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Deep Within-Class Covariance Analysis for Robust Audio Representation Learning

Convolutional Neural Networks (CNNs) can learn effective features, though have been shown to suffer from a performance drop when the distribution of the data changes from training to test data. In this paper we analyze the internal representations of CNNs and observe that the representations of unseen data in each class, spread more (with higher variance) in the embedding space of the CNN compared to representations of the training data. More importantly, this difference is more extreme if the unseen data comes from a shifted distribution. Based on this observation, we objectively evaluate the degree of representation's variance in each class via eigenvalue decomposition on the within-class covariance of the internal representations of CNNs and observe the same behaviour. This can be problematic as larger variances might lead to mis-classification if the sample crosses the decision boundary of its class. We apply nearest neighbor classification on the representations and empirically show that the embeddings with the high variance actually have significantly worse KNN classification performances, although this could not be foreseen from their end-to-end classification results. To tackle this problem, we propose Deep Within-Class Covariance Analysis (DWCCA), a deep neural network layer that significantly reduces the within-class covariance of a DNN's representation, improving performance on unseen test data from a shifted distribution. We empirically evaluate DWCCA on two datasets for Acoustic Scene Classification (DCASE2016 and DCASE2017). We demonstrate that not only does DWCCA significantly improve the network's internal representation, it also increases the end-to-end classification accuracy, especially when the test set exhibits a distribution shift. By adding DWCCA to a VGG network, we achieve around 6 percentage points improvement in the case of a distribution mismatch.

Efficient Online Bandit Multiclass Learning with $\tilde{O}(\sqrt{T})$ Regret

We present an efficient second-order algorithm with $\tilde{O}(\frac{1}{\eta}\sqrt{T})$ regret for the bandit online multiclass problem. The regret bound holds simultaneously with respect to a family of loss functions parameterized by $\eta$, for a range of $\eta$ restricted by the norm of the competitor. The family of loss functions ranges from hinge loss ($\eta=0$) to squared hinge loss ($\eta=1$). This provides a solution to the open problem of (J. Abernethy and A. Rakhlin. An efficient bandit algorithm for $\sqrt{T}$-regret in online multiclass prediction? In COLT, 2009). We test our algorithm experimentally, showing that it also performs favorably against earlier algorithms.

Local Communication Protocols for Learning Complex Swarm Behaviors with Deep Reinforcement Learning

Swarm systems constitute a challenging problem for reinforcement learning (RL) as the algorithm needs to learn decentralized control policies that can cope with limited local sensing and communication abilities of the agents. While it is often difficult to directly define the behavior of the agents, simple communication protocols can be defined more easily using prior knowledge about the given task. In this paper, we propose a number of simple communication protocols that can be exploited by deep reinforcement learning to find decentralized control policies in a multi-robot swarm environment. The protocols are based on histograms that encode the local neighborhood relations of the agents and can also transmit task-specific information, such as the shortest distance and direction to a desired target. In our framework, we use an adaptation of Trust Region Policy Optimization to learn complex collaborative tasks, such as formation building and building a communication link. We evaluate our findings in a simulated 2D-physics environment, and compare the implications of different communication protocols.

Towards exascale real-time RFI mitigation

We describe the design and implementation of an extremely scalable real-time RFI mitigation method, based on the offline AOFlagger. All algorithms scale linearly in the number of samples. We describe how we implemented the flagger in the LOFAR real-time pipeline, on both CPUs and GPUs. Additionally, we introduce a novel simple history-based flagger that helps reduce the impact of our small window on the data. By examining an observation of a known pulsar, we demonstrate that our flagger can achieve much higher quality than a simple thresholder, even when running in real time, on a distributed system. The flagger works on visibility data, but also on raw voltages, and beam formed data. The algorithms are scale-invariant, and work on microsecond to second time scales. We are currently implementing a prototype for the time domain pipeline of the SKA central signal processor.

Learning body-affordances to simplify action spaces

Controlling embodied agents with many actuated degrees of freedom is a challenging task. We propose a method that can discover and interpolate between context dependent high-level actions or body-affordances. These provide an abstract, low-dimensional interface indexing high-dimensional and time- extended action policies. Our method is related to recent ap- proaches in the machine learning literature but is conceptually simpler and easier to implement. More specifically our method requires the choice of a n-dimensional target sensor space that is endowed with a distance metric. The method then learns an also n-dimensional embedding of possibly reactive body-affordances that spread as far as possible throughout the target sensor space.

Cayley properties of the line graphs induced by of consecutive layers of the hypercube

Let $n >3$ and $ 0< k < \frac{n}{2} $ be integers. In this paper, we investigate some algebraic properties of the line graph of the graph $ {Q_n}(k,k+1) $ where $ {Q_n}(k,k+1) $ is the subgraph of the hypercube $Q_n$ which is induced by the set of vertices of weights $k$ and $k+1$. In the first step, we determine the automorphism groups of these graphs for all values of $k$. In the second step, we study Cayley properties of the line graph of these graphs. In particular, we show that for $ k>2, $ if $ 2k+1 \neq n$, then the line graph of the graph $ {Q_n}(k,k+1) $ is a vertex-transitive non Cayley graph. Also, we show that the line graph of the graph $ {Q_n}(1,2) $ is a Cayley graph if and only if $ n$ is a power of a prime $p$.

Beyond the technical challenges for deploying Machine Learning solutions in a software company

Recently software development companies started to embrace Machine Learning (ML) techniques for introducing a series of advanced functionality in their products such as personalisation of the user experience, improved search, content recommendation and automation. The technical challenges for tackling these problems are heavily researched in literature. A less studied area is a pragmatic approach to the role of humans in a complex modern industrial environment where ML based systems are developed. Key stakeholders affect the system from inception and up to operation and maintenance. Product managers want to embed "smart" experiences for their users and drive the decisions on what should be built next; software engineers are challenged to build or utilise ML software tools that require skills that are well outside of their comfort zone; legal and risk departments may influence design choices and data access; operations teams are requested to maintain ML systems which are non-stationary in their nature and change behaviour over time; and finally ML practitioners should communicate with all these stakeholders to successfully build a reliable system. This paper discusses some of the challenges we faced in Atlassian as we started investing more in the ML space.

Class-Splitting Generative Adversarial Networks

Generative Adversarial Networks (GANs) produce systematically better quality samples when class label information is provided., i.e. in the conditional GAN setup. This is still observed for the recently proposed Wasserstein GAN formulation which stabilized adversarial training and allows considering high capacity network architectures such as ResNet. In this work we show how to boost conditional GAN by augmenting available class labels. The new classes come from clustering in the representation space learned by the same GAN model. The proposed strategy is also feasible when no class information is available, i.e. in the unsupervised setup. Our generated samples reach state-of-the-art Inception scores for CIFAR-10 and STL-10 datasets in both supervised and unsupervised setup.

Dynamical system analysis of dark energy models in scalar coupled metric-torsion theories

We study the phase space dynamics of cosmological models in the theoretical formulations of non-minimal metric-torsion couplings with a scalar field, and investigate in particular the critical points which yield stable solutions exhibiting cosmic acceleration driven by the {\em dark energy}. The latter is defined in a way that it effectively has no direct interaction with the cosmological fluid, although in an equivalent scalar-tensor cosmological setup the scalar field interacts with the fluid (which we consider to be the pressureless dust). Determining the conditions for the existence of the stable critical points we check their physical viability, in both Einstein and Jordan frames. We also verify that in either of these frames, the evolution of the universe at the corresponding stable points matches with that given by the respective exact solutions we have found in an earlier work (arXiv: 1611.00654 [gr-qc]). We not only examine the regions of physical relevance for the trajectories in the phase space when the coupling parameter is varied, but also demonstrate the evolution profiles of the cosmological parameters of interest along fiducial trajectories in the effectively non-interacting scenarios, in both Einstein and Jordan frames.

J-MOD$^{2}$: Joint Monocular Obstacle Detection and Depth Estimation

In this work, we propose an end-to-end deep architecture that jointly learns to detect obstacles and estimate their depth for MAV flight applications. Most of the existing approaches either rely on Visual SLAM systems or on depth estimation models to build 3D maps and detect obstacles. However, for the task of avoiding obstacles this level of complexity is not required. Recent works have proposed multi task architectures to both perform scene understanding and depth estimation. We follow their track and propose a specific architecture to jointly estimate depth and obstacles, without the need to compute a global map, but maintaining compatibility with a global SLAM system if needed. The network architecture is devised to exploit the joint information of the obstacle detection task, that produces more reliable bounding boxes, with the depth estimation one, increasing the robustness of both to scenario changes. We call this architecture J-MOD$^{2}$. We test the effectiveness of our approach with experiments on sequences with different appearance and focal lengths and compare it to SotA multi task methods that jointly perform semantic segmentation and depth estimation. In addition, we show the integration in a full system using a set of simulated navigation experiments where a MAV explores an unknown scenario and plans safe trajectories by using our detection model.

The Calabi flow with rough initial data

In this paper, we prove that there exists a dimensional constant $\delta > 0$ such that given any background Kähler metric $\omega$, the Calabi flow with initial data $u_0$ satisfying \begin{equation*} \partial \bar \partial u_0 \in L^\infty (M) \text{ and } (1- \delta )\omega < \omega_{u_0} < (1+\delta )\omega, \end{equation*} admits a unique short time solution and it becomes smooth immediately, where $\omega_{u_0} : = \omega +\sqrt{-1}\partial \bar\partial u_0$. The existence time depends on initial data $u_0$ and the metric $\omega$. As a corollary, we get that Calabi flow has short time existence for any initial data satisfying \begin{equation*} \partial \bar \partial u_0 \in C^0(M) \text{ and } \omega_{u_0} > 0, \end{equation*} which should be interpreted as a "continuous Kähler metric". A main technical ingredient is Schauder-type estimates for biharmonic heat equation on Riemannian manifolds with time weighted Hölder norms.

Star Formation Activity in the molecular cloud G35.20$-$0.74: onset of cloud-cloud collision

To probe the star-formation (SF) processes, we present results of an analysis of the molecular cloud G35.20$-$0.74 (hereafter MCG35.2) using multi-frequency observations. The MCG35.2 is depicted in a velocity range of 30-40 km s$^{-1}$. An almost horseshoe-like structure embedded within the MCG35.2 is evident in the infrared and millimeter images and harbors the previously known sites, ultra-compact/hyper-compact G35.20$-$0.74N H\,{\sc ii} region, Ap2-1, and Mercer 14 at its base. The site, Ap2-1 is found to be excited by a radio spectral type of B0.5V star where the distribution of 20 cm and H$\alpha$ emission is surrounded by the extended molecular hydrogen emission. Using the {\it Herschel} 160-500 $\mu$m and photometric 1-24 $\mu$m data analysis, several embedded clumps and clusters of young stellar objects (YSOs) are investigated within the MCG35.2, revealing the SF activities. Majority of the YSOs clusters and massive clumps (500-4250 M$_{\odot}$) are seen toward the horseshoe-like structure. The position-velocity analysis of $^{13}$CO emission shows a blue-shifted peak (at 33 km s$^{-1}$) and a red-shifted peak (at 37 km s$^{-1}$) interconnected by lower intensity intermediated velocity emission, tracing a broad bridge feature. The presence of such broad bridge feature suggests the onset of a collision between molecular components in the MCG35.2. A noticeable change in the H-band starlight mean polarization angles has also been observed in the MCG35.2, probably tracing the interaction between molecular components. Taken together, it seems that the cloud-cloud collision process has influenced the birth of massive stars and YSOs clusters in the MCG35.2.

Oblivious Routing via Random Walks

We present novel oblivious routing algorithms for both splittable and unsplittable multicommodity flow. Our algorithm for minimizing congestion for \emph{unsplittable} multicommodity flow is the first oblivious routing algorithm for this setting. As an intermediate step towards this algorithm, we present a novel generalization of Valiant's classical load balancing scheme for packet-switched networks to arbitrary graphs, which is of independent interest. Our algorithm for minimizing congestion for \emph{splittable} multicommodity flow improves upon the state-of-the-art, in terms of both running time and performance, for graphs that exhibit good expansion guarantees. Our algorithms rely on diffusing traffic via iterative applications of the random walk operator. Consequently, the performance guarantees of our algorithms are derived from the convergence of the random walk operator to the stationary distribution and are expressed in terms of the spectral gap of the graph (which dominates the mixing time).

On Functional Graphs of Quadratic Polynomials

We study functional graphs generated by quadratic polynomials over prime fields. We introduce efficient algorithms for methodical computations and provide the values of various direct and cumulative statistical parameters of interest. These include: the number of connected functional graphs, the number of graphs having a maximal cycle, the number of cycles of fixed size, the number of components of fixed size, as well as the shape of trees extracted from functional graphs. We particularly focus on connected functional graphs, that is, the graphs which contain only one component (and thus only one cycle). Based on the results of our computations, we formulate several conjectures highlighting the similarities and differences between these functional graphs and random mappings.

Helmholtz decomposition theorem and Blumenthal's extension by regularization

Helmholtz decomposition theorem for vector fields is usually presented with too strong restrictions on the fields and only for time independent fields. Blumenthal showed in 1905 that decomposition is possible for any asymptotically weakly decreasing vector field. He used a regularization method in his proof which can be extended to prove the theorem even for vector fields asymptotically increasing sublinearly. Blumenthal's result is then applied to the time-dependent fields of the dipole radiation and an artificial sublinearly increasing field.

A homotopy decomposition of the fibre of the squaring map on $Ω^3S^{17}$

We use Richter's $2$-primary proof of Gray's conjecture to give a homotopy decomposition of the fibre $\Omega^3S^{17}\{2\}$ of the $H$-space squaring map on the triple loop space of the $17$-sphere. This induces a splitting of the mod-$2$ homotopy groups $\pi_\ast(S^{17}; \mathbb{Z}/2\mathbb{Z})$ in terms of the integral homotopy groups of the fibre of the double suspension $E^2:S^{2n-1} \to \Omega^2S^{2n+1}$ and refines a result of Cohen and Selick, who gave similar decompositions for $S^5$ and $S^9$. We relate these decompositions to various Whitehead products in the homotopy groups of mod-$2$ Moore spaces and Stiefel manifolds to show that the Whitehead square $[i_{2n}, i_{2n}]$ of the inclusion of the bottom cell of the Moore space $P^{2n+1}(2)$ is divisible by $2$ if and only if $2n=2, 4, 8$ or $16$.

Spaces of orders of some one-relator groups

We show that certain orderable groups admit no isolated left orders. The groups we consider are cyclic amalgamations of a free group with a general orderable group, the HNN extensions of free groups over cyclic subgroups, and a particular class of one-relator groups. In order to prove the results about orders, we develop perturbation techniques for actions of these groups on the line.

Adversarial Attacks on Neural Network Policies

Machine learning classifiers are known to be vulnerable to inputs maliciously constructed by adversaries to force misclassification. Such adversarial examples have been extensively studied in the context of computer vision applications. In this work, we show adversarial attacks are also effective when targeting neural network policies in reinforcement learning. Specifically, we show existing adversarial example crafting techniques can be used to significantly degrade test-time performance of trained policies. Our threat model considers adversaries capable of introducing small perturbations to the raw input of the policy. We characterize the degree of vulnerability across tasks and training algorithms, for a subclass of adversarial-example attacks in white-box and black-box settings. Regardless of the learned task or training algorithm, we observe a significant drop in performance, even with small adversarial perturbations that do not interfere with human perception. Videos are available at this http URL.

Stellar streams as gravitational experiments I. The case of Sagittarius

Tidal streams of disrupting dwarf galaxies orbiting around their host galaxy offer a unique way to constrain the shape of galactic gravitational potentials. Such streams can be used as leaning tower gravitational experiments on galactic scales. The most well motivated modification of gravity proposed as an alternative to dark matter on galactic scales is Milgromian dynamics (MOND), and we present here the first ever N-body simulations of the dynamical evolution of the disrupting Sagittarius dwarf galaxy in this framework. Using a realistic baryonic mass model for the Milky Way, we attempt to reproduce the present-day spatial and kinematic structure of the Sagittarius dwarf and its immense tidal stream that wraps around the Milky Way. With very little freedom on the original structure of the progenitor, constrained by the total luminosity of the Sagittarius structure and by the observed stellar mass-size relation for isolated dwarf galaxies, we find reasonable agreement between our simulations and observations of this system. The observed stellar velocities in the leading arm can be reproduced if we include a massive hot gas corona around the Milky Way that is flattened in the direction of the principal plane of its satellites. This is the first time that tidal dissolution in MOND has been tested rigorously at these mass and acceleration scales.

Tuning quantum non-local effects in graphene plasmonics

The response of an electron system to electromagnetic fields with sharp spatial variations is strongly dependent on quantum electronic properties, even in ambient conditions, but difficult to access experimentally. We use propagating graphene plasmons, together with an engineered dielectric-metallic environment, to probe the graphene electron liquid and unveil its detailed electronic response at short wavelengths.The near-field imaging experiments reveal a parameter-free match with the full theoretical quantum description of the massless Dirac electron gas, in which we identify three types of quantum effects as keys to understanding the experimental response of graphene to short-ranged terahertz electric fields. The first type is of single-particle nature and is related to shape deformations of the Fermi surface during a plasmon oscillations. The second and third types are a many-body effect controlled by the inertia and compressibility of the interacting electron liquid in graphene. We demonstrate how, in principle, our experimental approach can determine the full spatiotemporal response of an electron system.

Flows along arch filaments observed in the GRIS 'very fast spectroscopic mode'

A new generation of solar instruments provides improved spectral, spatial, and temporal resolution, thus facilitating a better understanding of dynamic processes on the Sun. High-resolution observations often reveal multiple-component spectral line profiles, e.g., in the near-infrared He I 10830 \AA\ triplet, which provides information about the chromospheric velocity and magnetic fine structure. We observed an emerging flux region, including two small pores and an arch filament system, on 2015 April 17 with the 'very fast spectroscopic mode' of the GREGOR Infrared Spectrograph (GRIS) situated at the 1.5-meter GREGOR solar telescope at Observatorio del Teide, Tenerife, Spain. We discuss this method of obtaining fast (one per minute) spectral scans of the solar surface and its potential to follow dynamic processes on the Sun. We demonstrate the performance of the 'very fast spectroscopic mode' by tracking chromospheric high-velocity features in the arch filament system.

Rethinking Information Sharing for Actionable Threat Intelligence

In the past decade, the information security and threat landscape has grown significantly making it difficult for a single defender to defend against all attacks at the same time. This called for introduc- ing information sharing, a paradigm in which threat indicators are shared in a community of trust to facilitate defenses. Standards for representation, exchange, and consumption of indicators are pro- posed in the literature, although various issues are undermined. In this paper, we rethink information sharing for actionable intelli- gence, by highlighting various issues that deserve further explo- ration. We argue that information sharing can benefit from well- defined use models, threat models, well-understood risk by mea- surement and robust scoring, well-understood and preserved pri- vacy and quality of indicators and robust mechanism to avoid free riding behavior of selfish agent. We call for using the differential nature of data and community structures for optimizing sharing.

More new classes of permutation trinomials over $\mathbb{F}_{2^n}$

Permutation polynomials over finite fields have wide applications in many areas of science and engineering. In this paper, we present six new classes of permutation trinomials over $\mathbb{F}_{2^n}$ which have explicit forms by determining the solutions of some equations.

Distributive Aronszajn trees

Ben-David and Shelah proved that if $\lambda$ is a singular strong-limit cardinal and $2^\lambda=\lambda^+$, then $\square^*_\lambda$ entails the existence of a normal $\lambda$-distributive $\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains valid after replacing the hypothesis $\square^*_\lambda$ by $\square(\lambda^+,{<}\lambda)$. As $\square(\lambda^+,{<}\lambda)$ does not impose a bound on the order-type of the witnessing clubs, our construction is necessarily different from that of Ben-David and Shelah, and instead uses walks on ordinals augmented with club guessing. A major component of this work is the study of postprocessing functions and their effect on square sequences. A byproduct of this study is the finding that for $\kappa$ regular uncountable, $\square(\kappa)$ entails the existence of a partition of $\kappa$ into $\kappa$ many fat sets. When contrasted with a classic model of Magidor, this shows that it is equiconsistent with the existence of a weakly compact cardinal that $\omega_2$ cannot be split into two fat sets.

Analytical solutions for the radial Scarf II potential

The real Scarf II potential is discussed as a radial problem. This potential has been studied extensively as a one-dimensional problem, and now these results are used to construct its bound and resonance solutions for $l=0$ by setting the origin at some arbitrary value of the coordinate. The solutions with appropriate boundary conditions are composed as the linear combination of the two independent solutions of the Schrödinger equation. The asymptotic expression of these solutions is used to construct the $S_0(k)$ s-wave $S$-matrix, the poles of which supply the $k$ values corresponding to the bound, resonance and anti-bound solutions. The location of the discrete energy eigenvalues is analyzed, and the relation of the solutions of the radial and one-dimensional Scarf II potentials is discussed. It is shown that the generalized Woods--Saxon potential can be generated from the Rosen--Morse II potential in the same way as the radial Scarf II potential is obtained from its one-dimensional correspondent. Based on this analogy, possible applications are also pointed out.

Gated Multimodal Units for Information Fusion

This paper presents a novel model for multimodal learning based on gated neural networks. The Gated Multimodal Unit (GMU) model is intended to be used as an internal unit in a neural network architecture whose purpose is to find an intermediate representation based on a combination of data from different modalities. The GMU learns to decide how modalities influence the activation of the unit using multiplicative gates. It was evaluated on a multilabel scenario for genre classification of movies using the plot and the poster. The GMU improved the macro f-score performance of single-modality approaches and outperformed other fusion strategies, including mixture of experts models. Along with this work, the MM-IMDb dataset is released which, to the best of our knowledge, is the largest publicly available multimodal dataset for genre prediction on movies.

Why Condorcet Consistency is Essential

In a single winner election with several candidates and ranked choice or rating scale ballots, a Condorcet winner is one who wins all their two way races by majority rule or MR. A voting system has Condorcet consistency or CC if it names any Condorcet winner the winner. Many voting systems lack CC, but a three step line of reasoning is used here to show why it is necessary. In step 1 we show that we can dismiss all the electoral criteria which conflict with CC. In step 2 we point out that CC follows almost automatically if we can agree that MR is the only acceptable system for elections with two candidates. In step 3 we make that argument for MR. This argument itself has three parts. First, in races with two candidates, the only well known alternatives to MR can sometimes name as winner a candidate who is preferred over their opponent by only one voter, with all others preferring the opponent. That is unacceptable. Second, those same systems are also extremely susceptible to strategic insincere voting. Third, in simulation studies using spatial models with two candidates, the best known alternative to MR picks the best or most centrist candidate significantly less often than MR does.

Birefringence induced by pp-wave modes in an electromagnetically active dynamic aether

In the framework of the Einstein-Maxwell-aether theory we study the birefringence effect, which can occur in the pp-wave symmetric dynamic aether. The dynamic aether is considered to be latently birefringent quasi-medium, which displays this hidden property if and only if the aether motion is non-uniform, i.e., when the aether flow is characterized by the non-vanishing expansion, shear, vorticity or acceleration. In accordance with the dynamo-optical scheme of description of the interaction between electromagnetic waves and the dynamic aether, we shall model the susceptibility tensors by the terms linear in the covariant derivative of the aether velocity four-vector. When the pp-wave modes appear in the dynamic aether, we deal with a gravitationally induced degeneracy removal with respect to hidden susceptibility parameters. As a consequence, the phase velocities of electromagnetic waves possessing orthogonal polarizations do not coincide, thus displaying the birefringence effect. Two electromagnetic field configurations are studied in detail: longitudinal and transversal with respect to the aether pp-wave front. For both cases the solutions are found, which reveal anomalies in the electromagnetic response on the action of the pp-wave aether mode.

On generalizations of $p$-sets and their applications

The $p$-set, which is in a simple analytic form, is well distributed in unit cubes. The well-known Weil's exponential sum theorem presents an upper bound of the exponential sum over the $p$-set. Based on the result, one shows that the $p$-set performs well in numerical integration, in compressed sensing as well as in UQ. However, $p$-set is somewhat rigid since the cardinality of the $p$-set is a prime $p$ and the set only depends on the prime number $p$. The purpose of this paper is to present generalizations of $p$-sets, say $\mathcal{P}_{d,p}^{{\mathbf a},\epsilon}$, which is more flexible. Particularly, when a prime number $p$ is given, we have many different choices of the new $p$-sets. Under the assumption that Goldbach conjecture holds, for any even number $m$, we present a point set, say ${\mathcal L}_{p,q}$, with cardinality $m-1$ by combining two different new $p$-sets, which overcomes a major bottleneck of the $p$-set. We also present the upper bounds of the exponential sums over $\mathcal{P}_{d,p}^{{\mathbf a},\epsilon}$ and ${\mathcal L}_{p,q}$, which imply these sets have many potential applications.

Robot human interface for housekepeer with wireless capabilities

This paper presents the design and implementation of a Human Interface for a housekeeper robot. It bases on the idea of making the robot understand the human needs without making the human go through the details of robots work, for example, the way that the robot implements the work or the method that the robot uses to plan the path in order to reach the work area. The interface commands based on idioms of the natural human language and designed in a manner that the user gives the robot several commands with their execution date/time.

Modified Frank-Wolfe Algorithm for Enhanced Sparsity in Support Vector Machine Classifiers

This work proposes a new algorithm for training a re-weighted L2 Support Vector Machine (SVM), inspired on the re-weighted Lasso algorithm of Candès et al. and on the equivalence between Lasso and SVM shown recently by Jaggi. In particular, the margin required for each training vector is set independently, defining a new weighted SVM model. These weights are selected to be binary, and they are automatically adapted during the training of the model, resulting in a variation of the Frank-Wolfe optimization algorithm with essentially the same computational complexity as the original algorithm. As shown experimentally, this algorithm is computationally cheaper to apply since it requires less iterations to converge, and it produces models with a sparser representation in terms of support vectors and which are more stable with respect to the selection of the regularization hyper-parameter.

Multi-Task Domain Adaptation for Deep Learning of Instance Grasping from Simulation

Learning-based approaches to robotic manipulation are limited by the scalability of data collection and accessibility of labels. In this paper, we present a multi-task domain adaptation framework for instance grasping in cluttered scenes by utilizing simulated robot experiments. Our neural network takes monocular RGB images and the instance segmentation mask of a specified target object as inputs, and predicts the probability of successfully grasping the specified object for each candidate motor command. The proposed transfer learning framework trains a model for instance grasping in simulation and uses a domain-adversarial loss to transfer the trained model to real robots using indiscriminate grasping data, which is available both in simulation and the real world. We evaluate our model in real-world robot experiments, comparing it with alternative model architectures as well as an indiscriminate grasping baseline.

Bounded Depth Ascending HNN Extensions and $π_1$-Semistability at $\infty$

A 1-ended finitely presented group has semistable fundamental group at $\infty$ if it acts geometrically on some (equivalently any) simply connected and locally finite complex $X$ with the property that any two proper rays in $X$ are properly homotopic. If $G$ has semistable fundamental group at $\infty$ then one can unambiguously define the fundamental group at $\infty$ for $G$. The problem, asking if all finitely presented groups have semistable fundamental group at $\infty$ has been studied for over 40 years. If $G$ is an ascending HNN extension of a finitely presented group then indeed, $G$ has semistable fundamental group at $\infty$, but since the early 1980's it has been suggested that the finitely presented groups that are ascending HNN extensions of {\it finitely generated} groups may include a group with non-semistable fundamental group at $\infty$. Ascending HNN extensions naturally break into two classes, those with bounded depth and those with unbounded depth. Our main theorem shows that bounded depth finitely presented ascending HNN extensions of finitely generated groups have semistable fundamental group at $\infty$. Semistability is equivalent to two weaker asymptotic conditions on the group holding simultaneously. We show one of these conditions holds for all ascending HNN extensions, regardless of depth. We give a technique for constructing ascending HNN extensions with unbounded depth. This work focuses attention on a class of groups that may contain a group with non-semistable fundamental group at $\infty$.

AirSim: High-Fidelity Visual and Physical Simulation for Autonomous Vehicles

Developing and testing algorithms for autonomous vehicles in real world is an expensive and time consuming process. Also, in order to utilize recent advances in machine intelligence and deep learning we need to collect a large amount of annotated training data in a variety of conditions and environments. We present a new simulator built on Unreal Engine that offers physically and visually realistic simulations for both of these goals. Our simulator includes a physics engine that can operate at a high frequency for real-time hardware-in-the-loop (HITL) simulations with support for popular protocols (e.g. MavLink). The simulator is designed from the ground up to be extensible to accommodate new types of vehicles, hardware platforms and software protocols. In addition, the modular design enables various components to be easily usable independently in other projects. We demonstrate the simulator by first implementing a quadrotor as an autonomous vehicle and then experimentally comparing the software components with real-world flights.

Hausdorff dimensions in $p$-adic analytic groups

Let $G$ be a finitely generated pro-$p$ group, equipped with the $p$-power series. The associated metric and Hausdorff dimension function give rise to the Hausdorff spectrum, which consists of the Hausdorff dimensions of closed subgroups of $G$. In the case where $G$ is $p$-adic analytic, the Hausdorff dimension function is well understood; in particular, the Hausdorff spectrum consists of finitely many rational numbers closely linked to the analytic dimensions of subgroups of $G$. Conversely, it is a long-standing open question whether the finiteness of the Hausdorff spectrum implies that $G$ is $p$-adic analytic. We prove that the answer is yes, in a strong sense, under the extra condition that $G$ is soluble. Furthermore, we explore the problem and related questions also for other filtration series, such as the lower $p$-series, the Frattini series, the modular dimension subgroup series and quite general filtration series. For instance, we prove, for odd primes $p$, that every countably based pro-$p$ group $G$ with an open subgroup mapping onto 2 copies of the $p$-adic integers admits a filtration series such that the corresponding Hausdorff spectrum contains an infinite real interval.

Real-time brain machine interaction via social robot gesture control

Brain-Machine Interaction (BMI) system motivates interesting and promising results in forward/feedback control consistent with human intention. It holds great promise for advancements in patient care and applications to neurorehabilitation. Here, we propose a novel neurofeedback-based BCI robotic platform using a personalized social robot in order to assist patients having cognitive deficits through bilateral rehabilitation and mental training. For initial testing of the platform, electroencephalography (EEG) brainwaves of a human user were collected in real time during tasks of imaginary movements. First, the brainwaves associated with imagined body kinematics parameters were decoded to control a cursor on a computer screen in training protocol. Then, the experienced subject was able to interact with a social robot via our real-time BMI robotic platform. Corresponding to subject's imagery performance, he/she received specific gesture movements and eye color changes as neural-based feedback from the robot. This hands-free neurofeedback interaction not only can be used for mind control of a social robot's movements, but also sets the stage for application to enhancing and recovering mental abilities such as attention via training in humans by providing real-time neurofeedback from a social robot.

City-Scale Road Audit System using Deep Learning

Road networks in cities are massive and is a critical component of mobility. Fast response to defects, that can occur not only due to regular wear and tear but also because of extreme events like storms, is essential. Hence there is a need for an automated system that is quick, scalable and cost-effective for gathering information about defects. We propose a system for city-scale road audit, using some of the most recent developments in deep learning and semantic segmentation. For building and benchmarking the system, we curated a dataset which has annotations required for road defects. However, many of the labels required for road audit have high ambiguity which we overcome by proposing a label hierarchy. We also propose a multi-step deep learning model that segments the road, subdivide the road further into defects, tags the frame for each defect and finally localizes the defects on a map gathered using GPS. We analyze and evaluate the models on image tagging as well as segmentation at different levels of the label hierarchy.

Mass and moment of inertia govern the transition in the dynamics and wakes of freely rising and falling cylinders

In this Letter, we study the motion and wake-patterns of freely rising and falling cylinders in quiescent fluid. We show that the amplitude of oscillation and the overall system-dynamics are intricately linked to two parameters: the particle's mass-density relative to the fluid $m^* \equiv \rho_p/\rho_f$ and its relative moment-of-inertia $I^* \equiv {I}_p/{I}_f$. This supersedes the current understanding that a critical mass density ($m^*\approx$ 0.54) alone triggers the sudden onset of vigorous vibrations. Using over 144 combinations of ${m}^*$ and $I^*$, we comprehensively map out the parameter space covering very heavy ($m^* > 10$) to very buoyant ($m^* < 0.1$) particles. The entire data collapses into two scaling regimes demarcated by a transitional Strouhal number, $St_t \approx 0.17$. $St_t$ separates a mass-dominated regime from a regime dominated by the particle's moment of inertia. A shift from one regime to the other also marks a gradual transition in the wake-shedding pattern: from the classical $2S$~(2-Single) vortex mode to a $2P$~(2-Pairs) vortex mode. Thus, auto-rotation can have a significant influence on the trajectories and wakes of freely rising isotropic bodies.

It Takes Two to Tango: Towards Theory of AI's Mind

Theory of Mind is the ability to attribute mental states (beliefs, intents, knowledge, perspectives, etc.) to others and recognize that these mental states may differ from one's own. Theory of Mind is critical to effective communication and to teams demonstrating higher collective performance. To effectively leverage the progress in Artificial Intelligence (AI) to make our lives more productive, it is important for humans and AI to work well together in a team. Traditionally, there has been much emphasis on research to make AI more accurate, and (to a lesser extent) on having it better understand human intentions, tendencies, beliefs, and contexts. The latter involves making AI more human-like and having it develop a theory of our minds. In this work, we argue that for human-AI teams to be effective, humans must also develop a theory of AI's mind (ToAIM) - get to know its strengths, weaknesses, beliefs, and quirks. We instantiate these ideas within the domain of Visual Question Answering (VQA). We find that using just a few examples (50), lay people can be trained to better predict responses and oncoming failures of a complex VQA model. We further evaluate the role existing explanation (or interpretability) modalities play in helping humans build ToAIM. Explainable AI has received considerable scientific and popular attention in recent times. Surprisingly, we find that having access to the model's internal states - its confidence in its top-k predictions, explicit or implicit attention maps which highlight regions in the image (and words in the question) the model is looking at (and listening to) while answering a question about an image - do not help people better predict its behavior.

On variation of dynamical canonical heights, and Intersection numbers

We study families of varieties endowed with polarized canonical eigensystems of several maps, inducing canonical heights on the dominating variety as well as on the "good" fibers of the family. We show explicitely the dependence on the parameter for global and local canonical heights defined by Kawaguchi when the fibers change, extending previous works of J. Silverman and others. Finally, fixing an absolute value $v \in K$ and a variety $V/K$, we descript the Kawaguchi`s canonical local height $\hat{\lambda}_{V,E,\mathcal{Q},}(.,v)$ as an intersection number, provided that the polarized system $(V,\mathcal{Q})$ has a certain weak Néron model over Spec$(\mathcal{O}_v)$ to be defined and under some conditions depending on the special fiber. With this we extend Néron's work strengthening Silverman's results, which were for systems having only one map.

Enhancing the Spectral Hardening of Cosmic TeV Photons by Mixing with Axionlike Particles in the Magnetized Cosmic Web

Large-scale extragalactic magnetic fields may induce conversions between very-high-energy photons and axionlike particles (ALPs), thereby shielding the photons from absorption on the extragalactic background light. However, in simplified "cell" models, used so far to represent extragalactic magnetic fields, this mechanism would be strongly suppressed by current astrophysical bounds. Here we consider a recent model of extragalactic magnetic fields obtained from large-scale cosmological simulations. Such simulated magnetic fields would have large enhancement in the filaments of matter. As a result, photon-ALP conversions would produce a significant spectral hardening for cosmic TeV photons. This effect would be probed with the upcoming Cherenkov Telescope Array detector. This possible detection would give a unique chance to perform a tomography of the magnetized cosmic web with ALPs.

Forecasting in the light of Big Data

Predicting the future state of a system has always been a natural motivation for science and practical applications. Such a topic, beyond its obvious technical and societal relevance, is also interesting from a conceptual point of view. This owes to the fact that forecasting lends itself to two equally radical, yet opposite methodologies. A reductionist one, based on the first principles, and the naive inductivist one, based only on data. This latter view has recently gained some attention in response to the availability of unprecedented amounts of data and increasingly sophisticated algorithmic analytic techniques. The purpose of this note is to assess critically the role of big data in reshaping the key aspects of forecasting and in particular the claim that bigger data leads to better predictions. Drawing on the representative example of weather forecasts we argue that this is not generally the case. We conclude by suggesting that a clever and context-dependent compromise between modelling and quantitative analysis stands out as the best forecasting strategy, as anticipated nearly a century ago by Richardson and von Neumann.

Adelic point groups of elliptic curves

We show that for an elliptic curve E defined over a number field K, the group E(A) of points of E over the adele ring A of K is a topological group that can be analyzed in terms of the Galois representation associated to the torsion points of E. An explicit description of E(A) is given, and we prove that for K of degree n, almost all elliptic curves over K have an adelic point group topologically isomorphic to a universal group depending on n. We also show that there exist infinitely many elliptic curves over K having a different adelic point group.

Position Aided Beam Alignment for Millimeter Wave Backhaul Systems with Large Phased Arrays

Wireless backhaul communication has been recently realized with large antennas operating in the millimeter wave (mmWave) frequency band and implementing highly directional beamforming. In this paper, we focus on the alignment problem of narrow beams between fixed position network nodes in mmWave backhaul systems that are subject to small displacements due to wind flow or ground vibration. We consider nodes equipped with antenna arrays that are capable of performing only analog processing and communicate through wireless channels including a line-of-sight component. Aiming at minimizing the time needed to achieve beam alignment, we present an efficient method that capitalizes on the exchange of position information between the nodes to design their beamforming and combining vectors. Some numerical results on the outage probability with the proposed beam alignment method offer useful preliminary insights on the impact of some system and operation parameters.

Deep & Cross Network for Ad Click Predictions

Feature engineering has been the key to the success of many prediction models. However, the process is non-trivial and often requires manual feature engineering or exhaustive searching. DNNs are able to automatically learn feature interactions; however, they generate all the interactions implicitly, and are not necessarily efficient in learning all types of cross features. In this paper, we propose the Deep & Cross Network (DCN) which keeps the benefits of a DNN model, and beyond that, it introduces a novel cross network that is more efficient in learning certain bounded-degree feature interactions. In particular, DCN explicitly applies feature crossing at each layer, requires no manual feature engineering, and adds negligible extra complexity to the DNN model. Our experimental results have demonstrated its superiority over the state-of-art algorithms on the CTR prediction dataset and dense classification dataset, in terms of both model accuracy and memory usage.

Fan-type spin structure in uni-axial chiral magnets

We investigate the spin structure of a uni-axial chiral magnet near the transition temperatures in low fields perpendicular to the helical axis. We find a fan-type modulation structure where the clockwise and counterclockwise windings appear alternatively along the propagation direction of the modulation structure. This structure is often realized in a Yoshimori-type (non-chiral) helimagnet but it is rarely realized in a chiral helimagnet. To discuss underlying physics of this structure, we reconsider the phase diagram (phase boundary and crossover lines) through the free energy and asymptotic behaviors of isolated solitons. The fan structure appears slightly below the phase boundary of the continuous transition of instability-type. In this region, there are no solutions containing any types of isolated solitons to the mean field equations.

Rotation of a synchronous viscoelastic shell

Several natural satellites of the giant planets have shown evidence of a global internal ocean, coated by a thin, icy crust. This crust is probably viscoelastic, which would alter its rotational response. This response would translate into several rotational quantities, i.e. the obliquity, and the librations at different frequencies, for which the crustal elasticity reacts differently. This study aims at modelling the global response of the viscoelastic crust. For that, I derive the time-dependency of the tensor of inertia, which I combine with the time evolution of the rotational quantities, thanks to an iterative algorithm. This algorithm combines numerical simulations of the rotation with a digital filtering of the resulting tensor of inertia. The algorithm works very well in the elastic case, provided the problem is not resonant. However, considering tidal dissipation adds different phase lags to the oscillating contributions, which challenge the convergence of the algorithm.

Direct estimation of density functionals using a polynomial basis

A number of fundamental quantities in statistical signal processing and information theory can be expressed as integral functions of two probability density functions. Such quantities are called density functionals as they map density functions onto the real line. For example, information divergence functions measure the dissimilarity between two probability density functions and are useful in a number of applications. Typically, estimating these quantities requires complete knowledge of the underlying distribution followed by multi-dimensional integration. Existing methods make parametric assumptions about the data distribution or use non-parametric density estimation followed by high-dimensional integration. In this paper, we propose a new alternative. We introduce the concept of "data-driven basis functions" - functions of distributions whose value we can estimate given only samples from the underlying distributions without requiring distribution fitting or direct integration. We derive a new data-driven complete basis that is similar to the deterministic Bernstein polynomial basis and develop two methods for performing basis expansions of functionals of two distributions. We also show that the new basis set allows us to approximate functions of distributions as closely as desired. Finally, we evaluate the methodology by developing data driven estimators for the Kullback-Leibler divergences and the Hellinger distance and by constructing empirical estimates of tight bounds on the Bayes error rate.

Experimental Evidence on a Refined Conjecture of the BSD type

Let $E/\mathbb{Q}$ be an elliptic curve of level $N$ and rank equal to $1$. Let $p$ be a prime of ordinary reduction. We experimentally study conjecture $4$ of B. Mazur and J. Tate in his article "Refined Conjectures of the Birch and Swinnerton-Dyer Type". We report the computational evidence.

The Tu--Deng Conjecture holds almost surely

The Tu--Deng Conjecture is concerned with the sum of digits $w(n)$ of $n$ in base~$2$ (the Hamming weight of the binary expansion of $n$) and states the following: assume that $k$ is a positive integer and $1\leq t<2^k-1$. Then \[\Bigl \lvert\Bigl\{(a,b)\in\bigl\{0,\ldots,2^k-2\bigr\}^2:a+b\equiv t\bmod 2^k-1, w(a)+w(b)<k\Bigr\}\Bigr \rvert\leq 2^{k-1}.\] We prove that the Tu--Deng Conjecture holds almost surely in the following sense: the proportion of $t\in[1,2^k-2]$ such that the above inequality holds approaches $1$ as $k\rightarrow\infty$. Moreover, we prove that the Tu--Deng Conjecture implies a conjecture due to T.~W.~Cusick concerning the sum of digits of $n$ and $n+t$.

Convergence Analysis of the Dynamics of a Special Kind of Two-Layered Neural Networks with $\ell_1$ and $\ell_2$ Regularization

In this paper, we made an extension to the convergence analysis of the dynamics of two-layered bias-free networks with one $ReLU$ output. We took into consideration two popular regularization terms: the $\ell_1$ and $\ell_2$ norm of the parameter vector $w$, and added it to the square loss function with coefficient $\lambda/2$. We proved that when $\lambda$ is small, the weight vector $w$ converges to the optimal solution $\hat{w}$ (with respect to the new loss function) with probability $\geq (1-\varepsilon)(1-A_d)/2$ under random initiations in a sphere centered at the origin, where $\varepsilon$ is a small value and $A_d$ is a constant. Numerical experiments including phase diagrams and repeated simulations verified our theory.

From bare interactions, low--energy constants and unitary gas to nuclear density functionals without free parameters: application to neutron matter

We further progress along the line of Ref. [Phys. Rev. {\bf A 94}, 043614 (2016)] where a functional for Fermi systems with anomalously large $s$-wave scattering length $a_s$ was proposed that has no free parameters. The functional is designed to correctly reproduce the unitary limit in Fermi gases together with the leading-order contributions in the s- and p-wave channels at low density. The functional is shown to be predictive up to densities $\sim0.01$ fm$^{-3}$ that is much higher densities compared to the Lee-Yang functional, valid for $\rho < 10^{-6}$ fm$^{-3}$. The form of the functional retained in this work is further motivated. It is shown that the new functional corresponds to an expansion of the energy in $(a_s k_F)$ and $(r_e k_F)$ to all orders, where $r_e$ is the effective range and $k_F$ is the Fermi momentum. One conclusion from the present work is that, except in the extremely low--density regime, nuclear systems can be treated perturbatively in $-(a_s k_F)^{-1}$ with respect to the unitary limit. Starting from the functional, we introduce density--dependent scales and show that scales associated to the bare interaction are strongly renormalized by medium effects. As a consequence, some of the scales at play around saturation are dominated by the unitary gas properties and not directly to low-energy constants. For instance, we show that the scale in the s-wave channel around saturation is proportional to the so-called Bertsch parameter $\xi_0$ and becomes independent of $a_s$. We also point out that these scales are of the same order of magnitude than those empirically obtained in the Skyrme energy density functional. We finally propose a slight modification of the functional such that it becomes accurate up to the saturation density $\rho\simeq 0.16$ fm$^{-3}$.

EgoCap: Egocentric Marker-less Motion Capture with Two Fisheye Cameras (Extended Abstract)

Marker-based and marker-less optical skeletal motion-capture methods use an outside-in arrangement of cameras placed around a scene, with viewpoints converging on the center. They often create discomfort by possibly needed marker suits, and their recording volume is severely restricted and often constrained to indoor scenes with controlled backgrounds. We therefore propose a new method for real-time, marker-less and egocentric motion capture which estimates the full-body skeleton pose from a lightweight stereo pair of fisheye cameras that are attached to a helmet or virtual-reality headset. It combines the strength of a new generative pose estimation framework for fisheye views with a ConvNet-based body-part detector trained on a new automatically annotated and augmented dataset. Our inside-in method captures full-body motion in general indoor and outdoor scenes, and also crowded scenes.

Diffusion Maps meet Nyström

Diffusion maps are an emerging data-driven technique for non-linear dimensionality reduction, which are especially useful for the analysis of coherent structures and nonlinear embeddings of dynamical systems. However, the computational complexity of the diffusion maps algorithm scales with the number of observations. Thus, long time-series data presents a significant challenge for fast and efficient embedding. We propose integrating the Nyström method with diffusion maps in order to ease the computational demand. We achieve a speedup of roughly two to four times when approximating the dominant diffusion map components.

Multiphase Flows of N Immiscible Incompressible Fluids: An Outflow/Open Boundary Condition and Algorithm

We present a set of effective outflow/open boundary conditions and an associated algorithm for simulating the dynamics of multiphase flows consisting of $N$ ($N\geqslant 2$) immiscible incompressible fluids in domains involving outflows or open boundaries. These boundary conditions are devised based on the properties of energy stability and reduction consistency. The energy stability property ensures that the contributions of these boundary conditions to the energy balance will not cause the total energy of the N-phase system to increase over time. Therefore, these open/outflow boundary conditions are very effective in overcoming the backflow instability in multiphase systems. The reduction consistency property ensures that if some fluid components are absent from the N-phase system then these N-phase boundary conditions will reduce to those corresponding boundary conditions for the equivalent smaller system. Our numerical algorithm for the proposed boundary conditions together with the N-phase governing equations involves only the solution of a set of de-coupled individual Helmholtz-type equations within each time step, and the resultant linear algebraic systems after discretization involve only constant and time-independent coefficient matrices which can be pre-computed. Therefore, the algorithm is computationally very efficient and attractive. We present extensive numerical experiments for flow problems involving multiple fluid components and inflow/outflow boundaries to test the proposed method. In particular, we compare in detail the simulation results of a three-phase capillary wave problem with Prosperetti's exact physical solution and demonstrate that the method developed herein produces physically accurate results.

Deadly dark matter cusps vs faint and extended star clusters: Eridanus II and Andromeda XXV

The recent detection of two faint and extended star clusters in the central regions of two Local Group dwarf galaxies, Eridanus II and Andromeda XXV, raises the question of whether clusters with such low densities can survive the tidal field of cold dark matter haloes with central density cusps. Using both analytic arguments and a suite of collisionless N-body simulations, I show that these clusters are extremely fragile and quickly disrupted in the presence of central cusps $\rho\sim r^{-\alpha}$ with $\alpha\gtrsim 0.2$. Furthermore, the scenario in which the clusters where originally more massive and sank to the center of the halo requires extreme fine tuning and does not naturally reproduce the observed systems. In turn, these clusters are long lived in cored haloes, whose central regions are safe shelters for $\alpha\lesssim 0.2$. The only viable scenario for hosts that have preserved their primoridal cusp to the present time is that the clusters formed at rest at the bottom of the potential, which is easily tested by measurement of the clusters proper velocity within the host. This offers means to readily probe the central density profile of two dwarf galaxies as faint as $L_V\sim5\times 10^5 L_\odot$ and $L_V\sim6\times10^4 L_\odot$, in which stellar feedback is unlikely to be effective.

Mutual Information, Relative Entropy and Estimation Error in Semi-martingale Channels

Fundamental relations between information and estimation have been established in the literature for the continuous-time Gaussian and Poisson channels, in a long line of work starting from the classical representation theorems by Duncan and Kabanov respectively. In this work, we demonstrate that such relations hold for a much larger family of continuous-time channels. We introduce the family of semi-martingale channels where the channel output is a semi-martingale stochastic process, and the channel input modulates the characteristics of the semi-martingale. For these channels, which includes as a special case the continuous time Gaussian and Poisson models, we establish new representations relating the mutual information between the channel input and output to an optimal causal filtering loss, thereby unifying and considerably extending results from the Gaussian and Poisson settings. Extensions to the setting of mismatched estimation are also presented where the relative entropy between the laws governing the output of the channel under two different input distributions is equal to the cumulative difference between the estimation loss incurred by using the mismatched and optimal causal filters respectively. The main tool underlying these results is the Doob--Meyer decomposition of a class of likelihood ratio sub-martingales. The results in this work can be viewed as the continuous-time analogues of recent generalizations for relations between information and estimation for discrete-time Lévy channels.

Testing redMaPPer centring probabilities using galaxy clustering and galaxy-galaxy lensing

Galaxy cluster centring is a key issue for precision cosmology studies using galaxy surveys. Mis-identification of central galaxies causes systematics in various studies such as cluster lensing, satellite kinematics, and galaxy clustering. The red-sequence Matched-filter Probabilistic Percolation (redMaPPer) estimates the probability that each member galaxy is central from photometric information rather than specifying one central galaxy. The redMaPPer estimates can be used for calibrating the off-centring effect, however, the centring algorithm has not previously been well-tested. We test the centring probabilities of redMaPPer cluster catalog using the projected cross correlation between redMaPPer clusters with photometric red galaxies and galaxy-galaxy lensing. We focus on the subsample of redMaPPer clusters in which the redMaPPer central galaxies (RMCGs) are not the brightest member galaxies (BMEM) and both of them have spectroscopic redshift. This subsample represents nearly 10% of the whole cluster sample. We find a clear difference in the cross-correlation measurements between RMCGs and BMEMs, and the estimated centring probability is 74$\pm$10% for RMCGs and 13$\pm$4% for BMEMs in the Gaussian offset model and 78$\pm$9% for RMCGs and 5$\pm$5% for BMEMs in the NFW offset model. These values are in agreement with the centring probability values reported by redMaPPer (75% for RMCG and 10% for BMEMs) within 1$\sigma$. Our analysis provides a strong consistency test of the redMaPPer centring probabilities. Our results suggest that redMaPPer centring probabilities are reliably estimated. We confirm that the brightest galaxy in the cluster is not always the central galaxy as has been shown in previous works.

Criterion of positivity for semilinear problems with applications in biology

The goal of this article is to provide an useful criterion of positivity and well-posedness for a wide range of infinite dimensional semilinear abstract Cauchy problems. This criterion is based on some weak assumptions on the non-linear part of the semilinear problem and on the existence of a strongly continuous semigroup generated by the differential operator. To illustrate a large variety of applications, we exhibit the feasibility of this criterion through three examples in mathematical biology: epidemiology, predator-prey interactions and oncology.

Axiomatic quantum mechanics: Necessity and benefits for the physics studies

The ongoing progress in quantum theory emphasizes the crucial role of the very basic principles of quantum theory. However, this is not properly followed in teaching quantum mechanics on the graduate and undergraduate levels of physics studies. The existing textbooks typically avoid the axiomatic presentation of the theory. We emphasize usefulness of the systematic, axiomatic approach to the basics of quantum theory as well as its importance in the light of the modern scientific-research context.

Kinetic modelling of competition and depletion of shared miRNAs by competing endogenous RNAs

Non-conding RNAs play a key role in the post-transcriptional regulation of mRNA translation and turnover in eukaryotes. miRNAs, in particular, interact with their target RNAs through protein-mediated, sequence-specific binding, giving rise to extended and highly heterogeneous miRNA-RNA interaction networks. Within such networks, competition to bind miRNAs can generate an effective positive coupling between their targets. Competing endogenous RNAs (ceRNAs) can in turn regulate each other through miRNA-mediated crosstalk. Albeit potentially weak, ceRNA interactions can occur both dynamically, affecting e.g. the regulatory clock, and at stationarity, in which case ceRNA networks as a whole can be implicated in the composition of the cell's proteome. Many features of ceRNA interactions, including the conditions under which they become significant, can be unraveled by mathematical and in silico models. We review the understanding of the ceRNA effect obtained within such frameworks, focusing on the methods employed to quantify it, its role in the processing of gene expression noise, and how network topology can determine its reach.

Shortening binary complexes and commutativity of $K$-theory with infinite products

We show that in Grayson's model of higher algebraic $K$-theory using binary acyclic complexes, the complexes of length two suffice to generate the whole group. Moreover, we prove that the comparison map from Nenashev's model for $K_1$ to Grayson's model for $K_1$ is an isomorphism. It follows that algebraic $K$-theory of exact categories commutes with infinite products.

Cost-Effective Seed Selection in Online Social Networks

We study the min-cost seed selection problem in online social networks, where the goal is to select a set of seed nodes with the minimum total cost such that the expected number of influenced nodes in the network exceeds a predefined threshold. We propose several algorithms that outperform the previous studies both on the theoretical approximation ratios and on the experimental performance. Under the case where the nodes have heterogeneous costs, our algorithms are the first bi- criteria approximation algorithms with polynomial running time and provable logarithmic performance bounds using a general contagion model. Under the case where the users have uniform costs, our algorithms achieve logarithmic approximation ratio and provable time complexity which is smaller than that of existing algorithms in orders of magnitude. We conduct extensive experiments using real social networks. The experimental results show that, our algorithms significantly outperform the existing algorithms both on the total cost and on the running time, and also scale well to billion-scale networks.

Fast Meta-Learning for Adaptive Hierarchical Classifier Design

We propose a new splitting criterion for a meta-learning approach to multiclass classifier design that adaptively merges the classes into a tree-structured hierarchy of increasingly difficult binary classification problems. The classification tree is constructed from empirical estimates of the Henze-Penrose bounds on the pairwise Bayes misclassification rates that rank the binary subproblems in terms of difficulty of classification. The proposed empirical estimates of the Bayes error rate are computed from the minimal spanning tree (MST) of the samples from each pair of classes. Moreover, a meta-learning technique is presented for quantifying the one-vs-rest Bayes error rate for each individual class from a single MST on the entire dataset. Extensive simulations on benchmark datasets show that the proposed hierarchical method can often be learned much faster than competing methods, while achieving competitive accuracy.

Vibrational Density Matrix Renormalization Group

Variational approaches for the calculation of vibrational wave functions and energies are a natural route to obtain highly accurate results with controllable errors. However, the unfavorable scaling and the resulting high computational cost of standard variational approaches limit their application to small molecules with only few vibrational modes. Here, we demonstrate how the density matrix renormalization group (DMRG) can be exploited to optimize vibrational wave functions (vDMRG) expressed as matrix product states. We study the convergence of these calculations with respect to the size of the local basis of each mode, the number of renormalized block states, and the number of DMRG sweeps required. We demonstrate the high accuracy achieved by vDMRG for small molecules that were intensively studied in the literature. We then proceed to show that the complete fingerprint region of the sarcosyn-glycin dipeptide can be calculated with vDMRG.

Identification and Off-Policy Learning of Multiple Objectives Using Adaptive Clustering

In this work, we present a methodology that enables an agent to make efficient use of its exploratory actions by autonomously identifying possible objectives in its environment and learning them in parallel. The identification of objectives is achieved using an online and unsupervised adaptive clustering algorithm. The identified objectives are learned (at least partially) in parallel using Q-learning. Using a simulated agent and environment, it is shown that the converged or partially converged value function weights resulting from off-policy learning can be used to accumulate knowledge about multiple objectives without any additional exploration. We claim that the proposed approach could be useful in scenarios where the objectives are initially unknown or in real world scenarios where exploration is typically a time and energy intensive process. The implications and possible extensions of this work are also briefly discussed.

Non-Asymptotic Analysis of Fractional Langevin Monte Carlo for Non-Convex Optimization

Recent studies on diffusion-based sampling methods have shown that Langevin Monte Carlo (LMC) algorithms can be beneficial for non-convex optimization, and rigorous theoretical guarantees have been proven for both asymptotic and finite-time regimes. Algorithmically, LMC-based algorithms resemble the well-known gradient descent (GD) algorithm, where the GD recursion is perturbed by an additive Gaussian noise whose variance has a particular form. Fractional Langevin Monte Carlo (FLMC) is a recently proposed extension of LMC, where the Gaussian noise is replaced by a heavy-tailed {\alpha}-stable noise. As opposed to its Gaussian counterpart, these heavy-tailed perturbations can incur large jumps and it has been empirically demonstrated that the choice of {\alpha}-stable noise can provide several advantages in modern machine learning problems, both in optimization and sampling contexts. However, as opposed to LMC, only asymptotic convergence properties of FLMC have been yet established. In this study, we analyze the non-asymptotic behavior of FLMC for non-convex optimization and prove finite-time bounds for its expected suboptimality. Our results show that the weak-error of FLMC increases faster than LMC, which suggests using smaller step-sizes in FLMC. We finally extend our results to the case where the exact gradients are replaced by stochastic gradients and show that similar results hold in this setting as well.

Spoken English Intelligibility Remediation with PocketSphinx Alignment and Feature Extraction Improves Substantially over the State of the Art

We use automatic speech recognition to assess spoken English learner pronunciation based on the authentic intelligibility of the learners' spoken responses determined from support vector machine (SVM) classifier or deep learning neural network model predictions of transcription correctness. Using numeric features produced by PocketSphinx alignment mode and many recognition passes searching for the substitution and deletion of each expected phoneme and insertion of unexpected phonemes in sequence, the SVM models achieve 82 percent agreement with the accuracy of Amazon Mechanical Turk crowdworker transcriptions, up from 75 percent reported by multiple independent researchers. Using such features with SVM classifier probability prediction models can help computer-aided pronunciation teaching (CAPT) systems provide intelligibility remediation.

Second-Order Analysis and Numerical Approximation for Bang-Bang Bilinear Control Problems

We consider bilinear optimal control problems, whose objective functionals do not depend on the controls. Hence, bang-bang solutions will appear. We investigate sufficient second-order conditions for bang-bang controls, which guarantee local quadratic growth of the objective functional in $L^1$. In addition, we prove that for controls that are not bang-bang, no such growth can be expected. Finally, we study the finite-element discretization, and prove error estimates of bang-bang controls in $L^1$-norms.

On the letter frequencies and entropy of written Marathi

We carry out a comprehensive analysis of letter frequencies in contemporary written Marathi. We determine sets of letters which statistically predominate any large generic Marathi text, and use these sets to estimate the entropy of Marathi.

Robust Orchestration of Concurrent Application Workflows in Mobile Device Clouds

A hybrid mobile/fixed device cloud that harnesses sensing, computing, communication, and storage capabilities of mobile and fixed devices in the field as well as those of computing and storage servers in remote datacenters is envisioned. Mobile device clouds can be harnessed to enable innovative pervasive applications that rely on real-time, in-situ processing of sensor data collected in the field. To support concurrent mobile applications on the device cloud, a robust and secure distributed computing framework, called Maestro, is proposed. The key components of Maestro are (i) a task scheduling mechanism that employs controlled task replication in addition to task reallocation for robustness and (ii) Dedup for task deduplication among concurrent pervasive workflows. An architecture-based solution that relies on task categorization and authorized access to the categories of tasks is proposed for different levels of protection. Experimental evaluation through prototype testbed of Android- and Linux-based mobile devices as well as simulations is performed to demonstrate Maestro's capabilities.

Anisotropy and multiband superconductivity in Sr2RuO4

Despite numerous studies the exact nature of the order parameter in superconducting Sr2RuO4 remains unresolved. We have extended previous small-angle neutron scattering studies of the vortex lattice in this material to a wider field range, higher temperatures, and with the field applied close to both the <100> and <110> basal plane directions. Measurements at high field were made possible by the use of both spin polarization and analysis to improve the signal-to-noise ratio. Rotating the field towards the basal plane causes a distortion of the square vortex lattice observed for H // <001>, and also a symmetry change to a distorted triangular symmetry for fields close to <100>. The vortex lattice distortion allows us to determine the intrinsic superconducting anisotropy between the c-axis and the Ru-O basal plane, yielding a value of ~60 at low temperature and low to intermediate fields. This greatly exceeds the upper critical field anisotropy of ~20 at low temperature, reminiscent of Pauli limiting. Indirect evidence for Pauli paramagnetic effects on the unpaired quasiparticles in the vortex cores are observed, but a direct detection lies below the measurement sensitivity. The superconducting anisotropy is found to be independent of temperature but increases for fields > 1 T, indicating multiband superconductvity in Sr2RuO4. Finally, the temperature dependence of the scattered intensity provides further support for gap nodes or deep minima in the superconducting gap.

Time-Reversal Breaking in QCD$_4$, Walls, and Dualities in 2+1 Dimensions

We study $SU(N)$ Quantum Chromodynamics (QCD) in 3+1 dimensions with $N_f$ degenerate fundamental quarks with mass $m$ and a $\theta$-parameter. For generic $m$ and $\theta$ the theory has a single gapped vacuum. However, as $\theta$ is varied through $\theta=\pi$ for large $m$ there is a first order transition. For $N_f=1$ the first order transition line ends at a point with a massless $\eta'$ particle (for all $N$) and for $N_f>1$ the first order transition ends at $m=0$, where, depending on the value of $N_f$, the IR theory has free Nambu-Goldstone bosons, an interacting conformal field theory, or a free gauge theory. Even when the $4d$ bulk is smooth, domain walls and interfaces can have interesting phase transitions separating different $3d$ phases. These turn out to be the phases of the recently studied $3d$ Chern-Simons matter theories, thus relating the dynamics of QCD$_4$ and QCD$_3$, and, in particular, making contact with the recently discussed dualities in 2+1 dimensions. For example, when the massless $4d$ theory has an $SU(N_f)$ sigma model, the domain wall theory at low (nonzero) mass supports a $3d$ massless $CP^{N_f-1}$ nonlinear $\sigma$-model with a Wess-Zumino term, in agreement with the conjectured dynamics in 2+1 dimensions.

Comparative Investigation of the High Pressure Autoignition of the Butanol Isomers

Investigation of the autoignition delay of the butanol isomers has been performed at elevated pressures of 15 bar and 30 bar and low to intermediate temperatures of 680-860 K. The reactivity of the stoichiometric isomers of butanol, in terms of inverse ignition delay, was ranked as n-butanol > sec-butanol ~ iso-butanol > tert-butanol at a compressed pressure of 15 bar but changed to n-butanol > tert-butanol > sec-butanol > iso-butanol at 30 bar. For the temperature and pressure conditions in this study, no NTC or two-stage ignition behavior were observed. However, for both of the compressed pressures studied in this work, tert-butanol exhibited unique pre-ignition heat release characteristics. As such, tert-butanol was further studied at two additional equivalence ratios ($\phi$ = 0.5 and 2.0) to help determine the cause of the heat release.

Selecting optimal minimum spanning trees that share a topological correspondence with phylogenetic trees

Choi et. al (2011) introduced a minimum spanning tree (MST)-based method called CLGrouping, for constructing tree-structured probabilistic graphical models, a statistical framework that is commonly used for inferring phylogenetic trees. While CLGrouping works correctly if there is a unique MST, we observe an indeterminacy in the method in the case that there are multiple MSTs. In this work we remove this indeterminacy by introducing so-called vertex-ranked MSTs. We note that the effectiveness of CLGrouping is inversely related to the number of leaves in the MST. This motivates the problem of finding a vertex-ranked MST with the minimum number of leaves (MLVRMST). We provide a polynomial time algorithm for the MLVRMST problem, and prove its correctness for graphs whose edges are weighted with tree-additive distances.

Noisy Natural Gradient as Variational Inference

Variational Bayesian neural nets combine the flexibility of deep learning with Bayesian uncertainty estimation. Unfortunately, there is a tradeoff between cheap but simple variational families (e.g.~fully factorized) or expensive and complicated inference procedures. We show that natural gradient ascent with adaptive weight noise implicitly fits a variational posterior to maximize the evidence lower bound (ELBO). This insight allows us to train full-covariance, fully factorized, or matrix-variate Gaussian variational posteriors using noisy versions of natural gradient, Adam, and K-FAC, respectively, making it possible to scale up to modern-size ConvNets. On standard regression benchmarks, our noisy K-FAC algorithm makes better predictions and matches Hamiltonian Monte Carlo's predictive variances better than existing methods. Its improved uncertainty estimates lead to more efficient exploration in active learning, and intrinsic motivation for reinforcement learning.

A Game of Life on Penrose tilings

We define rules for cellular automata played on quasiperiodic tilings of the plane arising from the multigrid method in such a way that these cellular automata are isomorphic to Conway's Game of Life. Although these tilings are nonperiodic, determining the next state of each tile is a local computation, requiring only knowledge of the local structure of the tiling and the states of finitely many nearby tiles. As an example, we show a version of a "glider" moving through a region of a Penrose tiling. This constitutes a potential theoretical framework for a method of executing computations in non-periodically structured substrates such as quasicrystals.

Single and Multiple Vortex Rings in Three-Dimensional Bose-Einstein Condensates: Existence, Stability and Dynamics

In the present work, we explore the existence, stability and dynamics of single and multiple vortex ring states that can arise in Bose-Einstein condensates. Earlier works have illustrated the bifurcation of such states, in the vicinity of the linear limit, for isotropic or anisotropic three-dimensional harmonic traps. Here, we extend these states to the regime of large chemical potentials, the so-called Thomas-Fermi limit, and explore their properties such as equilibrium radii and inter-ring distance, for multi-ring states, as well as their vibrational spectra and possible instabilities. In this limit, both the existence and stability characteristics can be partially traced to a particle picture that considers the rings as individual particles oscillating within the trap and interacting pairwise with one another. Finally, we examine some representative instability scenarios of the multi-ring dynamics including breakup and reconnections, as well as the transient formation of vortex lines.

Dimension-free Wasserstein contraction of nonlinear filters

For a class of partially observed diffusions, sufficient conditions are given for the map from initial condition of the signal to filtering distribution to be contractive with respect to Wasserstein distances, with rate which has no dependence on the dimension of the state-space and is stable under tensor products of the model. The main assumptions are that the signal has affine drift and constant diffusion coefficient, and that the likelihood functions are log-concave. Contraction estimates are obtained from an $h$-process representation of the transition probabilities of the signal reweighted so as to condition on the observations.

Vortex Nucleation Limited Mobility of Free Electron Bubbles in the Gross-Pitaevskii Model of a Superfluid

We study the motion of an electron bubble in the zero temperature limit where neither phonons nor rotons provide a significant contribution to the drag exerted on an ion moving within the superfluid. By using the Gross-Clark model, in which a Gross-Pitaevskii equation for the superfluid wavefunction is coupled to a Schrödinger equation for the electron wavefunction, we study how vortex nucleation affects the measured drift velocity of the ion. We use parameters that give realistic values of the ratio of the radius of the bubble with respect to the healing length in superfluid $^4$He at a pressure of one bar. By performing fully 3D spatio-temporal simulations of the superfluid coupled to an electron, that is modelled within an adiabatic approximation and moving under the influence of an applied electric field, we are able to recover the key dynamics of the ion-vortex interactions that arise and the subsequent ion-vortex complexes that can form. Using the numerically computed drift velocity of the ion as a function of the applied electric field, we determine the vortex-nucleation limited mobility of the ion to recover values in reasonable agreement with measured data.

Radio variability and non-thermal components in stars evolving toward planetary nebulae

We present new JVLA multi-frequency measurements of a set of stars in transition from the post-AGB to the Planetary Nebula phase monitored in the radio range over several years. Clear variability is found for five sources. Their light curves show increasing and decreasing patterns. New radio observations at high angular resolution are also presented for two sources. Among these is IRAS 18062+2410, whose radio structure is compared to near-infrared images available in the literature. With these new maps, we can estimate inner and outer radii of 0.03$"$ and 0.08$"$ for the ionised shell, an ionised mass of $3.2\times10^{-4}$ M$_\odot$, and a density at the inner radius of $7.7\times 10^{-5}$ cm$^{-3}$, obtained by modelling the radio shell with the new morphological constraints. The combination of multi-frequency data and, where available, spectral-index maps leads to the detection of spectral indices not due to thermal emission, contrary to what one would expect in planetary nebulae. Our results allow us to hypothesise the existence of a link between radio variability and non-thermal emission mechanisms in the nebulae. This link seems to hold for IRAS 22568+6141 and may generally hold for those nebulae where the radio flux decreases over time.

Sequential testing for structural stability in approximate factor models

We develop an on-line monitoring procedure to detect a change in a large approximate factor model. Our statistics are based on a well-known property of the $% \left( r+1\right) $-th eigenvalue of the sample covariance matrix of the data (having defined $r$ as the number of common factors): whilst under the null the $\left( r+1\right) $-th eigenvalue is bounded, under the alternative of a change (either in the loadings, or in the number of factors itself) it becomes spiked. Given that the sample eigenvalue cannot be estimated consistently under the null, we regularise the problem by randomising the test statistic in conjunction with sample conditioning, obtaining a sequence of \textit{i.i.d.}, asymptotically chi-square statistics which are then employed to build the monitoring scheme. Numerical evidence shows that our procedure works very well in finite samples, with a very small probability of false detections and tight detection times in presence of a genuine change-point.

Susceptibility Propagation by Using Diagonal Consistency

A susceptibility propagation that is constructed by combining a belief propagation and a linear response method is used for approximate computation for Markov random fields. Herein, we formulate a new, improved susceptibility propagation by using the concept of a diagonal matching method that is based on mean-field approaches to inverse Ising problems. The proposed susceptibility propagation is robust for various network structures, and it is reduced to the ordinary susceptibility propagation and to the adaptive Thouless-Anderson-Palmer equation in special cases.

Performance Analysis of Ultra-Dense Networks with Elevated Base Stations

This paper analyzes the downlink performance of ultra-dense networks with elevated base stations (BSs). We consider a general dual-slope pathloss model with distance-dependent probability of line-of-sight (LOS) transmission between BSs and receivers. Specifically, we consider the scenario where each link may be obstructed by randomly placed buildings. Using tools from stochastic geometry, we show that both coverage probability and area spectral efficiency decay to zero as the BS density grows large. Interestingly, we show that the BS height alone has a detrimental effect on the system performance even when the standard single-slope pathloss model is adopted.

Learning to Drive in a Day

We demonstrate the first application of deep reinforcement learning to autonomous driving. From randomly initialised parameters, our model is able to learn a policy for lane following in a handful of training episodes using a single monocular image as input. We provide a general and easy to obtain reward: the distance travelled by the vehicle without the safety driver taking control. We use a continuous, model-free deep reinforcement learning algorithm, with all exploration and optimisation performed on-vehicle. This demonstrates a new framework for autonomous driving which moves away from reliance on defined logical rules, mapping, and direct supervision. We discuss the challenges and opportunities to scale this approach to a broader range of autonomous driving tasks.

Strong-coupling of WSe2 in ultra-compact plasmonic nanocavities at room temperature

Strong-coupling of monolayer metal dichalcogenide semiconductors with light offers encouraging prospects for realistic exciton devices at room temperature. However, the nature of this coupling depends extremely sensitively on the optical confinement and the orientation of electronic dipoles and fields. Here, we show how plasmon strong coupling can be achieved in compact robust easily-assembled gold nano-gap resonators at room temperature. We prove that strong coupling is impossible with monolayers due to the large exciton coherence size, but resolve clear anti-crossings for 8 layer devices with Rabi splittings exceeding 135 meV. We show that such structures improve on prospects for nonlinear exciton functionalities by at least 10^4, while retaining quantum efficiencies above 50%.

Stigmergy-based modeling to discover urban activity patterns from positioning data

Positioning data offer a remarkable source of information to analyze crowds urban dynamics. However, discovering urban activity patterns from the emergent behavior of crowds involves complex system modeling. An alternative approach is to adopt computational techniques belonging to the emergent paradigm, which enables self-organization of data and allows adaptive analysis. Specifically, our approach is based on stigmergy. By using stigmergy each sample position is associated with a digital pheromone deposit, which progressively evaporates and aggregates with other deposits according to their spatiotemporal proximity. Based on this principle, we exploit positioning data to identify high density areas (hotspots) and characterize their activity over time. This characterization allows the comparison of dynamics occurring in different days, providing a similarity measure exploitable by clustering techniques. Thus, we cluster days according to their activity behavior, discovering unexpected urban activity patterns. As a case study, we analyze taxi traces in New York City during 2015.

BiHom-Lie colour algebras structures

BiHom-Lie Colour algebra is a generalized Hom-Lie Colour algebra endowed with two commuting multiplicative linear maps. The main purpose of this paper is to define representations and a cohomology of BiHom-Lie colour algebras and to study some key constructions and properties. Moreover, we discuss $\alpha^{k}\beta^l$-generalized derivations, $\alpha^{k}\beta^l$-quasi-derivations and $\alpha^{k}\beta^l$-quasi-centroid. We provide some properties and their relationships with BiHom-Jordan colour algebra.

Clustering of Gamma-Ray bursts through kernel principal component analysis

We consider the problem related to clustering of gamma-ray bursts (from "BATSE" catalogue) through kernel principal component analysis in which our proposed kernel outperforms results of other competent kernels in terms of clustering accuracy and we obtain three physically interpretable groups of gamma-ray bursts. The effectivity of the suggested kernel in combination with kernel principal component analysis in revealing natural clusters in noisy and nonlinear data while reducing the dimension of the data is also explored in two simulated data sets.

Bounded gaps between primes in short intervals

Baker, Harman, and Pintz showed that a weak form of the Prime Number Theorem holds in intervals of the form $[x-x^{0.525},x]$ for large $x$. In this paper, we extend a result of Maynard and Tao concerning small gaps between primes to intervals of this length. More precisely, we prove that for any $\delta\in [0.525,1]$ there exist positive integers $k,d$ such that for sufficiently large $x$, the interval $[x-x^\delta,x]$ contains $\gg_{k} \frac{x^\delta}{(\log x)^k}$ pairs of consecutive primes differing by at most $d$. This confirms a speculation of Maynard that results on small gaps between primes can be refined to the setting of short intervals of this length.

Handover analysis of the Improved Phantom Cells

Improved Phantom cell is a new scenario which has been introduced recently to enhance the capacity of Heterogeneous Networks (HetNets). The main trait of this scenario is that, besides maximizing the total network capacity in both indoor and outdoor environments, it claims to reduce the handover number compared to the conventional scenarios. In this paper, by a comprehensive review of the Improved Phantom cells structure, an appropriate algorithm will be introduced for the handover procedure of this scenario. To reduce the number of handover in the proposed algorithm, various parameters such as the received Signal to Interference plus Noise Ratio (SINR) at the user equipment (UE), users access conditions to the phantom cells, and users staying time in the target cell based on its velocity, has been considered. Theoretical analyses and simulation results show that applying the suggested algorithm the improved phantom cell structure has a much better performance than conventional HetNets in terms of the number of handover.

Bayesian Joint Topic Modelling for Weakly Supervised Object Localisation

We address the problem of localisation of objects as bounding boxes in images with weak labels. This weakly supervised object localisation problem has been tackled in the past using discriminative models where each object class is localised independently from other classes. We propose a novel framework based on Bayesian joint topic modelling. Our framework has three distinctive advantages over previous works: (1) All object classes and image backgrounds are modelled jointly together in a single generative model so that "explaining away" inference can resolve ambiguity and lead to better learning and localisation. (2) The Bayesian formulation of the model enables easy integration of prior knowledge about object appearance to compensate for limited supervision. (3) Our model can be learned with a mixture of weakly labelled and unlabelled data, allowing the large volume of unlabelled images on the Internet to be exploited for learning. Extensive experiments on the challenging VOC dataset demonstrate that our approach outperforms the state-of-the-art competitors.

Psychological model of the investor and manager behavior in risk

All people have to make risky decisions in everyday life. And we do not know how true they are. But is it possible to mathematically assess the correctness of our choice? This article discusses the model of decision making under risk on the example of project management. This is a game with two players, one of which is Investor, and the other is the Project Manager. Each player makes a risky decision for himself, based on his past experience. With the help of a mathematical model, the players form a level of confidence, depending on who the player accepts the strategy or does not accept. The project manager assesses the costs and compares them with the level of confidence. An investor evaluates past results. Also visit the case where the strategy of the player accepts the part.

Constraints on Super-Earths Interiors from Stellar Abundances

Modeling the interior of exoplanets is essential to go further than the conclusions provided by mean density measurements. In addition to the still limited precision on the planets' fundamental parameters, models are limited by the existence of degeneracies on their compositions. Here we present a model of internal structure dedicated to the study of solid planets up to ~10 Earth masses, i.e. Super-Earths. When the measurement is available, the assumption that the bulk Fe/Si ratio of a planet is similar to that of its host star allows us to significantly reduce the existing degeneracy and more precisely constrain the planet's composition. Based on our model, we provide an update of the mass-radius relationships used to provide a first estimate of a planet's composition from density measurements. Our model is also applied to the cases of two well-known exoplanets, CoRoT-7b and Kepler-10b, using their recently updated parameters. The core mass fractions of CoRoT-7b and Kepler-10b are found to lie within the 10-37% and 10-33% ranges, respectively, allowing both planets to be compatible with an Earth-like composition. We also extend the recent study of Proxima Centauri b, and show that its radius may reach 1.94 Earth radii in the case of a 5 Earth masses planet, as there is a 96.7% probability that the real mass of Proxima Centauri b is below this value.

Software correlator for Radioastron mission

In this paper we discuss the characteristics and operation of Astro Space Center (ASC) software FX correlator that is an important component of space-ground interferometer for Radioastron project. This project performs joint observations of compact radio sources using 10 meter space radio telescope (SRT) together with ground radio telescopes at 92, 18, 6 and 1.3 cm wavelengths. In this paper we describe the main features of space-ground VLBI data processing of Radioastron project using ASC correlator. Quality of implemented fringe search procedure provides positive results without significant losses in correlated amplitude. ASC Correlator has a computational power close to real time operation. The correlator has a number of processing modes: "Continuum", "Spectral Line", "Pulsars", "Giant Pulses","Coherent". Special attention is paid to peculiarities of Radioastron space-ground VLBI data processing. The algorithms of time delay and delay rate calculation are also discussed, which is a matter of principle for data correlation of space-ground interferometers. During 5 years of Radioastron space radio telescope (SRT) successful operation, ASC correlator showed high potential of satisfying steady growing needs of current and future ground and space VLBI science. Results of ASC software correlator operation are demonstrated.

Isogenies for point counting on genus two hyperelliptic curves with maximal real multiplication

Schoof's classic algorithm allows point-counting for elliptic curves over finite fields in polynomial time. This algorithm was subsequently improved by Atkin, using factorizations of modular polynomials, and by Elkies, using a theory of explicit isogenies. Moving to Jacobians of genus-2 curves, the current state of the art for point counting is a generalization of Schoof's algorithm. While we are currently missing the tools we need to generalize Elkies' methods to genus 2, recently Martindale and Milio have computed analogues of modular polynomials for genus-2 curves whose Jacobians have real multiplication by maximal orders of small discriminant. In this article, we prove Atkin-style results for genus-2 Jacobians with real multiplication by maximal orders, with a view to using these new modular polynomials to improve the practicality of point-counting algorithms for these curves.

On the self-duality of rings of integers in tame and abelian extensions

Let $L/K$ be a tame and Galois extension of number fields with group $G$. It is well-known that any ambiguous ideal in $L$ is locally free over $\mathcal{O}_KG$ (of rank one), and so it defines a class in the locally free class group of $\mathcal{O}_KG$, where $\mathcal{O}_K$ denotes the ring of integers of $K$. In this paper, we shall study the relationship among the classes arising from the ring of integers $\mathcal{O}_L$ of $L$, the inverse different $\mathfrak{D}_{L/K}^{-1}$ of $L/K$, and the square root of the inverse different $A_{L/K}$ of $L/K$ (if it exists), in the case that $G$ is abelian. They are naturally related because $A_{L/K}^2 = \mathfrak{D}_{L/K}^{-1} = \mathcal{O}_L^*$, and $A_{L/K}$ is special because $A_{L/K} = A_{L/K}^*$, where $*$ denotes dual with respect to the trace of $L/K$.

Forecasting Transformative AI: An Expert Survey

Transformative AI technologies have the potential to reshape critical aspects of society in the near future. However, in order to properly prepare policy initiatives for the arrival of such technologies accurate forecasts and timelines are necessary. A survey was administered to attendees of three AI conferences during the summer of 2018 (ICML, IJCAI and the HLAI conference). The survey included questions for estimating AI capabilities over the next decade, questions for forecasting five scenarios of transformative AI and questions concerning the impact of computational resources in AI research. Respondents indicated a median of 21.5% of human tasks (i.e., all tasks that humans are currently paid to do) can be feasibly automated now, and that this figure would rise to 40% in 5 years and 60% in 10 years. Median forecasts indicated a 50% probability of AI systems being capable of automating 90% of current human tasks in 25 years and 99% of current human tasks in 50 years. The conference of attendance was found to have a statistically significant impact on all forecasts, with attendees of HLAI providing more optimistic timelines with less uncertainty. These findings suggest that AI experts expect major advances in AI technology to continue over the next decade to a degree that will likely have profound transformative impacts on society.

Change of grading, injective dimension and dualizing complexes

Let $G,H$ be groups, $\phi: G \rightarrow H$ a group morphism, and $A$ a $G$-graded algebra. The morphism $\phi$ induces an $H$-grading on $A$, and on any $G$-graded $A$-module, which thus becomes an $H$-graded $A$-module. Given an injective $G$-graded $A$-module, we give bounds for its injective dimension when seen as $H$-graded $A$-module. Following ideas by Van den Bergh, we give an application of our results to the stability of dualizing complexes through change of grading.

Approximately certifying the restricted isometry property is hard

A matrix is said to possess the Restricted Isometry Property (RIP) if it acts as an approximate isometry when restricted to sparse vectors. Previous work has shown it to be NP-hard to determine whether a matrix possess this property, but only in a narrow range of parameters. In this work, we show that it is NP-hard to make this determination for any accuracy parameter, even when we restrict ourselves to instances which are either RIP or far from being RIP. This result implies that it is NP-hard to approximate the range of parameters for which a matrix possesses the Restricted Isometry Property with accuracy better than some constant. Ours is the first work to prove such a claim without any additional assumptions.