 order insofar as it authorizes collateral interviews of Jane Roe and John Roe as part of the mental examination of Jonnie Roe. The stay order issued March 12, 2015 is vacated. Petitioners are entitled to recover costs incurred in this writ proceeding. 7 In addition, if defendants designate Dr. Hall as an expert witness, other statutory rights of discovery may apply. (See e.g. §§ 2025.480, 2034.210 et seq., 2034.410.) 12  _________________________________ ELIA, J. WE CONCUR: _______________________________ RUSHING, P. J. _______________________________ WALSH, J.* Roe, a Minor, etc. et al. v. Superior Court H0420608 * Judge of the Santa Clara County Superior Court assigned by the Chief Justice pursuant to article VI, section 6 of the California Constitution. Filed 12/18/15 CERTIFIED FOR PUBLICATION IN THE COURT OF APPEAL OF THE STATE OF CALIFORNIA SIXTH APPELLATE DISTRICT JONNIE ROE, a Minor, etc., et al., H042060 (San Benito County Petitioners, Super. Ct. No. CU-14-00017) v. ORDER GRANTING REQUEST FOR PUBLICATION SUPERIOR COURT OF SAN BENITO COUNTY, Respondent; HOLLISTER SCHOOL DISTRICT et al., Real Parties in Interest. THE COURT: The opinion in the above-entitled matter filed on November 19, 2015, was not certified for publication in the Official Reports. Counsel for real parties in interest has requested the opinion be certified for publication. Counsel for petitioner and for California Attorneys of California have requested the opinion be certified for partial publication. It appears that the opinion meets the standards set forth in California Rules of Court, rule 8.1105(c). The court will grant full publication. The opinion is ordered published in the Official Reports. _________________________________________ ELIA, J. __________________________________________ RUSHING, P.J. 14 Trial Court: San Benito County Superior Court Superior Court No.: CU-14-00017 Trial Judge: Honorable Harry J. Tobias Counsel for Petitioners: Alan Charles Dell'Ario JONNIE ROE, a Minor, etc., et al. Alexis Susann McKenna Winer, McKenna & Burritt Counsel for Real Parties in Interest: Eric Shiu HOLLISTER SCHOOL DISTRICT et al., Lynch and Shupe Roe, a Minor, etc. et al. v. Superior Court H042060 

One Versus 2-stent Strategy for the Treatment of Bifurcation Lesions in the Context of a Coronary Chronic Total Occlusion. A Multicenter Registry. There is little evidence on the optimal strategy for bifurcation lesions in the context of a coronary chronic total occlusion (CTO). This study compared the procedural and mid-term outcomes of patients with bifurcation lesions in CTO treated with provisional stenting vs 2-stent techniques in a multicenter registry. Between January 2012 and June 2016, 922 CTO were recanalized at the 4 participating centers. Of these, 238 (25.8%) with a bifurcation lesion (side branch ≥ 2mm located proximally, distally, or within the occluded segment) were treated by a simple approach (n=201) or complex strategy (n=37). Propensity score matching was performed to account for selection bias between the 2 groups. Major adverse cardiac events (MACE) consisted of a composite of cardiac death, myocardial infarction, and clinically-driven target lesion revascularization. Angiographic and procedural success were similar in the simple and complex groups (94.5% vs 97.3%; P=.48 and 85.6% vs 81.1%; P=.49). However, contrast volume, radiation dose, and fluoroscopy time were lower with the simple approach. At follow-up (25 months), the MACE rate was 8% in the simple and 10.8% in the complex group (P=.58). There was a trend toward a lower MACE-free survival in the complex group (80.1% vs 69.8%; P=.08). After propensity analysis, there were no differences between the groups regarding immediate and follow-up results. Bifurcation lesions in CTO can be approached similarly to regular bifurcation lesions, for which provisional stenting is considered the technique of choice. After propensity score matching, there were no differences in procedural or mid-term clinical outcomes between the simple and complex strategies.

Q: Display all custom post types in archives.php How would I do this? archive.php only has this: wp_get_archives('type=monthly'); And wp_get_archives() does not have a parameter to display all post types. Also I think archive-[post_type].php is not the one I am looking for since I want all post types to be displayed in one archive page. Thanks! W A: If you set up the right parameters for your custom post type using 'has_archive' => true // Will use the post type slug, ie. example // or 'has_archive' => 'my-example-archive' // Explicitly setting the archive slug http://codex.wordpress.org/Function_Reference/register_post_type

Cover Reveal: Supernatural Fog Supernatural Fog by Louisa Klein About the book: 1) Learn how to use your new powers; 2) Find the other spirits; 3) Keep up with the training; 4) Defeat the Dark Cloud; 5) Don’t you ever, EVER fall in love with your best friend. Yeah, easier said than done. Supernatural Freak Robyn Wise is, well, freaking out. She’s trying to adjust to her new life as the Spirit of the Cat’s incarnation. But with little success. She cannot find the other animal spirits who are supposed to help her, nor can she master the tricky art of telekinesis. And then there’s James, her wizard best friend. They kissed in a moment of passion, right after she had slayed a powerful infernal monster. After that, being around James awakens a range of emotions she’s really not eager to analyse. She just wants to be back to normal, to be friends again. Trouble is, it’s not that easy. Especially when a mysterious Fog attacks London and the city’s survival depends on she teaming up with James. But it’s not a big deal, right? They can totally keep things friendly and professional, right? Right? RIGHT?

Human single chain Fv antibodies and a complementarity determining region-derived peptide binding to amyloid-beta 1-42. A library of phage-displayed human single-chain Fv (scFv) antibodies was selected against the human amyloid-beta peptide (Abeta42). Two new anti-Abeta42 phage-displayed scFvs antibodies were obtained, and the sequences of their V(H) and Vkappa genes were analyzed. A synthetic peptide based on the sequence of Ig heavy chain (V(H)) complementarity-determining region (HCDR3) of the clone with the highest recognition signal was generated and determined to bind to Abeta42 in ELISA. Furthermore, we showed for the first time that an HCDR3-based peptide had neuroprotective potential against Abeta42 neurotoxicity in rat cultured hippocampal neurons. Our results suggest that not only scFvs recognizing Abeta42 but also synthetic peptides based on the V(H) CDR3 sequences of these antibodies may be novel potential candidates for small molecule-based Alzheimer's disease (AD) therapy.

Eleonora cockatoo The Eleonora cockatoo, Cacatua galerita eleonora, also known as medium sulphur-crested cockatoo, is a subspecies of the sulphur-crested cockatoo. It is native to the Aru Islands in Indonesia, but has also been introduced to Kai Islands. It is common in aviculture. It is the smallest of the four subspecies of Cacatua galerita, at approx. 44 cm long and weighing in at between 404–602 grammes. Apart from the size difference, the Eleonora differs from the greater sulphur crested in that it doesn't have as prominent white eyerings (they often are a pale blue), the crest of an Eleonora is often less curved and it doesn't have the certain pointy upper mandible, which is only found in Cacatua galerita galerita. The Eleonora cockatoo often has pale yellow ear patches, and yellow diffusion throughout the body, especially under the wings and tail. The Eleonora also has a bald patch behind its crest. The Eleonora cockatoo was named by Dr. Otto Finsch. He discovered the subspecies in Amsterdam's Artis zoo and named it after Maria Eleonora van der Schroef, the wife of the then director of the zoo. Diet and habitat In the wild, the Eleonora cockatoo is found in open woodlands, forests, and semi-arid forested areas, as well as partially cleared forest areas. It feeds on nuts, berries, flower buds, flowers, seeds and insects. Reproduction The breeding season of this cockatoo is mainly from September to January. The birds build their nests in a tree hollow or rock crevice. The female lays 2–3 white oval eggs, which hatch after a period of 30 days. Both parents incubate the eggs and in turn provide for the chicks. The young fledge after about 75 days. Intelligence and beat perception One notable Eleonora cockatoo is Snowball, a bird recently demonstrated to be capable of beat induction – in other words, that the bird is capable of perceiving a musical beat and dancing to it. Like all cockatoos, the Eleonora cockatoo is widely considered to be very intelligent and emotionally complex. References External links ITIS Report Page Eleonora cockatoo Category:Parrots of Asia Category:Birds of the Aru Islands Eleonora cockatoo

export { default } from 'shared/utils/queue';

Q: How to resolve this "TypeError: pchstr must contain a $ as first char" from node-argon2? I got that TypeError when I'm trying to verify the password. The hash function works fine, but the verify not! this is the hash result: $argon2i$v=19$m=4096,t=3,p=1$8rKV3QWX0Y8GQ7ChOgVIRw$u+UEaGhG8Rvge4TvG17gnx/6jhdmePh9s7V3aK/asXA this verify function I use: function comparePassword(candidatePassword){ try { return argon2.verify candidatePassword, user.password } catch (err) { throw err } } And this is the hash function: try { hash = await argon2.hash(password) user.password = hash next() } catch (err) { next(err) } My enviremt Archlinux GNOME version 3.34.3 NodeJS v11.15.0 Argon2 v0.25.0 A: The error message gives you a hint: pchstr must contain a $ as first char. Every encoded representation of a hash generated by argon2 has its first part to be the variant of Argon2 being used, which in your case is argon2i. Your candidatePassword likely does not have '$' as its first character, and even if it did, you will have other problems. This is a start though! If you pay attention to the code example in npm package more closely, you will notice it is argon2.verify("<big long hash>", "password") and not argon2.verify("password","<big long hash>") as you have done. TLDR: Swap your arguments to match the parameters for argon2.verify.

feel bad for her, be the good wife for all the years and this what you get. Dildoes like us making fun of her on the interweb. What makes you assume she was the good wife? Just as easily she lost interest in sex fifteen years ago, didn't need it and so selfishly decided her husband didn't need it either. Satisfied her need for praise and attention by selling her "original hand-made shell fragment jewelry" on etsy.com and downing tubs of hagen daas.

Ceremonies mark opening of Musial Bridge Published 12:00 am CST, Saturday, February 8, 2014 ST LOUIS — The newest bridge spanning the Mississippi River is named after Stan Musial. You might have heard of him. Musial was a Hall-of-Fame first baseman for the St Louis Cardinals and a beloved figure in the St. Louis area. The bridge sharing his namesake is the third longest cable-stayed bridge in the country. The bridge is 1,500 feet across and 60 feet above the surface of the river. Part of the $700 million New Mississippi River Bridge Project, the bridge, which itself has a price tag of $229.5 million, spans from St. Clair County into just north of Downtown St. Louis through I-70. This is predicted to ease traffic on the Poplar Street Bridge as well as the Martin Luther King, Jr. Bridge. The Musial has four lanes with room to add an extra lane on either side. The opening of the bridge commenced with a ceremonial lighting on Friday night. That event featured speeches from local politicians including former area congressman Jerry Costello. Saturday morning allowed public admittance to the bridge. The morning included a cycling event at 10 and a 6K run at 8 a.m. At noon, the bridge was open to the public to walk or ride bicycles across it. A ceremonial ribbon cutting happened took place at 2 p.m. After that, a cruise of special cars were invited to do a “first crossing” event. Events Saturday concluded at 4 p.m. The bridge was then closed to the public at that point as well. The bridge opens to the public for crossing at noon Sunday.

Blogging Tips: Two Ways to Know Your Return on Investment Blogging has been a great outlet for me. I get to write about me and the kids, learn about new and fun products, save the family money and I actually have the opportunity to make some money too. To make money as a blogger you have to have ways to show what you are worth to other companies. You need to be able to show them what their return on investment would be. It’s also called an ROI. One way is to know your readers. You should be able to use a web form generator to create polls to find out what your readers are interested in. It’s also a great way to learn about your blog demographics. Knowing who your readers are is very valuable when it comes to working with certain companies. If you want to work with a baby company they are going to want to know if you’re readers are new moms or women that are expecting. Find out what your blog demographics are. Who is reading your blog, men or women, how old are they? Are they married or single? Another way is to have a newsletter, or mailing list. Last year, I worked with a company doing a very large giveaway, the Sleep Number Bed giveaway. I did this giveaway, one because I knew it would bring me a lot of traffic. Two, because I wanted to see if I could. One of the requirements I had to meet was that I had a acquire 2000, names, address and e-mail addresses. I thought the closest I would ever get to 2000 was 1000 and I have to admit that I thought that 1000 was stretching it. I had to create HTML forms and plug them into the giveaway so I could keep track of all the entries. It was basically a mailing list form. I ended up with 1500 unique addresses to give to the company I was working with. This was very valuable to them and they were extremely satisfied with my performance. Having a newsletter or mailing list is very valuable to companies because it’s another way that you can get information out to your followers on their behalf. Share on Yummly Recent Articles on Mom Start Thanks to The ONE for providing a Smart Keyboard Pro for review! My husband Jai is a self-taught pianist. He plays classical music by ear, inspired by his love of Chopin, and even recorded some of the music that we played during our wedding ceremony. He bought his first keyboard in 1996, and it served […]

Navigation A service is a process or application which is running in the background, either doing some predefined task or waiting for some event. If you remember our process chapter, we learned about systemd for the first time there. It is the first process to run in our system; it then starts all the required processes and services. To know about how the system boots up, read the bootup man page. Click here to read it online. If you look at Unix/Linux history, you will find the first process which starts up, is also known as init process. This process used to start other processes by using the rc files from /etc/rc.d directory. In the modern Linux systems, systemd has replaced the init system. Units are a standardized way for the systemd to manage various parts of a system. There are different kinds of units, .service is for system services, .path for path based ones. There is also .socket which are socket based systemd units. There are various other types, we can learn about those later. Even if you start a service, you’ll find that after you reboot the computer, the service did not start at the time of boot up. To do so, you will have to enable the service, or to stop a service from starting at boot, you will have to disable the service.

(Adapted from the Applicant?s Abstract) The purpose of the core is to provide the resources and expertise for the efficient generation and delivery into embryos of recombinant expression viruses (adenovirus and retroviruses) containing genes of interest to the project investigators. (End of Abstract) This core provides the critical adeno-viral and retro-viral support for the projects in this proposal. Most of the projects propose to either use lineage tracing or expression of certain genes utilizing either adeno-viral or retro-viral transfection into mouse or chick embryo cultures. This core is central to the experiments outlined in the various projects. The principal investigator and co-investigators have experience in the adeno-viral and retro-viral techniques proposed. Their approach is straight-forward and appropriate. They will maintain cell lines necessary for these experiments and generate the high titer viral stocks necessary for the experiments. They propose to make the core laboratory available to the investigators for them to learn as well as provide this service. The plans to provide direct infection of whole embryos in culture (mouse and chicken) are reasonable, and the investigators have experience with such techniques. There are overall no glaring difficulties with the proposed approach. The types of experiments proposed are now rather routine and will be useful for the various experiments outlined in the individual projects. The ability to infect specific tissues in whole embryo cultures is rather innovative, although it has been used successfully by other investigators. Nevertheless, it is not a common skill and it is certainly a strength that this core will have that ability. The prinicipal investigator and co-investigators have good experience, as they have demonstrated, utilizing retro-viral and adno-viral techniques. They have done these sorts of experiments for other purposes successfully, and should have no difficulty in performing the tasks outlined. Dr. Kubalak has had experience with mouse embryo culture and this will certainly be an asset to the program project grant. The environment for the core is strong and they appear to already have all the necessary equipment and technology to provide the core services outlined. There are no problems with the environment. This is a very important core for this program project and appears to be designed appropriately without any major flaws. The core has many strengths and will be a critical one for most of the projects. The availability of Dr. Mikawa as a consultant adds furthur strength to the ability of this core to troubleshoot and be effective.

1001 - 995 + 1315*a**3 + 12*a to the form j*a + z + v*a**3 + k*a**2 and give z. 6 Express 1735 - 3470 - 3*w**3 + w + 93*w**2 + 1732 - 2*w in the form g*w + l + z*w**3 + t*w**2 and give l. -3 Express -2 - 174*a**2 - 453*a - 2*a**4 + 343*a**2 + 132*a - 167*a**2 as r*a**2 + c*a**3 + d*a**4 + f*a + j and give c. 0 Express -398*g - 169 - 382*g - 397*g + 1172*g + (3*g + 3*g + g)*(-1 + 0 + 3) as l + k*g and give k. 9 Express 27*o**2 + 222 - 24*o**2 + 2*o - 2*o**4 - 232 - 2*o**3 in the form m*o**3 + a*o**2 + t*o**4 + d + s*o and give s. 2 Express 3333 - 2369 + 4*p + 5267 in the form i*p + y and give i. 4 Express (4 + 0 + 0)*(-3 + 3 - d**2 + (14*d + 19*d - 2*d)*(-2 + d + 2) + 24*d**2 - 7*d**2 + 9*d**2) as b*d + i + m*d**2 and give m. 224 Express -105*s**3 - 7 + 101*s**3 + 9*s**4 + 256*s**2 - 7*s**4 + 1 + 4 as h*s**4 + c*s**3 + y*s**2 + d + l*s and give d. -2 Express -208*f + 2547 - 10*f - 2542 - 594*f as a + n*f and give n. -812 Express 14740 - 2804*b + 10555*b + 3363*b - 14740 as i + a*b and give a. 11114 Express 17639*p**3 + 3*p**4 - 8821*p**3 + p**2 + 100*p - 8818*p**3 in the form f + w*p**3 + s*p + q*p**2 + h*p**4 and give s. 100 Rearrange (-2*q + q - q)*(1 + 2 + 0)*(-176*q**2 + 82*q**2 + 50*q**2) to the form m*q**2 + y*q**3 + x*q + u and give y. 264 Express 138*u**3 - 279*u**3 + 84*u**3 + 16*u**2 as q + j*u**2 + h*u + w*u**3 and give w. -57 Rearrange 5*g**4 + 29336 - 29337 + 7*g**4 - 33*g**3 + 85*g**2 - 13*g**4 to w*g + y + i*g**3 + u*g**4 + m*g**2 and give y. -1 Rearrange (4 - 1 - 5 + (1 + 4 - 3)*(1 - 1 - 2))*(3 - 1 + 0)*(51*r**3 - 52*r**3 + 30*r**3) to l*r**3 + s + j*r + i*r**2 and give l. -348 Express (7478 - 28509 - 92735 - 90894 + 20280)*(o**3 + o**4 - o**3) in the form b*o + v*o**4 + a*o**2 + n + m*o**3 and give v. -184380 Express 119*q - 1033619 + 5*q**2 - 2*q**2 + 48*q + 1033617 in the form y*q**2 + j + o*q and give j. -2 Rearrange -328678*q - 192*q**2 + 328678*q - 1 to v*q**2 + a + k*q and give a. -1 Rearrange 57*z - 37*z**2 + 39*z + 49*z**2 + 86*z + 46*z to a*z**2 + d*z + v and give v. 0 Rearrange -339*r + 22396*r - 10260*r + 23885*r + 2753*r to the form d + m*r and give m. 38435 Rearrange 27*n + 4 - 23*n - 3*n**3 + 18*n - 24*n to the form j*n + u*n**2 + i*n**3 + g and give g. 4 Express (3*k**3 - k**3 - k**3)*(1551*k - 1365*k + 2 - 6) as f + x*k**4 + h*k**2 + c*k**3 + u*k and give x. 186 Rearrange (-70 - 32 + 24 - 5 - 14)*(-65 + 65 - u) to d + s*u and give s. 97 Express -2728*f**3 + 3497*f**3 + 3 - 4*f**4 + f**4 as w*f**2 + h*f + l + j*f**4 + y*f**3 and give j. -3 Express (-7604*r**4 + 12132*r**4 - 7006*r**4)*(-5 + 1 + 2) + 2*r**4 + 5*r**3 - 5*r**3 as l*r + v*r**4 + n*r**3 + y + w*r**2 and give v. 4958 Express 66*v - 26*v**2 + 2 - 7*v**3 - 40*v + 3*v**3 - 28*v as q*v + s + k*v**2 + o*v**3 and give k. -26 Express 262*q - 910 + 526 + 376 as l*q + t and give l. 262 Express -9375685 + 9375684 - 3*x**2 - 53*x**3 + 109*x**4 + 3*x**2 in the form y*x**2 + l*x + c*x**4 + a*x**3 + g and give c. 109 Rearrange -3*a - 6*a + 10 + 23*a + 21*a - 8*a to the form k*a + t and give k. 27 Express -2*s - s - 6*s - 109*s + 956 - 956 + 3*s - 4*s + 3*s + (3 + 1 - 2)*(0 + 0 - s) + 2*s - s + 5*s in the form r + i*s and give i. -112 Express (245985 - 245985 + 2328*g)*(11*g - 7*g**2 - 11*g)*(-5 + 4 + 2) as p*g + o*g**2 + n*g**3 + m and give n. -16296 Express (21 - 21 - 3*j)*(-5*j + j + 3*j) + 421 - 421 - 766*j**2 + 2*j**2 + j**2 - j**2 in the form w + u*j + d*j**2 and give d. -761 Rearrange (5 - 10*o + 0*o + 13*o)*(-290*o + 23*o - 1006*o) to the form d + b*o + f*o**2 and give d. 0 Rearrange -25*c**3 + 15*c**4 + 8*c**3 + 15*c**3 - 2*c + 4*c**2 - 5*c**2 to r*c**4 + z*c + y*c**2 + w*c**3 + s and give s. 0 Rearrange (2 - 6 + 3)*(-2 + 1 + 0)*(-4 + 2 - 9)*(18*g - 8*g - 7*g) to u + i*g and give i. -33 Rearrange (98 + 44 + 16)*(-143*u - 130*u - 19*u + 15*u) to j*u + t and give j. -43766 Rearrange (-4*b + 0*b - 2*b - b - 2*b + 2*b + (0*b + 9*b + 3*b)*(0 + 0 - 2))*(6 - 3 + 0*b + 4*b) to d*b + a*b**2 + t and give d. -93 Express -4 + 4 + 4*y**2 + (-2*y**2 + 4*y**2 - y**2)*(-2 - 11 + 1) + (3 - 2 - 3)*(22*y**2 + 165 - 165) as z + u*y**2 + t*y and give u. -52 Rearrange (-1 + 0 - 1)*(-6 + 7*l + 6 + (2*l + l - 2*l)*(13 - 1 - 2))*(-8*l**3 - 35*l + 35*l) to r + g*l + u*l**2 + w*l**4 + b*l**3 and give w. 272 Rearrange 151 + 18 + 68 - 3*h - 22 to r + j*h and give r. 215 Rearrange -36*b**3 + 7*b - b**2 - 17*b**3 - 2*b**4 + 2*b**4 - 3*b**4 + 50*b**3 to the form m*b**4 + a*b**3 + z + v*b + d*b**2 and give v. 7 Rearrange 82*j + 74*j - 6461 - 158*j - 7284 to the form p + h*j and give h. -2 Express (3*n - 7*n + 0*n)*(-2371*n**2 - 62203*n + 62203*n) as r*n + t*n**3 + k*n**2 + w and give t. 9484 Rearrange -119 + 21 - 20*y + 58*y to the form t + x*y and give t. -98 Express -129 + 38*w - 105 - 7 + 524 - 47 in the form c + t*w and give t. 38 Express -97905*y + 195805*y - 282 - 97924*y in the form c*y + i and give i. -282 Rearrange (-3*t + 7*t + 9*t)*(-3*t - 51 - 1186 + 4*t - 499) to z*t**2 + x*t + h and give x. -22568 Express 18*s**2 - 18*s**2 - 4*s**3 + 5 - 5 + 5*s**3 + (6*s + 5 - 5)*(s**2 + 8*s**2 - 4*s**2) as a*s**3 + c*s + n*s**2 + q and give a. 31 Express l**3 - 4*l**3 + 3427317*l - 26*l**2 - 3427314*l in the form y*l**3 + t*l**2 + q*l + u and give y. -3 Express -27870*m**4 + 2 - 4*m**2 + 55840*m**4 - 27915*m**4 in the form o*m**3 + l*m + q*m**2 + h + c*m**4 and give c. 55 Express -3 - 277*t**2 + 79*t - 267*t**2 + 532*t**2 + 2 - t**3 in the form h*t + l + b*t**3 + r*t**2 and give b. -1 Express (-n - 8*n - 12*n)*(69*n**2 - 122*n**2 - 276*n**2) in the form t*n**3 + k + b*n**2 + q*n and give t. 6909 Express (-4*z**2 + 0*z**2 + z**2)*(234*z**2 + 1032*z**2 + 926*z**2 - 112*z**2) as i*z**2 + g*z**4 + u*z**3 + k*z + p and give k. 0 Rearrange (-13 + 12 + 3*s - 37*s)*((3 - 2*s - 3)*(0*s - s - s) - 2*s**2 - 2*s**2 + 8*s**2 - 2*s**2 - 9 + 9) to the form k*s**3 + q*s + z*s**2 + x and give q. 0 Rearrange 39*d**2 - d - 44*d**2 - 2 - 33*d**2 + 71*d**3 - 64*d**3 to l*d**2 + a + s*d + k*d**3 and give k. 7 Express (143*g**2 - 76*g**2 + 99*g**2)*(1 - 1 + 1) + (3 - 3 + g**2)*(4 + 6 - 6) in the form x + v*g**2 + z*g and give v. 170 Rearrange (4*o**2 - 3*o**2 + 0*o**2)*(1 - 3 + 3) + (5 + 6 - 4 + o)*((-8 - 10 + 11)*(-o - 4*o - 2*o) + 0*o + 5*o - 4*o) to s*o**2 + j + v*o and give j. 0 Express -79*l**3 - 1 - 6 + 4992*l**2 - 4987*l**2 - 25*l**3 as c + b*l**3 + q*l**2 + g*l and give b. -104 Rearrange -v + 9 + 132 - 51 - 2*v**2 + 6*v to z + h*v**2 + g*v and give z. 90 Rearrange t**3 - 31 - t - 3*t**3 + 22*t**2 + 17839*t**4 - 17838*t**4 to v*t**4 + s*t**2 + z*t**3 + i*t + c and give c. -31 Express 1125*f**3 + 1120*f**3 + 7*f**2 - 2*f - 2 - 2257*f**3 as x*f + z*f**2 + v*f**3 + m and give x. -2 Express 4553 - 4553 - 349*j**2 + (-1 + 1 + j)*(-4 - 2*j + 4) - 9*j**2 + 18*j - 18*j as l*j + p + a*j**2 and give a. -360 Rearrange -6*x - 9*x**3 - 15*x + 2355943*x**4 - 2355940*x**4 - 6*x**2 to the form i*x + q*x**3 + y*x**4 + f*x**2 + l and give f. -6 Rearrange -6 - 657*w**3 - 108*w**2 + 650*w**3 + 41*w + 48*w - 89*w to the form r*w + o + i*w**3 + h*w**2 and give o. -6 Express (3506*j**3 + 496*j**2 - 3473*j**3 - 173*j**2)*(1 - 2 - 1) as s + o*j**3 + h*j**2 + d*j and give h. -646 Rearrange -52185 + 103012 - 52117 + 2*k to the form i + w*k and give w. 2 Rearrange 6*v**3 - 2*v**4 - 22*v**3 - v**2 - 20*v**3 + 5*v - 11*v - 67*v**3 to the form t*v**4 + g*v**3 + d + r*v + w*v**2 and give r. -6 Rearrange (4424 + 4437 - 12885)*(p**2 - p + p) to the form v + s*p + t*p**2 and give t. -4024 Express (70*p - 3 - 107*p - 34*p)*(0*p + 0*p + p**2) in the form t + d*p + b*p**2 + c*p**3 and give t. 0 Rearrange 5*m**3 - 23 + 26293*m**2 - 26291*m**2 + 33 + m to w + h*m + i*m**3 + y*m**2 and give i. 5 Rearrange (29632 + 19607 + 586 + 24504 + 19962)*(0 + 0 - a**2)*(-3*a - a**2 + 3*a) to n*a**2 + j + m*a**3 + d*a + c*a**4 and give n. 0 Express -30213*q**2 + 7924*q**2 + 124 + 122 - 246 in the form l + a*q**2 + t*q and give a. -22289 Rearrange 2 - 30*q**4 - 3*q - q - q**2 + 3 - 6 + 0*q**3 + 2*q**3 to s*q**3 + t*q**4 + r*q**2 + n + i*q and give t. -30 Rearrange 17055*b**4 - 8 + 5*b - b**2 - 2*b - 17039*b**4 + 2*b**3 + b**2 to d*b**4 + q*b**2 + z*b + u + f*b**3 and give d. 16 Express 2151 - 4303 + 2152 + 5009*u**2 in the form h*u**2 + t*u + o and give h.

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1. Field of the Invention The present invention relates in general to a shifting mechanism for an automotive vehicle and more particularly to shift forks utilized therein. 2. Description of the Prior Art FIG. 4 shows a prior art shifting mechanism for an automotive transmission with parts removed to better illustrate the portion with which the present invention is concerned. In the drawing, 10 is a transmission case, 12 a shaft, 14 a collar mounted on the shaft 12, 16 a shift fork and 18 a fork rod located at the lower part of the shift fork 16. In the above structure, dropping or dripping oil 20 for lubrication of the sliding surfaces of the tip 16a of the shift fork 16 and the collar 14 tends to come down along the course indicated by the arrow A in the drawing since the shift fork 16 is so constructed and arranged to have a branch whose upper end face 16b is normal to the collar-engaging surface of the tip 16a, resulting in that the amount of lubricant for the sliding surfaces of the shift fork tip and the collar becomes insufficient.

--- abstract: 'We study the problem of designing a data structure that reports the positions of the distinct $\\tau$-majorities within any range of an array $A[1,n]$, without storing $A$. A $\\tau$-majority in a range $A[i,j]$, for $0<\\tau< 1$, is an element that occurs more than $\\tau(j-i+1)$ times in $A[i,j]$. We show that $\\Omega(n\\log(1/\\tau))$ bits are necessary for any data structure able just to count the number of distinct $\\tau$-majorities in any range. Then, we design a structure using $O(n\\log(1/\\tau))$ bits that returns one position of each $\\tau$-majority of $A[i,j]$ in $O((1/\\tau)\\log\\log_w(1/\\tau)\\log n)$ time, on a RAM machine with word size $w$ (it can output any further position where each $\\tau$-majority occurs in $O(1)$ additional time). Finally, we show how to remove a $\\log n$ factor from the time by adding $O(n\\log\\log n)$ bits of space to the structure.' address: - 'Department of Computer Science, University of Chile,Chile.' - 'Georgia Institute of Technology, USA.' author: - Gonzalo Navarro - 'Sharma V. Thankachan' bibliography: - 'paper.bib' title: Optimal Encodings for Range Majority Queries --- Introduction ============ Given an array $A[1, n]$ of $n$ arbitrary elements, an *array range query* problem asks us to build a data structure over $A$, such that whenever a range $[i, j]$ with $1 \\leq i \\leq j \\leq n$ arrives as an input, we can efficiently answer queries on the elements in $A[i, j]$ [@skala]. Many array range queries arise naturally as subproblems of combinatorial problems, and are also of direct interest in data mining applications. Well-known examples are range minimum queries (RMQs, which seek the smallest element in $A[i, j]$) [@BV93], top-$k$ queries (which report the $k$ largest elements in $A[i, j]$) [@bro], range selection queries (which report the $k$th largest element in $A[i,j]$) [@CW13], and colored top-$k$ queries (which report the $k$ largest distinct elements in $A[i,j]$) [@NNN]. An [*encoding*]{} for array range queries is a data structure that answers the queries without accessing $A$. This is useful when the values of $A$ are not of interest themselves, and thus $A$ may be deleted, potentially saving a lot of space. It is also useful when array $A$ does not fit in main memory, so it can be kept in secondary storage while a much smaller encoding can be maintained in main memory, speeding up queries. In this setting, instead of reporting an element in $A$, we only report a position in $A$ containing the element. Otherwise, in many cases we would be able to reconstruct $A$ via queries on the encodings, and thus these could not be small (e.g., $A[i]$ would be the only answer to the range query $A[i,i]$ for all the example queries given above). As examples of encodings, RMQs can be solved in constant time using just $2n+o(n)$ bits [@RMQ1] and, using $O(n\\log k)$ bits, top-$k$ queries can be solved in $O(k)$ time [@grossi] and range selection queries in $O(\\log k / \\log\\log n)$ time [@NRR14]. Frequency-based array range queries, in particular variants of heavy-hitter-like problems, are very popular in data mining. Queries such as finding the most frequent element in a range (known as the range mode query) are known to be harder than problems like RMQs. For range mode queries, known data structures with constant query time require nearly quadratic space [@R2]. The best known linear-space solution requires $O(\\sqrt{n/\\log n})$ query time [@stacs], and conditional lower bounds given in that paper show that a significant improvement is highly unlikely. Still, efficient solutions exist for some useful variants of the range mode problem. An example are approximate range mode queries, where we are required to output an element whose number of occurrences in $A[i, j]$ is at least $1/(1+\\epsilon)$ times the number of occurrences of the mode in $A[i, j]$ [@lbo; @lboo]. In this paper we focus on a popular variant of range mode queries called *range $\\tau$-majority queries*, which ask to report any element that occurs more than $\\tau(j-i+1)$ times in $A[i,j]$. A version of the problem useful for encodings can be stated as follows (other variants are possible). Given an array $A[1,n]$, a [*range $\\tau$-majority query*]{} receives a range $[i,j]$ and returns one position in the range where each $\\tau$-majority in $A[i,j]$ occurs. A [*$\\tau$-majority*]{} is any element that occurs more than $\\tau(j-i+1)$ times in $A[i,j]$. When $\\tau=1/2$ we simply call it a [*majority*]{}. Range majority queries can be answered in constant time by maintaining a linear space (i.e., $O(n)$-word or $O(n\\log n)$-bit) data structure [@Steph]. Similarly, range $\\tau$-majority queries can be solved in time $O(1/\\tau)$ and linear space if $\\tau$ is fixed at construction time, or $O(n\\log\\log n)$ space (i.e., $O(n\\log n\\log\\log n)$ bits) if $\\tau$ is given at query time [@wads]. In this paper, we focus for the first time on [*encodings for range $\\tau$-majority queries*]{}. In this scenario, a valid question is how much space is necessary for an encoding that correctly answers such queries (we recall that $A$ itself is not available at query time). We answer that question in Section \\[sec:lb\\], proving a lower bound for any encoding that solves even a weaker query. \\[thm:lb\\] Given a real number $0<\\tau<1$, any encoding able to count the number of range $\\tau$-majorities in any range $A[i,j]$ must use $\\Omega(n\\log(1/\\tau))$ bits. Since when using $O(n\\log n)$ bits we have sufficient space to store $A[1,n]$[^1] (and achieve the optimal $O(1/\\tau)$ time [@wads]), encodings for range $\\tau$-majorities are asymptotically interesting only for $\\log(1/\\tau) = o(\\log n)$. In Section \\[sec:nlglgn\\] we show how range $\\tau$-majority queries can be solved using $O((n/\\tau)\\log\\log n)$ bits of space and $O((1/\\tau)\\log n)$ query time. In Section \\[sec:nbits\\] we reduce the space to the optimal $O(n\\log(1/\\tau))$ bits and slightly increase the time. After spending this time, the structure can report [*any*]{} of the positions of any majority in optimal time (e.g., the leftmost position of each $\\tau$-majority in a negligible $O(1/\\tau)$ time). In Section \\[sec:constr\\] we show how to build our structure in $O(n\\log n)$ time. All the results hold on the RAM model with word size $w=\\Omega(\\log n)$ bits. \\[thm:main\\] Given a real number $0<\\tau<1$, there exists an encoding using the optimal $O(n\\log(1/\\tau))$ bits that answers range $\\tau'$-majority queries, for any $\\tau \\le \\tau' < 1$, in time $O((1/\\tau)\\log\\log_w(1/\\tau)\\log n)$, where $w=\\Omega(\\log n)$ is the RAM word size in bits. It can report any $occ$ further occurrence positions of the majorities in $O(occ)$ time. The encoding can be built in $O(n\\log n)$ time. We note that the query time is simply $O((1/\\tau)\\log n)$ for polylogarithmic values of $1/\\tau$. We also note that the time depends on $\\tau$, not $\\tau'$. In Section \\[sec:constr\\] we also show how to obtain a query time that is a function of $\\tau'$, yet using $O(n\\log^2(1/\\tau))$ bits of space. Finally, in Section \\[sec:optimal\\] we derive a new variant that may use more space but slashes the $\\log n$ term from the time complexity. \\[thm:optimal\\] Given a real number $0<\\tau<1$, there exists an encoding using $O(n\\log(1/\\tau)+n\\log\\log n)$ bits that answers range $\\tau'$-majority queries, for any $\\tau \\le \\tau' < 1$, in time $O((1/\\tau)\\log\\log_w(1/\\tau))$, where $w=\\Omega(\\log n)$ is the RAM word size in bits. It can report any $occ$ further occurrence positions of the majorities in $O(occ)$ time. The encoding can be built in $O(n\\log n)$ time. By combining the results of Theorems \\[thm:main\\] and \\[thm:optimal\\], we obtain the combinations given in Table \\[tab:final\\]. ------------------------------------------------------- ------------------------- --------------------------------- Condition Space (bits) Query time \\[-1.5ex\\] \\[-1.5ex\\] $1/\\tau = \\omega(\\operatorname{polylog}n)$   $O(n\\log(1/\\tau))$ \\* $O((1/\\tau)\\log\\log_w(1/\\tau))$ \\[-1.5ex\\] $1/\\tau = \\Theta(\\operatorname{polylog}n)$   $O(n\\log(1/\\tau))$ \\* $O(1/\\tau)~*$ \\[-1.5ex\\] $1/\\tau = o(\\operatorname{polylog}n)$   $O(n\\log(1/\\tau))$ \\* $O((1/\\tau)\\log n)$ \\[-1.5ex\\] $1/\\tau = o(\\operatorname{polylog}n)$ $O(n\\log\\log n)$ $O(1/\\tau)~*$ ------------------------------------------------------- ------------------------- --------------------------------- : Space-time tradeoffs achieved. We mark the optimal spaces and times with a \\*.[]{data-label="tab:final"} Related Work ============ In this section we first cover the state of the art for answering range $\\tau$-majority queries. Then, we survey a few results on bitmap representation, and give a new result that will be useful for this paper. Again, all these results hold on the RAM model with word size $w=\\Omega(\\log n)$ bits. Range Majorities ---------------- Range $\\tau$-majority queries were introduced by Karpinski and Nekrich [@KarpinskiN08], who presented an $O(n/\\tau)$-words structure with $O((1/\\tau)(\\log\\log n)^2)$ query time. Durocher et al. [@Steph] improved their word-space and query time to $O(n\\log(1/\\tau))$ and $O(1/\\tau)$, respectively. Gagie et al. [@spire] presented another trade-off, where the space is $O(n(H+1))$ [*bits*]{} and the query time is $O((1/\\tau)\\log\\log n)$. Here $H\\le\\lg n$ denotes the empirical entropy of the distribution of elements in $A$ (we use $\\lg$ to denote the logarithm in base 2). The best current result in general is by Belazzougui et al. [@wads], where the space is $O(n)$ words and the query time is $O(1/\\tau)$. All these results assume that $\\tau$ is fixed at construction time. For the case where $\\tau$ is also a part of the query input, data structures of space (in words) $O(n(H+1))$ and $O(n\\log n)$ were proposed by Gagie et al. [@spire] and Chan et al. [@swat], respectively. Very recently, Belazzougui et al. [@wads] brought down the space occupancy to $O(n\\log\\log\\sigma)$ words, where $\\sigma$ is the number of distinct elements in $A$. The query time is $O(1/\\tau)$ in all cases. Belazzougui et al. [@wads] also presented a compressed solution using $nH+o(n\\log \\sigma)$ bits, with slightly higher query time. All these solutions include a (sometimes compressed) representation of $A$, thus they are not encodings. As far as we know, ours is the first encoding for this problem. For further reading, we recommend the recent survey by Skala [@skala]. Bitmap Representations {#sec:bitmaps} ---------------------- Given a bitmap $B[1,m]$ with $n$ 1s, the operation $rank(B,i)$ returns the number of 1s in $B[1,i]$, whereas operation $select(B,j)$ gives the position of the $j$th 1 in $B$. Both operations can be solved in constant time by storing $o(m)$ bits in addition to $B$ [@Mun96; @Cla96]. When $n$ is significantly smaller than $m$, another useful representation [@RRR07] compresses $B$ to $n\\lg\\frac{m}{n}+O(n)+o(m)$ bits and retains constant time for both operations. When $n$ is much smaller than $m$, even the $o(m)$ extra bits of that compressed representation [@RRR07] are troublesome, and an Elias-Fano-based [@Fan71; @Eli74] compressed representation [@OS07] is useful. It requires $n\\lg\\frac{m}{n} + O(n)$ bits, solves $select$ in $O(1)$ time and $rank$ in $O(\\log\\frac{m}{n})$ time. The representation considers the positions of all the 1s in $B$, $x_i = select(B,i)$, and encodes the lowest $b = \\lceil \\lg\\frac{m}{n} \\rceil$ bits of each $x_i$ in an array $L[1,n]$, $L[i] = x_i~\\mathrm{mod}~2^b$. Then it defines a bitmap $H[1,2n]$ that encodes the highest bits of the $x_i$ values: all the bits at positions $i+(x_i ~\\mathrm{div}~ 2^b)$ are set in $H$. Bitmap $H$ is indexed for constant-time $rank$ and $select$ queries [@Mun96; @Cla96]. The space for $L[1,n]$ is $n\\lceil \\lg\\frac{m}{n} \\rceil$ and $H$ uses $2n+o(n)$ bits. Now, $select(B,j) = 2^b (select(H,j)-j) + L[i]$ can be computed in constant time. For $rank(B,i)$, we observe that the $h$th 0 in $H$ represents the point where the position $B[2^b h]$ is reached in the process of setting the 1s at positions $i+(x_i ~\\mathrm{div}~ 2^b)$, that is, $x_{i-1} < 2^b h \\le x_i$. The number of 1s in $H$ up to that position is $rank(B,2^b h)$. Therefore, if we write $i = 2^b h + l$, then $rank(B,i)$ is between $j_1 = rank(H,select_0(H,h))+1$ and $j_2 = rank(H,select_0(H,h+1))$, where $select_0(H,h)$ gives the position of the $h$th 0 in $H$ and is also computed in constant time and $o(n)$ bits [@Mun96; @Cla96]. Now we binary search for $l$ in $L[j_1,j_2]$, which is increasing in that range. The range is of length at most $2^b$, so the search takes $O(b)=O(\\log\\frac{m}{n})$ time. The final position $j$ returned by the search is $rank(B,i)$. The time can be improved to $O(\\log\\log_w\\frac{m}{n}+\\log s)$ on a RAM machine of $w$ bits by sampling, for each increasing interval of $L$ of length more than $s$, one value out of $s$. Predecessor data structures are built on the samples of each interval, taking at most $O((n/s)\\log\\frac{m}{n})$ bits. Then we first run a predecessor query on $L[j_1,j_2]$, which takes time $O(\\log\\log_w\\frac{m}{n})$ [@PT08], and finish with an $O(\\log s)$-time binary search between the resulting samples. \\[lem:bitmap\\] A bitmap $B[1,m]$ with $n$ 1s can be stored in $n\\log\\frac{m}{n} + O((n/s)\\log\\frac{m}{n} + n)$ bits, so that $select$ queries take $O(1)$ time and $rank$ queries take $O(\\log\\log_w\\frac{m}{n}+\\log s)$, for any $s$, on a RAM machine of $w$ bits. Lower Bounds {#sec:lb} ============ We derive a lower bound on the minimum size range $\\tau$-majority encodings may have, even if we just ask them to count the number of distinct $\\tau$-majorities present in any range. The idea is to show that we can encode a certain combinatorial object in the array $A$, so that the object can be recovered via range $\\tau$-majority queries. Therefore, in the worst case, the number of bits needed to solve such queries must be at least the logarithm of the number of distinct combinatorial objects that can be encoded. Consider a sequence of $m$ permutations on $[3k]$. There are $(3k)!^m$ such sequences, thus any encoding for them must use at least $m\\lg ((3k)!)$ bits in the worst case. Now consider the following encoding. Array $A$ will have length $n=36\\cdot k\\cdot m$. To encode the $i$th permutation, $\\pi_i = (x_1~x_2~\\ldots~x_{3k})$, we will write 9 chunks on $A[36k(i-1)+1,36ki]$: $$\\begin{aligned} 1,2,3,\\ldots,k, & {-}1,{-}2,{-}3,\\ldots,{-}2k, & x_1,x_2,x_3,\\ldots,x_k \\\\ k{+}1,k{+}2,k{+}3,\\ldots,2k,& {-}1,{-}2,{-}3,\\ldots,{-}2k,& x_1,x_2,x_3,\\ldots,x_k \\\\ 2k{+}1,2k{+}2,2k{+}3,\\ldots,3k,& {-}1,{-}2,{-}3,\\ldots,{-}2k,& x_1,x_2,x_3,\\ldots,x_k \\\\ 1,2,3,\\ldots,k,& {-}1,{-}2,{-}3,\\ldots,{-}2k,& x_{k{+}1},x_{k{+}2},x_{k{+}3},\\ldots,x_{2k} \\\\ k{+}1,k{+}2,k{+}3,\\ldots,2k,& {-}1,{-}2,{-}3,\\ldots,{-}2k,& x_{k{+}1},x_{k{+}2},x_{k{+}3},\\ldots,x_{2k} \\\\ 2k{+}1,2k{+}2,2k{+}3, \\ldots,3k,& {-}1,{-}2,{-}3,\\ldots,{-}2k,& x_{k{+}1},x_{k{+}2},x_{k{+}3},\\ldots,x_{2k} \\\\ 1,2,3,\\ldots,k,& {-}1,{-}2,{-}3,\\ldots,{-}2k,& x_{2k{+}1},x_{2k{+}2},x_{2k{+}3},\\ldots,x_{3k} \\\\ k{+}1,k{+}2,k{+}3,\\ldots,2k,& {-}1,{-}2,{-}3,\\ldots,{-}2k,& x_{2k{+}1},x_{2k{+}2},x_{2k{+}3},\\ldots,x_{3k} \\\\ 2k{+}1,2k{+}2,2k{+}3,\\ldots,3k,& {-}1,{-}2,{-}3,\\ldots,{-}2k,& x_{2k{+}1},x_{2k{+}2},x_{2k{+}3},\\ldots,x_{3k} \\\\\\end{aligned}$$ We will set $\\tau = 1/(2k+2)$ and perform $\\tau$-majority queries on parts of $A$ to recover any permutation. Let us start obtaining $\\pi_i(1)=x_1$. Let $C[1,36] = A[36k(i-1)+1,36ki]$. Consider an interval of the form $$C[\\ell,3k+g] = \\ell,\\ell+1,\\ldots,k, {-}1,{-2},\\ldots,{-}2k,x_1,x_2,\\ldots,x_g,$$ for $1 \\le \\ell,g \\le k$. Note that $x_1,\\ldots,x_g$ are the only values that may appear twice in $C[\\ell,3k+g]$, precisely, if they belong to $\\{\\ell,\\ldots,k\\}$. Note that elements appearing once in $C[\\ell,3k+g]$ are not $\\tau$-majorities, since $1 \\le \\tau(3k+g-\\ell+1)$ for any values $k,\\ell,g$. On the other hand, if an element appears twice in $C[\\ell,3k+g]$, then it is a $\\tau$-majority, since $2 > \\tau(3k+g-\\ell+1)$ for any values $k,\\ell,g$. With this tool, we can discover $x_1$ as follows. First, we ask whether there is a $\\tau$-majority in $C[1,3k+1]$. If there is none, then $x_1 \\not\\in \\{1,\\ldots,k\\}$, and we have to look for it elsewhere (in $C[4k+1,8k]$ or $C[8k+1,12k]$). Assume there is a $\\tau$-majority in $C[1,3k+1]$; then $x_1 \\in \\{1,\\ldots,k\\}$. Now we query the range $C[2,3k+1]$. If there is no $\\tau$-majority, then $x \\not\\in \\{2,\\ldots,k\\}$, and we conclude that $x_1=1$. If there is, then $x \\in \\{2,\\ldots,k\\}$ and we query the range $C[3,3k+1]$. If there is no $\\tau$-majority, then $x \\not\\in \\{3,\\ldots,k\\}$ and we conclude that $x_1=2$, and so on. The process is continued, if necessary, until querying the range $C[k,3k+1]$. If, instead, we had originally found out that $x \\not\\in \\{1,\\ldots,k\\}$, then we look for it analogously in $C[4k+1,8k]$ or $C[8k+1,12k]$. To look for $x_2$, we consider similarly ranges of the form $C[\\ell,3k+2]$, with identical reasoning. This time, it is possible that element $x_1$ is also counted as an answer, but since we already know the value of $x_1$, we simply subtract 1 from the count in any range $C[\\ell,3k+2]$ with $\\ell \\le x_1$. This process continues analogously until we identify $x_k$. The other two thirds of $\\pi_i$ are extracted analogously from $C[12k+1,24k]$ and $C[24k+1,36k]$. Consider encoding $m=1$ permutation $\\pi = (1~5~3~9~2~4~6~8~7)$, of size $3k=9$. Then we set $\\tau=1/8$ and the array $A[1,108]$ is as follows: $$\\begin{aligned} 1,2,3, & {-}1,{-}2,{-}3,{-4},{-}5,{-}6,& 1,5,3 \\\\ 4,5,6,& {-}1,{-}2,{-}3,{-4},{-}5,{-}6,& 1,5,3 \\\\ 7,8,9,& {-}1,{-}2,{-}3,{-4},{-}5,{-}6,& 1,5,3 \\\\ 1,2,3,& {-}1,{-}2,{-}3,{-4},{-}5,{-}6,& 9,2,4 \\\\ 4,5,6,& {-}1,{-}2,{-}3,{-4},{-}5,{-}6,& 9,2,4 \\\\ 7,8,9,& {-}1,{-}2,{-}3,{-4},{-}5,{-}6,& 9,2,4 \\\\ 1,2,3,& {-}1,{-}2,{-}3,{-4},{-}5,{-}6,& 6,8,7 \\\\ 4,5,6,& {-}1,{-}2,{-}3,{-4},{-}5,{-}6,& 6,8,7 \\\\ 7,8,9,& {-}1,{-}2,{-}3,{-4},{-}5,{-}6,& 6,8,7 \\\\\\end{aligned}$$ Now we will find $x_1$ (which is 1, but we do not know it yet). Since $A[1,10]$ has a $\\tau$-majority, we know that $x_1 \\in \\{ 1,2,3 \\}$. Since $A[2,10]$ has no $\\tau$-majority, we know that $x_2 \\not\\in \\{ 2,3\\}$, thus we learn $x_1=1$. Now let us find $x_2$. Since $A[1,11]$ has one $\\tau$-majority, which we know corresponds to $x_1=1$, we conclude that $x_2 \\not\\in \\{ 1,2,3 \\}$. Thus we will have to find it analogously in $A[13,24]$ or in $A[25,36]$. Now let us find $x_3$. Since $A[1,12]$ has two $\\tau$-majorities, one of which we know corresponds to $x_1=1$, and the other we know does not correspond to $x_2$, we conclude that $x_3 \\in \\{ 1,2,3\\}$. Now $A[2,12]$ has one $\\tau$-majority. We know it does not correspond to $x_1=1$ (as it falls outside the range) nor to $x_2$ (as it is not in this subset). Then it follows that $x_3 \\in \\{ 2,3\\}$. Finally, since $A[3,12]$ still has one $\\tau$-majority, we conclude $x_3 \\in \\{ 3 \\}$, thus $x_3=3$. Element $x_2$ will be found in $A[13,24]$. Elements $x_4,x_5,x_6$ will be obtained from $A[37,72]$ and elements $x_7,x_8,x_9$ from $A[73,108]$. Now, since $n=36km$ and $\\tau=1/(2k+2)$, we have that any encoding able to answer the above queries requires at least $$m\\lg \\left((3k)!\\right) > m\\left(3k \\lg (3k) - 3k \\lg e + 1\\right) > \\frac{n}{12}\\left(\\lg\\left(\\frac{3}{2}\\frac{1}{\\tau}-3\\right) - \\lg e\\right)$$ bits[^2]. This is $\\Omega(n\\log(1/\\tau))$ unless $1/\\tau \\le 2+\\frac{2}{3}e = O(1)$, thus it is sufficient that we show that $\\Omega(n)$ is a lower bound for any constant $\\tau \\ge 1/(2+\\frac{2}{3}e) > 1/4$. To show that $\\Omega(n)$ bits are necessary for any $\\tau \\ge 1/4$, consider encoding a bitmap $B[1,m]$ in an array $A[1,4m]$ so that, if $B[i]=0$, then $A[4(i-1)+1]=1$, $A[4(i-1)+2]=2$, $A[4(i-1)i+3]=3$, and $A[4i]=4$. Instead, if $B[i]=1$, then $A[4(i-1)+1,4i]=1$. Then, for any $\\tau \\ge 1/4$, there is a $\\tau$-majority in $A[4(i-1)+1,4i]$ iff $B[i]=1$. As there are $2^m$ possible bitmaps $B$ and our array is of length $n=4m$, we need at least $m = n/4 = \\Omega(n)$ bits for any encoding. Then the proof of Theorem \\[thm:lb\\] is complete. An $O((n/\\tau)\\log\\log n)$ Bits Encoding for Range $\\tau$-Majorities {#sec:nlglgn} ==================================================================== In this section we obtain an encoding using $O((n/\\tau)\\log\\log n)$ bits and solving $\\tau$-majority queries in $O((1/\\tau)\\log n)$ time. In the next section we improve the space usage. We assume that $\\tau$ is fixed at construction time. At query time, we will be able to solve any $\\tau'$-majority query for any $\\tau \\le \\tau' < 1$. The Basic Idea -------------- Consider each distinct symbol $x$ appearing in $A[1,n]$. Now consider the set of all the segments $S_x$ within $[1,n]$ where $x$ is a $\\tau$-majority (this includes, in particular, all the segments $[k,k]$ where $A[k]=x$). Segments in $S_x$ may overlap each other. Now let $A_x[1,n]$ be a bitmap such that $A_x[k]=1$ iff position $k$ belongs to some segment in $S_x$. We define a second bitmap related to $x$, $M_x$, so that if $A_x[k]=1$, then $M_x[rank(A_x,k)]=1$ iff $A[k]=x$, where operation $rank$ was defined in Section \\[sec:bitmaps\\]. Let our running example array be $A[1,7] = \\langle 1~3~2~3~3~1~1\\rangle$, and $\\tau=1/2$. Then we have the segments $S_x$: $$\\begin{aligned} S_1 &=& \\{ [1,1], [6,6], [7,7], [6,7], [5,7] \\},\\\\ S_2 &=& \\{ [3,3] \\},\\\\ S_3 &=& \\{ [2,2], [4,4], [5,5], [4,5], [2,4], [3,5], [4,6], [2,5], [1,5], [2,6] \\},\\end{aligned}$$ and the corresponding bitmaps $A_x$: $$A_1 ~=~ \\langle 1~0~0~0~1~1~1 \\rangle, ~~~ A_2 ~=~ \\langle 0~0~1~0~0~0~0 \\rangle, ~~~ A_3 ~=~ \\langle 1~1~1~1~1~1~0 \\rangle.$$ Finally, the corresponding bitmaps $M_x$ are: $$M_1 ~=~ \\langle 1~0~1~1 \\rangle, ~~~ M_2 ~=~ \\langle 1 \\rangle, ~~~ M_3 ~=~ \\langle 0~1~0~1~1~0 \\rangle.$$ Then, the following result is not difficult to prove. \\[lem:Ax\\] An element $x$ is a $\\tau'$-majority in $A[i,j]$ iff $A_x[k]=1$ for all $i\\le k\\le j$, and 1 is a $\\tau'$-majority in $M_x[rank(A_x,i),rank(A_x,j)]$. If $x$ is a $\\tau'$-majority in $A[i,j]$, then it is also a $\\tau$-majority. Thus, by definition, $[i,j] \\in S_x$, and therefore all the positions $k \\in [i,j]$ are set to 1 in $A_x$. Therefore, the whole segment $A_x[i,j]$ is mapped bijectively to $M_x[rank(A_x,i),rank(A_x,j)]$, which is of the same length. Finally, the number of occurrences of $x$ in $A[i,j]$ is the number of occurrences of 1 in $M_x[rank(A_x,i),$ $rank(A_x,j)]$, which establishes the result. Conversely, if $A_x[k]=1$ for all $i\\le k\\le j$, then $A[i,j]$ is bijectively mapped to $M_x[rank(A_x,i),rank(A_x,j)]$, and the 1s in this range correspond one to one with occurrences of $x$ in $A[i,j]$. Therefore, if 1 is a $\\tau'$-majority in $M_x[rank(A_x,i),$ $rank(A_x,j)]$, then $x$ is a $\\tau'$-majority in $A[i,j]$. Value 1 is a majority in $A[5,7]$, and it holds that $A_1[5,7] = \\langle 1~1~1 \\rangle$ and $M_1[rank(A_1,5),rank(A_1,7)] = M_1[2,4] = \\langle 0~1~1 \\rangle$, where 1 is a majority. Thus, with $A_x$ and $M_x$ we can determine whether $x$ is a majority in a range. \\[lem:algox\\] It is sufficient to have $rank$-enabled bitmaps $A_x$ and $M_x$ to determine, in constant time, whether $x$ is a $\\tau'$-majority in any $A[i,j]$. We use Lemma \\[lem:Ax\\]. We compute $i'=rank(A_x,i)$ and $j'=rank(A_x,j)$. If $j'-i' \\not= j-i$, then $A_x[k]=0$ for some $i \\le k \\le j$ and thus $x$ is not a $\\tau$-majority in $A[i,j]$, hence it is also not a $\\tau'$-majority. Otherwise, we find out whether 1 is a $\\tau'$-majority in $M_x[i',j']$, by checking whether $rank(M_x,j')-rank(M_x,i'-1)>\\tau'(j'-i'+1)$. To find any position $i \\le k \\le j$ where $A[k]=x$, we need the operation $select(B,j)$, defined in Section \\[sec:bitmaps\\]. Then, for example, if $x$ is a $\\tau'$-majority in $A[i,j]$, its leftmost occurrence in $A[i,j]$ is $i-i'+select(M_x,rank(M_x,i'-1)+1)$. In general, for any $1 \\le t \\le rank(M_x,j')-rank(M_x,i'-1)$, we can retrieve the $t$th occurrence with $i-i'+select(M_x,rank(M_x,i'-1)+t)$. Coalescing the Bitmaps ---------------------- We cannot afford to store (and probe!) all the bitmaps $A_x$ and $M_x$ for all $x$, however. The next lemma is the first step to reduce the total space to slightly superlinear. \\[lem:five1s\\] For any position $A[k]=x$ there are at most $2\\lceil 1/\\tau\\rceil$ 1s in $A_x$. Consider a process where we start with $A[k]=\\,\\perp$ for all $k$, and set the values $A[k]=x$ progressively. We will distinguish three kinds of changes. #### [(1) New segments around $A[k]$ are created in $S_x$]{} Setting $A[k]=x$ creates in $S_x$ all the segments of the form $[k-k_l,k+k_r]$ for $1>\\tau(k_r+k_l+1)$, or $k_l+k_r < 1/\\tau-1$. Their union is the area $A_x[k-\\lceil 1/\\tau\\rceil+2,\\ldots, k+\\lceil 1/\\tau\\rceil-2]=1$, which may increase the number of 1s in $A_x$ by up to $2\\lceil 1/\\tau\\rceil-3$. #### [(2) Segments already covering $A[k]$ are extended]{} Any maximal segment $[l,r] \\in S_x$ covering $A_x[k]$ contains $c > \\tau(r-l+1)$ occurrences of $x$, but it holds that $c \\le \\tau(r-l+2)$, otherwise there would also exist segments $[l-1,r]$ and $[l,r+1]$ in $S_x$, and $[l,r]$ would not be maximal. Therefore, adding one more occurrence, $A[k]=1$, we get $c+1 \\le \\tau(r-l+2+1/\\tau)$ occurrences in $[l,r]$. Now it holds that $x$ may be a $\\tau$-majority in segments $[l-k_l,r+k_r]$ for all $0 \\le k_l+k_r < 1+1/\\tau$ (i.e., where $c+1 > \\tau(r-l+1+k_l+k_r)$, using only that $c+1 \\le \\tau(r-l+2+1/\\tau)$), and therefore we can extend $[l,r]$ to the left by up to $\\lceil 1/\\tau\\rceil$, or to the right by up to $\\lceil 1/\\tau\\rceil$. #### [(3) Segments reaching close to $A[k]$ are extended]{} The same reasoning as for the previous case applies, even if $[l,r]$ does not originally contain position $k$. There are more restrictions, since now $[l-k_l,r+k_r]$ must be so that it contains $k$, and the same limit $0 \\le k_l+k_r < 1+1/\\tau$ applies. Thus, in addition to being possible to extend them by at most $\\lceil 1/\\tau\\rceil$ cells in either direction, position $k$ must lie within the extended area. #### Total extension The three cases above are superimposed. Let $\\ell_l$ and $\\ell_r$ the closest positions $\\ell_l \\le k \\le \\ell_r$ where $A_x[\\ell_l] = A_x[\\ell_r] = 1$. Then, if $\\ell_l=k$, we can set at most $\\lceil 1/\\tau\\rceil$ new 1s in $A_x$ to the left of $k$ by extending segments using case (2). Otherwise, if $k-\\ell_l \\le \\lceil 1/\\tau\\rceil$, we can cover the area $A_x[\\ell_l+1,\\ldots,k]$ and add up to $\\lceil 1/\\tau\\rceil-(k-\\ell_l)$ further cells to the left, using case (3). Otherwise, if $k-\\ell_l > \\lceil 1/\\tau\\rceil$, we set $\\lceil 1/\\tau\\rceil-2$ cells to the left, apart from $k$, using case (1). The same reasoning applies to the right, and therefore $2 \\lceil 1/\\tau\\rceil$ is an upper bound to the number of 1s in $A_x$ produced by each new occurrence of $x$ in $A$. The lemma shows that all the $A_x$ bitmaps add up to $O(n/\\tau)$ 1s, and thus the lengths of all the $M_x$ bitmaps add up to $O(n/\\tau)$ as well (recall that $M_x$ has one position per 1 in $A_x$). Therefore, we can store all the $M_x$ bitmaps within $O(n/\\tau)$ bits of space. We cannot, however, store all the $A_x$ bitmaps, as they may add up to $O(n^2)$ 0s (note there can be $O(n)$ distinct symbols $x$), and we still cannot probe all the $A_x$ bitmaps for all $x$ in $o(n)$ time. Instead, we will [*coalesce*]{} all the bitmaps $A_x$ into a smaller number of bitmaps $A'_r$ (which will be called coalesced bitmaps). Coalescing works as follows. Let us write $A[i,j]=b$ to mean $A[\\ell]=b$ for all $i \\le \\ell \\le j$. We start with all $A'_r[1,n]=0$ for all $r$. Then we take each maximal area of all 1s of each bitmap, $A_x[i,j]=1$, choose some $r$ such that $A'_r[i-1,j+1]=0$, and set $A'_r[i,j]=1$. That is, we copy the run of 1s from $A_x$ to some coalesced bitmap $A'_r$ such that the run does not overlap nor touch other previous runs already copied (i.e., there must be at least one 0 between any two copied runs of 1s). We associate to each such $A'_r$ a bitmap $M'_r$ where the areas of each $M_x$ corresponding to each coalesced area of $A_x$ are concatenated, in the same order of the coalesced areas. That is, if $A'_r[i_t,j_t]=1$, the $t$th left-to-right run of 1s in $A'_r$, was copied from $A_x$, then $M_x[rank(A_x,i_t),rank(A_x,j_t)]$ will be the $t$th segment appended to $M'_r$. We can coalesce the whole bitmaps $A_1$ and $A_2$ into $A' = \\langle 1~0~1~0~1~1~1 \\rangle$, with the corresponding bitmap $M' = \\langle 1~1~0~1~1 \\rangle$. The coalesced bitmaps $A'_r$ and $M'_r$ will replace the original bitmaps $A_x$ and $M_x$. At query time, we check for the area $[i,j]$ of each coalesced bitmap using Lemma \\[lem:algox\\]. We cannot confuse the areas of different symbols $x$ because we force that there is at least one 0 between any two areas. We cannot report the same $\\tau'$-majority $x$ in more than one coalesced bitmap, as both areas should overlap on $[i,j]$ and then they would have been merged as a single area in $A_x$. If we find one $\\tau'$-majority in one coalesced bitmap, we know that there is a $\\tau'$-majority $x$ and can spot all of its occurrences (or the leftmost, if desired) in optimal time, even if we cannot know the identity of $x$. Moreover, we will find all the distinct $\\tau'$-majorities in this way. Bounding the Number of Coalesced Bitmaps ---------------------------------------- This scheme will work well if we obtain just a few coalesced bitmaps overall. Next we show how to obtain only $O((1/\\tau)\\log n)$ coalesced bitmaps. \\[lem:2lgn\\] At most $2\\log_{1+\\tau} n$ distinct values of $x$ can have $A_x[k]=1$ for a given $k$. First, $A[k]=x$ is a $\\tau$-majority in $A[k,k]$, thus $A_x[k]=1$. Now consider any other element $x' \\not=x$ such that $A_{x'}[k]=1$. This means that $x'$ is a $\\tau$-majority in some $[i,j]$ that contains $k$. Since $A[k]\\not=x'$, it must be that $x'$ is a $\\tau$-majority in $[i,k-1]$ or in $[k+1,j]$ (or in both). We say $x'$ is a left-majority in the first case and a right-majority in the second. Let us call $y_1, y_2, \\ldots$ the $x'$ values that are left-majorities, and $i_1, i_2, \\ldots$ the starting points of their segments (if they are $\\tau$-majorities in several segments covering $k$, we choose one arbitrarily). Similarly, let $z_1, z_2, \\ldots$ be the $x'$ values that are right-majorities, and $j_1, j_2, \\ldots$ the ending points of their segments. Assume the left-majorities are sorted by decreasing values of $i_r$ and the right-majorities are sorted by increasing values of $j_r$. If a same value $x'$ appears in both lists, we arbitrarily remove one of them. As an exception, we will start both lists with $y_0 = z_0 = x$, with $i_0=j_0=k$. It is easy to see by induction that $y_r$ must appear at least $(1+\\tau)^r$ times in the interval $[i_r,k]$ (or in $[i_r,k-1]$, which is the same). This clearly holds for $y_0 = x$. Now, by the inductive hypothesis, values $y_0, y_1, \\ldots, y_{r-1}$ appear at least $(1+\\tau)^0, (1+\\tau)^1,\\ldots,(1+\\tau)^{r-1}$ times within $[i_{r-1},k-1]$ (which contains all the intervals), adding up to $\\frac{(1+\\tau)^r-1}{\\tau}$ occurrences. Thus $k-1-i_{r-1}+1 \\ge \\frac{(1+\\tau)^r-1}{\\tau}$. In order to be a left-majority, element $y_r$ must appear strictly more than $\\tau(k-i_{r-1}) \\ge (1+\\tau)^r-1$ times in $[i_r,k-1]$, to outweight all the occurrences of the previous symbols. The case of right-majorities is analogous. This shows that there cannot be more than $\\log_{1+\\tau} n$ left-majorities and $\\log_{1+\\tau} n$ right-majorities. In the following it will be useful to define $C_x$ as the set of maximal contiguous areas of 1s in $A_x$. That is, $C_x$ is obtained by merging all the segments of $S_x$ that touch or overlap. Note that segments of $C_x$ do not overlap, unlike those of $S_x$. Since a segment of $C_x$ covers a position $k$ iff some segment of $S_x$ covers position $k$ (and iff $A_x[k]=1$), it follows by Lemma \\[lem:2lgn\\] that any position is covered by at most $2\\log_{1+\\tau} n$ segments of $C_x$ of distinct symbols $x$. Note that a pair of consecutive positions $A[k]=x$ and $A[k+1]=y$ is also covered by at most $2\\log_{1+\\tau} n$ such segments: the right-majorities for $A[k]$ either are $y$ or are also right-majorities for $A[k+1]$, and those are already among the $\\log_{1+\\tau} n$ right-majorities of $A[k+1]$. And vice versa. We obtain $O(\\log_{1+\\tau} n)$ coalesced bitmaps as follows. We take the union of all the sets $C_x$ of all the symbols $x$ and sort the segments by their starting points. Then we start filling coalesced bitmaps. We check if the current segment can be added to an existing bitmap without producing overlaps (and leaving a 0 in between). If we can, we choose any appropriate bitmap, otherwise we start a new bitmap. If at some point we need more than $2\\log_{1+\\tau} n$ bitmaps, it is because all the last segments of the current $2\\log_{1+\\tau} n$ bitmaps overlap either the starting point of the current segment or the previous position, a contradiction. We have $C_1 = \\{ [1,1], [5,7]\\}$, $C_2 = \\{ [3,3] \\}$, and $C_3 = \\{ [1,6] \\}$. Now, we take $C_1 \\cup C_2 \\cup C_3 = \\{ [1,1], [1,6], [3,3], [5,7] \\}$, and the process produces precisely the coalesced bitmaps $A'$, corresponding to the set $\\{ [1,1], [3,3], [5,7] \\}$, and $A_3$, corresponding to $\\{ [1,6] \\}$. Note that in general the coalesced bitmaps may not correspond to the union of complete original bitmaps $A_x$, but areas of a bitmap $A_x$ may end up in different coalesced bitmaps. Therefore, the coalescing process produces $O(\\log_{1+\\tau} n) = O((1/\\tau)\\log n)$ bitmaps. Consequently, we obtain $O((1/\\tau)\\log n)$ query time by simply checking the coalesced bitmaps one by one using Lemma \\[lem:algox\\]. Finally, representing the $O((1/\\tau)\\log n)$ coalesced bitmaps $A'$, which have total length $O((n/\\tau)\\log n)$ and contain $O(n/\\tau)$ 1s, requires $O((n/\\tau)\\log\\log n)$ bits if we use a compressed bitmap representation [@RRR07] that still offers constant-time $rank$ and $select$ queries (recall Section \\[sec:bitmaps\\]). The coalesced bitmaps $M'$ still have total length $O(n/\\tau)$. This completes the first part of our result. Next, we will reduce the space usage of our encoding. Reducing the Space to $O(n\\log(1/\\tau))$ Bits {#sec:nbits} ============================================= We introduce a different representation of the coalesced bitmaps that allows us to store them in $O(n\\log(1/\\tau))$ bits, while retaining the same mechanism described above. We note that, although there can be $O(n/\\tau)$ bits set in the bitmaps $A_x$, each new element $x$ produces at most one new [*run*]{} of contiguous 1s (case (1) in the proof of Lemma \\[lem:five1s\\]). Therefore there are at most $n$ runs in total. We will use a representation of coalesced bitmaps that takes advantage of these runs. We will distinguish segments of $C_x$ by their lengths, separating lengths by ranges between $\\lceil 2^\\ell/\\tau \\rceil$ and $\\lceil 2^{\\ell+1}/\\tau\\rceil -1$, for any [*level*]{} $0 \\le \\ell \\le \\lg(\\tau n)$ (level $0$ is special in that it contains lengths starting from 1). In the process of creating the coalesced bitmaps described in the previous section, we will have separate coalesced bitmaps for inserting segments within each range of lengths; these will be called bitmaps of level $\\ell$. There may be several bitmaps of the same level. It is important that, even with this restriction, our coalescing process will still generate $O((1/\\tau)\\log n)$ bitmaps, because only $O(1/\\tau)$ coalesced bitmaps of each level $\\ell$ will be generated. \\[lem:8lev\\] There can be at most $4/\\tau$ segments of any $C_x$, of length between $\\lceil 2^\\ell/\\tau \\rceil$ and $\\lceil 2^{\\ell+1}/\\tau \\rceil -1$, covering a given position $k$, for any $\\ell$. Any such segment must be contained in the area $A[k-\\lceil 2^{\\ell+1}/\\tau\\rceil+1, k+\\lceil 2^{\\ell+1}/\\tau\\rceil-1]$, and if $x$ is a $\\tau$-majority in it, it must appear more than $\\tau \\lceil 2^\\ell / \\tau \\rceil \\ge 2^\\ell $ times. There can be at most $4/\\tau$ different values of $x$ appearing more than $2^\\ell$ times in an area of length less than $2^{\\ell+2}/\\tau$. Consider a coalesced bitmap $A'[1,n]$ of level $\\ell$. All of its 1s come in runs of lengths at least $b = \\lceil 2^\\ell/\\tau\\rceil$. We cut $A'$ into [*chunks*]{} of length $b$ and define two bitmaps: $A'_1[1,n/b]$ will have $A'_1[i]=1$ iff the $i$th chunk of $A'$ is all 1s, and $A'_2[1,n/b]$ will have $A'_2[i]=1$ iff the $i$th chunk of $A'$ has 0s and 1s. Note that, since the runs of 1s are of length at least $b$, inside a chunk with 0s and 1s there can be at most one 01 and at most one 10, and the 10 can only come before the 01. Let $p_{10}[j]$ be the position, in the $j$th chunk with 0s and 1s, of the 1 preceding a 0, where $p_{10}[j]=0$ if the chunk starts with a 0. Similarly, let $p_{01}[j]$ be the position of the 0 preceding a 1, with $p_{01}[j]=b$ if the chunk ends with a 0. It always holds that $p_{10}[j] < p_{01}[j]$, and the number of 1s in the chunk is $r(j)=p_{10}[j]+(b-p_{01}[j])$. Also, the rank up to position $k$ in the chunk, $r(j,k)$, is $k$ if $k \\le p_{10}[j]$, $p_{10}[j]$ if $p_{10}[j] < k \\le p_{01}[j]$, and $p_{10}[j]+(k-p_{01}[j])$ if $k > p_{01}[j]$. Then it holds that $$\\begin{aligned} && rank(A',i) ~~=~~ b\\cdot r_1 ~+~ \\sum_{j=1}^{r_2} r(j) ~+~ \\\\ && ~~~~~~~~~~~~~~~ [\\mathbf{if}~A'_2[1+\\lfloor i/b \\rfloor]=1~\\mathbf{then}~ r(r_2+1,k)~\\mathbf{else}~ A'_1[1+\\lfloor i/b \\rfloor]\\cdot k],\\end{aligned}$$ where $r_1 = rank(A'_1,\\lfloor i/b\\rfloor)$, $r_2 = rank(A'_2,\\lfloor i/b\\rfloor)$, and $k = i~\\mathrm{mod}~b$. Note this can be computed in constant time as long as we have constant-time $rank$ data structures on $A'_1$ and $A'_2$, and constant-time access and sums on $p_{10}$ and $p_{01}$. Using $b=2^\\ell$ to make it more interesting, we would have three coalesced bitmaps: $A' = \\langle 1~0~1~0~0~0~0 \\rangle$, of level $\\ell=0$, for the segments $[1,1]$ and $[3,3]$; $A'' = \\langle 0~0~0~0~1~1~1 \\rangle$, of level $\\ell=1$, for the segment $[5,7]$; and $A''' = \\langle 1~1~1~1~1~1~0 \\rangle$, of level $\\ell=2$, for the segment $[1,6]$. Consider level $\\ell=0$ and $b=2$, and let us focus on $A'$. Then, we would have $A'_1 = \\langle 0~0~0~0 \\rangle$, $A'_2 = \\langle 1~1~0~0 \\rangle$, $p_{10} = \\langle 1~1 \\rangle$, and $p_{01} = \\langle 2~2 \\rangle$. To have constant-time sums on $p_{10}$ ($p_{01}$ is analogous), we store its values in a bitmap $A'_{10}$, where we set all the bits at positions $r + \\sum_{j=1}^r p_{10}[j]$ to 1, for all $r$. Then we can recover $\\sum_{j=1}^r p_{10}[j] = select(A'_{10},r)-r$. We use a bitmap representation [@OS07] that solves $select$ in constant time (recall Section \\[sec:bitmaps\\]). Let $n'$ be the number of segments $C_x$ represented in bitmap $A'$. Then there are at most $2n'$ chunks with 0s and 1s, and $A'_{10}$ contains at most $2n'$ 1s and $2n'b$ 0s (as $0 \\le p_{10}[j] \\le b$). The size of the bitmap representation [@OS07] is in this case $O(n'\\log b) = O(n'(\\ell + \\log(1/\\tau)))$ bits. On the other hand, bitmaps $A'_1$ and $A'_2$ are represented in plain form [@Mun96; @Cla96], requiring $O(n/b) = O(n\\tau/2^\\ell)$ bits. Considering that there are $O(n/\\tau)$ 1s overall, and that the runs of level $\\ell$ are of length at least $2^\\ell/\\tau$, we have that there can be at most $n/2^\\ell$ runs across the $O(1/\\tau)$ bitmaps of level $\\ell$. Therefore, adding up the space over the bitmaps of level $\\ell$, we have $O(n(\\ell+\\log(1/\\tau))/2^\\ell)$ bits. Added over all the levels $\\ell$, this gives $O(n\\log(1/\\tau))$ bits. Let us now consider the representation of the coalesced bitmaps $M'$. They have total length $O(n/\\tau)$ and contain $n$ 1s overall, therefore using the representation of Lemma \\[lem:bitmap\\] with $s=1$, we have $O(n\\log(1/\\tau))$ bits of space. They solve $rank$ queries in time $O(\\log\\log_w(1/\\tau))$, and $select$ in constant time. As we have to probe $O((1/\\tau)\\log n)$ coalesced bitmaps $M'$ in the worst case, this raises our query time to $O((1/\\tau)\\log\\log_w(1/\\tau)\\log n)$. This concludes the proof of Theorem \\[thm:main\\], except for the construction time (see the next section). In our previous work [@NT14], we had obtained $O((1/\\tau)\\log n)$ time, but using $O((n/\\tau)\\log^*n)$ bits of space. It is not hard to obtain that time, using $O(n/\\tau)$ bits, by simply representing the coalesced bitmaps $M'$ using plain $rank$/$select$ structures [@Cla96; @Mun96], or even using $O(n\\log(1/\\tau) + (n/\\tau)/\\operatorname{polylog}n)$ bits, for any $\\operatorname{polylog}n$, using compressed representations [@Pat08]. The extra $O(\\log\\log_w(1/\\tau))$ time factor arises when we insist in obtaining the optimal $O(n\\log(1/\\tau))$ bit space. We note that this time penalty factor vanishes when $1/\\tau = w^{O(1)}$, which includes the case where $1/\\tau$ grows polylogarithmically with $n$. Construction {#sec:constr} ============ The most complex part of the construction of our encoding is to build the sets $C_x$. Once these are built, the structures described in Section \\[sec:nbits\\] can be easily constructed in $o(n\\log n)$ time: 1. The $O(n)$ segments $C_x$ belong to $[1,n]$, so they are sorted by starting point in $O(n)$ time. 2. We maintain a priority queue for each level $\\ell$, containing the last segment of each coalesced bitmap. We use the queue to find the segment that finishes earliest in order to try to add the new segment of $C_x$ after it. We carry out, in total, $O(n)$ operations on those queues, and each contains $O(1/\\tau)$ elements, thus they take total time $O(n\\log(1/\\tau))=o(n\\log n)$. 3. The bitmaps $A'$ of each level $\\ell$, represented with $A'_1$, $A'_2$, $A'_{01}$ and $A'_{10}$, are easily built in $O(n/b)=O(n\\tau/2^\\ell)$ time. Added over the $O(1/\\tau)$ coalesced bitmaps of level $\\ell$ this is $O(n/2^\\ell)$, and added over all the levels $\\ell$ this gives $O(n)$ total time. 4. The coalesced bitmaps $M'$ have $O(n)$ 1s overall, so their representation (Lemma \\[lem:bitmap\\]) is also built in $O(n)$ time, except for the predecessor structures, which need construction of deterministic dictionaries. This can be done in $o(n\\log n)$ total time [@Ruz08]. Now we show that the sets $C_x$ can be built in $O(n\\log n)$ time, thus finishing the proof of Theorem \\[thm:main\\]. We build the set of increasing positions $P_x$ where $x$ appears in $A$, for each $x$, in $O(n\\log n)$ total time (the elements of $A$ can be of any atomic type, so we only rely on a comparison-based dictionary to maintain the set of different $x$ values and their $P_x$ lists). Now we build $C_x$ from each $P_x$ using a divide-and-conquer approach, in $O(|P_x|\\log|P_x|)$ time, for a total construction time of $O(n\\log n)$. We pick the middle element $k \\in P_x$ and compute in linear time the segment $[l,r] \\in C_x$ that contains $k$. To compute $l$, we find the leftmost element $p_l \\in P_x$ such that $x$ is a $\\tau$-majority in $[p_l,k_r]$, for some $k_r \\in P_x$ with $k_r \\ge k$. To find $p_l$, we note that it must hold that $(w(p_l,k-1)+w(k,k_r))/(k_r-p_l+1) > \\tau$, where $w(i,j)$ is the number of occurrences of $x$ in $A[i,j]$. The condition is equivalent to $w(p_l,k-1)/\\tau + p_l - 1 > k_r - w(k,k_r)/\\tau$. Thus we compute in linear time the minimum value $v$ of $k_r - w(k,k_r)/\\tau$ over all those $k_r \\in P_x$ to the right of $k$, and then traverse all those $p_l \\in P_x$ to the left of $k$, left to right, to find the first one that satisfies $w(p_l,k-1)/\\tau + p_l + 1 > v$, also in linear time. Once we find the proper $p_l$ and its corresponding $k_r$, the starting position of the segment is slightly adjusted to the left of $p_l$, to be the smallest value that satisfies $w(p_l,k_r)/(k_r-l+1) > \\tau$, that is, $l$ satisfies $l > -w(p_l,k_r)/\\tau +k_r+1$, or $l = k_r - \\lceil w(p_l,k_r)/\\tau \\rceil + 2$. Once $p_r$ and then $r$ are computed analogously, we insert $[l,r]$ into $C_x$ and continue recursively with the elements of $P_x$ to the left of $p_l$ and to the right of $p_r$. Upon return, it might be necessary to join $[l,r]$ with the rightmost segment of the left part and/or with the leftmost segment of the right part, in constant time. The total construction time is $T(n) = O(n) + 2T(n/2) = O(n\\log n)$. #### Building multiple structures In order to answer $\\tau'$-majority queries for any $\\tau \\le \\tau' < 1$ in time related to $1/\\tau'$ and not to $1/\\tau$, we build the encoding of Theorem \\[thm:main\\] for values $\\tau'' = 1/2, 1/4, 1/8, \\ldots, 1/2^{\\lceil \\lg 1/\\tau \\rceil}$. Then, a $\\tau'$-majority query is run on the structure built for $\\tau'' = 1/2^{\\lceil \\lg 1/\\tau' \\rceil}$. Since $\\tau'/2 < \\tau'' \\le \\tau'$, the query time is $O((1/\\tau'')\\log\\log_w(1/\\tau'')\\log n)=O((1/\\tau')\\log\\log_w(1/\\tau')\\log n)$. As for the space, we build $O(\\log(1/\\tau))$ structures, so we use $O(n\\log^2(1/\\tau))$ bits, and the construction time is $O(n\\log(1/\\tau)\\log n)$. \\[cor:vartau\\] Given a real number $0<\\tau<1$, there exists an encoding using $O(n\\log^2(1/\\tau))$ bits that answers range $\\tau'$-majority queries, for any $\\tau \\le \\tau' < 1$, in time $O((1/\\tau')\\log\\log_w(1/\\tau')\\log n)$, where $w=\\Omega(\\log n)$ is the RAM word size in bits. The structure can be built in time $O(n\\log(1/\\tau)\\log n)$. A Faster Data Structure {#sec:optimal} ======================= In this section we show how, by adding $O(n\\log\\log n)$ bits to our data structure, we can slash a $\\log n$ factor from the query time, that is, we prove Theorem \\[thm:optimal\\]. The result, as discussed in the Introduction, yields the optimal query time $O(1/\\tau)$ when $1/\\tau = O(\\operatorname{polylog}n)$, although the resulting space may not be optimal anymore. The idea is inspired in a previous non-encoding data structure for majority queries [@wads]. Consider a value $\\ell$. Then we will cut $A$ into consecutive pieces of length $2^\\ell$ (said to be of [*level*]{} $\\ell$) in two overlapped ways: $A[2^\\ell k+1,2^\\ell(k+1)]$ and $A[2^\\ell k+2^{\\ell-1}+1,2^\\ell(k+1)+2^{\\ell-1}]$, for all $k \\ge 0$. We carry out this partitioning for every $\\lceil \\lg(1/\\tau) \\rceil \\le \\ell \\le \\lceil \\lg n \\rceil$. Note that there are $O(n/2^\\ell)$ pieces of level $\\ell$, and any interval $A[i,j]$ of length up to $2^\\ell/2$ is contained in some piece $P$ of level $\\ell$. Now, given a query interval $A[i,j]$, let $\\ell = \\lceil \\lg(j-i+1)\\rceil+1$. Then, not only $A[i,j]$ is contained in a piece $P$ of level $\\ell$, but also any $\\tau$-majority $x$ in $A[i,j]$ must be a $\\tau/4$-majority in $P$: Since $j-i+1 > 2^\\ell/4$, $x$ occurs more than $\\tau(j-i+1) > (\\tau/4)2^\\ell$ times in $A[i,j]$, and thus in $P$. Consider a $\\tau/4$-majority $x$ in a given piece $P$ of level $\\ell$ that is also a $\\tau$-majority for some range $A[i,j]$ within $P$, where $2^\\ell/4 < j-i+1 \\le 2^\\ell/2$. By construction of our previous structures, there exists a maximal segment $C_x$ that contains the range $[i,j]$. If there is another range $A[i',j']$ within $P$ where $x$ is a $\\tau$-majority, then there exists another maximal segment $C'_x$ for the same $x$ within $P$. By our construction, if $C'_x \\neq C_x$, then $C'_x$ is disjoint with $C_x$, and thus each of them contains at least $(\\tau/4)2^\\ell$ distinct occurrences of $x$. Obviously, segments $C_y$ for $\\tau$-majorities $y \\neq x$ contain other $(\\tau/4)2^\\ell$ occurrences disjoint from those of $x$. Therefore, the number of distinct maximal segments $C$ that contain $\\tau$-majorities at any range $A[i,j]$ (with $j-i+1 > 2^\\ell/4$) within $P$ is upper bounded by $4/\\tau$. We will say those segments $C$ are [*relevant*]{} to $P$. Therefore, for each piece $P$ of level $\\ell$, we will store the index $r$ of the coalesced bitmap $A'_r$ (and its companion $M'_r$) to which each maximal segment $C$ that is relevant to $P$ belongs. Since there are at most $4/\\tau$ such coalesced bitmaps to record, out of a total of $O((1/\\tau)\\log n)$ coalesced bitmaps, $\\gamma$-codes on a differential encoding of the subset values requires $O((1/\\tau)\\log\\log n)$ bits.[^3] Added up over the $O(n/2^\\ell)$ pieces of level $\\ell \\ge \\lceil \\lg(1/\\tau)\\rceil$, this yields $\\sum_{\\ell \\ge \\lceil\\lg(1/\\tau)\\rceil} O((n/2^\\ell) (1/\\tau) \\log\\log n) = O(n\\log\\log n)$ bits. This information reduces the search effort to that of verifying $O(1/\\tau)$ coalesced bitmaps $A'_r$ and $M'_r$ for the range $[i,j]$, and thus to $O((1/\\tau)\\log\\log_w (1/\\tau))$ query time. However, for ranges shorter than $1/\\tau$, where no piece structure has been built, we still have the original query time. To speed up this case, we build a second structure where, for each element $A[k]$, we identify the coalesced bitmap where the maximal segment $C_{A[k]}$ containing the segment $A[k,k]$ belongs, and store the identifier $r$ of the corresponding coalesced bitmap $A'_r$ (and $M'_r$) associated to $k$. This requires $O(n\\log((1/\\tau)\\log n)) = O(n\\log(1/\\tau) + n\\log\\log n)$ further bits, and allows checking only one coalesced bitmap $A'_r$ (and $M'_r$) for each of the $O(1/\\tau)$ positions that need to be checked. To finish the proof we must consider the construction time. The second structure (for short ranges) is easily built with the general structure, taking no additional time, by keeping track of which maximal segment $C_{A[k]}$ contains each segment $A[k,k]$ and which coalesced bitmap it is assigned. With this, the structure for long ranges can be built as follows: for each position $A[k]$ contained in a piece $P$ of level $\\ell$, consider the maximal segment $C_{A[k]}$ that contains it and determine whether it is relevant to $P$. A weak test for this is to consider the coalesced bitmap $M'$ where $C_{A[k]}$ is represented (which is precisely what the first structure stores associated to $k$) and ask whether $M'$ contains more than $(\\tau/4)2^\\ell$ 1s in the range of $P$. This must be the case if $C_{A[k]}$ is relevant to $P$. Although including the identifier of each $M'$ that passes the test may add some nonrelevant ones, we still cannot include more than $4/\\tau$ coalesced bitmaps in the set, as the 1s in the $M'$ bitmaps are disjoint. The $rank$ operations on bitmaps $M'$ take $O(\\log\\log_w(1/\\tau))$ time, so we avoid them to count how many 1s does $M'$ contain in the range of $P$. Instead, we perform a preprocessing pass over $P$ as follows: We initialize to zero a set of $O((1/\\tau)\\log n)$ counters, one per coalesced bitmap $M'$, and process $P$ left to right. We increase the counter associated to the bitmap $M'$ of each element $A[k]$ in $P$. At the end, we know all the desired values. This takes $O(2^\\ell)$ time, and a similar postprocessing pass clears the counter for the next piece. Therefore, we process all the pieces $P$ of level $\\ell$ in time $O(2^\\ell)$, which amounts to $O(n)$ time per level. Added over all the levels, this gives $O(n\\log n)$ total time. This concludes the proof of Theorem \\[thm:optimal\\]. Conclusions {#sec:concl} =========== A $\\tau$-majority query on array $A[1,n]$ receives a range $[i,j]$ and returns all the elements appearing more than $\\tau(j-i+1)$ times in $A[i,j]$. We have obtained the first results about [*encodings*]{} for answering range $\\tau$-majority queries. Encodings are data structures that use less space than what is required to store $A$ and answer queries without accessing $A$ at all. In the encoding scenario we do not report the $\\tau$-majorities themselves, but one of their positions in $A[i,j]$. We have proved that $\\Omega(n\\log(1/\\tau))$ bits are necessary for any such encoding, even if it can only count the number of $\\tau$-majorities in any range. Then we presented an encoding that uses the optimal $O(n\\log(1/\\tau))$ bits, and answers queries in $O((1/\\tau)\\log\\log_w(1/\\tau)\\log n)$ time in the RAM model with word size $w=\\Omega(\\log n)$ bits. We also showed that this time can be divided by $\\log n$ if we add $O(n\\log\\log n)$ bits to the space. This yields various space/time tradeoffs, shown in Table \\[tab:final\\]. Our encoding can actually report any occurrence of each $\\tau$-majority, in optimal extra time. The structure is built in $O(n\\log n)$ time. An open question is whether it is possible to achieve optimal query time within optimal space for all values of $1/\\tau$. As seen in Table \\[tab:final\\], we reach this only for $\\log(1/\\tau)=\\Theta(\\log\\log n)$. This is also possible when $\\log (1/\\tau) = \\Omega(\\log n)$, where we leave the non-encoding scenario [@wads]. Instead, our results for $\\log(1/\\tau)$ between $\\log\\log n$ and $\\log n$ have a small factor $O(\\log\\log_w (1/\\tau))$ over the optimal time, and those for $\\log(1/\\tau)$ below $\\log\\log n$ either require nonoptimal $O(n\\log\\log n)$ bits of space, or an $O(\\log n)$ factor over the optimal time. It is not clear whether combined optimality can be reached. Another open question is whether we can do better for weaker versions of the problem we have not studied. For example, if we are only required to report [*any*]{} occurrence of [*any*]{} $\\tau$-majority (or, even less, telling whether or not there exists a $\\tau$-majority), our lower bound based on representing a bitmap $B$ shows that $\\Omega(n)$ bits are necessary, but we do not know if this bound is tight. [^1]: Or an equivalent array where each element is replaced by an identifier in $[1,n]$. [^2]: Bounding $\\lg (3k)!$ with integrals one obtains $3k \\lg(3k/e) + 1 \\le \\lg (3k)! \\le (3k+1)\\lg((3k+1)/e)+1$. [^3]: We could also afford to store them in plain form using $O((1/\\tau)(\\log(1/\\tau)+\\log\\log n))$ bits.

Sandava Sandava is a genus of moths of the family Erebidae. The genus was erected by Francis Walker in 1863. Species Sandava micrastigma (Kaye, 1901) Trinidad Sandava scitisignata (Walker, 1862) Queensland Sandava xylistis Swinhoe, 1900 Australia References Category:Calpinae Category:Moth genera

Generally, data is always recorded in a document recorded on paper (described a paper document hereinafter) so that people can visually and easily understand it. Accordingly, a paper document itself has a role as a recording medium for recording data thereon and also has a role as a displaying means for displaying data, whereby excellent characteristics are provided in ease in reading, convenience in portability, ease in handling, applicable circumstances, and continuity with actual work. On the other hand, in recent years, electronization of documents has been promoted by improving the computer-related technology and man-machine interface as well as by upgrading the network environment, whereby distribution of a paperless system has been accelerated in offices. Concretely, various types of documents are prepared (electronized) on a screen of a personal computer work station, and the electronized document can be edited, copied, transferred, shared in common, filed, proofread, and searched or the like in the computer (in a digital world or virtual reality). Especially with development of the network, an electronized document can be distributed (transferred) to a personal address as is without outputting it by a printer or the like, so that the paperless system in an office is achieving further progress. Also, electronized documents can automatically and systematically be managed with a document data administrating system constructed in a computer, so that there are such advantages such as that classifying documents to be stored and searching documents to be referred to can easily be carried out, and furthermore that a total volume of documents can be reduced due to increasing of documents held in common, security of confidential documents due to use of a pass word or the like can be improved, and data between documents can be related to each other. However, although there are many advantages in an electronized document, in a case where it is compared to a document outputted onto an actual sheet of paper (described as a paper document hereinafter), there are various types of restrictions relating to ease in reading, convenience in portability, ease in handling, applicable circumstances, and continuity with actual work or the like. Thus in a case where the electronized document is used in actual work, it is sometimes more efficient to use the document as a paper document after it is outputted onto a sheet of record paper by a printer or the like once. Accordingly, a paper document and an electronized document each used according to an object of work will coexist in an office environment in the future. However, with the conventional technology described above, there have been some problems as described below because there are no continuity and no relation of data as digital data between the digital world such as a computer or the like and the paper document. Firstly, even in a case where a document electronized is put under control by the document data administrating system constructed in the digital world, when the electronized document is outputted as a paper document, related data which the electronized document has, for instance, address data in the document data administrating system, security data such as a pass word, linking data with other documents or the like are eliminated, so that a paper document has no value except one as only an output from the document data administrating system. Secondarily, it is impossible to directly access digital world by using a paper document as a medium, so that a user is required to access the digital world by operating a keyboard or the like, which is convenient. It should be noted that there is a method of directly accessing the digital world with paper like a mark sheet as a medium in conventional technology, but mark sheets which are previously formed in one particular pattern are used, so that there are various types of restriction therein, and for this reason mark sheets can not be used as an ordinary type of document. Thirdly, a hyper text document exists in the digital world as an advanced concept of an electronized document, but in a case where this hyper text document is outputted as a paper document, only a plane data (visualized two-dimensional data) is outputted, so that data which the original hyper text has is lost, which causes a loss in data and reduction of the convenience. More specifically, a hyper text is a collection of linked (related) texts (electronized documents), and a basic concept of multi-media software allowing reference to each text hierarchically and multi-dimensionally related to each other in an arbitrary order through the linked construction. Accordingly, this hyper text includes data for forming the linked construction (namely, data as a hyper text) other than data visually provided to a user. However, when a hyper text document is once outputted as a paper document, the data as hyper text is eliminated, so that the outputted paper document does not have features of a hyper text document. It should be noted that, in conventional technology, hyper text documents can exist only as electronized documents, so that the concept of a hyper text itself was used only in the digital world (virtual document) in which electronized documents were handled. Accordingly, there has not existed such a concept that a paper document can be handled as a hyper text document and the hyper text is realized by using the paper document in the real world (this concept is defined as a paper hyper text, and described as paper hyper text hereinafter). With a paper document based on conventional technology, it is assumed that data is always recorded so that people can easily and visually understand it, and for this reason, a quantity of data recordable on a sheet of paper document is physically restricted according to the size of a visible character and the size of a sheet of paper, and also the number of pages (the number of sheets of paper) is increased in proportion to quantity of increased data in an entire document, whereby much more space is required for storing paper documents. With the paper document based on conventional technology, the data recorded on paper was used as final output data which people could easily and visually understand, which means that the data was not generally used for any other purposes. On the other hand, in the digital world, a hyper text document exists as an advanced concept of an electronized document. More specifically, the hyper text is a collection of linked (related) texts (electronized documents), and a basic concept of multimedia software in which texts hierarchically and multi-dimensionally related to each other can be referred in a given order through a linked construction. Accordingly, data for forming a linked construction (namely, data as a hyper text) is included in this hyper text document other than the data visually provided to users. However, in conventional technology, the hyper text document exists as an electronized document, so that the concept of the hyper text itself was used only in the digital world (virtual document) in which electronized documents were handled. Accordingly, there has not existed until now such a concept as that a paper document can be handled as a hyper text document and the hyper text is realized by using the paper document in the real world (this concept is defined as a paper hyper text, and described as paper hyper text hereinafter).

The Magician's Birthday The Magician's Birthday is the fifth album by British rock band Uriah Heep, released in November 1972 by Bronze Records in the UK and Mercury Records in the US. The concept was "based loosely on a short story" written by keyboardist Ken Hensley in June and July 1972. The original vinyl release was a gatefold sleeve, the front designed again by Roger Dean. The inner fold had pictures of the band, with the album itself housed in a liner on which were printed the lyrics. The single "Sweet Lorraine" / "Blind Eye" reached No. 91 in the US Hot 100 chart. The single "Spider Woman" reached No. 14 in Germany. The Magician's Birthday was certified gold by the RIAA on 22 January 1973. The album was remastered and reissued by Castle Communications in 1996 with two bonus tracks, and again in 2003 in an expanded deluxe edition. In 2017, Sanctuary Records released a two-disc version. Reception The Magician's Birthday received mixed reviews from contemporary critics. Mike Saunders, writing for Creem, called the album "a package full of dreck", finding the first side of the LP "listenable" despite poor production and side two downright "irritating". Village Voice critic Robert Christgau described the songs on the album as "third-hand heavy metal fantasies (...) hooked to some clean, powerful arrangements, and a good melody or two." Modern reviews are more positive. AllMusic reviewer remarked the album's prog elements and wrote that "The Magician's Birthday never quite hits the consistent heights of Look at Yourself or Demons and Wizards, but remains a solid listen for Uriah Heep fans". Joe Geesein of Record Collector praised the musicians and the good sound of the album's reissue, but wrote that most of the songs "don’t stand up quite out so well" in comparison with opener "Sunrise" or the single "Spider Woman". Canadian journalist Martin Popoff called The Magician's Birthday "another colourful, mystical journey", although "somewhat disjointed, less accessible and in total much less metallic" than previous efforts, "culminating in the band's most harrowing, nightmarish epic of them all, the ten minute title track." Track listings Personnel Credits adapted from album liner notes Uriah Heep David Byron – lead vocals Mick Box – guitars Ken Hensley – keyboards, guitars, Moog synthesizer, kazoo (8) Gary Thain – bass Lee Kerslake – drums, percussion Additional musicians Brian Cole – pedal steel guitar on "Tales" Production Gerry Bron – producer Peter Gallen – engineer Ashley Howe – assistant engineer Gilbert Kong – mastering Mike Brown and Robert Corich – remastering (1996 and 2003 reissues) Charts Album Singles Certifications References Category:1972 albums Category:Uriah Heep (band) albums Category:Albums with cover art by Roger Dean (artist) Category:Albums produced by Gerry Bron Category:Bronze Records albums Category:Mercury Records albums

Q: Android: How to bind spinner to custom object list? In the user interface there has to be a spinner which contains some names (the names are visible) and each name has its own ID (the IDs are not equal to display sequence). When the user selects the name from the list the variable currentID has to be changed. The application contains the ArrayList Where User is an object with ID and name: public class User{ public int ID; public String name; } What I don't know is how to create a spinner which displays the list of user's names and bind spinner items to IDs so when the spinner item is selected/changed the variable currentID is set to appropriate value. I would appreciate if anyone could show the solution of the described problem or provide any link useful to solve the problem. Thanks! A: I know the thread is old, but just in case... User object: public class User{ private int _id; private String _name; public User(){ this._id = 0; this._name = ""; } public void setId(int id){ this._id = id; } public int getId(){ return this._id; } public void setName(String name){ this._name = name; } public String getName(){ return this._name; } } Custom Spinner Adapter (ArrayAdapter) public class SpinAdapter extends ArrayAdapter<User>{ // Your sent context private Context context; // Your custom values for the spinner (User) private User[] values; public SpinAdapter(Context context, int textViewResourceId, User[] values) { super(context, textViewResourceId, values); this.context = context; this.values = values; } @Override public int getCount(){ return values.length; } @Override public User getItem(int position){ return values[position]; } @Override public long getItemId(int position){ return position; } // And the "magic" goes here // This is for the "passive" state of the spinner @Override public View getView(int position, View convertView, ViewGroup parent) { // I created a dynamic TextView here, but you can reference your own custom layout for each spinner item TextView label = (TextView) super.getView(position, convertView, parent); label.setTextColor(Color.BLACK); // Then you can get the current item using the values array (Users array) and the current position // You can NOW reference each method you has created in your bean object (User class) label.setText(values[position].getName()); // And finally return your dynamic (or custom) view for each spinner item return label; } // And here is when the "chooser" is popped up // Normally is the same view, but you can customize it if you want @Override public View getDropDownView(int position, View convertView, ViewGroup parent) { TextView label = (TextView) super.getDropDownView(position, convertView, parent); label.setTextColor(Color.BLACK); label.setText(values[position].getName()); return label; } } And the implementarion: public class Main extends Activity { // You spinner view private Spinner mySpinner; // Custom Spinner adapter (ArrayAdapter<User>) // You can define as a private to use it in the all class // This is the object that is going to do the "magic" private SpinAdapter adapter; @Override public void onCreate(Bundle savedInstanceState) { super.onCreate(savedInstanceState); setContentView(R.layout.main); // Create the Users array // You can get this retrieving from an external source User[] users = new User[2]; users[0] = new User(); users[0].setId(1); users[0].setName("Joaquin"); users[1] = new User(); users[1].setId(2); users[1].setName("Alberto"); // Initialize the adapter sending the current context // Send the simple_spinner_item layout // And finally send the Users array (Your data) adapter = new SpinAdapter(Main.this, android.R.layout.simple_spinner_item, users); mySpinner = (Spinner) findViewById(R.id.miSpinner); mySpinner.setAdapter(adapter); // Set the custom adapter to the spinner // You can create an anonymous listener to handle the event when is selected an spinner item mySpinner.setOnItemSelectedListener(new OnItemSelectedListener() { @Override public void onItemSelected(AdapterView<?> adapterView, View view, int position, long id) { // Here you get the current item (a User object) that is selected by its position User user = adapter.getItem(position); // Here you can do the action you want to... Toast.makeText(Main.this, "ID: " + user.getId() + "\\nName: " + user.getName(), Toast.LENGTH_SHORT).show(); } @Override public void onNothingSelected(AdapterView<?> adapter) { } }); } } A: Simplest Solution After scouring different solutions on SO, I found the following to be the simplest and cleanest solution for populating a Spinner with custom Objects. Here's the full implementation: User.java public class User{ public int ID; public String name; @Override public String toString() { return this.name; // What to display in the Spinner list. } } res/layout/spinner.xml <?xml version="1.0" encoding="utf-8"?> <TextView xmlns:android="http://schemas.android.com/apk/res/android" android:layout_width="fill_parent" android:layout_height="wrap_content" android:padding="10dp" android:textSize="14sp" android:textColor="#FFFFFF" android:spinnerMode="dialog" /> res/layout/your_activity_view.xml <?xml version="1.0" encoding="utf-8"?> <LinearLayout xmlns:android="http://schemas.android.com/apk/res/android" android:layout_width="fill_parent" android:layout_height="fill_parent" android:orientation="vertical"> <Spinner android:id="@+id/user" /> </LinearLayout> In Your Activity List<User> users = User.all(); // This example assumes you're getting all Users but adjust it for your Class and needs. ArrayAdapter userAdapter = new ArrayAdapter(this, R.layout.spinner, users); Spinner userSpinner = (Spinner) findViewById(R.id.user); userSpinner.setAdapter(userAdapter); userSpinner.setOnItemSelectedListener(new AdapterView.OnItemSelectedListener() { @Override public void onItemSelected(AdapterView<?> parent, View view, int position, long id) { // Get the value selected by the user // e.g. to store it as a field or immediately call a method User user = (User) parent.getSelectedItem(); } @Override public void onNothingSelected(AdapterView<?> parent) { } }); A: For simple solutions you can just Overwrite the "toString" in your object public class User{ public int ID; public String name; @Override public String toString() { return name; } } and then you can use: ArrayAdapter<User> dataAdapter = new ArrayAdapter<User>(mContext, android.R.layout.simple_spinner_item, listOfUsers); This way your spinner will show only the user names.

Introduction ============ Metal nanoparticles with at least one dimension approximately 1-100 nm have received considerable attention in both scientific and technological areas due to their unique and unusual physico-chemical properties compared with that of bulk materials \\[[@B1]\\]. Phenomena at the nanoscale are likely to be a completely new world, where properties may not be predictable from those observed at large size scales, on account of quantum size effect and surface effects. Synthesis of nanoparticles has been a rapidly growing field in solid state chemistry \\[[@B2]\\]. Metal nanoparticles are particularly interesting because they can easily be synthesized and modified chemically as well as can suitably be applied for device fabrication \\[[@B3]-[@B5]\\]. Due to the specific size, shape, and distribution, nanoparticles are used in the production of novel systems such as nanosensors \\[[@B6]\\], nanoresonators \\[[@B7]\\], nanoactuators \\[[@B8]\\], nanoreactors \\[[@B9]\\], single electron tunneling devices \\[[@B10]\\], plasmonics \\[[@B11]\\], and nanowire based devices \\[[@B12]\\] etc. Among the various metal nanostructures, noble metal nanoparticles have attracted much attention, due to their superior physical and chemical properties. Nowadays, a lot of researches have been focused on silver nanoparticles because of their important scientific and technological applications in color filters \\[[@B13],[@B14]\\], optical switching \\[[@B15]\\], optical sensors \\[[@B16],[@B17]\\], and especially in surface-enhanced Raman scattering \\[[@B18]-[@B20]\\]. Such properties and applications strongly depend on the morphology, crystal structure, and dimensions of silver nanostructures. Over recent years, silver thin films have been a subject of intensive investigations because of excellent optical, electrical, catalytic, sensing, and antibacterial properties \\[[@B21],[@B22]\\] and subsequent applications. The synthesis of silver nanoparticles with controlled morphology is important for uncovering their specific properties and for achieving their practical applications. Silver nanoparticles are of current importance because of its easy preparation process and unique optical, electrical, and thermal properties. The electrical conductivity of polyaniline-silver nanocomposite increases with increase in silver nanoparticles content than that of pure polyaniline \\[[@B23],[@B24]\\]. Pillai et al. \\[[@B25]\\] demonstrated that solar cells employing metallic nanoparticles can dramatically enhance the near infrared absorption due to the presence of surface plasmons. The excited surface plasmons can eject electrons into a surrounding conductive medium resulting in effective charge separation. D. Basak et al. \\[[@B26]\\] observed significant modifications in the electrical properties of poly (methyl methacrylate) thin films upon dispersion of silver nanoparticles. So far as the electrical properties are concerned, it is necessary to throw some light on the structural and morphological characteristics of silver nanoparticles. In the synthesis of nanoparticles, it is very important to control not only the particle size but also the particle shape and particle size distribution as well. In the present investigation, the synthesis of silver nanoparticles and thin films by wet chemical solution route \\[[@B27]\\] has been discussed. The prepared silver nanoparticles have been examined using X-ray diffraction (XRD), field emission transmission scanning electron microscope (FESEM), field emission transmission electron microscope (FETEM), high-resolution transmission electron microscope (HRTEM), two-probe direct-current (dc) resistivity measurement and thermogravimetric analysis/differential thermal analysis (TGA/DTA) thermal system. Experimental details -------------------- All the chemicals employed in the synthesis have been of analytical reagent grade. We used them without further purification. The nanoparticles of silver have been prepared according to the conventional procedure \\[[@B28]\\]. The aqueous solution (20 ml) containing glucose (9 mmol), polyvinylpyrrolidone (12 mmol), and sodium hydroxide (7 mmol) has been heated at 60°C for 30 min under vigorous stirring at 3,000 rpm. After that, 10 ml aqueous solution of AgNO~3~(1 mol/l) has been dropped in the previous solution. After refluxing for 60 min, the colloidal solution has been allowed to cool slowly to room temperature. The resultant solution has been undertaken to centrifugation at 8,000 rpm for 90 min. After filtration, the precipitate so obtained has been washed many times with deionized water using centrifugation for 15 min each time. Finally, the precipitate has been collected and powdered finely, and identified as silver nanoparticles using characterization tools. These silver nanoparticles have been re-dispersed in ethanol for the preparation of silver film. The films have been deposited on ultra-clean quartz substrates using dip-coating method. The quartz substrate has been immersed vertically into the ethanol solution of silver nanoparticles (25 mg/ml). After that, the container has been placed in a vacuum chamber (10^-3^torr) at room temperature for 24 h; the smooth, uniform, and bright silver film has been obtained on the quartz substrate due to the evaporation of the solvent (ethanol) under reduced pressure. The film shows good adhesion to the substrate. Prior to the deposition of silver film, the quartz slide has been immersed in chromic-sulfuric acid for a day in order to clean the surface and to enhance its hydrophilicity; and then rinsed many times with deionized water and dried in air. The morphology and crystal structure of silver nanoparticles powder has been evaluated by FESEM, FETEM, HRTEM, SAED, energy dispersive spectroscopy (EDX), and XRD. SEM images were obtained using a field emission scanning electron microscope (JSM-7600F, JEOL, Tokyo Japan) at an accelerating voltage of 15 kV. The fine powder of silver nanoparticles has been dispersed in ethanol on a carbon coated copper grid and TEM images were obtained with ultra-high resolution FETEM (JEOL, JEM-2100F) at an accelerating voltage of 200 kV. The reaction type and weight loss have been confirmed using TGA/DTA thermal system (DTG-60, Shimadzu, Kyoto, Japan). The XRD pattern was recorded by X-ray diffractometer (PANalytical X\\'Pert, Almelo, The Netherlands) equipped with Ni filter and CuKα (*λ*= 1.54056 Å) radiation source. For dc resistivity measurements, silver film with deposited contacts has been mounted in a specially designed metallic sample holder where a vacuum of about 10^-3^torr could be maintained throughout the measurements. A voltage (1.5 V, DC) was applied across the film and the resulting current was measured by a digital electrometer (Keithley 617, Keithley Instruments, Inc., Cleveland OH, USA). The temperature was measured by mounting a calibrated copper-constantan thermocouple near the sample. Results and discussion ====================== Structural properties --------------------- Figure [1](#F1){ref-type="fig"} shows the XRD pattern of powder silver nanoparticles. The presence of peaks at 2*θ*values 38.1°, 44.09°, 64.36°, 77.29°, 81.31°, 97.92°, 110.81° and 114.61° corresponds to (111), (200), (220), (311), (222), (400), (331), and (420) planes of silver, respectively. Thus, the XRD spectrum confirmed the crystalline structure of silver nanoparticles. No peaks of other impurity crystalline phases have been detected. All the peaks in XRD pattern can be readily indexed to a face-centered cubic structure of silver as per available literature (JCPDS, File No. 4-0783). The lattice constant calculated from this pattern has been found to be *a*= 0.4085 nm, which is consistent with the standard value a = 0.4086 nm. The crystallite size (*L*) of the material of thin film has been evaluated by Scherrer\\'s formula \\[[@B29]\\] {#F1} where *λ*is wavelength (0.15418 Å) of X-rays used, *β*is broadening of diffraction line measured at half of its maximum intensity (in radian), and *θ*is Bragg\\'s diffraction angle (in degree). The crystallite size of silver nanoparticles has been found to be 16.37 nm. In order to distinguish the effect of crystallite size induced broadening and strain induced broadening at FWHM of XRD profile, Williamson-Hall plot \\[[@B30]\\] has been drawn which is shown in inset of Figure [1](#F1){ref-type="fig"}. The crystallite size and strain can be obtained from the intercept at y-axis and the slope of line, respectively. where *β*is FWHM in radian, *t*is the grain size in nm, *ε*is the strain, *λ*is X-ray wavelength in nanometers, and *C*is a correction factor taken as 0.94. The grain size and strain of the sample have been found to be 16.37 nm and 3.98 × 10^-3^, respectively. The intrinsic stress (*σ*~s~) developed in nanoparticles due to the deviation of measured lattice constant of silver nanoparticles over the bulk has been calculated using the relation \\[[@B31]\\] Here, *Y*is the Young\\'s modulus of Ag (83 GPa), *a*is the lattice constant (in nanometers) measured from XRD data, *a*~0~is the bulk lattice constant (0.5406 nm) and *γ*is the Poisson\\'s ratio (0.37) for Ag. The dislocation density (*δ*) in the nanoparticles has been determined using expression \\[[@B32]\\] The X-ray line profile analysis has been was used to determine the intrinsic stress and dislocation density of silver nanoparticles and found to be as 0.275 GPa and 7.0 × ^-14^m^-2^respectively. Figure [2](#F2){ref-type="fig"} shows the FESEM image of silver nanoparticles. It exhibits that almost all the nanoparticles are of spherical shape with no agglomeration. FETEM and HRTEM images of the same sample are shown in Figure [3a, b](#F3){ref-type="fig"}, respectively. Figure [3a](#F3){ref-type="fig"} shows that silver nanoparticles are spherical in shape having smooth surface and are well dispersed. The average diameter of silver nanoparticles is found to be approximately 35 nm. TEM image also shows that the produced nanoparticles have more or less narrow size distribution. HRTEM image (Figure [3b](#F3){ref-type="fig"}) has given us further insight into the microstructure and crystallinity of as-prepared silver nanoparticles. The clear and uniform lattice fringes confirmed that the spherical particles are highly crystallized. The lattice spacing of 0.232 nm corresponds to (111) planes of silver. The results show that the dominant faces of silver spheres are (111). The SAED pattern has been obtained by directing the electron beam perpendicular to one of the spheres. The hexagonal symmetry of diffraction spots pattern shown in the inset of Figure [3b](#F3){ref-type="fig"} confirmed that the spherical particles are well crystalline, and its face is indexed to (111) planes. Both HRTEM image and SAED pattern confirmed that the prepared spherical silver nanoparticles are single crystals. {#F2} {#F3} The elemental analysis of sample has been performed using EDX spectroscopy. Inset of Figure [2](#F2){ref-type="fig"} shows EDX spectrum of silver nanoparticles. The peaks observed at 3.0, 3.2, and 3.4 keV correspond to the binding energies of Ag *L~α~*, Ag *L~β~*, and Ag *L~β~*~2~respectively; while the peaks situated at the binding energies of 0.85, 1.0, 8.05, and 8.95 keV belong to Cu*L*~1~, Cu*L~α~*, Cu*K~α~*, and Cu*K~β~*, respectively. In addition, a peak at 0.25 keV corresponding to carbon (C*K~α~*) has been observed. The copper and the carbon peaks correspond to the carbon coated copper grid of TEM. No peaks of other impurity have been detected. Therefore, the EDX profile of sample (inset of Figure [2](#F2){ref-type="fig"}) indicates that the silver nanoparticles sample contain pure silver, with no oxide. Thermal properties ------------------ TGA and DTA spectra have been recorded in temperature range from room temperature to 700°C using simultaneous thermal system (Shimadzu, DTG-60). A ceramic (Al~2~O~3~) crucible was used for heating and measurements were carried out in nitrogen atmosphere at the heating rate of 10°C/min. TGA and DTA curves of powder silver nanoparticles are given in Figure [4](#F4){ref-type="fig"}. It is observed from TGA curve that dominant weight loss of the sample occurred in temperature region between 200 and 300°C. There is almost no weight loss below 200°C and above 300°C. It can be generally attributed to the evaporation of water and organic components. Overall, TGA results show a loss of 14.58% upto 300°C. DTA plot displays an intense exothermic peak between 200°C and 300°C which mainly attributed to crystallization of silver nanoparticles. DTA profiles show that complete thermal decomposition and crystallization of the sample occur simultaneously. {#F4} Electrical properties --------------------- The temperature dependence of dc electrical resistivity of thin films of silver nanoparticles in the temperature range 100-300 K has been shown in Figure [5](#F5){ref-type="fig"}. It is evident from the figure that the resistivity decreases with increase in temperature, which shows the semiconducting nature of the sample. In these semiconductors, there are additional energy levels in the band gap, which are localized and close to either the conduction or the valence band. Since the energy difference between these levels and band edges is very small, a slight thermal excitation is sufficient to accept or donate electrons; thereby the electrical resistivity decreases with increase in temperature. Electron transport in the nanocrystalline silver thin film at relatively low temperature could be explained by thermally activated hopping between localized states near the Fermi level. In the variable range hopping (VRH) process \\[[@B33]\\], it becomes favorable for an electron to jump from one localized state to another where the overlapping of wave functions exists. The difference in corresponding eigen energies is compensated by the absorption or emission of phonons. Thus, the variation of electrical resistivity with temperature can be described by three-dimensional Mott\\'s variable range hopping model \\[[@B34]\\], {#F5} where ρ~o~is the high temperature limit of resistivity (in *Ω*-*m*)and *T*~o~is Mott\\'s characteristic temperature (in kelvin) associated with the degree of localization of the electronic wave function. The Mott\\'s characteristic temperature *T*~o~for three-dimensional hopping transport is given by, where *k*~B~is the Boltzmann constant (in electronvolt per kelvin), *N*(*E*~F~) is the density of states (in per electron volt per cubic meter), 1/γ is the decay length of electronic wave function which typically varies in the range 3-30 Å and *C*~o~is a dimensionless constant, which has a value in the range 16-310 \\[[@B35]\\]. It is clear from Figure [5](#F5){ref-type="fig"} and its inset that the sample exhibits a good fitting over the entire temperature range 100-300 K. Here, we have taken the localization length *γ*= 3 Å as reported by Maddison et al. \\[[@B36]\\]. From the fitted values of *T*~o~, we have found the value of density of states at the Fermi level *N*(*E*~F~) approximately 3.732 × 10^24^eV^-1^m^-3^for silver nanoparticles. Conclusions =========== The present wet chemical solution method for the preparation of silver nanoparticles and their thin films is simple, convenient, and viable which allows nanocrystalline silver particles of spherical shape and almost narrow size distribution. The x-ray diffraction pattern of sample shows a face-centered cubic crystalline phase of silver with lattice constant 0.4085 nm. The average particle size, as obtained from FETEM analysis, is 17.5 nm that agreed with XRD results. TGA/DTA study shows that the dominant weight loss occurs between 200°C and 300°C; and the reaction is of exothermic type. The temperature dependence of resistivity of silver film exhibits semiconducting behavior of the sample. The electrical conduction is due to the activated VRH in the localized states near the Fermi level. Competing interests =================== The authors declare that they have no competing interests. Authors\\' contributions ======================= MAMK participated in the design of the study and performed the electrical studies. SK and MA carried out the structural studies. SAA and MSA performed the thermal studies. MAMK and MA also involved in writing of the manuscript. All authors read and approved the final manuscript. Acknowledgements ================ Thanks are due to King Abdul Aziz City for Science and Technology (KAACST), Riyadh, Saudi Arabia (Grant No.: 10-NAN1001-02) for providing financial assistance in the form of major research project.

This summer, WizKids will debut an all-new line of Dungeons & Dragons pre-painted miniatures that complement the recently announced Tyranny of Dragons adventure theme. FEBRUARY 07, 2014 (Hillside, NJ) – Adding to the excitement of the recently announced Tyranny of Dragons from Wizards of the Coast, WizKids Games, a division of National Entertainment Collectibles Association, Inc., is excited…

End of an Era The term End of an Era may be used: Books End of an Era, poem by Adrienne Rich 1961 End of an Era, science fiction novel by Robert J. Sawyer 1994 End of an Era (comics), an American comic book Film and TV End of an Era (film) (Greek: Τέλος Εποχής / Telos Epokhis), a Greek film released in 1994 Music Songs "End of an Era", a song from Never Back Down by Close to Home "End of an Era", a song from Turn Against This Land by Dogs "End of an Era", a song from The Way by Zack Hemsey "End of an Era", a song from Between Heaven and Hell by Firewind "End of an Era", a song by Vira (band) "The End of an Era", a song from Temple of Rock by German hard rock band Michael Schenker Group Albums End of an Era (Nightwish album), an album of Finnish metal band Nightwish Professional wrestling The Undertaker versus Stone Cold Steve Austin at Fully Loaded (1999) The Undertaker versus Triple H at WrestleMania XXVIII

My Account Statistics Spaital query processing for location based services View/Open Author Liu, Yaqiong Date of Issue 2016-04-16 School School of Computer Engineering Research Centre Center for Advanced Information Systems Abstract With the rapid development of wireless communications, location-based services (LBSs) have received extensive researchers' attention. Many LBSs are dependent on the tracking of continuously varying positions of a large set of mobile users, which are also called mobile objects or clients. In this thesis, we consider three spatial queries based on three related LBSs. First, given a road network, a group of moving objects together with their friendships, and a network distance threshold for each pair of friends, the problem of proximity detection in road networks is to find friend pairs whose network distance is within the threshold. The problem of proximity detection is often encountered in massively multiplayer virtual games and friend-locator applications. Because of the limited battery power and bandwidth, we need a solution which incurs low communication cost. Hence, the primary goal of this problem is to reduce the total communication cost. However, most existing proximity detection solutions focus on the Euclidean space which cannot be used in road network space and the solutions for road networks incur substantial communication costs. Motivated by this, we propose two types of solutions to the proximity detection problem in road networks. In the first type of solution, each mobile client is assigned a mobile region of a fixed size. We design algorithms with a fixed radius for the server and client respectively, with the purpose of reducing unnecessary probing messages and updating messages. Second, we present a self-adjustment strategy to automatically adjust the size of the mobile region for the purpose of minimizing the communication cost. Experiments show that our second type of solution works efficiently and robustly with a much lower communication cost with respect to various parameters. In addition, we propose server-side computational cost optimization techniques to reduce the total computational cost. Second, points of interest (POI) recommendation with real-world applications is another research issue that has attracted researchers' much attention. Given a set of moving users, i.e., moving objects, and their historical GPS trajectories, the POI recommendation problem is to recommend semantic POIs, based on the GPS trajectories of the users. We first develop a novel algorithm, namely, SEM-DTBJ-Cluster, which stands for semantics-enhanced density-based clustering, for extracting semantic points of interest from GPS trajectories. We subsequently take three different factors (popularity, temporal influence and geographical influence) into consideration, and describe the impacts of popularity, temporal and geographical information, by deriving three different scoring functions based on three recommendation models. We finally combine the three scoring functions together and obtain a unified framework PTG-Recommend for recommending candidate POIs to a moving user. Our work is the first that considers the influence of popularity, the influence of temporal features, and the influence of geographical features of a POI together. Results of experiments on two GPS trajectory datasets not only prove the effectiveness of our framework, but also show that it performs better than the baseline POI recommendation methods with regard to precision and recall. Third, route queries are important problems that find applications in many location-based services. Considerable existing studies address routing problems in static road networks. However, the travel costs on edges in road networks always change over time. Such road networks are referred as time-dependent road networks. Most existing studies on time-dependent road networks focus on simply finding a shortest path with the minimum travel time without considering waiting at some nodes, or fuel consumption and toll fee. In fact, waiting at a node is likely to happen and one edge can be traversed at different speeds. Additionally, traveling along a route consumes both fuels and toll fee. In many cases, an optimal route is the minimum-cost route under time and speed constraints. Motivated by this, we study the Cost-Optimal routing problem in Time-dEpendent Road networks with time and speed constraints, denoted as COTER for short, where the travel cost of a route is composed of fuel cost and toll fees. We utilize two fuel consumption models and compute the minimum fuel consumption of an edge under the constraint that the travel time on this edge is exactly the given time, for helping users determine optimal speeds on each edge. We allow the toll fee to be an arbitrary single-valued time-dependent function of the departure time for each edge. We define a time-dependent OC function (Optimal Cost function) for each node n_i, and derive the recurrence relation formula between n_i's incoming neighbors' OC-functions and n_i's OC-function. We propose a five-step approximate algorithm, namely, ALG-COTER, which answers COTER using optimized single-source shortest-path algorithm, topological sorting, dynamic programming, nonlinear programming and backtrack algorithms. Experimental results show that our algorithm answers COTER queries efficiently and our algorithm is scalable with respect to different parameters that have influences on the running time.

Q: How to combine the results of two DTOs in C# into one list of one type I have a C# web app that is currently pulling data from two databases. One of the databases has a table called resources that contains employee details and the other contains a view to details collected in a company web app. I need to create a list of each 'active' employee that also lists their web app history. I want to return a List of type ResourceDTO with the results of the WebAppDTO in another list per user. Ideally I will be able to manipulate this in Angular, Create a table listing employee names and in the next column "tally" up how many times they have participated. Each of the tally's will be a link that then uses the webappID to display the details for that employee. C# Question for Satckoverflow //Web Api public List<ResourceDTO> GetWebAppLeaders() { List<ResourceDTO> webappLeaders = new List<ResourceDTO>(); //Linq to get a list of employees that take part of Web App var people = from x in _staffCtx.Resources where (x.Active.HasValue && x.Active.Value && x.ManagerID.HasValue && x.FirstName.Length > 0) select new ResourceDTO() { FirstName = x.FirstName, LastName = x.LastName, ResourceID = x.ResourceID, }; webappLeaders = people.ToList(); //currently loops through each member of staff in list above and grabs their web app history. foreach (var person in people) { int personID = person.ResourceID; var webappHistory = from u in _webappCtx.CompanyWebAppViews where (u.PupilID == personID || u.TeacherID == personID) select new WebAppDTO() { webappDate = u.webappDate.ToString(), webappID = u.ID, }; webappHistory.ToList(); } //webappLeaders.ToList(); // successfully returns list of Employees as filtered out by where clause. return webappLeaders; } '//ResourceDTO.cs public class ResourceDTO { public int ResourceID { get; set; } public string Email { get; set; } public string FirstName { get; set; } public string LastName { get; set; } public string JobTitle { get; set; } public string ExtensionNumber { get; set; } public string MobileNumber { get; set; } public string MobileSpeedDial { get; set; } public string IMAddress { get; set; } public int? ManagerID { get; set; } public string ManagerName { get; set; } public string DepartmentType { get; set; } // Other field you may need //web app specific public List<WWebAppDTO> webappPupil { get; set; } public List<WebAppsDTO> webappTeacher { get; set; } } //WebAppDTO.cs public class WebAppDTO { public int webappID { get; set; } public string pupilName { get; set; } public string teacherName { get; set; } public string webappDate { get; set; } public string pupilLearnt { get; set; } public string pupilComments { get; set; } public string teacherComments { get; set; } } Apologies in advance if I have miss understood some vital concepts, C# MVC is new to me. I would greatly appreciate some example code. Thanks. A: The following changes to the code resolved the issue for me. //WebApi public List<ResourceDTO> GetWebAppLeaders() { List<ResourceDTO> webappLeaders = new List<ResourceDTO>(); //Linq to get a list of employees that take part of WebApp var people = from x in _staffCtx.Resources where (x.Active.HasValue && x.Active.Value && x.ManagerID.HasValue && x.FirstName.Length > 0) select new ResourceDTO() { FirstName = x.FirstName, LastName = x.LastName, ResourceID = x.ResourceID, }; webappLeaders = people.ToList(); foreach (var person in webappLeaders) { int personID = person.ResourceID; person.webappPupil = from u in _webappCtx.CompanyWebAppViews where (u.PupilID == personID) select new WebappDTO() { webappID = u.ID, }; person.webappPupil.ToList(); person.webappTeacher = from u in _webappCtx.CompanyWebAppViews where (u.TeacherID == personID) select new WebappDTO() { webappID = u.ID, }; person.webappTeacher.ToList(); } return webappLeaders.ToList(); } //ResourceDTO public class ResourceDTO { public int ResourceID { get; set; } public string Email { get; set; } public string FirstName { get; set; } public string LastName { get; set; } public string JobTitle { get; set; } public string ExtensionNumber { get; set; } public string MobileNumber { get; set; } public string MobileSpeedDial { get; set; } public string IMAddress { get; set; } public int? ManagerID { get; set; } public string ManagerName { get; set; } public string DepartmentType { get; set; } //WebApp specific public IQueryable<WebAppDTO> webappPupil { get; set; } public IQueryable<WebAppDTO> webappTeacher { get; set; } } //WebAppDTO public class WebAppDTO { public int webappID { get; set; } public string pupilName { get; set; } public string teacherName { get; set; } public string webappDate { get; set; } public string pupilLearnt { get; set; } public string pupilComments { get; set; } public string teacherComments { get; set; } public List<WebAppDTO> WebApp { get; set; } } Extending Stephen Vakil's answer, the for each loop complained about IQeuryable type conversion to List type. To resolve this two methods of type IQueryable where created in the ResourceDTO, to then be able to convert the result to list a method of tpye List was created in WebAppDTO, the final step involved taking the assignment webappLeaders = people.ToList() and feeding this into the foreach loop. The results now return a list of employees with further lists of their web app history.

Q: Find next word and replace in file I have file which contains sentences: File1.txt: "I like Banana" I want to find the word appears after "like" and replace it. I tried with string and works fine String = "orange" Text = 'I like Banana' list_of_words = Text.split() for u, word in enumerate(list_of_words): if 'like ' == word: next_word= list_of_words[u+ 1] Text = Text.replace(next_word,String) print(Text) prints : I like orange But when I apply it on file it only replace (like): with open(file, 'r') as open_file: read_file = open_file.readlines() output_lines = [] for line in read_file: words = line.split() output_line = [] for u,word in enumerate(words): if 'like' == word: new_word = words[u + 1] word = word.replace(new_word,"Orange") output_line.append(word) #-------------------------------------------------------- output_lines.append(' '.join(output_line)) with open(file, 'w') as open_file: open_file.write(' '.join(output_lines)) It replaces Like with orange: I Orange Banana Any idea why?!!!! A: In your if condition, you are confusing word with words. You replace being done on 'like', not ['I', 'like', 'bananas']. Since like does not contain 'oranges', that line is a no-op. I think you want something more like this. Although this still needs to check boundaries (what if u + 1 is out of range?). output_line = [] for line in read_file: words = line.split() for u,word in enumerate(words): if 'like' == word: words[u + 1] = 'Orange' output_line.append(' '.join(words)) Good luck!

Opinions of the United 1994 Decisions States Court of Appeals for the Third Circuit 7-7-1994 Reich v. Chez Robert, Inc. et al. Precedential or Non-Precedential: Docket 93-5619 Follow this and additional works at: http://digitalcommons.law.villanova.edu/thirdcircuit_1994 Recommended Citation "Reich v. Chez Robert, Inc. et al." (1994). 1994 Decisions. Paper 76. http://digitalcommons.law.villanova.edu/thirdcircuit_1994/76 This decision is brought to you for free and open access by the Opinions of the United States Court of Appeals for the Third Circuit at Villanova University School of Law Digital Repository. It has been accepted for inclusion in 1994 Decisions by an authorized administrator of Villanova University School of Law Digital Repository. For more information, please contact Benjamin.Carlson@law.villanova.edu.  UNITED STATES COURT OF APPEALS FOR THE THIRD CIRCUIT _______________ No. 93-5619 _______________ ROBERT REICH, Secretary of Labor, United States Department of Labor, Appellant v. CHEZ ROBERT, INC., ROBERT SLIWOWSKI, individually and as Owner and President Appellee _______________ On Appeal From the United States District Court for the District of New Jersey (D.C. Civil No. 87-2219) _______________ Submitted Under Third Circuit LAR 34.1(a) May 12, 1994 Before: BECKER AND LEWIS, Circuit Judges and POLLAK, District Judge1. (Filed July 7, 1994) LAURISTON H. LONG WILLIAM J. STONE United States Department of Labor 200 Constitution Avenue, N.W. Washington, DC 20210 Attorneys for Appellant ROBERT SLIWOWSKI 45 Covington Lane Voorhees, NJ 08043 1 Honorable Louis H. Pollak, United States District Judge for the Eastern District of Pennsylvania, sitting by designation. 1  Appellee _______________ OPINION OF THE COURT _______________ Pollak, District Judge. Secretary of Labor Robert Reich ("Secretary") here appeals from a judgment of the United States District Court for the District of New Jersey in an action brought under the Fair Labor Standards Act, 29 U.S.C. § 201 et seq. The Secretary contends that the court erred in reducing the statutory liability of defendants -- a restaurant and its owner -- for back wages by improperly taking into account tips earned by employees during the violation period.2 For the reasons set forth below, we agree with the Secretary, and we remand for further proceedings consistent with this opinion. Background: The facts, insofar as relevant for this appeal, are as follows.3 This suit to enforce the Fair Labor Standards Act ("the Act") was commenced in 1987. The defendants are Chez Robert, Inc., an "upscale" restaurant in New Jersey, and its owner Robert Sliwowski. The complaint alleged violations of the minimum wage, overtime, and record-keeping provisions of the 2 Defendants-appellees have not filed a responsive brief in this appeal. We therefore have before us only the brief of appellant, Secretary Reich. 3 The complete factual background and the many facets of the underlying case are amply set forth in the district court's comprehensive opinion, Reich v. Chez Robert, Inc., 821 F.Supp. 967 (D.N.J. 1993). 2 Act. After a bench trial that began in March, 1992, the district court held that the defendants had willfully violated the wage, overtime and record-keeping provisions of the Act. The court awarded both damages and injunctive relief, and found defendants liable for two kinds of damages: (1) "actual damages" -- i.e. unpaid hours, underpaid overtime, and uniform maintenance expenses -- in the amount of $177,809.66, and (2) tip credit remunerations -- i.e. the cumulative amount by which the wages of Chez Robert's employees fell short of the minimum wage -- in the amount of $229,794.19. The total damages came to $407,603.85. The court reduced the award to $305,702.88 to reflect tips earned by employees during the relevant period. The Secretary contends that the district court's decision to discount defendants' liability was erroneous. As framed by the Secretary's brief, the only issue before this court is "whether the district court erred as a matter of law by sua sponte reducing, across the board, the back wage awards to individual employees by 25% from the amounts which the court found otherwise owed to them as a result of defendants' violation of the [Act]." Appellant's Br. at 2. Discussion: The Secretary bases his appeal upon Section 3(m) of the Fair Labor Standards Act, which provides that . . . In determining the wage of a tipped employee, the amount paid such employee by his employer shall be deemed to be increased on account of tips by an amount determined by the employer . . . except that the amount of the increase on account of tips determined by the employer may not exceed the value of tips actually received by the employee. The previous sentence shall not apply with respect to any tipped employee unless (1) such employee has been informed by the employer of the provisions of this subsection, and (2) all tips 3  received by such employee have been retained by the employee . . . 29 U.S.C. § 203 (m). Section 3(m) therefore allows an employer to reduce a tipped employee's wage below the statutory minimum by an amount to be made up in tips, but only if the employer informs the tipped employee that her wage is being decreased under section 3(m)'s tip-credit provision. If the employer cannot show that it has informed employees that tips are being credited against their wages, then no tip credit can be taken and the employer is liable for the full minimum-wage ($3.35/hr in this case). Martin v. Tango's Restaurant, Inc., 969 F.2d 1319, 1322-23 (1st Cir. 1992). At trial, defendants argued, pursuant to section 3(m), that their liability for back wages should be calculated at $2.01/hour, the rate at which Chez Robert's employees were apparently paid. Defendants argued that they were entitled to a tip credit of $1.34/hour for the balance of the $3.35 per hour statutory minimum wage.4 The district court rejected defendants' argument. The court found that defendants had not notified employees of the tip credit as required under the Act, and therefore were not entitled to the offset. Chez Robert, 821 F.Supp. at 977. Using the statutory minimum wage of $3.35/hour, the court calculated defendants' liability for back wages to be $177,809.66 in unpaid wages, underpaid overtime and uniform 4 The minimum wage applicable until March 31, 1990, was $3.35 per hour. The violations by Chez Robert and its owner occurred prior to that date. The current statutory minimum wage, which became effective on March 31, 1991, is $4.35 per-hour. 29 U.S.C. § 206(a)(1). 4 maintenance, plus $229,794.19 in disallowed tip credit deductions, for a total of $407,603.85. Id. at 985. The Secretary does not challenge this initial determination. The Secretary takes issue with what the district court did next. Notwithstanding that the court found defendants not to be entitled to the tip deduction under section 3(m), the court made the following ruling: the Secretary has made no provisions . . . for tips actually received by employees. Certainly no precise amount can be determined. . . . Chez Robert is an expensive "upscale" restaurant and certainly capable of generating income that would have supplemented employees' incomes to a great degree. Since the Secretary did not account for tips actually received, the Court must apply a discount rate to the damages owed to each employee. . . . The Court has adjusted Defendants' liability to account for this inflating factor. The $177,809.66 in actual damages and the $229,794.19 in tip credit remunerations will be reduced by 25%. Therefore, after discounting, Defendants' [sic] are obligated to pay total damages, actual and tip credit, in the amount of $305,702.88. Id. at 985. Appellant argues that the above ruling was erroneous because it essentially gives defendants a tip credit which the court had already determined they were statutorily barred from claiming. The pertinent cases support the Secretary's argument. In Tango's Restaurant, the First Circuit held that "Congress chose to allow employers a partial tip credit if, but only if, certain conditions are met." 969 F.2d at 1322. The notice requirement is a firm one: It may at first seem odd to award back pay against an employer, doubled by liquidated damages, where the employee has actually received and retained base wages and tips that together amply satisfy the minimum wage requirements. Yet Congress has in section 3(m) 5  expressly required notice as a condition of the tip credit and the courts have enforced the requirement. . . . If the penalty for omitting notice appears harsh, it is also true that notice is not difficult for the employer to provide. Id. at 1323 (internal citations omitted). In this case, the district court did exactly what Tango's Restaurant instructs against doing: that is, alleviate the harsh results of the notice requirement by reducing damages out of an equitable sense that some offset for tips should be allowed. 821 F.Supp. at 985. If such a ruling were permissible, the district courts would effectively have discretion to waive the notice requirement in the interests of perceived fairness to the employer. While that is perhaps not in itself an undesirable power for the district courts to have, it is not, as the First Circuit tells us, what the statute permits. The First Circuit's view is shared by other courts that have addressed the section 3(m) notice requirement. In Richard v. Marriott Corp., 549 F.2d 303 (4th Cir. 1977), the Fourth Circuit held that the district court erred when it allowed a partial tip credit for Marriott "out of a vague sense of fairness and a feeling that $5.43 and up per hour is enough for a wait[e]r[ess]", when it was established that "Marriott never informed its employees of the provisions of Section 3(m) of the [Act]." Id. at 305. The Fifth Circuit has likewise held that where it was agreed that a restaurant did not inform waiters that a tip-credit was being deducted from their wages, "the district court properly found that the employees were entitled to the full minimum wage 6 for every hour" at issue. Barcellona v. Tiffany English Pub, 597 F.2d 464, 467-68 (5th Cir. 1979); see also Marshall v. Gerwill, inc., 495 F.Supp. 744, 753 (D.Md. 1980) (without section 3(m) notice, "retaining of tips by the [employees] cannot offset the failure to pay the applicable minimum wage."); Bonham v. Copper Cellar Corp., 476 F.Supp. 98, 101-02 (E.D.Tenn. 1979) (barring tip credit for employer who failed to explain provisions of section 3(m) to employees, even though employer acted in good faith). We have not previously had occasion to address whether the notice requirement of section 3(m) may be waived by the district court when there is evidence of actual tips received. Now faced with that question, we agree with the interpretation of the statute reached by the First Circuit in Tango's Restaurant. When the employer has not notified employees that their wages are being reduced pursuant to the Act's tip-credit provision, the district court may not equitably reduce liability for back wages to account for tips actually received. Accordingly, we find that the district court erred in reducing defendants' liability from $407,603.85 to $305,702.88. The judgment of the district court is vacated and the case is remanded to the district court for proceedings consistent with this opinion. 7 

The role of cell adhesion proteins--laminin and fibronectin--in the movement of malignant and metastatic cells. Metastasizing tumor cells must traverse diverse extracellular matrices during dissemination. Extracellular matrices consist of two basic types, interstitial stroma and basement membranes. Extracellular matrices are chemically complex structures that interact with cell surfaces by a number of mechanisms. There has been a great deal of effort in recent years to understand the molecular nature of extracellular matrices, especially as it relates to the adhesion of normal and malignant cell types. Adhesive noncollagenous glycoproteins, such as laminin and fibronectin, serve pivotal roles in basement membrane and stromal matrices, respectively. These proteins participate in establishing the architecture of extracellular matrices as well as in attaching to the surface of cells and affecting cellular phenotype. This phenotypic effect ranges from adhesion and motility to growth and differentiation. Changes in adhesive characteristics and motility of cells have long been suspected to play a role in mediating the spread of malignant neoplasms. This article is designed to review extracellular matrix constituents that are currently known that can mediate the adhesion and motility of malignant neoplasms. The adhesion of normal and malignant cells to matrices is a complex process mediated by several distinct mechanisms which are initially manifested by changes in cytoskeletal architecture. The topic of normal and malignant cell adhesion to matrices will also be discussed in this regard, since any explanation of tumor cell migration must account for the complex dynamic interactions of the cell surface with the substratum as well as with the cytoskeleton. Finally, current efforts designed to understand the molecular nature of tumor cell:matrix interactions that contribute to metastatic behavior will also be discussed. The rationale behind these studies is that selective inhibition of specific tumor:extracellular matrix interactions can provide an avenue for therapeutic intervention of metastatic cancer.

Synthesis of NAG-thiazoline-derived inhibitors for β-N-acetyl-d-hexosaminidases. β-N-Acetyl-d-hexosaminidases are responsible for the metabolism of glycoconjugates in diverse physiological processes that are important targets for medicine and pesticide development. Fourteen new NAG-thiazoline derivatives were synthesized by cyclization and click reaction using d-glucosamine hydrochloride as the starting material. All the compounds created were characterized by NMR and HRMS spectra. A preliminary bioassay, using four enzymes from two β-N-acetyl-d-hexosaminidase families, showed that most of the compounds synthesized exhibit selective inhibition of GH84 β-N-acetyl-d-hexosaminidase. Among the compounds tested, compounds 5a (IC50=12.6 μM, hOGA) and 5e (IC50=12.5 μM, OfOGA) proved to be a highly selective and potent inhibitor.

<?xml version="1.0" encoding="UTF-8"?> <project xmlns="http://maven.apache.org/POM/4.0.0" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:schemaLocation="http://maven.apache.org/POM/4.0.0 http://maven.apache.org/xsd/maven-4.0.0.xsd"> <parent> <groupId>org.springframework.boot</groupId> <artifactId>spring-boot-starter-parent</artifactId> <version>2.1.3.RELEASE</version> <relativePath/> <!-- lookup parent from repository --> </parent> <modelVersion>4.0.0</modelVersion> <artifactId>lab-15-spring-data-elasticsearch</artifactId> <dependencies> <!-- 自动化配置 Spring Data Elasticsearch --> <dependency> <groupId>org.springframework.boot</groupId> <artifactId>spring-boot-starter-data-elasticsearch</artifactId> </dependency> <!-- 方便等会写单元测试 --> <dependency> <groupId>org.springframework.boot</groupId> <artifactId>spring-boot-starter-test</artifactId> <scope>test</scope> </dependency> </dependencies> </project>

Data mining a small molecule drug screening representative subset from NIH PubChem. PubChem is a scientific showcase of the NIH Roadmap Initiatives. It is a compound repository created to facilitate information exchange and data sharing among the NIH Roadmap-funded Molecular Library Screening Center Network (MLSCN) and the scientific community. However, PubChem has more than 10 million records of compound information. It will be challenging to conduct a drug screening of the whole database of millions of compounds. Thus, the purpose of the present study was to develop a data mining cheminformatics approach in order to construct a representative and structure-diverse sublibrary from the large PubChem database. In this study, a new chemical diverse representative subset, rePubChem, was selected by whole-molecule chemistry-space matrix calculation using the cell-based partition algorithm. The representative subset was generated and was then subjected to evaluations by compound property analyses based on 1D and 2D molecular descriptors. The new subset was also examined and assessed for self-similarity analysis based on 2D molecular fingerprints in comparing with the source compound library. The new subset has a much smaller library size (540K compounds) with minimum similarity and redundancy without loss of the structural diversity and basic molecular properties of its parent library (5.3 million compounds). The new representative subset library generated could be a valuable structure-diverse compound resource for in silico virtual screening and in vitro HTS drug screening. In addition, the established subset generation method of using the combined cell-based chemistry-space partition metrics with pairwised 2D fingerprint-based similarity search approaches will also be important to a broad scientific community interested in acquiring structurally diverse compounds for efficient drug screening, building representative virtual combinatorial chemistry libraries for syntheses, and data mining large compound databases like the PubChem library in general.