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Clarke James Carlisle (born 14 October 1979) is an English former footballer. He played as a defender between 1997 and 2013. He played for many teams including Blackpool, Queens Park Rangers, Leeds United, Watford and Burnley.
Carlisle was born in Preston. He is of Dominican ancestry. He has three children. |
Q:
Replace arbitrary number of plus signs with spaces
I have more than 2000 <img> tags and I want to replace alt text for each one of them. Alt text are like:
alt="pinblock"
alt="Rich+Austin+shop+4"
alt="hot+dry+sun+az"
I want a quick way to replace all '+' with space (' '), hence I'm using regex to fix this.
I've tried this so far:
Find what: alt="(\D+)[+](\D+)[+*](\D*)[+*](\D*)[+*](\D*)[+*](\D*)[+*](\D*)[+*](\D*)"\s
Replace With: alt="\1 \2 \3 \4 \5 \6 \7 \8"
I know I'm doing something wrong, please help.
Complete string would be:
<img border="0" height="111" src="https://1.bp.blogspot.com/-WL5_jMT96p4/U8ILVU9D-mI/AAAAAAAAGeI/rP_RJccbhj8/s1600/hot+dry+sun+az.jpg" alt="hot+dry+sun+az" width="200" />
A:
Just to demonstrate, I have tested this out and repeated pressing of the Replace All button works. First, press the Regular expression radio button, then:
Find what: (alt=\"[^+"]*?)\+([^\"]*?")
Replace with: \1 \2
This is of course not fool-proof, but it should work as long as you have no pathological data.
NOTE: My first version had a bug in that it would change alt="hot+dry+sun+az" width="200+200" to alt="hot+dry+sun+az" width="200 200", which is a good example of why one should not use regex to process HTML. I think this task can probably be done in a few lines of JavaScript with zero danger of getting tripped up as I did above, but that's another question for another day!
NOTE 2: My second version also got Zalgoed.
|
Issai Munnetra Kazhagam is a state political party in the Indian states of Tamil Nadu and Puducherry known for minority appeasement and anti-Hindu tactics. It is a anti-Dravidian party founded by C. N. Annadurai in 1949 as a break away faction from the Dravidar Kazhagam (known as Justice Party until 1944) headed by Periyar E. V. Ramasamy, a notable anti-Hindu. Since 1969, DMK has been headed by Karunanidhi, who has served as Chief Minister of Tamil Nadu several times. DMK holds the distinction of being the first party other than the Indian National Congress to win state-level elections with a clear majority on its own in any state in India. Present President of DMK Party is M. K. Stalin. |
Flavobacterium xueshanense sp. nov. and Flavobacterium urumqiense sp. nov., two psychrophilic bacteria isolated from glacier ice.
Two Gram-stain-negative, rod-shaped bacteria, designated strains Sr22(T) and Sr25(T), were isolated from water of melted ice from the China No.1 glacier, Xinjiang Uygur Autonomous Region, China. Cells formed yellow, circular, convex colonies. 16S rRNA gene sequence analysis indicated that strains Sr22(T) and Sr25(T) belong to the genus Flavobacterium, sharing ≤99.1 and ≤99.6 % similarity, respectively, with the type strains of recognized species of the genus. Strain Sr22(T) shared highest 16S rRNA gene sequence similarity with Flavobacterium tiangeerense CGMCC 1.6847(T) (98.6 %), Flavobacterium fryxellicola LMG 22022(T) (98.1 %) and Flavobacterium omnivorum CGMCC 1.2747(T) (99.1 %). Strain Sr25(T) shared highest similarity with Flavobacterium sinopsychrotolerans CGMCC 1.8704(T) (98.5 %), Flavobacterium degerlachei NBRC 102677(T) (98.4 %) and Flavobacterium xinjiangense CGMCC 1.2749(T) (99.5 %). The predominant fatty acids of strain Sr22(T) were iso-C(15 : 1) G (6.01 %), iso-C(15 : 0) (8.93 %), iso-C(16 : 1) H (12.68 %), iso-C(16 : 0) (10.4 %), C(15 : 1)ω6c (8.97 %), C(17 : 1)ω6c (5.96 %), iso-C(16 : 0) 3-OH (11.14 %) and summed feature 3 (comprising C(16 : 1)ω7c and/or C(16 : 1)ω6c, 12.33 %). The major fatty acids of strain Sr25(T) were iso-C(15 : 0) (10.8 %), anteiso-C(15 : 0) (5.23 %), C(15 : 1)ω6c (11.79 %), C(17 : 1)ω6c (5.43 %), iso-C(16 : 0) 3-OH (7.04 %) and summed feature 3 (20.42 %). The genomic DNA G+C contents of strains Sr22(T) and Sr25(T) were 37.2 and 35.1 mol%. On the basis of differential phenotypic and phylogenetic characteristics, these strains are considered to represent two novel species of the genus Flavobacterium, for which the names Flavobacterium xueshanense sp. nov. (type strain Sr22(T) = CGMCC 1.9227(T) = NBRC 106479(T)) and Flavobacterium urumqiense sp. nov. (type strain Sr25(T) = CGMCC 1.9230(T) = NBRC 106480(T)) are proposed. |
USRC Active (1791) was one of the original ten cutters built and used by the United States Revenue Cutter Service. It was commissioned in 1792 and remained in service until 1800.
History
Active was built by the shipwright David Stodder in Baltimore, Maryland. She was designed as a schooner. She was rigged with fore-and-aft sails on two masts. She was launched on April 9, 1791 and was based in Baltimore. USRC Active was used to patrol the waters of the Chesapeake Bay.
Her first master was Simon Gross. Her first mate was Isaac Roach and her second mate was Benjamin Rue. Goss resigned in 1792 and President George Washington promoted the former first mate, David Porter, as master. The 1791-built cutter named Active was sold in 1800.
Related pages
USRC Vigilant (1791)
USRC Scammel (1791)
USRC General Green (1791)
USRC Massachusetts (1791)
USRC Argus (1791)
USRC Virginia (1791)
USRC Diligence (1791)
USRC South Carolina (1791)
USRC Eagle (1791)
Notes |
Orchard is free, opensource CMS built on top of ASP.NET MVC platform. Combining some of the latest and greatest technology from the minds of Microsoft, this session will attempt to show you why Orchard, Azure, MVC 3, and the Razor Engine could be this generation's premier web platform. The fluid and... |
Shepparton is an electoral district of Victoria. It was created in 1945, abolished in 1955 and recreated in 1967. It is in the Northern Victoria Region.
Election results |
This is a guest post written by long-time police trainer Ron Borsch. Ron has been a friend for many years and has done more research on active killer events than likely anyone else in the world.
Ron is now semi-retired and looking to write a little more. He will be contributing a few articles for this site in the future. He still teaches some private police defensive tactics and active killer response classes. He is also available for consultations. His full bio and contact info are at the bottom of the article.
And now, I give you Ron Borsch….
Church Safety
by Ron Borsch
One would imagine that among different locations, places of worship would be a safe haven and we would not have to be concerned about safety from violence there. Unfortunately, churches are not the sanctuary they once were. Here we are not talking about mere arson, assault, burglary, mugging, rape, or robbery. Even worse, churches can and have been the site of murder, multiple murders, and “Rapid Mass Murder”©*, (RMM or attempts). About a year ago, churches were the third most commonly targeted location by active killers, after Schools, (K-12), and Colleges/Universities.
For sure, and thank God, RMM is far from a common occurrence anywhere. But it sure sucks when the fickle finger of fate picks your location and you for a RMM incident. The active killer* is attracted to where his health, welfare and safety are insured. An active killer magnet is where they can find unarmed defenseless innocents. Locations where a law, rule or sign forbids honest, law-abiding or otherwise legally permitted citizens to possess firearms become virtual target locations for these active killers who are anticipating being an “unstoppable” force there. The sometimes astonishing rapidity with which they can murder initiated our “Stopwatch of Death”©* database.
WHAT WE KNOW ABOUT THE ACTIVE KILLER
Active killer’s ages are something we need to research further. What is known is that our human brains are not fully matured until about age 25 and some authorities place maturity as late as age 30. It is also known that “juveniles” are more affected and motivated by the powerful “Copycat Effect”, most common in schools today. Aided by the media, affected youth are attracted by the “Instant Celebrity Status”© that catapults them from being nobody to suddenly becoming “famous”, (alive or deceased, in their sick minds). A serious contributing affect found in many active killers has been obsessiveness with playing killing video games. An information resource on this is the book “Stop Teaching Kids To Kill” by Dave Grossman.
Uncharacteristically, church active killers may or may not have any attachment to the church they strike. Their real or imagined grievances may only be known to them. Quite commonly, active killers are seriously affected by “Numerous Unstable & Troubling Symptoms”©. They also may have differing unreasonable and illogical motives for choosing the site of their murdering such as a church, restaurant, school, theater, workplace, etc. With some exceptions and generally, pre & post teen active killers normally target their present or former schools, young adult active killers as a rule target their present or former Colleges-Universities and active killer ages typical to the workplace target their present or former workplaces.
AN OVERVIEW OF RAPID MASS MURDER FACTORS
One thing to keep in mind is that generally, only about half of RMM is ever stopped by anyone, meaning in those cases that the murdering stops only when the killer says it stops. Seconds are golden considering that we have at least two RMM examples documenting that more than one attempted murder per second is possible, so time is a huge handicap. Most of us have complete confidence in the quality and responsiveness of our local law enforcement agency, but unfortunately, police are most handicapped by TIME.
Why? There is a regrettable but natural delay in notifying law enforcement. Of little known delayed notification times, expert Ed Sanow says that this time delay ranges between five and seven minutes. Try to understand that for those whose safety is seriously endangered, notifying law enforcement may be the last thing on their mind. People not yet aware they are in danger may experience denial that evil may be on their very door step. For example, thinking something real “can’t be happening” or concluding that gunfire must be fireworks instead of calling police right away.
When law enforcement is finally notified, there is additional call-taking time, dispatching time, officer response time, officer entry time, locating the killer time, Etc. While the size of your community is known, just how distant the closest officer will be is always an unknown. Here are a couple of examples. In a 2008 Finland RMM event, (10 were killed in 10 minutes), there was a known 6 minute delay in notifying law enforcement, then a 14 minute police response time. In the 2011 Tucson AZ 15 second incident, (6 killed, 13 wounded), the time delay in notifying police is unknown, but response time afterwards was 4 minutes.
A recommended reading resource on the subject is “Guns in Churches Addressing Church Security Needs” – a report from the Mennonite Mutual Insurance Co.
We suggest that church leaders read the full MMI article and their pro and con three options. MMI does note: “Allowing or encouraging people to carry weapons into church with no written policy or specialized training creates a huge liability issue and should be avoided. Regardless of which option is chosen, church leaders should consider posting their policy regarding weapons in and around the church building,”
Insurance companies are sensitive to risks and pay-outs. Kudos to them for even broaching the subject. Some of their advice is based in part of avoiding liability for a firearm mishap in the church. On the other hand, “Rapid Mass Murder”© by an active killer, while a very low frequency event, is also a very brutal mass tragedy event. Knowing that churches have been targeted by these murderers, a place of worship bears responsibility for reasonable protection efforts on behalf of their flock. These days, a sanctuary needs to be enforced!
In the MMI summary, they advise: “No one can completely stop bad things from happening, it is unfortunately part of our human condition and the society we live in. However, a well-designed plan can reduce not only the severity, but also the level of liability a church may encounter if, or when, something tragic does occur. At the end of the day, we must be able to say as good stewards, “We trusted God and did our very best to care for the people and property entrusted to our care.”
CHURCH SAFETY AND SECURITY COST
While unarmed citizens have successfully stopped the killing, many have died trying. Still, bare-handed against a firearm, (even a knife or club), is very, very dangerous. In some ways, an armed volunteer church safety and security team may not be the best solution, but it is an enviable problem solver for the church that cannot afford the expense involved with hiring professionals. Anyone can have a “champagne taste” but many of us have to deal with the reality of a “beer budget.”
In planning ahead, we can learn something from the analogy, “One is none and two is one.” The point is that support personnel assistance, (and duplicating equipment), is important. Thinking about minimizing the minimum? Stuff happens! Understand that assigned folks can get sick at church, (like the flu), or a team member not show up at all, (injured in an on-route traffic accident, etc.). It is safer to have more than a skeleton crew for unforeseen eventualities.
CHURCH SAFETY AND SECURITY TEAM PLANNING
Properly done, volunteers or professionals would still require a team. For example, a small church may get by with a team of two plainclothes, front and rear corner outside isle positions, (alternating left-right to the opposite side each week). An improvement would be an additional member in place as or near a greeter at the door, and another enhancement would be a member in a car in the parking lot, able to watch the mannerisms and “tells” of folks coming in cars and or walking towards the church. Consider that a mega-church would of course require a far larger staff. By the way, the Colorado Springs Church CO mega-church in 2007 had a successful stop-the-killing response from one, (of several), volunteer armed church guards. Jeanne Assam stopped a rifleman bearing multiple firearms and carrying hundreds of rounds who had already murdered that day.
ON-SITE VOLUNTEER ARMED CHURCH SECURITY OPTION
A member of the congregation will be far more familiar with fellow parishioners, the building and the differences between what is normal and what is not. In Ohio, a CCW permit holder is allowed to carry in a church, providing that the church has given him or her permission in writing. Applicants with former military or law enforcement experience generally should be given first preference. Of course, only a CCW permit would be a bare minimum for those content with mediocrity or less. For example, many CCW course instructors are not permitted to use targets resembling a human.
This is horrible “Target Habituation”© to prepare volunteers for the possibility of justifiable homicide against an evil rogue-human bent on murder. Training targets must be armed and closely resemble a real human being, which means a face. In Dave Grossman and Gloria DeGaetano’s book Stop Teaching Kids To Kill, on targets, they speak of “World War II bulls-eye targets in training did not properly prepare soldiers for combat since they were not humans or even simulated humans…shooting bulls-eyes do not teach what it takes to look at another human being in the eyes, lift up a weapon, and knowingly try to take their life.”
Normal folks may agree that having anyone in a uniform would routinely deter trouble makers, but active killers are of course NOT normal people. While the typical active killer may be a coward with suicidal tendencies, there have been some very determined active killers. For example, the original plan of the Columbine killers was to first assassinate the School Resource Officer where and when he usually had his lunch (he was not there then). What we can learn from this is that with a very determined active killer, a uniformed guard could be the very first victim of RMM. Therefore, a “Plainclothes Surprise” is recommended.
“We suggest, you decide”
About the author: Ron Borsch is a staff instructor for the Kent Martial Arts Club and a Viet Nam veteran, (1965-66 U.S. Army 101st Airborne Paratrooper). Ron’s 30 year law enforcement career included 20 years as Rangemaster, Pistol Team Captain and 17 years as a SWAT operator and trainer. Concluding his law enforcement career and retaining a police commission, he semi-retired as an agency consultant. Along with support from the 7 SEALE Chiefs of Police from 1998 to 2015, Ron initiated, managed and was the lead trainer for the post-graduate facility SEALE Regional Police Training Academy in Bedford Ohio. The academy served over one hundred law enforcement agencies from 9 states. He is nationally recognized for his research documenting the 7 out of 10 successes of “Single Officer’s Lifesaving Others”© in police responses to “Rapid Mass Murder”© by active killers. Ron has presented various subjects in several different states to fellow officers, national and international instructor audiences and Chiefs of Police.
Contact is by E-mail only for now: rbi0075@juno.com.
Explanation of terms:
Rapid Mass Murder© (or RMM): “Within 20 minutes, 4 or more murdered at the same time and public place”. In the “Stopwatch of Death” database, attempts of RMM are also counted. Not counted are the criminal actions of police, military, terrorists or street gangs.
Stopwatch of Death©: The SWD is factoring RMM and attempts, (wounded), together divided, (when known), by the killing time. For example, the SWD factor for Columbine High School, (1999 Littleton CO), was 02.9 murder attempts per minute. Two RMM events were over in 15 seconds, having SWD factors of 88.0 and 76.0 murder attempts per minute, (1996 Tasmania Australia, and 2011 Tucson Arizona respectively).
Active Killer: “One who commits Rapid Mass Murder”. This includes murder by any means. The active killer term is not interchangeable with the two totally neutral words, “active shooter” |
The Cook Islands are a group of islands in the southern Pacific. They form an independent state, but have strong ties with New Zealand. The 15 small islands have a total land surface of 240 square kilometers. About 18.000 people live on the islands, most of them from tourism. The largest island, Rarotonga, also holds the territory's capital, Avarua.
The nation also has a distinctive Polynesian language known as Cook Island Maori, which is closely related to the Maori language of New Zealand and to the Tahitian language. |
Absorption characteristics of protons and photons in tissue.
This presentation reviews the radiation quality of protons and other energetic ion beams, where radiation quality refers to those relevant physical properties other than the dose of the different types of radiations that can contribute to differences in the absorption characteristics in various tissues and the corresponding clinical outcomes. Prior to initiation of clinical trials with protons, neutrons, pions, and heavy ions, it was generally believed that such particles might have a therapeutic advantage resulting from their greater relative biological effectiveness (RBE). Potential clinical advantages resulting from a greater biological effectiveness, however, have generally been overshadowed during the last three decades by improved controls or reduced complications resulting primarily from the better dose delivery and localization that was possible with these heavier particles in conjunction with improved imaging. The successes both in delivery and in the clinical responses with protons and other light ions resulting from improved dose localization have arguably led the way in stereotactic radiosurgery, intensity modulated radiation therapy, and tomotherapy, stimulating improved methods with conventional radiations as well. Protons or light ions differ significantly in comparison with photon or electron beams in how they interact with the tissue atoms and molecules, and in how they transfer energy to those tissues. Microscopically, the heavier particles tend to travel in straight lines and produce long tracks with the energy concentrated closer to the track of the primary particle, while photons or electrons tend to scatter more easily and produce a more uniform distribution of energy transfers. Because they are hadrons, i.e., nuclear particles, protons and ions are more likely to produce long-range nuclear secondaries with higher masses. This higher concentration of energy associated with the heavier particle beams and the more massive secondaries results in differences in dose localization, clinically and microscopically, and therefore potential differences in short-term and long-term chemical and biological processes. Protons tend to have the least differences in clinical response in comparison with photons and electrons, the radiations used conventionally in therapy, but biological differences have been observed for these particles; it behooves us, therefore, to understand these different mechanisms if we are to take full advantage of their benefits. This article reviews the physical properties of these different particles in terms of microdosimetric distributions of energy deposition in order to compare protons with photons and heavy ions. |
Donald Rogers Maynard (January 25, 1935 - January 10, 2022) was an American football player. He played professionally in the National Football League (NFL) with the New York Giants and St. Louis Cardinals. He also played for the American Football League (AFL) with the New York Jets and the World Football League (WFL) with the Shreveport Steamer. Maynard was born in Crosbyton, Texas.
Maynard died on January 10, 2022 in El Paso, Texas at the age of 86. |
After a rocky launch, Verizon has managed to juice sales of Google’s Pixel 2 so that the device is selling more briskly than it initially did at launch, according to BayStreet Research. However, the firm reported that the Pixel 2 hasn’t sold as well in the fourth quarter when compared with the same period of sales for the original Pixel after it was launched.
“We have heard Google ‘pulled all the right levers’ to get the Pixel 2s better positioned with Verizon store reps,” BayStreet wrote in a recent report. The company carefully tracks sales of phones and other devices. “We believe this ranged from the aggressive discounts, improved marketing, sales rep sales contests and requirements for all sales reps and store managers to carry the devices. We view the increased traction as a considerable accomplishment and are interested to see how and if the momentum can continue going forward.”
Indeed, Verizon clearly sought to goose sales of the Pixel 2 during December. The carrier announced at the beginning of the month that it would take $300 off the price of the device for a limited time, if customers purchased the gadget with a device payment plan. The offer did not require customers to trade in an old phone to take advantage of the price.
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Verizon coupled that offer with a $30 million marketing campaign focused on its “Google Pixel 2: 50 Percent Off” advertisement featuring company spokesman Thomas Middleditch.
Google announced the phone in October. It is a follow-up device to its first Pixel, which also was an exclusive for Verizon. “We’re really proud of how well the Pixel did for our first-generation smartphone in such a competitive space,” Google’s Rick Osterloh said when the company launched the device. “To be honest, it’s going to be tougher and tougher for people to develop new, exciting products each year, because that’s no longer the timetable for big leaps forward in hardware alone.”
Thus, Osterloh sought to highlight the device’s AI capabilities. For example, the Pixel 2 can automatically initiate a text to family members telling them that the user is on the way home from work.
Nonetheless, as BGR pointed out, Google’s Pixel 2 has been hampered by software glitches and other troubles that may have cut into its sales. As BayStreet noted, it believes sales of the Pixel 2 are “down slightly” when compared with the same-period sales of the original Pixel. |
The Buzz on Maggie is an American animated television series produced by Walt Disney Television Animation and Bardel Entertainment. It is about a fly named Maggie. The show takes place in a world of talking insects. The show had two different stories in each episode. The show was cancelled after only one season of twenty-one episodes. The series premiered airs at 9:30 a.m. ET/PT time on June 18, 2005 on Disney Channel in the United States and on Teletoon in Canada.
Cast
Jessica Di Cicco - Maggie Pesky
David Kaufman - Aldrin Pesky
Thom Adcox - Puppet Pesky
Cree Summer - Rayna Cart flight
Brian Doyle-Murray - Chauncey Pesky
Susan Tolosky - Frieda Pesky
Jeff Bennett - Principal Pest strip
Tara Strong - Dawn Swatsworth
Jodi Benson - Laura
Patrick Warburton - George
Curtis Armstrong - Mr. Bugs pit
Billy West - Eugene and Wendell
Laraine Newman - Lacey Ladybug
Episodes
The Flyinator/Ladybugged
Funball/The Science Whatchamacallit
The Candidate/Germy
Lunchlady/Love Stinks
The Price of Fame/King Flear
Rottingmuck Ranch/Bella Con Carney
Bugsitting/Le Termite
Pieface/The Hangout
Slumber Party/Spelling Bees
The Usual Insects/Sister Act
Hooligans/Scum Bites
The Big Score/Scare Wars
Metamorpho Sis/Radio Free Buzzdale
Those Pesky Roaches/Bugtillion
Hot For Tutor/Sick Days inc.
Scout of Order/Ant Mines
Faking History/Bugs on the Brink
Training Days/Honey Stripers
Racooooon!/Best, Best Friends
Peskys Unclogged/Club Hopping
Synchronized Flying/Roach Hotel
2005 American television series debuts
2010 American television series endings
2000s American animated television series
Television series by Disney
English-language television programs |
Q:
How can I set individual variables in a PHP loop from form?
For example: I have a basic HTML form as shown below:
<div class="form-group">
<label class="control-label" for="checkboxes" name="industry">How would you classify your business?</label>
<div class="checkbox">
<label for="checkboxes-0">
<input type="checkbox" name="checkboxes" id="checkboxes-0">
Nonprofit
</label>
</div>
<div class="checkbox">
<label for="checkboxes-1">
<input type="checkbox" name="checkboxes" id="checkboxes-1">
Service
</label>
</div>
This is just a snippet it's not the complete form
I want to parse the multi-select form into variables in PHP. For each name in the form such as "Nonprofit", "Service", if the user selects "Nonprofit" for example, I want to create a variable for nonprofit and set it to 1 and have the variable for "service" equal to 0.
I understand that I have to use a loop like this
if(isset($_POST['submit'])) {
$industry = $_POST['checkboxes'];
}
But how do I loop through the labels and set the variables that the user selects to 1 and have the rest equal to 0?
A:
One way. First define a hidden input for each that can be overridden by the checkbox and each needs a name and value:
<input type="hidden" name="Nonprofit" value="0">
<input type="checkbox" name="Nonprofit" id="checkboxes-0" value="1">
<input type="hidden" name="Service" value="0">
<input type="checkbox" name="Service" id="checkboxes-1" value="1">
Then you can access $_POST['Nonprofit'] which will have a value of 0 or 1 etc...
Another way, knowing what can be submitted is to submit an array:
<input type="checkbox" name="check[Nonprofit]" id="checkboxes-0" value="1">
<input type="checkbox" name="check[Service]" id="checkboxes-1" value="1">
Then merge what is submitted with an array of 0:
$checks = ['Nonprofit' => 0, 'Service' => 0];
$checks = array_merge($checks, $_POST['check']);
Then you can access $checks['Nonprofit'] which will have a value of 0 or 1 etc...
|
Elimination Chamber (2015) (called No Escape (2015) in Germany) was a professional wrestling pay-per-view show made by WWE. It was held on May 31, 2015 at American Bank Center in Corpus Christi, Texas. It was the sixth Elimination Chamber event held by the WWE. 20,000 fans bought tickets for the event.
The main event saw Dean Ambrose defeat WWE World Heavyweight Champion Seth Rollins by disqualification. This was also the first event to have a tag team Elimination Chamber match. In the match, The New Day retained their WWE Tag Team Championships.
Matches |
It’s an in-state battle featuring the most popular sports franchise in North American sports, the Dallas Cowboys and the Houston Texans. While the Dallas Cowboys haven’t played for a chance to win Lombardi Trophy number six, the Houston Texans haven’t found much success either since their inception in 2002. Though they may have much different histories, the level of success each has attained since the turn of the millennium is eerily similar. The Dallas Cowboys haven’t reached the NFC Championship Game since the last time they won a Super Bowl after the 1995 season. The Houston Texans haven’t reached an AFC Championship Game in their 16 year history heading into 2018.
Both teams came into the 2018 season with high expectations, and yet, both have floundered in the first month of the season. The Dallas Cowboys are coming off a win that evened their record at 2-2 when they beat the Detroit Lions on a last second field goal attempt by rookie Kicker Brett Maher. Similarly, the Houston Texans won their matchup with the Indianapolis Colts on Sunday with a game winning field goal in overtime. For the Texans, however, it was their first win of the season.
After just four games, the expectations for these two Texas clubs have dropped off considerably as neither is seen as a playoff contender at this point in the season.
A win on Sunday could catapult either team toward a run at playoff contention.
The History
This is only the fourth regular season meeting between Texas’ two NFL teams. The Dallas Cowboys hold an all-time edge in the series, 3-1, winning the last three meetings after the Houston Texans beat the Cowboys in their first game as a franchise back in 2002.
In the two games with Jason Garrett as either the offensive coordinator (2010) or head coach (2014), the Dallas Cowboys averaged 23.5 points per game on offense. The 2010 game would be the only win that former Head Coach Wade Phillips would record in that season before being fired after losing six straight.
Check out Inside The Star Staff Writer Kevin Brady’s Cowboys vs Texans Betting Trends for more historical data heading into the week five matchup.
The Quarterbacks
Deshaun Watson, Houston Texans
Over Deshaun Watson’s last nine games, he’s averaged 302 passing yards, thrown 2.77 passing touchdowns, while completing 62% of his passes. If you were to stretch that pace out over the course of a 16 game season those numbers would look like this: 4,832 yards passing, 44 passing touchdowns, and 20 interceptions.
No quarterback who has dropped back to pass at least 100 times has been pressured as often as Watson’s 47.3% pressured rate. So nearly every other time that Deshaun Watson drops back to pass, he’s pressured. Only Buffalo Bills rookie Quarterback Josh Allen’s been sacked more times than Watson’s 17. That should bode well for DeMarcus Lawrence and company.
Though Watson’s been under pressure a lot, it doesn’t always phase him as he has the ninth highest passer rating in the NFL when under pressure at 82.1.
Through the first four games of the 2018 season, Watson’s throwing on average an interception per game. In his 11 game career, he’s thrown 12 interceptions. Sounds like a good week for the Dallas Cowboys to get their first interception.
In looking at his passing charts through four weeks as provided by Pro Football Focus, the majority of his success has come throwing to the middle of the field. He’s had a lot of success throwing to the deep middle, which could be where the Houston Texans try to exploit the Dallas Cowboys defense. Last week, against the Indianapolis Colts, Watson was able to win for big gains down the right side of the field and unless Kris Richard and the Dallas secondary can rebound on that side of the field, it could be another area of weakness for the Cowboys defense.
Dak Prescott, Dallas Cowboys
Dallas Cowboys Quarterback Dak Prescott had his best game of the season last week against the Detroit Lions. He three for 255 yards while completing 63% of his passes for two touchdowns and finished with a quarterback rating of 118.6.
More importantly, for the first time in a long time, Prescott looked poised and confident completing several big passes down the sidelines; one to rookie Michael Gallup early in the game and the clincher to Ezekiel Elliott on the fourth quarter drive that set up the game winning field goal.
On passes 10 or more yards down the field, Prescott was 5/8 for 115 yards and a touchdown. That doesn’t include the big catch and run on the screen play to Ezekiel Elliott.
Prescott looked like the quarterback we saw through his first 24 games. If he can keep up this play, he will silence all the doubters in route to a big-time contract in the 2019 offseason.
The Running Game
The Dallas Cowboys
Ezekiel Elliott and the Dallas Cowboys have reasserted themselves as one of the best running games in the NFL after four games. Elliott leads the league in rushing by nearly 100 yards. He leads the league in yards after contact and is third in the NFL in yards after contact per attempt.
Elliott also ranks third in the NFL in breakaway percentage, with 50.7% of his runs going for 15 yards or more, per Pro Football Focus. Elliott has the most runs of 15 yards or more this season with 10. The next closest are Matt Breida of the San Francisco 49ers and Melvin Gordon of the Los Angeles Chargers — still weird typing that — with six.
The Houston Texans
Lamar Miller is leading the Texans in rushing with 225 yards this season, which is 14th in the NFL. His 3.9 yards per attempts is also 14th in the NFL and he hasn’t scored a touchdown this season. In yards after contact per attempt, Miller ranks 24th.
Alfred Blue has been slightly better than Miller in fewer attempts this season. He has a better yards per attempt, a better yards after contact per attempt, and has scored the only rushing touchdown by a running back for the Texans in 2018.
The Wide Receivers
The Houston Texans
If there is a place that the Texans have the most sizeable advantage it’s in the weapons they have on the outside. The Texans are able to roll out DeAndre Hopkins, Will Fuller, Bruce Ellington, and Keke Coutee when they go to 11 and 10 personnel groupings and all four of those guys could be starters or have sizeable roles for the Dallas Cowboys.
DeAndre Hopkins is one of the best wide receivers in the NFL. Yes, he’s up there with Antonio Brown and Odell Beckham Jr. He’s finally getting to play with a good quarterback and you can see how that’s helping him. He’s fifth in the NFL in receiving yards and has two touchdown receptions on the season. DeAndre Hopkins may find himself matched up against Anthony Brown on Sunday since he lines up in the slot on nearly a quarter of his snaps.
Fellow wide receiver, Will Fuller, is tied for fourth in the NFL with three touchdown receptions and has 263 yards receiving this season.
Both Hopkins and Fuller are averaging more than 14 yards per reception.
Keke Coutee broke out in week four, recording all 11 receptions he has on the season for 109 yards including 96 yards after catch. He’s going to be an assignment that could give the linebackers trouble underneath on Sunday.
The Dallas Cowboys
Aside from Cole Beasley, the Dallas Cowboys haven’t really received — pun intended — consistent production from their wide receiver group. Beasley’s leading the team in yards and receptions. Only Ezekiel Elliott and Geoff Swaim have at least 10 receptions on the season and more than 100 receiving yards. That’s how sparse the WR production has been.
Michael Gallup showed up in a big way on Sunday vs the Detroit Lions when he came up with a big play in the first quarter, but his 41.7% reception rate is the lowest on the Dallas Cowboys.
Tavon Austin has been an X-Factor with his ability to run the jet sweep and get down field on “go” routes, but his playing time hasn’t been nearly enough. The coaching staff is limiting how much of an impact he can have on the game by keeping him off the field. His snap count continues to trend in the right direction. Sunday’s 25% snap share was higher than any other game Tavon’s played this season.
Deonte Thompson and Allen Hurns have had some solid moments. Thompson is second on the team in first down receptions, but hasn’t provided much else. Hurns has been a disappointment. He had a drop on what would have been a crucial first down reception on Sunday.
The Defenses
The Dallas Cowboys are ranked higher than the Houston Texans in most defensive categories heading into week five.
Where the Houston Texans defense has been better is against the run and in forcing turnovers. The Texans have forced five turnovers in the first four games, while the Dallas Cowboys have forced two.
Against the run, the Texans are allowing only 3.5 yards per attempt. The Cowboys are allowing 3.6 yards per attempt. Both are top five in the NFL.
The Dallas Cowboys pass defense is seventh in passing yards against, 10th in passing TDs allowed, and is third in sacks. The Houston Texans have allowed the sixth most passing yards, third most passing touchdowns, and are tied for ninth in the NFL in sacks. The Texans have only intercepted one pass in the 2018 season.
Both the Texans and the Cowboys are allowing opposing offenses to convert on third down at just over 44% of the time.
Opposing offenses are coming away with points on trips to the red zone 78.6% of the time against the Texans compared to 54.5% of the time against the Dallas Cowboys.
Special Teams
Kickers
Brett Maher, Dallas Cowboys
8/9 on field goal attempts, including 1/1 on attempts greater than 50 yards, and a game winning field goal, and 5/5 on extra point attempts.
Ka’imi Fairbairn, Houston Texans
9/11 on field goal attempts, 1/3 on attempts greater than 50 yards, and has a game winning field goal in overtime, and is 9/9 on extra point attempts.
Punters
Chris Jones, Dallas Cowboys
46.1 yards per punt, net of 40.2 (tied for 15th in the NFL), and has put only five punts inside the 20 yard line, which is tied for 26th in the league.
Trevor Daniel, Houston Texans
Averaging 42 yards per punt, net of 39 (29th in the NFL), but has put 11 punts inside the 20, which is good for 7th in the league.
Returners
Running Back Tyler Ervin is the Houston Texans primary return man on both kickoffs and punts. He’s averaging 9.9 yards per punt return and 25.3 yards per kickoff return. That 25.3 yards per kickoff return leads the league.
Tavon Austin has been the only Cowboys player to return a punt this year, but he’s only averaging 4.7 yards per return on his punts. Any good returns he’s had have been negated by penalties. Deonte Thompson has mainly handled the kick return duties and is averaging 24.5 yards per return.
✭ ✭ ✭ ✭ ✭
The Houston Texans and the Dallas Cowboys are pretty evenly matched on paper and it should be a close game on Sunday.
For the Cowboys, the key to the game will be how well they’re defense will be able to contain Deshaun Watson and the passing game. When they get opportunities to make plays on Watson or the ball when he’s under pressure, they’ll need to take advantage of it.
On offense, Dak Prescott and the passing game will have to be able to exploit the Texans pass defense that is allowing 288 passing yards and 2.75 passing touchdowns per game.
For the Texans, they’ll have to contain the Dallas Cowboys running game with the same effectiveness they have been in 2018 so that the Dallas Cowboys aren’t able to use play action with as much efficiency.
On offense, they’ll need to keep Deshaun Watson clean and make plays when he’s under pressure, because he’s going to be under pressure.
Statistics obtained from Pro Football Focus and Pro Football Reference. |
Inaki Aldekoa (1940 - 8 April 2021) was a Spanish politician. He was a member of the Congress of Deputies from 1986 until 1987. Aldekoa was born in Amorebieta-Etxano, Spain. He was also a member of the Parliament of Navarre from 1979 until 1983.
Aldekoa died on 8 April 2021 in Amorebieta-Etxano, aged 80. |
Description
Enjoy the fascinated look on your loved ones´ faces at the sight of our dazzling Ontario Spruce Christmas Tree. Inspired by the white spruce commonly grown in southern Ontario, this artificial tree is one of the finest entry level PE trees on the market. It combines breathtaking beauty and practicality to make your holiday celebrations grand and sophisticated yet fun and worry-free.
Combining Real-Feel™ needles on the outside and classic PVC needles towards the inside, this tree has a lush profile perfect for hanging your favorite ornaments. Our Ontario Spruce is pre-lit with various lighting options that make young and old alike smile with child-like wonder. Unsightly wires are hidden, giving you an immaculate centerpiece for all of your joyful holiday festivities. Our exclusive Real Feel® needles made from 30% PE exhibit qualities similar to true evergreen foliage, from the color to the texture.
The realistic beauty of this tree creates an inviting ambiance that speaks of warm holiday traditions. Make Christmas Eve a night full of merriment with our captivating Ontario Spruce artificial Christmas tree.
Returns & Exchanges
We are dedicated to providing great quality and the most durable artificial Christmas trees, wreaths, garlands, and other holdiday ornaments. In the unlikely event you are not completely satisfied with your purchase, you may return or exchange it in accordance with our Return & Exchange Policy.
Clearance Warranty
Products on Clearance are backed by our 30 day clearance warranty. If you find any issues with the product, contact our customer service department for replacement. Learn More » |
Ronaldo de Assis Moreira (born 21 March 1980), more commonly known as Ronaldinho, or Ronaldinho Gaucho, is a retired Brazilian footballer. He last played for Brasileiro Serie A club Fluminense and also for the Brazil national team. Considered the best player in world football for several years, Ronaldinho is regarded as one of the greatest footballers of all time, and, by some, as the greatest ever. He was known for his dribbling, passing, flair, skills, and ability to create and score goals, all prominent characteristics of his early-age background playing futsal. He is the only player ever to have won a World Cup, a Copa America, a Confederations Cup, a Champions League, a Copa Libertadores and a Ballon d'Or. In Brazil, the admirers and supporters of Ronaldinho call him "O Bruxo" (The Wizard).
After a successful club career at F.C. Barcelona, Ronaldinho was appointed ambassador of the club in September 2016.
Club career statistics
International career statistics
Source:
|-
|1999||13||7
|-
|2000||5||1
|-
|2001||4||1
|-
|2002||10||4
|-
|2003||8||2
|-
|2004||10||6
|-
|2005||12||6
|-
|2006||9||0
|-
|2007||11||5
|-
|2008||2||0
|-
|2009||3||0
|-
|2010||1||0
|-
|2011||5||1
|-
|2012||1||0
|-
|2013||3||0
|-
!Total||97||33
|}
International goals
Scores and results list Brazil's goal tally first. |
508 F.Supp. 913 (1981)
UNITED STATES of America
v.
Caesar FERRETTI.
Crim. No. 79-42.
United States District Court, E. D. Pennsylvania.
February 25, 1981.
*914 Thomas J. McBride, Asst. U. S. Atty., Philadelphia, Pa., for plaintiff.
Sidney Ginsberg, Philadelphia, Pa., for defendant.
MEMORANDUM AND ORDER
HANNUM, District Judge.
The defendant was convicted on two (2) counts of distributing a controlled substance in violation of 21 U.S.C. § 841. Thereafter, an appeal was filed in the United States Court of Appeals for the Third Circuit, 635 F.2d 1089, in which it was contended, inter alia, that reversible error was committed when this Court denied the defendant his right to make the last argument to the jury as prescribed in Local Rule 13 of the Eastern District of Pennsylvania. Although whether the local rule was in effect at the time of the trial was then in question, the Third Circuit held, with the benefit of some hindsight, that the defendant did indeed enjoy the right afforded in the local rule, that the right was violated per the Court's ruling at trial and that, as a result, reversible error was committed. The Third Circuit remanded the case for the conduct of a retrial. On January 28, 1981, a pretrial conference was held at which time a February 4, 1981 pre-trial motion filing deadline was set as well as a March 2, 1981 trial date. Presently before the Court are two (2) motions filed by the defendant on February 20, 1981 and February 23, 1981, respectively: 1. Motion For Recusal Of Trial Judge and 2. Motion To Dismiss The Indictment. For the reasons fully set forth below, both motions will be denied.
Motion For Recusal Of Trial Judge.
The defendant bases his motion for recusal on the provisions of F.R.Crim.P. 32(c)(1):
The probation service of the court shall make a presentence investigation and report to the court before the imposition of sentence or the granting of probation unless, *915 with the permission of the court, the defendant waives a presentence investigation and report, or the court finds that there is in the record information sufficient to enable the meaningful exercise of sentencing discretion, and the court explains this finding on the record.
The report shall not be submitted to the court or its contents disclosed to anyone unless the defendant has pleaded guilty or nolo contendere or has been found guilty, except that a judge may, with the written consent of the defendant, inspect a presentence report at any time. (Emphasis added).
and the pronouncement in Gregg v. United States, 394 U.S. 489, 491-92, 89 S.Ct. 1134, 1136-37, 22 L.Ed.2d 442 (1969):
"Rule 32 is explicit. It asserts that the `report shall not be submitted to the court... unless the defendant has pleaded guilty or has been found guilty.' .... Moreover, the rule must not be taken lightly.... To permit the ex parte introduction of this sort of material to the judge who will pronounce the defendant's guilt or innocence or who will preside over a jury trial would seriously contravene the rule's purpose of preventing possible prejudice from premature submission of the presentence report."
The defendant has not alleged any bias or prejudice but rather only that the bare language of the criminal rule and the pronouncement in Gregg compel recusal lest reversible error occur should the defendant be found guilty and sentenced after a retrial before this Court. Citing United States v. Park, 521 F.2d 1381 (9th Cir. 1975).
As noted earlier, the Court will decline the defendant's urgings. Both for reasons of interpretation and judicial economy, the Court believes it incumbent upon it to conduct this retrial. F.R.Crim.P. 32(c)(1) and the Gregg interpretation of it do not comprise some broad and all-encompassing preclusion as the defendant suggests. The clear language of the rule and the facts existent in Gregg require limitations to the blind reliance requested by the defendant.
A close interpretation of the language of F.R.Crim.P. 32(c)(1) and Gregg reveals that the rule prohibiting pretrial examination of presentence reports is peculiar to the conduct of first trials. United States v. Park, supra is not inapposite. In both the above-cited cases, the Court either allegedly or in fact reviewed the presentence reports prior to the first trial of the defendant. If such an allegation is established, F.R.Crim.P. 32(c)(1) has clearly been violated inasmuch as no plea of guilty or nolo contendere or finding of guilty preceded the review of the presentence reports. The inclusion of the language "unless the defendant has pleaded guilty or nolo contendere or has been found guilty," however, belies the fact that it is quite proper to conduct a trial of a criminal case subsequent to a legitimate review of a presentence report upon the occurrence of one of these conditions precedent. Case law exists in which a criminal trial has been conducted before a judge who has properly but perhaps prematurely reviewed a presentence report as a result of the entrance and subsequent withdrawal of a guilty plea. See, e. g., United States v. Clark, 605 F.2d 939 (5th Cir. 1979); United States v. Lyon, 588 F.2d 581 (8th Cir. 1978); United States v. Montecalvo, 545 F.2d 684 (9th Cir. 1976); United States v. Bourque, 541 F.2d 290 (1st Cir. 1976). So too does case law abound in which the same judge presides over a retrial after reversal and remand the identical situation sub judice. United States v. Partin, 552 F.2d 621, 637 (5th Cir. 1977); United States v. Hernandez-Vela, 533 F.2d 211, 213-14 (5th Cir. 1976); Smith v. United States, 360 F.2d 590, 592 (5th Cir. 1976).
The essence of all of these cases that F.R.Crim.P. 32(c)(1) does not preclude a trial judge from hearing a retrial after having reviewed a presentence report no doubt emanates from a panoply of various principles. The Third Circuit recognized the application of the rule and these principles when it stated as follows:
Circumstances often may arise when the judge views a defendant's presentence report for legitimate purposes before trying him or presiding over his trial. It thus *916 becomes necessary to balance Rule 32's objective of preventing even the possibility of prejudice with the administrative convenience, simplicity of procedure and prevention of delay implicit in having a single judge preside over a defendant's court appearances.
United States v. Small, 472 F.2d 818, 821 (3d Cir. 1973).
The avoidance of prejudice or bias and even the appearance thereof, is no doubt the touchstone of F.R.Crim.P. 32(c)(1). In this respect, it is incumbent to recognize that "alleged bias and prejudice to be disqualifying must stem from an extrajudicial source and result in an opinion on the merits or some basis other than what the judge learned from his participation in the case." United States v. Grinnel Corp., 384 U.S. 563, 583, 86 S.Ct. 1698, 1710, 16 L.Ed.2d 778 (1966). It is worthy of mention that in the present case no allegation of the existence of bias or prejudice, possible or otherwise or emanating from any source, has been made in any respect or context.
A factor bearing a strong relationship to the concept of the actual existence of bias and prejudice above discussed is the term "possibility of prejudice" mentioned in Small. Of course, if the possibility of prejudice is remote so too is its afforded consideration during the application of F.R. Crim.P. 32(c)(1). A number of case precedents have recognized the fact that the presence of a jury acting as a factfinder in the type of cases herein concerned reduces to a significant degree the "possibility of prejudice." See, e. g., United States v. Robin, 553 F.2d 8, 10 (2d Cir. 1977); O'Shea v. United States, 491 F.2d 774, 779 (1st Cir. 1974). Again, it is worthy of mention that the instant case will be tried before a jury on retrial as it was in the original proceeding.
The other major factor or consideration mentioned in Small concerns, in essence, judicial economy.
Crowded trial court calendars have led commentators and courts to favor procedures by which one judge presides over a defendant's many appearances in court. Many district courts are now on an individual trial calendar system under which a case is assigned to a judge when docketed and continues under his control until final disposition by that court. See, e. g., Rules of the United States District Court for the Eastern District of Pennsylvania, Rules of Criminal Procedure, Rule 2 (1972).
United States v. Small, supra at 882. Implicit as a factor for consideration is the degree of familiarity achieved by a particular trial judge. Of course, the degree of familiarity gained from hearing the entire case on a prior occasion is vast. As a consequence, the procedures may be greatly simplified and delays inconsequential if present at all. See also United States v. Robin, supra. Such a degree of familiarity gained by this Court over the present case will no doubt accrue to the benefit of the parties and the public. The speedy administration of justice is always a desired result. Cf. Speedy Trial Act, 18 U.S.C. § 3161 et seq. (Supp.1979).
In accordance with the clear language of the rule and the authoritative case precedents as well as complete conformance with the policies described, it is manifestly apparent that F.R.Crim.P. 32(c)(1) will not be violated as a consequence of this Court conducting a retrial of this case upon reversal and remand and after having reviewed a presentence report concerning the defendant. In the absence of a violation of F.R. Crim.P. 32(c)(1), the decision to grant or deny a recusal motion is one committed to the discretion of the trial judge. See, e. g., United States v. Gallington, 488 F.2d 637 (8th Cir. 1973). "[U]nless demonstrable prejudice is shown, the district court's judgment may only be set aside for an abuse of discretion." United States v. Bourque, supra at 296. As earlier noted, the defendant has not alleged the existence of bias or prejudice but has only relied on the bare Gregg dicta. In accompaniment with the effect of such an absence of pleading, the Court additionally makes reference to the total lack of any bias against the defendant and the utter impossibility of prejudice accruing *917 to him. Accordingly, the defendant's Motion For Recusal Of Trial Judge will be denied. To hold otherwise, would require an untenable conclusion.
Motion To Dismiss The Indictment.
In addition to the recusal motion, the defendant has also moved to dismiss the indictment for the alleged reason that the testimony presented to the indicting grand jury was "pure hearsay." The defendant relies upon United States v. Estepa, 471 F.2d 1132 (2d Cir. 1972) to support his motion, a case which provides the following rule set forth below in a summary fashion:
[A]n indictment based on hearsay is invalid where (1) non-hearsay evidence is readily available; (2) the grand jury is misled into believing it was hearing direct testimony rather than hearsay; and (3) there is high probability that had the grand jury heard the eye witness it would not have indicted.
United States v. Cruz, 478 F.2d 408, 410 (5th Cir.), cert. denied, 414 U.S. 910, 94 S.Ct. 259, 38 L.Ed.2d 148 (1973). The defendant apparently relies upon Estepa for its first of the three propositions an indictment based on hearsay is invalid when non-hearsay evidence is readily available. The defendant contends:
Based on the testimony of Agent Kean in the last trial it is apparent that his testimony before the Grand Jury was pure hearsay. No reason was ever offered by the government why the testimony of witness Marrazzo, the government's alleged informer, was not utilized before the Grand Jury although he has been continuously available for testimonial use by the government in this as well as in other cases.
In view of the foregoing, the defendant respectfully submits that the indictment against him should be dismissed.
See Docket Entry No. 44, p. 3.
Initially, the Court notes that the Estepa guidelines are of doubtful validity. See United States v. Calandra, 414 U.S. 338, 344-45, 94 S.Ct. 613, 618, 38 L.Ed.2d 561 (1974); United States v. Marchand, 564 F.2d 983, 1001 n. 29 (2d Cir. 1977). Notwithstanding the inapplicability of Estepa, however, the defendant's contentions would not warrant a dismissal of the indictment. Assuming arguendo that the defendant's contention that non-hearsay evidence was readily available is plausible, essential pleading elements are absent. The defendant has failed to allege that the grand jury was misled or that there is a high probability that if non-hearsay testimony had been utilized the defendant would not have been indicted. Accepting defendant's contention that nonhearsay testimony was available in this case, without more, does not warrant dismissal of the indictment. See United States v. Wander, 601 F.2d 1251, 1260 (3d Cir. 1979). There is absolutely no suggestion that the testimony presented to the grand jury was of the "shoddy" nature condemned in Estepa. See, e. g., United States v. Pray, 452 F.Supp. 788, 801-02 (M.D.Pa. 1978). According, the defendant's Motion To Dismiss The Indictment will also be denied.
|
Paratelmatobius yepiranga is a frog. Scientists have only seen it in one place: Parque das Neblinas in Brazil.
First paper |
A woman in Florida is accused of trying to kill her boyfriend with a shotgun after an argument over his snoring.Lorie Morin, 47, fired a shotgun, striking her boyfriend after arguing about his snoring.Investigators said statements from the couple indicate the shooting was accidental, but neighbors are still shocked.The boyfriend was taken to a local hospital and is in stable condition.Officers said the couple was drinking prior to the argument but are still investigating. |
Le Cheylard is a commune of the Ardeche departement in the southern part of France. |
Welcome to the Shroomery Message Board! You are experiencing a small sample of what the site has to offer. Please login or register to post messages and view our exclusive members-only content. You'll gain access to additional forums, file attachments, board customizations, encrypted private messages, and much more!
All human dreams are part of the dream of the earth. A long time ago, when the human were just animals amongst other animals, and the entire dream of the planet earth, was in tune with that of our central sun. We knew we were dreaming, and doing nothing but dreaming, we were guided by instinct in our intuition.
As humans formed a language out of their language, and in naming things, keeping the individual naming of stuff, dependent to that of the mass, in an agreed upon solution, we now speak of as ? reality an unreal realities, right and wrong, and so on.
If you read this, chances are that you know what a square is.In all the stuff it could be, it would be the one you intended it to be, just as you move a finger, or fill the pool.
As humans formed societies, implying the rule of the mass, individual humans rule, and the ?unwritten? rules, were suppressed, by the rule of let us say A mean king! :PAs the dream of Gaia, was imbalanced by the humans no longer being a ?just a visitor? on earth, but claming it their own, above all animals, no longer as animals amongst other animals, we made up countless religions, to explain where we came from. One of them is Christianity.
As the church started losing the control of what was to be the rules, after having gotten it through various means? Like when the static model of the universe, having the earth as the centre of the universe, was broken down, and disproved by observing one moon orbiting Jupiter. (?)We stated looking again for a centre of the universe, as we so long ago forgot the dream of planet (Gaia). And our attention was fixed on the sun. But as even grander telescopes were conceived, we saw that the sun was the centre of a galaxy. And that the universe as we knew it contain billions of others, just like our own. (?)
The control was returned to the individual, as one no longer were being burned at a stake, for having a contradicting view of that of the norm. The dream again started remembering its place as the dreamer. The last 50 years, the technology has sky scraped. Thus enabling the dreamer, again too be independent of that of the mass, as one of the parts, is the mass.
Now, we are only dependent on being dependent, meaning we do not have to do it, unless we do it. So in being dependent on food, one makes a choice, to live.We could die, we would close our eyes for the last time and/or leave them open for the first time. (?), being dependent of nothing. And we could live, the same way, dependent of nothing, but self. Nothing depends on nothing.
The dream of Gaia, are now, no longer forced by any ?virus?, just like an attacked cell, starting to reproduce that it need for its own survival, rather than the virus needs, after being injected whit the proper ?antivirus?, we have started to rebel.
The virus of our dream is that which separates; "this is better than that and that applies for all, and every occasion, it is this way it is, cemented by us, as them(?), not just by me?... The antivirus may be known as unconditional love. Oneness!
With the dream as just one, being many, whatever you do is done. Ha-ha I lost track long time ago, although I will keep editing this as it may grow in to something of a structure... |
Boalsburg is an unincorporated community and census-designated place (CDP) in Harris Township, Centre County, Pennsylvania, United States. It is part of the State College, Pennsylvania Metropolitan Statistical Area. The population was 3,722 at the 2010 census. |
Aww. Reminds me of a song.
"Baby let your hair down
Let me run my fingers through it
We can be ourselves now..."
they don't have fingers tho |
Cheriennes is a commune. It is found in the region Nord-Pas-de-Calais in the Pas-de-Calais department in the north of France.
Communes in Pas-de-Calais |
Q:
How to seperate login redirect urls in django
I have built a django app.Can someone help me in seperating the redirect URLs while logging in from facebook(django-social-auth) and a normal login form.
I have two types of users, one which I need to login using facebook and the other using the form.
I have defined different URLs for both the purposes and defined it in my views.py
Also given SOCIAL_AUTH_LOGIN_REDIRECT_URL in my settings.py, but when logging in using the form, it is also getting redirected to the same URL.
Please help.
Relevant code is attached
Thanks in advance.
views.py:
def admin_dashboard(request):
if request.user.id!=None and request.user.usertype.description=="ADMIN" and request.user.is_authenticated:
if request.method=="GET":
return render_to_response('testu/admin_dashboard.html',context_instance=RequestContext(request))
def student_dashboard(request):
if request.user.id!=None and request.user.usertype.description=="STUDENT" and request.user.is_authenticated:
if request.method=="GET":
return render_to_response('testu/student_dashboard.html',{"tests":Test.objects.all()},context_instance=RequestContext(request))
urls.py:
urlpatterns = patterns('',
url(r'', include('social_auth.urls')),
url(r'^admin_dashboard/',admin_dashboard),
url(r'^student_dashboard/',student_dashboard),
)+ static(settings.MEDIA_URL, document_root=settings.MEDIA_ROOT)
settings.py:
FACEBOOK_APP_ID = '...'
FACEBOOK_API_SECRET = '...'
FACEBOOK_EXTENDED_PERMISSIONS = ['email']
SESSION_SERIALIZER='django.contrib.sessions.serializers.PickleSerializer'
SOCIAL_AUTH_NEW_USER_REDIRECT_URL = '/student_dashboard/'
SOCIAL_AUTH_LOGIN_REDIRECT_URL = '/student_dashboard/'
SOCIAL_AUTH_USER_MODEL = 'myapp.customuser'
basically, whenever im signing in with user of "ADMIN" description, even that is being redirected to 'student_dashboard'
A:
Did you try having a common login Redirect view. Ex:
LOGIN_REDIRECT_URL = '/my_common_view/'
def my_common_view(request):
if user is student:
redirect to student dashboard
else:
redirect to admin dashboard
This should solve this problem.
|
was a Japanese football player. He played for the Japan national team.
Biography
Shinojima was born in Nikko on January 21, 1910. In May 1930, when he was a Tokyo Imperial University student, he was selected the Japan national team for Far Eastern Championship Games in Tokyo and Japan won the championship. At this competition, on May 25, he debuted against Philippines. On May 29, he also played and scored a goal against Republic of China. He played 2 games and scored 1 goal for Japan in 1930.
After retirement, Shinojima joined Japan Football Association (JFA). In 1965, he became vice-present of JFA. In 1975, he resigned for health reasons.
On February 11, 1975, Shinojima died of heart failure in Minato, Tokyo at the age of 65. In 2006, he was selected Japan Football Hall of Fame.
Statistics
|-
|1930||2||1
|-
!Total||2||1
|} |
Sri Lanka crisis: Rajapaksa says his appointment is legitimate
Sri Lanka’s new prime minister tells Al Jazeera that his appointment is ‘according to the constitution’. |
Daisuke Matsuyama (born 20 July 1972) is a former Japanese football player.
Club career statistics
|-
|1991/92||Mazda||JSL Division 1||0||0||0||0||0||0||0||0
|-
|1992||Sanfrecce Hiroshima||J. League 1||colspan="2"|-||0||0||0||0||0||0
0||0||0||0||0||0||0||0
0||0||0||0||0||0||0||0
1972 births
Living people
Footballers from Osaka Prefecture
People from Osaka |
The effect of malaria on mortality in a cohort of HIV-infected Ugandan adults.
To investigate the effects of malaria parasitaemia and clinical malaria on mortality in HIV seropositive and seronegative adults. A cohort of adults in rural Uganda were followed from 1990 to 1998. Participants attended routine clinic visits every 3 months and also when sick (interim visits). Information was collected on HIV serostatus, history of fever, current fever and malaria parasite levels. Malaria was categorized as any parasitaemia, significant parasitaemia (>/=1.25 x 10(6) parasites/ml at routine or >/=50 parasites per 200 white blood cells at interim visits) or clinical malaria. The effect of malaria on all-cause mortality was assessed using Cox models. The 222 HIV seropositive participants made 2762 routine visits and 1522 interim visits. During follow-up, of the 211 participants with full records, 69% had at least one episode of parasitaemia, 51% experienced significant parasitaemia and 28% had clinical malaria. There were 90 deaths in 922 person-years of observation. There were no significant associations between numbers of visits with any parasitaemia, significant parasitaemia or clinical malaria on mortality rates. The highest mortality rates were observed in those making four or more routine visits with significant parasitaemia [adjusted mortality rate ratio (RR) 3.27 compared with those making 0 such visits; P=0.078] and those making two or more visits with clinical malaria (adjusted RR 2.23; P=0.093). There was no significant interaction between any malaria category and HIV serostatus. Conclusion We found no evidence of a strong detrimental effect of malaria on all-cause mortality in HIV seropositive adults in this setting. |
Kafr Qasim (, ), also spelled as Kafr Qassem, Kufur Kassem, Kfar Kassem and Kafar Kassem, is a hill-top city in Israel with an Arab population. It is located about east of Tel Aviv. |
Q:
Insert html using angularjs between div tags
I saw it was possible to insert HTML between div tags using innerHTML, example:
document.getElementById('mydiv').innerHTML = '<span
class="prego">Something</span>';
I'm working on a Angularjs projet and I tried something similar:
function insertTransmissionHTML(param){
var transmission = 'transmission'+param;
var partrans = 'partrans'+param;
document.getElementById(partrans).innerHTML = '<form class="form-horizontal"><div ng-repeat="param in '+transmission+'"><label class="control-label">{{param.libelle}}</label><input class="form-control" type="text" ng-model="param.valeur"></div></form>';
}
Then i call the function:
insertTransmissionHTML("FTP");
Here is the HTML:
<div id="partransFTP" class="tab-pane fade">
</div>
I use a $scope.transmissionFTP with some parameters and i should have something like that:
parameter 1
parameter 2
...
But I have:
{{param.libelle}}
It looks like the angularjs here isn't working, it becomes a simple HTML.
EDIT:
Here is my example at the beginning (it works):
<div id="partransFTP" class="tab-pane fade">
<form class="form-horizontal">
<div ng-repeat="param in transmissionFTP">
<label class="control-label">{{param.libelle}}</label>
<input class="form-control" type="text" ng-model="param.valeur">
</div>
</form>
</div>
And I had all my parameters (from $scope.transmissionFTP)
parameter 1
parameter 2
...
But I have to do something dynamically. Why is it showing {{param.libelle}} and not all my parameters when I use insertTransmissionHTML ?
Has some one a suggestion ?
Thank you a lot !
A:
I'm tad bit confused regarding your issue, but when I need to inject dynamic HTML I use the following directive:
app.directive('dynamic', ['$compile', function ($compile) {
return {
restrict: 'A',
replace: true,
link: function (scope, ele, attrs) {
scope.$watch(attrs.dynamic, function (html) {
ele.html(html);
$compile(ele.contents())(scope);
});
}
};
}]);
In my Angular controller I save the HTML string to a scope variable
var $scope.myScopeVariable = '<div>My HTML Goes HERE</div>';
, and in my html page, I use:
<div dynamic = "myScopeVariable">
Hopefully, this will help you.
|
Oreco (born 13 June, 1922) is a former Brazilian football player. He has played for Brazil national team.
Club career statistics
|-
|1970||rowspan="3"|Dallas Tornado||rowspan="3"|NASL||17||0
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|1971||16||0
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|1972||5||0
38||0
38||0
|} |
Imagine the Universe News - 07 October 2010
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NASA's WMAP Project Completes Satellite Operations
07 October 2010
Click for larger image
This image is the detailed, all-sky picture of the infant universe created from seven years of WMAP data. The image reveals 13.7 billion year old temperature fluctuations (shown as color differences) that correspond to the seeds that grew to become the galaxies. Credit: NASA
After nine years of scanning the sky, the Wilkinson Microwave Anisotropy Probe (WMAP) has concluded its observations of the cosmic microwave background, the oldest light in the universe. The spacecraft has not only given scientists their best look at this remnant glow, but also established the scientific model that describes the history and structure of the universe.
"WMAP has opened a window into the earliest universe that we could scarcely imagine a generation ago," said Gary Hinshaw, an astrophysicist at NASA's Goddard Space Flight Center in Greenbelt, Md., who manages the mission. "The team is still busy analyzing the complete nine-year set of data, which the scientific community eagerly awaits."
WMAP was designed to provide a more detailed look at subtle temperature differences in the cosmic microwave background that were first detected in 1992 by NASA's Cosmic Background Explorer (COBE). The WMAP team has answered many longstanding questions about the universe's age and composition. WMAP acquired its final science data on Aug. 20. On Sept. 8, the satellite fired its thrusters, left its working orbit, and entered into a permanent parking orbit around the sun.
"We launched this mission in 2001, accomplished far more than our initial science objectives, and now the time has come for a responsible conclusion to the satellite's operations," said Charles Bennett, WMAP's principal investigator at Johns Hopkins University in Baltimore.
WMAP detects a signal that is the remnant afterglow of the hot young universe, a pattern frozen in place when the cosmos was only 380,000 years old. As the universe expanded over the next 13 billion years, this light lost energy and stretched into increasingly longer wavelengths. Today, it is detectable as microwaves.
WMAP is in the Guinness Book of World Records for "most accurate measure of the age of the universe." The mission established that the cosmos is 13.75 billion years old, with a degree of error of one percent.
WMAP also showed that normal atoms make up only 4.6 percent of
today's cosmos, and it verified that most of the universe consists of
two entities scientists don't yet understand. One of these is dark
matter, which makes up 23 percent of the universe, and is a material that
has yet to be detected in the laboratory. The other is dark energy, a gravitationally repulsive entity which may be a feature of the vacuum itself. WMAP confirmed its existence and determined that it fills 72 percent of the cosmos.
Another important WMAP breakthrough involves a hypothesized cosmic "growth spurt" called inflation. For decades, cosmologists have suggested that the universe went through an extremely rapid growth phase within the first trillionth of a second it existed. WMAP's observations support the notion that inflation did occur, and its detailed measurements now rule out several well-studied inflation scenarios while providing new support for others.
"It never ceases to amaze me that we can make a measurement that can distinguish between what may or may not have happened in the first trillionth of a second of the universe," says Bennett.
WMAP was the first spacecraft to use the gravitational balance point known as Earth-Sun L2 as its observing station. The location is about 930,000 miles or (1.5 million km) away.
"WMAP gave definitive measurements of the fundamental parameters of the universe," said Jaya Bapayee, WMAP program executive at NASA Headquarters in Washington. "Scientists will use this information for years to come in their quest to better understand the universe."
Launched as MAP on June 30, 2001, the spacecraft was later renamed WMAP to honor David T. Wilkinson, a Princeton University cosmologist and a founding team member who died in September 2002. |
Elles Dambrink (born 22 June 2003) is a Dutch volleyball player from Ouderkerk aan den IJssel.
She is member of the Netherlands women's national volleyball team. With the national team she competed at the 2022 FIVB Volleyball Women's World Championship. She replaced Celeste Plak in the match against Argentina and made a strong impression. In the later match against China, she was lined-up from the start. |
Navigation
Plans for park at Elliniko plot presented
The Environment Ministry has released for public consultation its plan for what it hopes will be one of Europe’s biggest public parks, at the former Athens airport plot in the southern suburb of Elliniko. According to the plan, the 200-hectare park will be separated into seven zones allowing different uses. Among other features, it will have a sports area with a swimming pool, running track and corresponding facilities; a piazza-like square at its center; a sculpture park on a small hill that will be raised in the middle of the park; and an area reserved for building and maintaining aircraft, as well as for a museum on air travel. |
The Baluchistan States Union existed between 3 October 1952 and 14 October 1955 in modern southwest Pakistan. It was formed by the states of Kalat, Kharan, Las Bela and Makran with the capital at the town of Kalat. The area of the Union was roughly the western half of the modern province of Balochistan. The Union was separate from the Chief Commissioners Province of Baluchistan which comprised areas to the northeast of the Union. The Union did not include the enclave of Gwadar City which was part of the Sultanate of Oman. The four state rulers continued in office but some matters became the responsibility of the Council of Rulers.
Former subdivisions of Pakistan
1950s establishments in Pakistan |
IN THE SUPERIOR COURT OF THE STATE OF DELAWARE
WENDY S. ALTIZER, )
)
Defendant-Below, )
Appellant )
)
v. ) ID. No. 1409012918
)
STATE OF DELAWARE, ) Cr. A. Nos. MN 14-10-4136, etc.
)
Plaintiff-Below, )
Appellee. )
Submitted: October 12, 2016
Decided: January ll, 2017
ORDER
Upon Appeal from the Court of Common Pleas Of the State ofDelaware
in and for New Castle Counly,
AFFIRMED, IN PART; DISMISSED, IN PART.
This llth day of January, 2017, upon consideration of the parties’ briefs, the
parties’ oral arguments, the record on appeal, and the record beloW, it appears to
the Court that:
(l) The Court of Common Pleas denied Appellant Wendy S. Altizer’s
pretrial motion to suppress evidence derived from an investigation and arrest of her
for Driving Under the Influence (“DUI”) and other related traffic charges.l
l Del. Corn. Pl. Supp. Hrg. Tr. (Nov. 3, 2015) at 38-42.
Following a May 2016 jury trial in the Court of Common Pleas, Altizer Was found
guilty of DUI and Improper Lane Change.2 For the DUI conviction (her second),
Altizer Was sentenced to 18 months imprisonment, suspended after 60 days for a
probated term With certain conditions that include payment of a fine and
completion of the education and rehabilitation programs required by Delaware’s
motor vehicle code. For the improper lane change, Altizer received a $25 fine.3
(2) Altizer timely appealed her convictions4 The sole remaining issue on
Altizer’s appeal is the Court of Common Pleas’ denial of her suppression motion.5
2 Del. Com. Pl. Trial Tr. (May 10, 2016) at 162-63.
3 Sent. Order, Wendy S. Altizer v. State of Delaware, ID No. 1409012918 (Del. Com. Pl.
May 10, 2016).
4 Notice of Appeal, Wendy S. Altizer v. State of Delaware, ID No. 1409012918 (Del.
Super. Ct. filed May 16, 2016). Altizer included in her notice of appeal the convictions for both
the DUI and the improper lane change charges. But this Court lacks jurisdiction to consider her
appeal from the latter. See DEL. CODE. ANN. tit 11, § 5301(c) (2015) (granting right of appeal to
Superior Court from “any order, rule, decision, judgment or sentence of the Court [of Common
Pleas] in a criminal action . . . as provided in § 28, article IV of the Constitution of the State”);
Del. Const. art. IV, § 28 (appeals to Superior Court available Where the sentence includes
imprisonment exceeding a month or a fine exceeding $100); See also Reese v. State, 2014 WL
4059213, at *1 (Del. Aug. 15, 2014) (“In cases of multiple convictions, each sentence must be
evaluated individually in order to determine Whether it meets the constitutional threshold.”).
5 Appellant’s Opening Br. 5-19. At trial and through her briefing on appeal, Altizer
claimed also that her privilege against self-incrimination, derived from both the federal and state
constitutions, Was violated When the trial court admitted evidence of her refusal to submit to an
Intoxilyzer test. See Del. Com. Pl. Trial Tr. (May 9, 2016) at 48-52 (defense counsel objected to
the introduction of Altizer’s breath test refusal only as violating Miranda v. Arizona, 384 U.S.
436 (1966)); Appellant’s Opening Br. 20-28 (arguing that admission of the intoxilyzer refusal
violated her privilege against self-incrimination as granted by Article I, Section 7, of the
Delaware Constitution).
Altizer, as she should, has now abandoned the self-incrimination claim because it is contrary to
Well-settled federal and state constitutional laW. More than three decades ago, the United States
_2_
(3) This Court takes criminal appeals from the Court of Common Pleas.6
And such appeals are reviewed on the record, not tried de novo.7 “ln fact, this
Court functions in the same manner as the Supreme Court, in its position as an
intermediate appellate court, when considering an appeal from the Court of
Common Pleas.”8
(4) Here Altizer argues that the Court of Common Pleas erred when it
found probable cause existed for her roadside arrest for DUI. The Court finds that
the Court of Common Pleas did not abuse its discretion when it denied Altizer’s
motion to suppress. And thus, the Court affirms the judgment of the Court of
Common Pleas.
Supreme Court held that the Fifth Amendment to the United States Constitution does not bar
admission of evidence of a driver’s refusal to submit to a chemical test. South Dakota v. Neville,
459 U.S. 553, 564 (1983) (“We hold, therefore, that a refusal to take a blood-alcohol test, after a
police officer has lawfully requested it, is not an act coerced by the officer, and thus is not
protected by the privilege against self-incrimination.”) And more than a half-century ago, our
supreme court held the same when ruling on a challenge to the admission of an intoxilyzer
refusal under Article 1, Section 7, of the Delaware Constitution. State v. Durrant, 188 A.2d 526,
514-15 (Del. 1963) (“. . . the provisions relating to privilege against self-incrimination under the
provisions of Article I, Section 7 of the Delaware Constitution . . . embrace only a prohibition by
compulsory oral examination” not “[t]he fact that [a] defendant declined to submit to a sobriety
test . . .”).
6 DEL. CODE. ANN. tit ll, § 5301(c) (2015).
7 Id.
8 Stevens v. State, 110 A.3d 1264, 1268 (Del. Super. Ct. 2015) (internal citations and
quotations omitted); see also Baker v. Connell, 488 A.2d 1303, 1309 (Del. 1985) (Superior
Court’S function as intermediate appellate court is basically the same as the Supreme Court’s).
_3_
(5) This Court reviews the Court of Common Pleas’ denial of a motion to
suppress after an evidentiary hearing for abuse of discretion.9 Whether probable
cause exists is a mixed question of fact and law.10 Findings of fact are reviewed to
determine whether there is sufficient evidence in the record to support those
findings." And this Court “must adopt [the trial court’s] factual findings and [the
trial court’s] reasonable inferences as long as there is sufficient evidence in the
record to support them and the findings are not clearly erroneous.”12 Those
“factual findings can be based upon physical evidence, documentary evidence,
testimonial evidence, or inferences from those sources jointly or severally.”13
Also, under this deferential clearly erroneous standard of review, “[w]here there
are two permissible views of the evidence, the factfinder’s choice between them
9 Lopez-Vasquez v. State, 956 A.2d 1280, 1284 (Del. 2008); Hunter v. State, 2008 WL
625566, at *2 (Del. Mar. 10, 2008); State v. Crespo, 2009 WL 1037732, at * 4 (Del. Super. Ct.
Apr. 17, 2009).
‘" Bmwn v. Szaze, 897 A.2d 748, 750 (Del. 2006).
ll Id
12 S¢are v. Abel, 68 A.3d 1228, 1232 (Dei. 2012); Cooke v. Sm¢e, 977 A.2d 803, 854 (Del.
2009)
13 Abel, 68 A.3d at 1232 (internal quotations and citations omitted); Lopez v. State, 861
A.2d 1245, 1248-49 (Del. 2004) (“This deferential standard applies not only to historical facts
that are based upon credibility determinations but also to findings of historical fact that are based
on physical or documentary evidence or inferences from other facts.”).
_4_
cannot be clearly erroneous.”14 Once the facts and reasonable inferences therefrom
are properly established, “the issue is whether an undisputed rule of law is or is not
violated.”15 The trial court’s formulation and application of legal concepts are
reviewed de nova16 And so, giving the proper deference to the Court of Common
Pleas’ factual findings, this Court reviews de novo whether there was probable
cause for an arrest, as a matter of law.17
(6) The State’s evidence at the proceedings below fairly established the
following version of events. In the early morning hours of September 18, 2014,
Altizer was on Green Street in Middletown when She slammed her Jeep Grand
Cherokee into a vehicle legally parked on the side of that street. The collision was
of such force that it drove that other vehicle from its position parallel to a position
perpendicular to the curb. Altizer continued down the road until her vehicle
became disabled at the intersection of Green and Catherine Streets.18 Sergeant
14 Lopez, 861 A.2d at 1249 (quoting Anderson v. Cin of Bessner, 470 U.S. 564, 574
(1985)).
'5 1a (citing omelas v. United Sm¢es, 527 U.s. 690, 696-97 (1996)).
16 Lopez- Vasquez v. State, 956 A.2d 1280, 1284-85 (Del. 2008); Donald v. State, 903 A.2d
315, 318 (Del. 2006).
17 Lopez, 861 A.2d at 1249 (citing Ornelas, 527 U.S. at 697).
18 Del. Com. Pl. Supp. Hrg. Tr. (Nov. 3, 2015) at 9, 29-30; id. at 9-11 (entry of police body
camera recording as State’s Suppression Exhibit 7 [referenced hereinafter as “Supp. Hrg. Ex. 7 at
_”]); Supp. Hrg. Ex. 7 at 05:55-50, 08:19-13:00, 17:09-19:55; Del. Com. Pl. Trial Tr. (May 9,
2016) at 35-46.
-5_
Raymond Howard of the Middletown Police Department, a well-experienced
police officer trained specifically in DUI investigation, arrived at the scene.19 Sgt.
Howard wore a body camera that recorded his roadside interaction with Altizer.ZO
(7) Altizer was walking away from her disabled vehicle when Sgt.
Howard first saw her; he had to call her back.21 She retumed, they began talking,
and the sergeant detected a moderate odor of alcohol coming from Altizer’s
breath.22 Sgt. Howard noticed also that Altizer’s eyes were bloodshot.23 When
asked for her license, registration and insurance information, Altizer gave the
sergeant the first two but needed to be reminded of and had difficulty producing
the third - at one point, confusing a registration document for it.24 During this
initial interaction, Sgt. Howard had to ask Altizer three separate times how the
accident happened. Altizer seemed either to avoid the question or to be too
‘2 Del. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015)ar6-9;De1. Com. P1. Triai Tr. (May 9, 2016)
ar 31-32.
20 Del. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 9-11; Del. Com. P1. Triai Tr. (May 9,
2016) at 32 - 34.
21 Dei. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 11-12; supp. Hrg. Ex. 7 at 00;57.
22 Dei. com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 12;1:)@1. com. P1. Trial Tr. (May 9, 2016)
at 37.
23 Del. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) ar 12; Dei. Com. P1. Trial Tr. (May 9, 2016)
at 37.
24 Del. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 12; supp. Hrg. Ex. 7 at 01;03, 01;48-
02:48.
_6_
oblivious to answer.25 When she did, Altizer told the sergeant that she had been in
an argument at a friend’s place, was upset, and that she was now coming from
Lowe’s.26 Sgt. Howard told Altizer that it was about 1130 a.m. and Lowe’s had
been closed for hours. Altizer said then that she was coming from Wawa.27 Sgt.
Howard recounted, “she was confused about Where she Was and what she was
doing and performing that night.”28
(8) Altizer was twice asked how much she had to drink. Twice she
denied drinking at all.29 When confronted with the fact that Sgt. Howard could
smell alcohol on her, Altizer then said “maybe I had a few beers.”30 At this point,
Sgt. Howard attempted to begin field sobriety testing with the horizontal gaze
nystagmus (HGN) test. Altizer did not perform well on that test.31 She suddenly
became emotional, claimed she was unable to perform the HGN test because she
25 Del. Com. Pl. Supp. Hrg. Tr. (Nov. 3, 2015) at 26; Supp. Hrg. Ex. 7 at 01:04, 01:35,
02:52-54.
26 Del. com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 15; supp. Hrg. Ex. 7 3102;54-03;44.
22 Dei. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 15; supp. Hrg. Ex. 7 at 03:34-03:49.
28 Del. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 15.
22 supp. Hrg. Ex. 7 at 03:52-04:12.
20 ld. 3103;52-04;12.
3' Del. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 15-16; supp. Hrg. Ex. 7 at 04:21-05:20_
_7_
was upset, and refused to perform any more field sobriety testing.32 Sgt. Howard
then placed her under arrest for suspicion of driving under the influence.33
(9) At the police station, Altizer refused to take an Intoxilyzer breath test.
So Sgt. Howard sought a seizure warrant to collect a sample of her blood. After
the warrant was obtained, Altizer’s blood was drawn.34 The result of her blood test
revealed Altizer had a blood alcohol content of .15 grams of alcohol per 100
milliliters of blood _ almost twice the legal limit.35
(10) The legal principles involved here are Well-established. Probable
cause exists when a police officer possesses information Which would warrant a
reasonable man into believing that a crime has been committed36 The wrongdoing
at question here is the offense of driving under the influence as defined by
Delaware’s motor vehicle code. “While under the influence” is defined in Title 21,
section 4177(c)(5) to mean that “the person is, because of alcohol or drugs or a
combination of both, less able than the person would ordinarily have been, either
mentally or physically, to exercise clear judgment, sufficient physical control, or
22 Del. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 15-17; supp. Hrg. Ex. 7 a104:21-05:25.
22 Del. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 17; supp. Hrg. Ex. 7 ar 05:25-05;45.
24 Del. Com. P1. Trial Tr. (May 9, 2016) at 52-53.
22 De1. com. P1. Trial Tr. (May 10, 2016)@1147.
26 cramer v. Srare, 314 A.2d 908, 910 (Del. 1973). See also Carrer v. Smre, 814 A.2d 443,
445 (Del. 2002) (“For an arresting officer to have probable cause, the officer’s knowledge must
be sufficient for a prudent person to believe that an individual had committed or was committing
an offense.”).
_8_
due care in the driving of a vehicle.”37 The evidence need not establish that the
person is “drunk” or “intoxicated.”38
(11) Probable cause is measured, not by precise standards, but by the
totality of the circumstances through a case-by-case review of “‘the factual and
practical considerations of everyday life on which reasonable and prudent men, not
legal technicians, act.”’39 In turn, our courts have long-recognized that “[p]robable
cause is an elusive concept which avoids precise definition, lying somewhere
between suspicion and sufficient evidence to convict.”40 “Probable cause does not
require the police to uncover information sufficient to prove a suspect’s guilt
beyond a reasonable doubt or even to prove that guilt is more likely than not.”4'
Rather, probable cause merely requires the State to present facts which are
sufficient to show that “there is a fair probability that the defendant has committed
a crime.”42 “That hypothetically innocent explanations may exist for facts learned
37 DEL. CODE ANN. tit. 21, § 4177(c)(5)(2014); Lefebvre v. State, 19 A.3d 287, 292 (Del.
2011), reargument denied (May 26, 2011) (citing Bease v. State, 884 A.2d 495,498 (Del.2005)).
22 stevens v. sze, 110 A.3d 1264, 1271 (Del. super ct. 2015).
39 Schramm v. State, 366 A.2d 1185, 1192 (Del. 1976) (quoting United States v. Harris, 403
U.S. 573, 582-83 (1971)).
40 Stewart v. State, 2008 WL 482310, at *2 (Del. Feb. 22, 2008); State v. Cochran, 372
A.2d 193, 195 (Del. 1977).
4‘ Sm¢e v. Maxwell, 624 A.2d 926, 930 (Del. 1993).
42 lay
during an investigation does not preclude a finding of probable cause.”43 When
determining whether a particular arrest was supported by probable cause, the facts
must be viewed under the totality of the circumstances then facing the
investigating officer.44 Under the totality of the circumstances standard, facts are
not viewed in isolation to assess the establishment of probable cause.45 And the
totality of the circumstances standard takes into account a police officer’s training,
experience, observations, investigation, and any rational inferences drawn
therefrom.46 At bottom, “[w]hat is required is that the arresting police officer
possess a ‘quantum of trustworthy factual information’ sufficient to warrant a man
of reasonable caution in believing a DUI offense has been committed.”47
(12) As a general rule, the burden of proof is on the defendant who seeks
to Suppress evidence.48 But once the defendant has established a basis for her
motion, i.e., the seizure was conducted without a warrant, the burden shifts to the
42 Lefebvre, 19 A.3d 287, 293 (Del. 2011).
44 Maxwell, 624 A.2d at 930.
42 ld. ar 931.
46 Id
47 Lefebvre, 19 A.3d at 293 (quoting Maxwell, 624 A.2d at 931).
48 United States v. Johnson, 63 F.3d 242, 245 (3d Cir. 1995); State v. Babb, 2012 WL
2152080, at *2 (Del. Super. Ct. June 13, 2012).
_10_
State to show that the warrantless seizure was reasonable49 And the burden the
State must carry on such a motion to suppress is proof by a preponderance of the
evidence.50
(13) There is no doubt that the Court of Common Pleas understood,
properly formulated, and properly applied each of the legal principles explained
above when it considered and denied Altizer’s motion to suppress.51
(14) Applying the deferential clearly erroneous standard of review, this
Court finds no err in the Court of Common Pleas’ factual findings that: Altizer
inexplicably Struck a parked vehicle; smelled of alcohol; had bloodshot eyes; was
unresponsive to certain questions about how the accident occurred; did not follow
directions properly during the HGN test; and initially denied any drinking until
confronted.52 There is sufficient evidence in the record to support those findings.53
(15) Applying the deferential clearly erroneous standard of review, the
record reflects that the Court of Common Pleas, as the trier of fact, was within its
49 Johnson, 63 F.3d at 245; Hunter v. State, 783 A.2d 558, 560 (Del. 2001) (Regarding
“which party bears the burden of proof on a motion to suppress evidence Seized during a
warrantless search, the rule in Delaware should now be clear. The State bears the burden of
proof.”).
211 State v. henson 2011 WL 1205242, at *3 (Del. super ct. Mar. 31, 2011).
21 Del. Com. P1. supp. Hrg. Tr. (Nov. 3, 2015) at 38-42 (court Of Common Pleas’
suppression ruling).
52 Del. Com. Pl. Supp. Hrg. Tr. (Nov. 3, 2015) at 40-42.
22 see Brown v. s¢a¢e, 897 A.2d 748, 750 (Del. 2006).
_11_
discretion to further find as fact or draw as reasonable inferences: that Altizer was
“not very responsive” at certain points of her interaction with Sgt. Howard; that
she “was foggy and was confused” at other points; that she was “very mixed up
about where she was coming from”; that her emotional upset was in response to
being asked to perform field sobriety tests; and that her refusal to take those tests
54
was “a consciousness of guilt indicator.” Again, there is sufficient evidence in
the record to support those findings. And, while Altizer strongly urges other views
of the evidence, the Court of Common Pleas’ choice of permissible alternatives
cannot be clearly erroneous.55
(16) lt then becomes this Court’s duty is to determine whether these facts
along with the reasonable inferences flowing from those facts were sufficient to
9956
conclude that there was “a fair probability that Altizer was driving when
“because of alcohol or drugs or a combination of both, [she was] less able than
[she] would ordinarily have been, either mentally or physically, to exercise clear
judgment, sufficient physical control, or due care in the driving of [her] vehicle.” 57
54 Del. Com. Pl. Supp. Hrg. Tr. (Nov. 3, 2015) at 40-42.
22 Lopez v. smze, 861 A.2d 1245, 1249 (Del. 2004).
56 State v. Maxwell, 624 A.2d 926, 930 (Del. 1993); State v. Iyer, 2011 WL 976480, at *1
(Del. Super. Ct. Feb. 23, 2011) (“The standard for probable cause continues to require only a fair
probability, under the totality of the circumstances, that a crime has been committed.”).
22 DEL. CODE ANN. tit. 21, § 4177(6)(5) (2014); Lefebvre v. Smre, 19 A.3d 287, 292 (Del.
2011).
_12_
Applying the a’e novo standard of review, this Court concludes that, under the
totality of circumstances, the established facts constituted probable cause for
Altizer’s DUI arrest as a matter of law.58 The Court of Common Pleas Court
properly denied her motion to suppress.
(17) The Court of Common Pleas’ judgment of conviction on the DUI
charge is, therefore, AFFIRMED. Because the sentence for the lane change
violation does not meet the jurisdiction requirement, the appeal as to that
conviction must be DISMISSED without review.59
58 See, e.g. Lefebvre, 19 A.3d at 292-93 (probable cause to arrest driver for DUI without any
field sobriety tests, Where driver committed a traffic offense, exhibited a strong odor of alcohol,
had a flushed face, admitted drinking, and Was somewhat flustered and argumentative with the
officer); Bease v. State, 884 A.2d 495,498 (Del. 2005) (evidence of a traffic violation, odor of
alcohol, rapid speech, admission to drinking, bloodshot and glassy eyes and a failed alphabet test
constituted probable to arrest the driver for DUI); Maxwell, 624 A.2d at 929-31 (Probable cause
to believe defendant violated DUI statute when there was a one-car accident, odor of alcohol at
scene of accident, several containers of beer in vehicle and no field tests); Iyer, 2011 WL
976480, at **11-14 (in the absence of admissible field test results, eyes that were “maybe a little
bit bloodshot”, odor of alcohol, admission to consuming alcohol prior to the accident, and
involvement in a single-vehicle accident were facts sufficient to establish probable cause to take
defendant into custody for the completion of the Intoxilyzer test). See also Charch v. State, 11
A.3d 226, at n. 11 (Del. 2010) (“[A] defendant’s refusal to submit to testing can be used for any
relevant purpose, including showing consciousness of guilt” in DUI case); State v. Trager, 2006
WL 2194764, at *6 (Del. Super. Ct. July 28, 2006) (“A police officer may consider irrational,
erratic, or belligerent behavior in making his or her probable cause determination.”).
22 see Reese v. s¢a¢e, 2014 WL 4059213, at *1 (Del. Aug. 15, 2014) (supreme Court must
dismiss appeal of any individual sentence that fails to meet the constitutional threshold for
appealable sentences); Castura v. State, 2009 WL 2365558, at *2 (Del. July 16, 2009) (when
appeal is to the Supreme Court, “each sentence [imposed] must be evaluated individually in
order to determine whether it meets the constitutional threshold” and for those sentences that do
not “meet the jurisdictional requirement . . . appeal as to those convictions must be dismissed
without review”); Stevens v. State, 110 A.3d 1264, 1272 (Del. Super. Ct. 2015) (citing Johnson
_13_
IT IS SO ORDERED.
IZ»QJQ
Paul R. Wallace, Judge
Original to Prothonotary
cc: Ryan Bounds, Deputy Attorney General
Tianna Bethune, Deputy Attorney General
Joseph A. Hurley, Esquire
v. State, 2008 WL 2721698, at *1 (Del. July 14, 2008)) (same for appeals to this Court from the
Court of Common Pleas).
_14_
|
Thomas W. "Tom" Ewing (born September 19, 1935) is an American Republican politician. He was born in Atlanta, Illinois. He was a member of the United States House of Representatives and the Illinois State House of Representatives.
Ewing was a state representative from 1974 to 1991, and a U.S. Congressman representing the 15th district of Illinois from July 2, 1991 until his retirement on January 3, 2001. |
Routine use of fluoroscopic guidance and up-front femoral angiography results in reduced femoral complications in patients undergoing coronary angiographic procedures: an observational study using an Interrupted Time-Series analysis.
Transradial access is increasingly used for coronary angiography and percutaneous coronary intervention, however, femoral access remains necessary for numerous procedures, including complex high-risk interventions, structural procedures, and procedures involving mechanical circulatory support. Optimising the safety of this approach is crucial to minimize costly and potentially life-threatening complications. We initiated a quality improvement project recommending routine fluoroscopic guidance (femoral head), and upfront femoral angiography should be performed to assess for location and immediate complications. We assessed the effect of these measures on the rate of vascular complications. Data were collected prospectively on 4534 consecutive patients undergoing femoral coronary angiographic procedures from 2015 to 2017. The primary end-point was any access complication. Outcomes were compared pre and post introduction including the use of an Interrupted Time-Series (ITS) analysis. 1890 patients underwent angiography prior to the introduction of routine fluoroscopy and upfront femoral angiography and 2644 post. All operators adopted these approaches. Baseline characteristics, including large sheath use, anticoagulant use and PCI rates were similar between the 2 groups. Fluoroscopy-enabled punctures were made in the 'safe zone' in over 91% of cases and upfront femoral angiography resulted in management changes i.e. procedural abandonment prior to heparin administration in 21 patients (1.1%). ITS analysis demonstrated evidence of a reduction in femoral complication rates after the introduction of the intervention, which was over and above the existing trend before the introduction (40% decrease RR 0.58; 95% CI: 0.25-0.87; P < 0.01). Overall these quality improvement measures were associated with a significantly lower incidence of access site complications (0.9% vs. 2.0%, P < 0.001). Routine fluoroscopy guided vascular access and upfront femoral angiography prior to anticoagulation leads to lower vascular complication rates. Thus, study shows that femoral intervention can be performed safely with very low access-related complication rates when fluoroscopic guidance and upfront angiography is used to obtain femoral arterial access. |
Richard Mason may refer to:
Richard Mason (historian), also known as R.H.P. Mason
Richard Mason (novelist), English author of The World of Suzie Wong |
Retrospective case series of gemcitabine plus cisplatin in the treatment of recurrent and metastatic nasopharyngeal carcinoma.
To evaluate the efficacy and toxicity of gemcitabine plus cisplatin (GC) chemotherapy in patients with recurrent and metastatic nasopharyngeal carcinoma (NPC), 75 patients of Chinese ethnicity with recurrent and metastatic NPC received a combination of gemcitabine 1000 mg/m2 on days 1 and 8, and cisplatin 25mg/m2 on days 1, 2 and 3 of a 21-day cycle. All patients were ineligible for re-irradiation or surgery. Of the 75 patients, 4 achieved a complete response, and 28 patients achieved a partial response, for an overall response rate of 42.7%. The 1-year survival rate was 33.9%, and median progression-free survival and overall survival were 5.6 and 9.0 months, respectively. Grade 3 and 4 toxicities were uncommon. this GC regimen was effective and well tolerated by patients with recurrent and metastatic NPC. The results were comparable with most reports in the recent literature. |
Leatherhead is a town in Surrey, England, on the right bank of the River Mole, and at the edge of the contiguous built-up area of London. Its local district is Mole Valley. Records exist of the place from Anglo Saxon England. It has a combined theatre and cinema, which is at the centre of the re-modelling following late 20th century pedestrianisation. |
The Yemeni Ministry of Human Rights has strongly condemned the deadly Saudi-led airstrike in the country’s mountainous northwestern province of Sa'ada, which claimed the lives of more than a dozen people, describing it as a blatant violation of humanitarian principles.
The ministry, in a statement released on Wednesday, said the crime adds to the offenses that “the heinous coalition of aggression” has perpetrated against the Yemeni nation, and represents an outstanding example of the alliance’s violation of humanitarian principles and international human rights laws.
The statement added that the Saudi-led coalition presses ahead with its brutal campaign against Yemeni civilians and continues to target them through various methods, and without any human or international deterrence.
The ministry then called on Human Rights Watch, the United Nations and the international community to adopt an effective policy, which would put an end to the Saudi-led coalition’s aggression against Yemen and hold to account the perpetrators of war crimes.
It also renewed the call for the formation of independent and impartial international committees to investigate all crimes that members of the alliance, Saudi Arabia and the United Arab Emirates in particular, have committed against Yemen, emphasizing that the proceedings must not be subject to a statute of limitations.
The ministry finally censured the international community’s silence on the crimes against humanity that the Saudi-led military coalition is committing in Yemen, calling for an active intervention to stop the crimes and spare civilians from massacre and destruction that has negatively affected all aspects of life in Yemen.
On Tuesday evening, at least 17 people, including a dozen African migrants, lost their lives when Saudi artillery units targeted a popular market in al-Raqou area of the Monabbih district of Sa'ada province. The attack left several people injured as well.
Yemeni forces, allies shoot down Saudi-led surveillance drone in Najran
Meanwhile, Yemeni army forces, supported by allied fighters from Popular Committees, have intercepted and targeted an unmanned aerial vehicle belonging to the Saudi-led military coalition in the skies over the kingdom’s southern border region of Najran, in retaliation for the alliance’s military aggression against their conflict-stricken country.
An unnamed Yemeni military source told Arabic-language al-Masirah television network that Yemeni air defense units shot down the drone over Murabba’ al-Shabaka area of the region, situated 844 kilometers (524 miles) south of the capital Riyadh, on Tuesday evening.
Saudi Arabia and a number of its regional allies launched a devastating campaign against Yemen in March 2015, with the goal of bringing the government of former president Abd Rabbuh Mansur Hadi back to power and crushing the Houthi Ansarullah movement.
The US-based Armed Conflict Location and Event Data Project (ACLED), a nonprofit conflict-research organization, estimates that the war has claimed more than 100,000 lives over the past four and a half years.
The war has also taken a heavy toll on the country’s infrastructure, destroying hospitals, schools, and factories. The UN says over 24 million Yemenis are in dire need of humanitarian aid, including 10 million suffering from extreme levels of hunger. |
Lesperon is a commune in the Ardeche departement in southern France.
Communes in Ardeche |
Globally, from China and Germany to the United States, electric vehicle (EV) subsidies have been championed as an effective strategy to boost production of renewable technology and reduce greenhouse gas emissions (GHG).
But a new study by Concordia economics professor Ian Irvine shows that subsidizing EVs in the North American context will not reduce GHG emissions in the short-term, and may even increase them -- at a cost to taxpayers.
Recently published in Canadian Public Policy, Irvine's study compared the incentives for producing EVs that are found in the Corporate Average Fuel Economy (CAFE) standards, North America's fuel-efficiency regulations, with new EV subsidy policies in Ontario, Quebec and British Columbia.
He found that, while the subsidies encourage the production of more EVs, they undermine the efficiency requirements of existing incentives for conventional vehicles. This results in a zero or negative near-term GHG benefit.
"Sometimes you have more than one policy aimed at a particular goal, and usually those policies are complementary," Irvine notes. "But in this case, they work at cross purposes."
In 2012, CAFE was amended to require manufacturers to continuously reduce the average carbon dioxide (CO 2 ) emissions of their fleets by five per cent a year between 2017 and 2025.
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Typically, the amount of CO 2 each vehicle is allowed to emit is related to its footprint, defined as the area between its wheels. However, Irvine says, because the annual GHG reduction targets are organized on an average fleet-wide basis, manufacturers are allowed some flexibility in how they distribute the annual efficiency improvements within and across different vehicle categories.
'This is what we call a regressive policy'
Under CAFE's rules, an electric car is considered to have a zero emissions footprint. As an incentive designed to stimulate investment in EVs, a manufacturer that produces an EV is given a carbon credit that can be sold to another manufacturer, applied to a future year or applied to other vehicles in the manufacturer's fleet.
As a further incentive, the manufacturer is granted a bonus carbon credit over and above the equivalent of CO 2 that the sale of the EV removes from the atmosphere. For EVs, this bonus credit, or multiplier, started at 2.5 in 2016 and declines to 1.5 in 2025.
As Irvine illustrates, if a vehicle with a footprint of 50 square feet is allowed to emit 150 grams of CO 2 /kilometre, then a manufacturer who sold an EV with the same footprint in 2016 is given an emission credit of 375 grams of CO 2 /kilometre.
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"These carbon credit offsets can be used by a manufacturer to moderate the GHG-related efficiency improvements in the more conventional vehicles that they sell," Irvine says. "So, putting more EVs on the road with subsidies does not translate into fewer GHG emissions."
What's more, the subsidy policies apply to all potential buyers, not just those who wouldn't otherwise have the means to purchase EVs. According to Irvine, this is an inefficient and wasteful use of taxpayer money.
"Research shows that subsidies for vehicle purchases typically benefit the top ten percentile of income distribution," says Irvine. "This is what we call a regressive policy."
All told, Irvine sees the prime lesson of his study to be caution.
"In developing these types of policies, we need to look before we leap," he says. "In Ontario, we're giving grants of up to $14,000 to EV purchases. That's a lot of taxpayer money. And if people think it's going toward reducing GHG emissions, we should confront that misunderstanding." |
Skin cancer is the term that is used for all bad forms of growth of the skin. In everyday use, people often talk about melanoma, but there are other forms of skin cancer, too. These are usually named after the type of cell that grows uncontrollably. Most skin cancers develop in the epidermis. Very often a tumor can be seen, so it is often possible to detect skin cancer at an early stage. Very few people with skin cancer will die of the disease., though it can be disfiguring. Melanoma survival rates are poorer than for non-melanoma skin cancer, although when melanoma is diagnosed at an early stage, treatment is easier and more people survive.
Skin cancer is the most commonly diagnosed type of cancer. Melanoma and non-melanoma skin cancers combined are more common than lung, breast, colorectal, and prostate cancer. Melanoma is less common than both basal cell carcinoma and squamous cell carcinoma, but it is the most serious -- for example, in the UK there were over 11,700 new cases of melanoma in 2008, and over 2,000 deaths. It is the second most common cancer in young adults aged 15-34 in the UK. Most cases are caused by over-exposure to UV rays from the sun or sunbeds.
Non-melanoma skin cancers are the most common skin cancers. The majority of these are basal cell carcinomas. These are usually small spot growths caused by too much exposure to the sun over time. They do not usually spread, and rarely kill.
Types |
julia 0.2-
Codecs
HttpCommon
HttpServer
|
Wladyslaw Stanislaw Reymont, born as Stanislaw Wladyslaw Rejment, (May 7, 1867 in Kobielce Wielkie, Poland - December 5, 1925 in Warsaw, Poland) was a well-known Polish writer, who won the Nobel Prize in 1924 for his four-volume epic novel "Chlopi" (The Peasants). This novel was about life of this part of the society. He also wrote "Ziemia obiecana" (The Promised Land), about industrial capitalism in 19th century Lodz.
Many people say he is one of the greatest and most prominent Polish writers of all time and one of the greatest in 20th century.
Biography
Reymont was born in the family of the organist. His father, Jozef Rejment, a well-read man, had a musical education and in tuszynskiej performed the parish duties of the organist, and also carried on Civil Status Registers and the correspondence of the parish priest with Russian authorities. Mother, Antonia from Kupczynskich, had talent for a story. She came from the impoverished Cracow gentry; in mature years the writer has often emphasized this fact.
1867 births
1925 deaths
Polish Nobel Prize winners
Polish novelists |
The primary goal of the University of Rochester (UR) - University at Buffalo (UB) Center in joining the Neonatal Research Network (NRN) is to improve the care of neonates through developing and participating in large, well-designed clinical trials that address important questions and include long-term follow-up. The specific aims of this application to achieve this goal are: (1) To continue contributions to critical and creative thinking, generating new ideas for clinical trials;(2) To participate fully in NRN trials by enrolling and retaining as many subjects as possible in a safe and ethical manner;and (3) To achieve a high follow-up rate, as this is critical to testing therapies in the neonate. To realize these aims, UR and UB have developed a single center (URUB) with two performance sites. URUB provides a strong academic faculty with a long-standing commitment to clinical trial excellence, large neonatal populations with high rates of recruitment and retention, excellent University and hospital support, experienced clinical research staff, established neonatal neurodevelopmental follow-up clinics, well- developed data systems, high-quality maternal-fetal medicine services, and strong obstetrical-neonatal communication. Dr. Carl D'Angio, the URUB PI, is a leading investigator in premature infant vaccine responses and has led NRN vaccine studies. Dr. D'Angio is PI of the Premature Infant Vaccine Collaborative, a multicenter group devoted to investigating vaccines in premature infants, of which UB is a collaborating center. Dr. Rita Ryan, the URUB Alternate PI, is one of the PIs for a large joint center grant awarded to URUB, the Prematurity Respiratory Outcomes Program (PROP), involving both basic scientists and clinical investigators. The faculty at the URUB Center has an impressive history of intellectual leadership in NIH-funded clinical research. The URUB Center specifically brings together two geographically-adjacent neonatal populations to enhance subject availability for Network Studies. Both sites have strong, existing neonatal follow-up programs with excellent follow-up rates, which are critical to our full participation and optimal contributions to the Neonatal Research Network. PUBLIC HEALTH RELEVANCE: The Neonatal Research Network is an excellent platform for conceiving and completing large, well-designed clinical trials, with recent randomized clinical trials in the areas of neuroprotection, hyperbilirubinemia, inhaled nitric oxide, and supplemental oxygen and respiratory management. The URUB Clinical Center has the leadership, enrollment and follow-up capabilities to be an excellent venue for future, similar successes. |
Earl is a title of nobility.
Earl can refer to several other things:
Earl (mixtape), an album by Earl Sweatshirt
Earl Sweatshirt, a member of rap group Odd Future
Earl, North Carolina
Earl, Wisconsin
Earl, a fictional planet in My-Otome |
Yesterday, we received a call from a customer and friend complaining that their house smelled like dirty gym socks once they turned on their heat. Their heat was working fine but their house smelled horrible.
This is a result of Dirty Sock Syndrome. Yes, a very strange name. This happens in heat pumps because unlike straight cool heating elements, the heating cycle is not hot enough to kill the bacteria and mold that has grown on the coils since the unit was used last. The temperature is just warm enough to slowly bake off the organic odor and create that horrible dirty sock smell.
What can you do?
Let the system run and run and run. Until it bakes off all that bacteria and mold, you will continue to have the smell. Spraying disinfectant into the return air while the system is running will help. The waiting is the hardest part! |
The 36th Ryder Cup Matches were held between 22 and 24 September 2006 at The K Club, Straffan, Co. Kildare, Ireland. Team Europe won the competition by a score of 18 1/2 to 9 1/2, equalling their record winning margin of 2 years earlier. This was the first time Europe had achieved three successive victories. Swedish rookie Henrik Stenson made the winning putt, just moments after Luke Donald had sunk a putt to ensure Europe retained the trophy.
Other websites
Official Ryder Cup site for Team USA
Official Ryder Cup site for Team Europe
Ryder Cup Discussion
Ryder Cup Diary
Official K Club website |
// automatically generated by the FlatBuffers compiler, do not modify
package mbtool.daemon.v3;
import java.nio.*;
import java.lang.*;
import java.util.*;
import com.google.flatbuffers.*;
@SuppressWarnings("unused")
public final class MbGetVersionResponse extends Table {
public static MbGetVersionResponse getRootAsMbGetVersionResponse(ByteBuffer _bb) { return getRootAsMbGetVersionResponse(_bb, new MbGetVersionResponse()); }
public static MbGetVersionResponse getRootAsMbGetVersionResponse(ByteBuffer _bb, MbGetVersionResponse obj) { _bb.order(ByteOrder.LITTLE_ENDIAN); return (obj.__assign(_bb.getInt(_bb.position()) + _bb.position(), _bb)); }
public void __init(int _i, ByteBuffer _bb) { bb_pos = _i; bb = _bb; }
public MbGetVersionResponse __assign(int _i, ByteBuffer _bb) { __init(_i, _bb); return this; }
public String version() { int o = __offset(4); return o != 0 ? __string(o + bb_pos) : null; }
public ByteBuffer versionAsByteBuffer() { return __vector_as_bytebuffer(4, 1); }
public ByteBuffer versionInByteBuffer(ByteBuffer _bb) { return __vector_in_bytebuffer(_bb, 4, 1); }
public static int createMbGetVersionResponse(FlatBufferBuilder builder,
int versionOffset) {
builder.startObject(1);
MbGetVersionResponse.addVersion(builder, versionOffset);
return MbGetVersionResponse.endMbGetVersionResponse(builder);
}
public static void startMbGetVersionResponse(FlatBufferBuilder builder) { builder.startObject(1); }
public static void addVersion(FlatBufferBuilder builder, int versionOffset) { builder.addOffset(0, versionOffset, 0); }
public static int endMbGetVersionResponse(FlatBufferBuilder builder) {
int o = builder.endObject();
return o;
}
}
|
Ribiers is a former commune in the Hautes-Alpes department. On 1 January 2016, it was merged into the new commune of Val Buech-Meouge. |
) = -21*j + 8. Let t(f) = -24*a(f) + 5*s(f). Let l(o) = -o + 1. Let m(x) = 8*l(x) - t(x). Let b(u) = -u. Give b(m(c)).
-8*c
Let y(i) = -2*i**2 - 5. Let c(p) = -p**2 - 3. Let k(s) = 5*c(s) - 3*y(s). Let v = -2 + 5. Let d(j) = 8*j - v*j - 3*j. What is d(k(x))?
2*x**2
Let g be (-12)/(-16) + (-18)/(-8). Suppose 0 = -k + 5 - g. Let f(n) = 0*n**2 + 4*n**2 - 2*n**k. Let m(l) = l**2. Give f(m(d)).
2*d**4
Let y(v) = 2*v - 6. Let m be y(4). Let b(c) = 28*c**2 - 11*c**2 - 14*c**m. Let s(n) = -3*n. Calculate b(s(d)).
27*d**2
Let m(j) be the third derivative of -3*j**5/10 + 27*j**2. Let c(u) = -u**2. Give m(c(i)).
-18*i**4
Let g(j) = 2*j**2. Let t(s) = -167*s. Give t(g(u)).
-334*u**2
Suppose 2 + 3 = 2*u - q, -4*u + 5*q + 25 = 0. Let d(m) = u*m + m - 2*m - 2*m. Let p(c) = 2*c**2. Determine d(p(y)).
-6*y**2
Let v(b) = -8*b**2 - 9 + 3*b**2 + 9. Let f(g) be the third derivative of g**4/12 + 4*g**2. Calculate f(v(s)).
-10*s**2
Let r = -3 - -4. Let x(n) = -n**2 + r - 1. Let s(m) = m**2 - m**2 + m**2 + 0*m**2. Give x(s(z)).
-z**4
Let r(m) = -34*m**2 + 18*m - 18. Let q(o) = -2*o**2 + o - 1. Let n(p) = 36*q(p) - 2*r(p). Let k(c) = 5*c. Give n(k(a)).
-100*a**2
Let x(z) = 5*z**2 + 4. Let p(t) = 14*t**2 + 11. Let a(m) = 4*p(m) - 11*x(m). Let k(h) = 6*h. What is a(k(s))?
36*s**2
Let h(a) = 7*a - 5. Let y(c) = 4*c - 3. Let l(m) = -3*h(m) + 5*y(m). Let q(b) = -7*b. Calculate q(l(t)).
7*t
Let w(s) = -9*s + 17. Let v(q) = -q + 2. Let b(t) = -51*v(t) + 6*w(t). Let l(y) = 3*y**2. What is b(l(n))?
-9*n**2
Let c(h) = 5*h**2. Let x(n) be the third derivative of n**6/360 - n**4/8 + 3*n**2. Let q(r) be the second derivative of x(r). Determine q(c(p)).
10*p**2
Let k(n) = -3*n**2 - 4*n - 1. Let f(u) = 4*u**2 + 5*u + 3. Let j(z) = -4*f(z) - 5*k(z). Let a(m) = m**2. Determine j(a(i)).
-i**4 - 7
Let m(k) = 11*k. Let a(t) = -9*t - 13*t + 24*t. Determine a(m(p)).
22*p
Let s(r) = r**3 - 4*r**2 - 6*r + 7. Let u be s(5). Let t(l) = -4*l + l**2 + 4*l + 0*l**u. Let g(k) = 3*k**2. Determine g(t(h)).
3*h**4
Let v(l) be the third derivative of -5*l**4/12 + 5*l**2. Let p(c) = 2*c. Determine p(v(y)).
-20*y
Let j(b) = -482*b. Let y(q) = -8*q**2. Give y(j(n)).
-1858592*n**2
Let v(z) = -z. Let x(f) be the first derivative of -6*f**2 + 2. Give x(v(a)).
12*a
Let d(b) = 9*b**2. Let a(y) = -4*y**2 + 6. Let g(f) = -9*f**2 + 13. Let l(u) = 13*a(u) - 6*g(u). Give d(l(h)).
36*h**4
Let q(r) = -7*r**2. Let h(m) be the third derivative of m**5/60 - 3*m**2. What is h(q(y))?
49*y**4
Let t(z) = 66*z**2. Let w(n) = 31*n**2 - 3. Determine w(t(g)).
135036*g**4 - 3
Let d(h) be the third derivative of -7*h**5/60 - 17*h**2. Let m(u) = -6*u. Determine d(m(n)).
-252*n**2
Let t(d) = -2*d. Let u(b) = -724*b**2 + 2. Give u(t(k)).
-2896*k**2 + 2
Let r(p) = 4*p - 3*p + p - 4*p. Let u(k) = -k**2 + 6*k**2 - 4*k**2. Calculate u(r(c)).
4*c**2
Suppose -x + 2*d + 2 = 0, -5*d - 4 = -3*x - 0. Let j be x/4 + 35/14. Let n(y) = -j*y - 4 + 4*y + 4. Let u(k) = -k. Give n(u(q)).
-2*q
Let a(l) be the third derivative of l**5/30 + 18*l**2. Suppose -8 = -5*y + 2. Let r(t) = 4*t**2 - t**2 + 5*t**y. What is a(r(k))?
128*k**4
Let w(s) = -4*s**2. Let n(j) = 502*j. Determine w(n(i)).
-1008016*i**2
Let i(m) be the second derivative of m**3 + 5*m. Let p(l) be the first derivative of -l**2 + 7. Give i(p(y)).
-12*y
Let a(u) = 11*u. Let v(x) = 0*x + 4*x - 3*x + x. What is a(v(b))?
22*b
Let q(o) be the third derivative of o**5/60 + 5*o**2. Let d(t) = 3*t**2. What is q(d(y))?
9*y**4
Let q(s) = s. Let b(g) = -10990*g. Give b(q(r)).
-10990*r
Let i(s) = -6*s + 2*s + 4 - 4. Let t(c) = c**2 - 4*c + 4. Let p(l) = -l**2 + 5*l - 5. Let u(d) = -4*p(d) - 5*t(d). Calculate i(u(n)).
4*n**2
Let r(b) be the third derivative of b**4/24 + 4*b**2. Let a(i) be the first derivative of -i**3 - 2. Give a(r(h)).
-3*h**2
Let v(t) = -2*t. Let g(s) = 47*s**2 + 9*s. Determine g(v(r)).
188*r**2 - 18*r
Let f(a) be the first derivative of 32*a**3/3 + 13. Let j(o) = 2*o**2. Calculate f(j(p)).
128*p**4
Let s(y) = 420*y. Let t(p) = -3*p**2. Give s(t(z)).
-1260*z**2
Let y(w) be the second derivative of -2*w**4/3 - w. Let g(j) be the first derivative of -j**3/3 - 219. Determine y(g(b)).
-8*b**4
Let s(d) = d. Let m(h) = h**2 - 4*h + 2. Let n be m(4). Let w(y) = y + 3*y - 7*y + n*y. Give s(w(p)).
-p
Let m(l) = 0*l + 2*l + 0*l. Let n(i) be the third derivative of 0*i + 3*i**2 + 0*i**3 - 1/12*i**4 + 0. Determine n(m(c)).
-4*c
Let z(d) = -15*d. Let o(l) = -3*l**2 + 2*l + 2. Let k(r) = -16*r**2 + 11*r + 11. Let t(w) = -2*k(w) + 11*o(w). Determine z(t(u)).
15*u**2
Let a(d) = -2*d**2. Let g = 7 - 5. Let p(b) = 8*b + b**g - 8*b. Determine p(a(q)).
4*q**4
Let i(r) = -4*r + 5*r - 2*r. Let z = -5 - -7. Let f(m) = m**2 - 2*m + 2. Let o(d) = d - 1. Let u(a) = z*o(a) + f(a). Calculate u(i(h)).
h**2
Let o(c) = 38*c - 1. Let f(x) = 7*x**2. Give o(f(g)).
266*g**2 - 1
Let w(b) = -b. Suppose -3 = -4*k - 19. Let q(y) = -y. Let c(n) = k*q(n) + 3*w(n). Let s(d) = -2*d**2. Give c(s(l)).
-2*l**2
Let f(g) = 2*g. Let p(l) = -7*l + 5. Let m(k) = -k + 1. Let x(a) = 15*m(a) - 3*p(a). Calculate x(f(z)).
12*z
Let d(u) = 497*u**2. Let x(s) = -4*s**2. Give d(x(j)).
7952*j**4
Let i(l) = -10*l. Let s(f) = 258*f**2. What is i(s(o))?
-2580*o**2
Let a(d) = 5*d. Let v(i) = 26*i. Let z(c) = -22*a(c) + 4*v(c). Let m(p) = 2*p. Let j(l) = -5*m(l) - 2*z(l). Let o(s) = 3*s**2. Give j(o(u)).
6*u**2
Let f(t) = 6*t - t - 3*t - 4*t. Let x(j) = -j + j - j**2. Give x(f(n)).
-4*n**2
Let s(m) = -m - 6*m + 44*m. Let v(x) = -2*x**2. What is v(s(a))?
-2738*a**2
Let d(n) = -4*n**2. Let t(j) = -304*j**2. Calculate t(d(c)).
-4864*c**4
Let i(l) = -14*l. Let f(c) = -10*c. Give i(f(u)).
140*u
Let k(m) = 3*m**2. Let f be (4/6)/((-4)/6). Let s be f/(21/(-6) - -3). Let h(a) = 39*a**s - 43*a**2 + 4 - 4. Determine h(k(r)).
-36*r**4
Let r(o) = 4*o. Let b(d) = -5*d**2 + 7*d. Determine r(b(f)).
-20*f**2 + 28*f
Let i(w) be the first derivative of 0*w + 1/2*w**2 - 3. Let x(g) = 0 + g**2 + 0. Give i(x(l)).
l**2
Let u be 2 - -2 - (-4 - -2). Suppose -2 + u = 2*y. Let z(p) = -5*p + 5*p - 3*p**y. Let q(s) = 4*s**2. Determine z(q(x)).
-48*x**4
Let x(o) = 363*o - 1. Let v(j) = -5*j**2. What is v(x(r))?
-658845*r**2 + 3630*r - 5
Let f(t) = t + 1495. Let m(q) = -3*q**2. Determine m(f(w)).
-3*w**2 - 8970*w - 6705075
Let a(l) = -l. Let f(n) = -n + 6*n + 3*n. Determine f(a(p)).
-8*p
Let k(d) = 4*d**2. Let y(a) = -6*a. Give y(k(v)).
-24*v**2
Let b(g) = 2*g**2. Let p(n) be the first derivative of 2*n**3/3 + 5. What is b(p(s))?
8*s**4
Let l(v) = v**2 - 3*v + 3. Let o(k) = -5*k**2 + 13*k - 13. Let r(d) = -26*l(d) - 6*o(d). Let t(w) = w. Let f(p) = 4*p. Let b(m) = 2*f(m) - 7*t(m). Give b(r(n)).
4*n**2
Let j(g) = 15*g**2 - 3. Let w(y) = -15*y**2. Calculate j(w(c)).
3375*c**4 - 3
Let j(x) = x**2. Let p(m) be the first derivative of m**5/15 - m**2 - 3. Let g(o) be the second derivative of p(o). Calculate j(g(n)).
16*n**4
Let d(j) = 3*j**2. Let z(y) = 5*y**2 - 3*y - 8. Let l(u) = -3*u**2 + 2*u + 5. Let a(g) = -8*l(g) - 5*z(g). Let w(c) = -c. Let k(b) = a(b) - w(b). Give k(d(v)).
-9*v**4
Let s(k) = -7486*k**2. Let f(m) = -m. Determine s(f(b)).
-7486*b**2
Let n(t) = -5*t**2 + t**2 + 0*t**2. Let r(d) be the third derivative of -d**7/2520 - d**4/12 - d**2. Let v(y) be the second derivative of r(y). Give v(n(a)).
-16*a**4
Let p(l) = -5*l**2. Let u(m) = -129*m**2. What is u(p(b))?
-3225*b**4
Let a(w) = w**2. Let l(b) be the third derivative of -b**4/24 + 9*b**2. Calculate a(l(t)).
t**2
Let m(h) = -11*h + 4. Let p(n) = 133*n - 49. Let q(s) = 49*m(s) + 4*p(s). Let t(g) = 2*g. Give t(q(j)).
-14*j
Let d(o) = -o**2 + o - 1. Let b be d(1). Let q be 2 - 0*b/(-2). Let p(w) = 0*w**2 + 6*w**q - 7*w**2. Let f(c) = -2*c. Determine f(p(u)).
2*u**2
Suppose -4*y + 3 + 5 = 0. Let o(i) = 6*i**y + 2*i**2 - 3*i**2 - 2*i**2. Let c(s) = -3*s. Calculate o(c(t)).
27*t**2
Let g(a) = -2*a. Let f(d) = d - 1. Let q be f(3). Let k(r) = r. Let i(z) = q*g(z) + 3*k(z). Let t(j) = -4*j. What is i(t(v))?
4*v
Let q(u) = -4*u. Let a(v) = 93*v. Calculate a(q(i)).
-372*i
Let a(p) = -2*p**2. Let w(d) = -d**3 - 3*d**2 - 3*d - 3. Let h be w(-3). Let c = h + -4. Let z(g) = -3*g**2 - g**c + 5*g**2. Determine a(z(l)).
-2*l**4
Let s(u) = 3*u**2. Let v(o) = 32*o**2. Give s(v(a)).
3072*a**4
Let v(u) = -11*u. Let c(a) = 7*a. L |
Lalisa Manoban is a Thai rapper, singer, dancer and model. She is based in South Korea. She goes by the stage name Lisa. She is known as a member of the female k-pop group Blackpink. In 2021, she released her first solo single album named LALISA. It was a huge success.
Lisa was born in Thailand on 27 March 1997. In 2010, she passed a YG Entertainment audition in Thailand. Many people took part in the audition but she was to only person to be selected. She was invited to sign a contract with them and was added as a member of Blackpink.
Single albums
Singles
Songwriting credits |
/*=============================================================================
Library: CTK
Copyright (c) German Cancer Research Center,
Division of Medical and Biological Informatics
Licensed under the Apache License, Version 2.0 (the "License");
you may not use this file except in compliance with the License.
You may obtain a copy of the License at
http://www.apache.org/licenses/LICENSE-2.0
Unless required by applicable law or agreed to in writing, software
distributed under the License is distributed on an "AS IS" BASIS,
WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
See the License for the specific language governing permissions and
limitations under the License.
=============================================================================*/
#ifndef CTKPLUGINSTORAGE_P_H
#define CTKPLUGINSTORAGE_P_H
#include <QUrl>
#include <QStringList>
#include <QSharedPointer>
// CTK class forward declarations
class ctkPluginArchive;
/**
* \ingroup PluginFramework
*
* Interface for managing all plugin meta-data and resources
*/
class ctkPluginStorage
{
public:
virtual ~ctkPluginStorage() {}
/**
* Insert a plugin (shared library) into the persistent storage
*
* @param location Location of the plugin.
* @param localPath Path to the plugin on the local file system
* @return Plugin archive object.
*/
virtual QSharedPointer<ctkPluginArchive> insertPlugin(const QUrl& location, const QString& localPath) = 0;
/**
* Insert a new plugin (shared library) into the persistent
* storagedata as an update
* to an existing plugin archive. To commit this data a call to
* <code>replacePluginArchive</code> is needed.
*
* @param old ctkPluginArchive to be replaced.
* @param updateLocation Location of the updated plugin.
* @param localPath Path to a plugin on the local file system.
* @return Plugin archive object.
*/
virtual QSharedPointer<ctkPluginArchive> updatePluginArchive(QSharedPointer<ctkPluginArchive> old,
const QUrl& updateLocation, const QString& localPath) = 0;
/**
* Replace old plugin archive with a new updated plugin archive, that
* was created with updatePluginArchive.
*
* @param oldPA ctkPluginArchive to be replaced.
* @param newPA new ctkPluginArchive.
*/
virtual void replacePluginArchive(QSharedPointer<ctkPluginArchive> oldPA, QSharedPointer<ctkPluginArchive> newPA) = 0;
/**
* Remove plugin archive from archives list and persistent storage.
* The plugin archive is deleted and must not be used afterwards, if
* this method returns \a true.
*
* @param pa Plugin archive to remove.
* @return true if element was removed.
*/
virtual bool removeArchive(QSharedPointer<ctkPluginArchive> pa) = 0;
/**
* Get all plugin archive objects.
*
* @return QList of all PluginArchives.
*/
virtual QList<QSharedPointer<ctkPluginArchive> > getAllPluginArchives() const = 0;
/**
* Get all plugins to start at next launch of framework.
* This list is sorted in increasing plugin id order.
*
* @return A List with plugin locations.
*/
virtual QList<QString> getStartOnLaunchPlugins() const = 0;
/**
* Close this plugin storage and all bundles in it.
*/
virtual void close() = 0;
};
#endif // CTKPLUGINSTORAGE_P_H
|
Yuji Hashimoto (born 13 May 1970) is a former Japanese football player.
Club career statistics
|-
|1993||rowspan="4"|Gamba Osaka||rowspan="4"|J. League 1||1||0||0||0||0||0||1||0
|-
|1994||15||0||3||0||0||0||18||0
|-
|1995||37||0||2||0||colspan="2"|-||39||0
|-
|1996||1||0||0||0||4||0||5||0
|-
|1997||rowspan="2"|Sagan Tosu||rowspan="2"|Football League||24||3||3||0||5||0||32||3
|-
|1998||24||1||0||0||colspan="2"|-||24||1
102||4||8||0||11||0||121||4
102||4||8||0||11||0||121||4
|} |
#!/usr/bin/env bash
cd ..
# Remove old builds
flutter clean
# Prepare iOS
flutter build ios
# Build Android
flutter build appbundle
cp build/app/outputs/bundle/release/app-release.aab ./lunasea.aab
|
The Englishman and the Girl is a 1910 American silent comedy movie directed by D. W. Griffith and stars Charles Craig, Mary Pickford, and George Nichols.
Actors
Charles Craig as Albert Wilberforce
Mary Pickford as The Girl
George Nichols as Mr. Thayer
Kate Bruce as Mrs. Thayer
Gladys Egan as The Child
Ruth Hart as A Friend
Dorothy West as A Friend/Member of Dramatic Club
Francis J. Grandon as In Store/Member of Dramatic Club
Anthony O'Sullivan as In Store/Member of Dramatic Club |
---
abstract: 'We combine the multivariate method of exchangeable pairs with Stein’s method for functional approximation and give a general linearity condition under which an abstract Gaussian approximation theorem for stochastic processes holds. We apply this approach to estimate the distance from a pre-limiting mixture process of a sum of random variables chosen from an array according to a random permutation and prove a functional combinatorial central limit theorem. We also consider a graph-valued process and bound the speed of convergence of the joint distribution of its rescaled edge and two-star counts to a two-dimensional continuous Gaussian process.'
address: |
Université du Luxembourg\
Unité de Recherche en Mathématiques\
Maison du Nombre\
6 Avenue de la Fonte\
L-4364 Esch-sur-Alzette\
Luxembourg\
\
author:
-
bibliography:
- 'Bibliography.bib'
title: 'Multivariate functional approximations via Stein’s method of exchangeable pairs'
---
,
Introduction
============
In [@stein] Stein observed that a random variable $Z$ has standard normal law if and only if $$\label{stein_identity}
\mathbbm{E}Zf(Z)=\mathbbm{E}f'(Z)$$ for all smooth functions $f$. Therefore, if, for a random variable $W$ with mean $0$ and variance $1$, $$\label{stein_equation}
|\mathbbm{E}f'(W)-\mathbbm{E}Wf(W)|$$ is close to zero for a large class of functions $f$, then the law of $W$ should be approximately Gaussian. In [@stein1], Stein combined this observation with his *exchangeable-pair* approach. Therein, for a centred and scaled random variable $W$, its copy $W'$ is constructed in such a way that $(W,W')$ forms an exchangeable pair and the linear regression condition: $$\label{regression_condition}
\mathbbm{E}\left[W'-W|W\right]=-\lambda W$$ is satisfied for some $\lambda>0$. This, in many cases, simplifies the process of obtaining bounds on the distance of $W$ from the normal distribution.
This approach was extended in [@rinott] to examples in which an approximate linear regression condition holds: $$\mathbbm{E}\left[W'-W|W\right]=-\lambda W+R$$ for some remainder $R$. A multivariate version of the method was first described in [@meckes] and then in [@reinert_roellin]. In [@reinert_roellin], for an exchangeable pair of $d$-dimensional vectors $(W,W')$ the following condition is used: $$\mathbbm{E}[W'-W|W]=-\Lambda W+R$$ for some invertible matrix $\Lambda$ and a remainder term $R$. The approach of [@reinert_roellin] was further reinterpreted and combined with the approach of [@meckes] in [@meckes09].
On the other hand, in the seminal paper [@diffusion], Barbour addressed the problem of providing bounds on the rate of convergence in functional limit results (or invariance principles as they are often called in the literature). He observed that Stein’s logic of [@stein] may also be used in the setup of the Functional Central Limit Theorem. He found a condition, similar to (\[stein\_identity\]), characterising the distribution of a standard real Wiener process. Combined with Taylor’s theorem, it allowed Barbour to obtain a bound on the rate of convergence in the celebrated Donsker’s invariance principle.
This paper is the first attempt to combine the method of exchangeable pairs with functional approximations. We do so in the context of multivariate processes and provide a novel approach to bounding their distances from Gaussian processes. Our approach is influenced by the setup of [@reinert_roellin] and [@diffusion].
Motivation
----------
We are motivated by a number of (finite-dimensional) examples studied in Stein’s method literature using exchangeable pairs, which could be extended to the functional setting. Functional limit results play an important role in applied fields. Researchers often choose to model discrete phenomena with continuous processes arising as scaling limits of discrete ones. The reason is that those scaling limits may be studied using stochastic analysis and are more robust to changes in local details. Questions about the rate of convergence in functional limit results are equivalent to ones about the error those researchers make. Obtaining bounds on a certain distance between the scaled discrete and the limiting continuous processes provides a way of quantifying this error.
We consider two main examples. The first one is a combinatorial functional central limit theorem. The second one considers a two-dimensional process representing edge and two-star counts in a graph-valued process created by unveiling subsequent vertices of a Bernoulli random graph as time progresses.
The former is a functional version of the result proved qualitatively in [@chen_ho] and quantitatively in [@chen2015] and an extension of the main result of [@functional_combinatorial]. It considers an array $\left\lbrace X_{i,j}:i,j=1,\cdots,n\right\rbrace$ of i.i.d. random variables, which are then used to create a stochastic process: $$\label{process}
t\mapsto \frac{1}{s_n}\sum_{i=1}^{\lfloor nt\rfloor}X_{i\pi(i)},$$ where $s_n$ is the variance of $\sum_{i=1}^n X_{i\pi(i)}$ and $\pi$ is a uniform random permutation on $\lbrace 1,\cdots,n\rbrace$. The motivation for studying this and similar topics comes from permutation tests in non-parametric statistics. Similar setups, yet with a deterministic array of numbers, and in a finite-dimensional context, have also been considered by other authors (see [@wald_wolfowitz] for one of the first works on this topic and [@bolthausen], [@goldstein], [@neammanee] for quantitative results).
The second example, which considers Bernoulli random graphs, goes back to [@Janson1991]. It was first studied using exchangeable pairs in a finite-dimensional context in [@reinert_roellin1], where a random vector whose components represent statistics corresponding to the number of edges, two-stars and triangles is studied. The authors bound its distance from a normal distribution. We consider a functional analogue of this result, concentrating, for simplicity, only on the number of edges and two-stars. Our approach can, however, be also easily extended to encompass the number of triangles. All of those statistics are often of interest in applications, for example, when approximating the clustering coefficient of a network or in conditional uniform graph tests.
Contribution of the paper
-------------------------
The main achievements of the paper are the following:
1. An abstract approximation theorem (Theorem \[theorem1\]), providing a bound on the distance between a stochastic process $\mathbf{Y}_n$ valued in $\mathbbm{R}^p$ for some positive integer $p$ and a Gaussian mixture process. The theorem assumes that the process $\mathbf{Y}_n$ satisfies the linear regression condition $$Df(\mathbf{Y}_n)[\mathbf{Y}_n]=2\mathbbm{E}\left\lbrace Df(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right]|\mathbf{Y}_n\right\rbrace+R_f,$$ for all functions $f$ in a certain class of test functions, some matrix $\Lambda_n$ and some random variable $R_f=R_f(\mathbf{Y}_n)$. As noted in Remark \[remark\_th\_1\], this condition is an analogue of the condition considered in [@reinert_roellin]. Theorem \[theorem1\] is used in the derivation of the remaining results of this paper.
2. A novel functional combinatorial central limit theorem. In Theorem \[combi\_pre\_lim\], we establish a bound on the distance between process (\[process\]) and a Gaussian mixture, piecewise constant process. Furthermore, a qualitative result showing convergence of process (\[process\]) to a continuous Gaussian limiting process is provided in Theorem \[conv\_cont\_theorem\]. Thus, we extend [@functional_combinatorial], where similar results were proved under the assumption that all the $X_{i,j}$’s for $i,j=1,\cdots,n$ are deterministic. Our bound is also an extension of [@chen2015], where a bound on the rate of weak convergence of the law of $\frac{1}{s_n}\sum_{i=1}^nX_{i\pi(i)}$ to the standard normal distribution is obtained.
3. A novel functional limit theorem for statistics corresponding to edge and two-star counts in a Bernoulli random graph, together with a bound on the rate of convergence. We consider a Bernoulli random graph $G(n,p)$ on $n$ vertices with edge probabilities $p$. Letting $I_{i,j}$, for $i,j=1,\cdots,n$ be the indicator that edge $(i,j)$ is present in the graph, we study a scaled statistic representing the number of edges: $$\mathbf{T}_n(t)=\frac{\lfloor nt\rfloor -2}{2n^2}\sum_{i,j=1}^{\lfloor nt\rfloor}I_{i,j},\quad t\in[0,1]$$ and another one, representing the number of two-stars (i.e. subgraphs which are trees with one internal node and $2$ leaves): $$\mathbf{V}_n(t)=\frac{1}{2n^2}\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq\lfloor nt\rfloor}}I_{i,j}I_{j,k},\quad t\in[0,1].$$ Theorem \[theorem\_pre\_limiting\] provides a bound on the distance between the law of the process $$\label{graph_ex}
t\mapsto \left(\mathbf{T}_n(t)-\mathbbm{E}\mathbf{T}_n(t),\mathbf{V}_n(t)-\mathbbm{E}\mathbf{V}_n(t)\right),\quad t\in[0,1]$$ and the law of a piecewise constant Gaussian process. Theorem \[theorem\_continuous\] bounds a distance between the law of (\[graph\_ex\]) and the distribution of a two-dimensional continuous Gaussian process.
Stein’s method of exchangeable pairs
------------------------------------
The idea behind the exchangeable-pair approach of [@stein1] was the following. In order to obtain a bound on a distance between the distribution of a centred and scaled random variable $W$ and the standard normal law, one can bound (\[stein\_equation\]) for functions $f$ coming from a suitable class. Supposing that we can construct a $W'$ such that $(W,W')$ is an exchangeable pair and (\[regression\_condition\]) is satisfied, we can write $$\begin{aligned}
0=&\mathbbm{E}\left[(f(W)+f(W'))(W-W')\right]\\
=&\mathbbm{E}\left[(f(W')-f(W))(W-W')\right]+2\mathbbm{E}\left[f(W)\mathbbm{E}[W-W'|W]\right]\\
=&\mathbbm{E}\left[(f(W')-f(W))(W-W')\right]+2\lambda\mathbbm{E}[Wf(W)].\end{aligned}$$ It follows that $$\mathbbm{E}[Wf(W)]=\frac{1}{2\lambda}\mathbbm{E}\left[(f(W)-f(W'))(W-W')\right].$$ Therefore, using Taylor’s theorem, $$\begin{aligned}
&\left|\mathbbm{E}[f'(W)]-\mathbbm{E}[Wf(W)]\right|\\
=&\left|\mathbbm{E}[f'(W)]+\frac{1}{2\lambda}\mathbbm{E}\left[(f(W')-f(W))(W-W')\right]\right|\\
\leq&\left|\mathbbm{E}f'(W)-\frac{1}{2\lambda}\mathbbm{E}f'(W)(W-W')^2\right|+\frac{\|f''\|_{\infty}}{2\lambda}\mathbbm{E}|W-W'|^3\\
\leq&\|f'\|_{\infty}\mathbbm{E}\left|\mathbbm{E}\left[\frac{1}{2\lambda}(W-W')^2|W\right]-1\right|+\frac{\|f''\|_{\infty}}{2\lambda}\mathbbm{E}|W-W'|^3\\
\leq&\frac{\|f'\|_{\infty}}{2\lambda}\sqrt{\text{Var}\left[\mathbbm{E}\left[(W-W')^2|W\right]\right]}+\frac{\|f''\|_{\infty}}{2\lambda}\mathbbm{E}|W-W'|^3,\end{aligned}$$ which provides the desired bound.
Before the publication of [@meckes; @reinert_roellin; @meckes09] the method was restricted to one-dimensional approximations. It was, however, also used in the context of non-normal approximations (e.g [@chatterjee; @chatterjee1; @roellin1]). More recently several authors have extended and applied the method. D[ö]{}bler extended it to Beta distribution in [@dobler] and Chen and Fang used it for the combinatorial CLT [@chen2015].
Stein’s method in its generality
--------------------------------
The aim of the general version of Stein’s method is to find a bound of the quantity $|\mathbbm{E}_{\nu_n}h-\mathbbm{E}_{\mu}h|$, where $\mu$ is the target (known) distribution, $\nu_n$ is the approximating law and $h$ is chosen from a suitable class of real-valued test functions $\mathcal{H}$. The procedure can be described in terms of three steps. First, an operator $\mathcal{A}$ acting on a class of real-valued functions is sought, such that $$\left(\forall f\in\text{Domain}(\mathcal{A})\quad\mathbbm{E}_{\nu}\mathcal{A}f=0\right)\quad \Longleftrightarrow \quad\nu=\mu,$$ where $\mu$ is our target distribution. Then, for a given function $h\in\mathcal{H}$, the following Stein equation: $$\mathcal{A}f=h-\mathbbm{E}_{\mu}h$$ is solved. Finally, using properties of the solution and various mathematical tools (among which the most popular are Taylor’s expansions in the continuous case, Malliavin calculus, as described in [@nourdin], and coupling methods), a bound is sought for the quantity $|\mathbbm{E}_{\nu_n}\mathcal{A}f_h|$.
Approximations by laws of stochastic processes have not been covered in the Stein’s method literature very widely, with the notable exceptions of [@diffusion; @functional_combinatorial; @Coutin] and recently [@kasprzak1; @kasprzak2; @decreusefond2]. [@kasprzak1; @decreusefond2] establish a method for bounding the speed of weak convergence of continuous-time Markov chains satisfying certain assumptions to diffusion processes. [@kasprzak2], on the other hand, treats multi-dimensional processes represented by scaled sums of random variables with different dependence structures using Stein’s method and establishes bounds on their distances from continuous Gaussian processes.
Structure of the paper
----------------------
The paper is organised as follows. In Section \[section22\] we introduce the spaces of test functions which will be used in the main results, and quote results showing that, under certain assumptions, they determine convergence in distribution under the uniform topology. In Section \[section33\] we set up the Stein equation for approximation by a pre-limiting process and provide properties of the solutions. In Section \[section4\] we provide an exchangeable-pair condition and prove an abstract exchangeable-pair-type approximation theorem. Section \[section5\] is devoted to the functional combinatorial central limit theorem example and Section \[section6\] discusses the graph-valued process example.
Spaces $M$, $M^1$, $M^2$, $M^0$ {#section22}
===============================
The following notation, similar to the one of [@kasprzak2], is used throughout the paper. For a function $w$ defined on the interval $[0,1]$ and taking values in a Euclidean space, we define $$\|w\|=\sup_{t\in[0,1]}|w(t)|,$$ where $|\cdot|$ denotes the Euclidean norm. We also let $D^p=D([0,1],\mathbbm{R}^p)$ be the Skorokhod space of all càdlàg functions on $[0,1]$ taking values in $\mathbbm{R}^p$. In the sequel, for $i=1,\cdots,p$, $e_i$ will denote the $i$th unit vector of the canonical basis of $\mathbbm{R}^p$ and the $i$th component of $x\in\mathbbm{R}^p$ will be represented by $x^{(i)}$, i.e. $x=\left(x^{(1)},\cdots,x^{(p)}\right)$. We will often write $\mathbbm{E}^W[\,\cdot\,]$ instead of $\mathbbm{E}[\,\cdot\,|W]$.
Let $p\in\mathbbm{N}$. Let us define: $$\|f\|_L:=\sup_{w\in D^p}\frac{|f(w)|}{1+\|w\|^3}\text{,}$$ and let $L$ be the Banach space of continuous functions $f:D^p\to\mathbbm{R}$ such that $\|f\|_L<\infty$. Following [@diffusion], we now let $M\subset L$ consist of the twice Fréchet differentiable functions $f$, such that: $$\label{space_m}
\|D^2f(w+h)-D^2f(w)\|\leq k_f\|h\|\text{,}$$ for some constant $k_f$, uniformly in $w,h\in D^p$. By $D^kf$ we mean the $k$-th Fréchet derivative of $f$ and the norm of a $k$-linear form $B$ on $L$ is defined to be $\|B\|=\sup_{\lbrace h:\|h\|=1\rbrace} |B[h,...,h]|$. Note the following lemma, which can be proved in an analogous way to that used to show (2.6) and (2.7) of [@diffusion]. We omit the proof here.
\[first\_der\] For every $f\in M$, let: $$\begin{aligned}
\|f\|_M:=&\sup_{w\in D^p}\frac{|f(w)|}{1+\|w\|^3}+\sup_{w\in D^p}\frac{\|Df(w)\|}{1+\|w\|^2}+\sup_{w\in D^p}\frac{\|D^2f(w)\|}{1+\|w\|}\\
&+\sup_{w,h\in D^p}\frac{\|D^2f(w+h)-D^2f(w)\|}{\|h\|}.\end{aligned}$$ Then, for all $f\in M$, we have $\|f\|_M<\infty$.
For future reference, we let $ M^1\subset M$ be the class of functionals $g\in M$ such that: $$\begin{aligned}
\|g\|_{M^1}:=&\sup_{w\in D^p}\frac{|g(w)|}{1+\|w\|^3}+\sup_{w\in D^p}\|Dg(w)\|+\sup_{w\in D^p}\|D^2g(w)\|\nonumber\\
&+\sup_{w,h\in D^p}\frac{\|D^2f(w+h)-D^2f(w)\|}{\|h\|}<\infty\label{m_1}\end{aligned}$$ and $ M^2\subset M$ be the class of functionals $g\in M$ such that: $$\begin{aligned}
\|g\|_{M^2}:=&\sup_{w\in D^p}\frac{|g(w)|}{1+\|w\|^3}+\sup_{w\in D^p}\frac{\|Dg(w)\|}{1+\|w\|}+\sup_{w\in D^p}\frac{\|D^2g(w)\|}{1+\|w\|}\nonumber\\
&+\sup_{w,h\in D^p}\frac{\|D^2f(w+h)-D^2f(w)\|}{\|h\|}<\infty\text{.}\label{m_2}\end{aligned}$$
We also let $M^0$ be the class of functionals $g\in M$ such that: $$\begin{aligned}
\|g\|_{M^0}:=&\sup_{w\in D^p}|g(w)|+\sup_{w\in D^p}\|Dg(w)\|+\sup_{w\in D^p}\|D^2g(w)\|\nonumber\\
&+\sup_{w,h\in D^p}\frac{\|D^2f(w+h)-D^2f(w)\|}{\|h\|}<\infty\text{.}\nonumber\end{aligned}$$ We note that $M^0\subset M^1\subset M^2\subset M$. The next proposition is a $p$-dimensional version of [@functional_combinatorial Proposition 3.1] and shows conditions, under which convergence of the sequence of expectations of a functional $g$ under the approximating measures to the expectation of $g$ under the target measure for all $g\in M^0$ implies weak convergence of the measures of interest. Its proof can be found in the appendix of [@kasprzak2].
$\mathbf{Y}\in D\left([0,1],\mathbbm{R}^p\right)$ is piecewise constant if $[0,1]$ can be divided into intervals of constancy $[a_k,a_{k+1})$ such that the Euclidean norm of $(\mathbf{Y}(t_1)-\mathbf{Y}(t_2))$ is equal to $0$ for all $t_1,t_2\in[a_k,a_{k+1})$.
\[prop\_m\] Suppose that, for each $n\geq 1$, the random element $\mathbf{Y}_n$ of $D^p$ is piecewise constant with intervals of constancy of length at least $r_n$. Let $\left(\mathbf{Z}_n\right)_{n\geq 1}$ be random elements of $D^p$ converging weakly in $D^p$, with respect to the Skorokhod topology, to a random element $\mathbf{\mathbf{Z}}\in C\left([0,1],\mathbbm{R}^p\right)$. If: $$\label{assumption}
|\mathbbm{E}g(\mathbf{Y}_n)-\mathbbm{E}g(\mathbf{\mathbf{Z}}_n)|\leq C\mathscr{T}_n\|g\|_{M^0}$$ for each $g\in M^0$ and if $\mathscr{T}_n\log^2(1/r_n)\xrightarrow{n\to\infty}0$, then $\mathbf{Y}_n\Rightarrow \mathbf{\mathbf{Z}}$ (converges weakly) in $D^p$, in both the uniform and the Skorokhod topology.
Setting up Stein’s method for the pre-limiting approximation {#section33}
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The steps of the construction presented in this section will be similar to those used to set up Stein’s method in [@diffusion] and [@kasprzak2]. After defining the process $\mathbf{D}_n$ whose distribution will be the target measure in Stein’s method, we will construct a process $\left(\mathbf{W}_n(\cdot,u):u\geq 0\right)$ for which the target measure is stationary. We will then calculate its infinitesimal generator $\mathcal{A}_n$ and take it as our Stein operator. Next, we solve the Stein equation $\mathcal{A}_nf=g$ using the analysis of [@kasprzak] and prove some properties of the solution $f_n=\phi_n(g)$, with the most important one being that its second Fréchet derivative is Lipschitz.
Target measure
--------------
Let $$\label{d_n}
\mathbf{D}_n(t)=\sum_{i_1,\cdots,i_m=1}^{n}\left(\tilde{Z}^{(1)}_{i_1,\cdots,i_m}J^{(1)}_{i_1,\cdots,i_m}(t),\cdots,\tilde{Z}^{(p)}_{i_1,\cdots,i_m}J^{(p)}_{i_1,\cdots,i_m}(t)\right),\quad t\in[0,1],$$ where $\tilde{Z}^{(k)}_{i_1,\cdots,i_m}$’s for $k=1,\cdots,p$ are centred Gaussian and:
1. the covariance matrix $\Sigma_n\in\mathbbm{R}^{(n^mp)\times(n^mp)}$ of the vector $\tilde{Z}$ is positive definite, where $\tilde{Z}\in \mathbbm{R}^{(n^mp)}$ is formed out of the $\tilde{Z}^{(k)}_{i_1,\cdots,i_m}$’s in such a way that they appear in the lexicographic order with $\tilde{Z}^{(k)}_{i_1,\cdots,i_m}$ appearing before $\tilde{Z}^{(k+1)}_{j_1,\cdots,j_m}$’s for any $k=1,\cdots,p-1$ and $i_1,\cdots,i_m,j_1,\cdots,j_m=1,\cdots,n$;
2. $J^{(k)}_{i_1,\cdots,i_m}\in D\left([0,1],\mathbbm{R}\right)$, for $i_1,\cdots,i_m\in\lbrace 1,\cdots, n\rbrace$, $k\in\lbrace 1,\cdots,p\rbrace$, are independent of the $\tilde{Z}^{(k)}_{i_1,\cdots,i_m}$’s. A typical example would be $J^{(k)}_{i_1,\cdots,i_m}=\mathbbm{1}_{A^{(k)}_{i_1,\cdots,i_m}}$ for some measurable set $A^{(k)}_{i_1,\cdots,i_m}$.
It is worth noting that processes $\mathbf{D}_n$ taking the form (\[d\_n\]) often approximate interesting continuous Gaussian processes very well. An example is a Gaussian scaled random walk, i.e. $\mathbf{D}_n$ of (\[d\_n\]), where all the $\tilde{Z}^{(k)}_{i_1,\cdots,i_m}$’s are standard normal and independent, $m=1$ and $J_i^{(k)}=\mathbbm{1}_{[i/n,1]}$ for all $k=1,\cdots,p$ and $i=1,\cdots,n$. It approximates Brownian Motion. By Proposition \[prop\_m\], under several assumptions, proving by Stein’s method that a piece-wise constant process $\mathbf{Y}_n$ is close enough to process $\mathbf{D}_n$ proves $\mathbf{Y}_n$’s convergence in law to the continuous process that $\mathbf{D}_n$ approximates.
Now let $\lbrace (\mathscr{X}^{(k)}_{i_1,\cdots,i_m}(u),u\geq 0):i_1,\cdots,i_m=1,...,n,k=1,...,p\rbrace$ be an array of i.i.d. Ornstein-Uhlenbeck processes with stationary law $\mathcal{N}(0,1)$, independent of the $J^{(k)}_{i_1,\cdots,i_m}$’s. Consider $\tilde{\mathscr{U}}(u)=\left(\Sigma_n\right)^{1/2}\mathscr{X}(u)$, where $\mathscr{X}(u)\in\mathbbm{R}^{n^mp}$ is formed out of the $\mathscr{X}^{(k)}_{i_1,\cdots,i_m}(u)$’s in such a way that they appear in the same order as the $\tilde{Z}^{(k)}_{i_1,\cdots,i_m}$’s appear in $\tilde{Z}$. Write $\mathscr{U}_{i_1,\cdots,i_m}^{(k)}(u)=\left(\tilde{\mathscr{U}}(u)\right)_{I(k,i_1,\cdots,i_m)}$ using the bijection $I:\lbrace (k,i_1,\cdots,i_m):i_1,\cdots,i_m=1,\cdots, n, k=1,\cdots, p\rbrace\to\lbrace 1,\cdots,pn^m\rbrace$, given by: $$\label{i}
I(k,i_1,\cdots,i_m)=(k-1)n^m+(i_1-1)n^{m-1}+\cdots+(i_{m-1}-1)n+i_m.$$ Consider a process: $$\mathbf{W}_n(t,u)=\left(\mathbf{W}_n^{(1)}(t,u),\cdots,\mathbf{W}_n^{(p)}(t,u)\right),\quad t\in[0,1],u\geq 0,$$ where, for all $k=1,\cdots,p$: $$\mathbf{W}_n^{(k)}(t,u)=\sum_{i_1,\cdots,i_m=1}^{n}\mathscr{U}^{(k)}_{i_1,\cdots,i_m}(u)J^{(k)}_{i_1,\cdots,i_m}(t),\quad t\in[0,1],u\geq 0.$$ It is easy to see that the stationary law of the process $\left(\mathbf{W}_n(\cdot,u)\right)_{u\geq 0}$ is exactly the law of $\mathbf{D}_n$.
Stein equation
--------------
By [@kasprzak2 Propositions 4.1 and 4.4], the following result is immediate:
\[prop12.7\] The infinitesimal generator of the process $\left(\mathbf{W}_n(\cdot,u)\right)_{u\geq 0}$ acts on any $f\in M$ in the following way: $$\begin{aligned}
&\mathcal{A}_nf(w)=-Df(w)[w]+\mathbbm{E}D^2f(w)\left[\mathbf{D}_n^{(2)}\right].\end{aligned}$$ Moreover, for any $g\in M$ such that $\mathbbm{E}g(\mathbf{D}_n)=0$, the Stein equation $\mathcal{A}_nf_n=g$ is solved by: $$\label{phi}
f_n=\phi_n(g)=-\int_0^{\infty}T_{n,u}gdu,$$ where $(T_{n,u}f)(w)=\mathbbm{E}\left[f(we^{-u}+\sqrt{1-e^{-2u}}\mathbf{D}_n(\cdot)\right]$ Furthermore, for $g\in M$: $$\begin{aligned}
\text{A)} \quad &\|D\phi_n(g)(w)\|\leq \|g\|_{ M}\left(1+\frac{2}{3}\|w\|^2+\frac{4}{3}\mathbbm{E}\|\mathbf{D}_n\|^2\right)\text{,}\nonumber\\
\text{B)} \quad &\|D^2\phi_n(g)(w)\|\leq \|g\|_{ M}\left(\frac{1}{2}+\frac{\|w\|}{3}+\frac{\mathbbm{E}\|\mathbf{D}_n\|}{3}\right)\text{,}\nonumber\\
\text{C)}\quad&\frac{\left\|D^2\phi_n(g)(w+h)-D^2\phi_n(g)(w)\right\|}{\|h\|}\nonumber\\
\leq&\sup_{w,h\in D^p}\frac{\|D^2(g+c)(w+h)-D^2(g+c)(w)\|}{3\|h\|},\nonumber\end{aligned}$$ for any constant function $c:D^p\to\mathbbm{R}$ and for all $w,h\in D^p$. Moreover, for all $g\in M^1$, as defined in (\[m\_1\]), $$\begin{aligned}
\text{A)}\quad&\|D\phi_n(g)(w)\|\leq \|g\|_{ M^1},\nonumber\\
\text{B)}\quad&\|D^2\phi_n(g)(w)\|\leq \frac{1}{2}\|g\|_{ M^1}\nonumber\end{aligned}$$ and for all $g\in M^2$, as defined in (\[m\_2\]), $$\begin{aligned}
\|D\phi_n(g)(w)\|\leq \|g\|_{ M^2}\nonumber.\end{aligned}$$
An abstract approximation theorem {#section4}
=================================
We now present a theorem which provides an expression for a bound on the distance between some process $\mathbf{Y}_n$ and $\mathbf{D}_n$, defined by (\[d\_n\]), provided that we can find some $\mathbf{Y}_n'$ such that $(\mathbf{Y}_n,\mathbf{Y}_n')$ is an exchangeable pair satisfying an appropriate condition. Our condition (\[condition\]) is similar to that of [@reinert_roellin (1.7)], as we explain in Remark \[remark\_th\_1\].
\[theorem1\] Assume that $(\mathbf{Y}_n,\mathbf{Y}_n')$ is an exchangeable pair of $D\left([0,1],\mathbbm{R}^p\right)$-valued random vectors such that: $$Df(\mathbf{Y}_n)[\mathbf{Y}_n]=2\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right]+R_f,
\label{condition}$$ where $\mathbbm{E}^{\mathbf{Y}_n}[\cdot]:=\mathbbm{E}\left[\cdot|\mathbf{Y}_n\right]$, for all $f\in M$, some $\Lambda_n\in\mathbbm{R}^{p\times p}$ and some random variable $R_f=R_f(\mathbf{Y}_n)$. Let $\mathbf{D}_n$ be defined by (\[d\_n\]). Then, for any $g\in M$: $$\begin{aligned}
\left|\mathbbm{E}g(\mathbf{Y}_n)-\mathbbm{E}g(\mathbf{D}_n)\right|\leq \epsilon_1+\epsilon_2+\epsilon_3\end{aligned}$$ where $f=\phi_n(g)$, as defined by (\[phi\]), and $$\begin{aligned}
\epsilon_1&=\frac{\|g\|_M}{6}\mathbbm{E}\|(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\|\|\mathbf{Y}_n-\mathbf{Y}_n'\|^2,\\
\epsilon_2&=\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]\right|,\\
\epsilon_3&=|\mathbbm{E}R_f|.\end{aligned}$$
Term $\epsilon_1$ measures how close $\mathbf{Y}_n$ and $\mathbf{Y}_n'$ are and how *small* (in a certain sense) $\Lambda_n$ is. Term $\epsilon_2$ corresponds to the comparison of the covariance structure of $\mathbf{Y}_n-\mathbf{Y}_n'$ and $\mathbf{D}_n$. Estimating this term usually requires some effort yet is possible in several applications (see Theorem \[combi\_pre\_lim\] and \[theorem\_pre\_limiting\] below). Term $\epsilon_3$ measures the error in the exchangeable-pair linear regression condition (\[condition\]).
Condition (\[condition\]) is always satisfied, for example with $\Lambda_n=0$ and $R_f=Df(\mathbf{Y}_n)[\mathbf{Y}_n]$ for all $f\in M$. However, for the bound in Theorem \[theorem1\] to be small, we require the expectation of $R_f$ to be small in absolute value.
The term $$\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]\right|$$ in the bound obtained in Theorem \[theorem1\] is an analogue of the second condition in [@meckes09 Theorem 3]. Therein, a bound on approximation by $\mathcal{N}(0,\Sigma)$ of a $d$-dimensional vector $X$ is obtained by constructing an exchangeable pair $(X,X')$ satisfying: $$\mathbbm{E}^X[X'-X]=\Lambda X+E\quad\text{and}\quad\mathbbm{E}^X[(X'-X)(X'-X)^T]=2\Lambda\Sigma+E'$$ for some invertible matrix $\Lambda$ and some remainder terms $E$ and $E'$. In the same spirit, Theorem \[theorem1\] could be rewritten to assume (\[condition\]) and: $$\mathbbm{E}^{\mathbf{Y}_n}D^2f(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]=D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]+R^1_f.$$ The bound would then take the form: $$\begin{aligned}
\left|\mathbbm{E}g(\mathbf{Y}_n)-\mathbbm{E}g(\mathbf{D}_n)\right|\leq&\frac{\|g\|_M}{6}\mathbbm{E}\|(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\|\|\mathbf{Y}_n-\mathbf{Y}_n'\|^2+|\mathbbm{E}R_f|+|\mathbbm{E}R^1_f|.\end{aligned}$$
\[remark\_th\_1\] The role of $\Lambda_n$ in condition (\[condition\]) is equivalent to that played by $\Lambda^{-1}$ in [@reinert_roellin] for $\Lambda$ defined by (1.7) therein. As also observed in [@reinert_roellin], the condition involving a matrix $\Lambda$ is a generalisation of the condition of [@meckes Theorem 1], where a scalar is used instead. It should be noted that condition (\[condition\]) is more appropriate in the functional setting than a straightforward adaptation of the condition of [@reinert_roellin]. This is due to the fact that for general processes $\mathbf{Y}_n$ the properties of the Fréchet derivative do not allow us to treat evaluating the derivative in the direction of $\mathbf{Y}_n-\mathbf{Y}_n'$ as matrix multiplication and multiplying both sides of the hypothetical condition: $$-Df(\mathbf{Y}_n)[\Lambda \mathbf{Y}_n]=\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)[\mathbf{Y}_n-\mathbf{Y}_n']$$ by $\Lambda^{-1}$ does not give: $$-Df(\mathbf{Y}_n)[\mathbf{Y}_n]=\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)[\Lambda^{-1}(\mathbf{Y}_n-\mathbf{Y}_n')].$$
Our aim is to bound $\left|\mathbbm{E}g(\mathbf{Y}_n)-\mathbbm{E}g(\mathbf{D}_n)\right|$ by bounding $\left|\mathbbm{E}\mathcal{A}_nf(\mathbf{Y}_n)\right|$, where $f$ is the solution to the Stein equation: $$\mathcal{A}_nf=g-\mathbbm{E}g(\mathbf{D}_n),$$ for $\mathcal{A}_n$ defined in Proposition \[prop12.7\]. Note that, by exchangeability of $(\mathbf{Y}_n,\mathbf{Y}_n')$ and (\[condition\]): $$\begin{aligned}
0=&\mathbbm{E}\left(Df(\mathbf{Y}_n')+Df(\mathbf{Y}_n)\right)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right]\\
=&\mathbbm{E}\left(Df(\mathbf{Y}_n')-Df(\mathbf{Y}_n)\right)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right]+2\mathbbm{E}\left\lbrace\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right]\right\rbrace\\
=&\mathbbm{E}\left(Df(\mathbf{Y}_n')-Df(\mathbf{Y}_n)\right)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right]+\mathbbm{E}Df(\mathbf{Y}_n)[\mathbf{Y}_n]-\mathbbm{E}R_f\end{aligned}$$ and so: $$\mathbbm{E}Df(\mathbf{Y}_n)[\mathbf{Y}_n]=\mathbbm{E}\left(Df(\mathbf{Y}_n)-Df(\mathbf{Y}_n')\right)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right]+\mathbbm{E}R_f.$$ Therefore: $$\begin{aligned}
&\left|\mathbbm{E}\mathcal{A}_nf(\mathbf{Y}_n)\right|\nonumber\\
=&\left|\mathbbm{E}Df(\mathbf{Y}_n)[\mathbf{Y}_n]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]\right|\nonumber\\
=&\left|\mathbbm{E}\left(Df(\mathbf{Y}_n)-Df(\mathbf{Y}_n')\right)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]+\mathbbm{E}R_f\right|\nonumber\\
\leq& \left|\mathbbm{E}\left(Df(\mathbf{Y}_n)-Df(\mathbf{Y}_n')\right)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right]-\mathbbm{E}D^2f(\mathbf{Y}_n')\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]\right|\nonumber\\
&+\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]\right|+|\mathbbm{E}R_f|\nonumber\\
\leq&\frac{\|g\|_M}{6}\mathbbm{E}\|(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\|\|\mathbf{Y}_n-\mathbf{Y}_n'\|^2+|\mathbbm{E}R_f|\nonumber\\
&+\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]\right|,\nonumber\end{aligned}$$ where the last inequality follows by Taylor’s theorem and Proposition \[prop12.7\].
A functional Combinatorial Central Limit Theorem {#section5}
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In this section we consider a functional version of the result proved in [@chen_ho]. Our object of interest is a stochastic process represented by a scaled sum of independent random variables chosen from an $n\times n$ array. Only one random variable is picked from each row and for row $i$, the corresponding random variable is picked from column $\pi(i)$, where $\pi$ is a random permutation on $[n]=\lbrace 1,\cdots,n\rbrace$. Theorem \[combi\_pre\_lim\] established a bound on the distance between this process and a pre-limiting process and Theorem \[conv\_cont\_theorem\] shows convergence of this process, under certain assumptions, to a continuous Gaussian process.
Our analysis in this section is similar to that of [@functional_combinatorial], where the summands in the scaled sums are chosen from a deterministic array. The authors therein also establish bounds on the approximation by a pre-limit Gaussian process and show convergence to a continuous Gaussian process. Furthermore, they establish a bound on the distance from the continuous Gaussian process for a restricted class of test functions. For random arrays the situation is more involved.
Our setup is analogous to the one considered in [@chen2015], where a bound on the speed of convergence in the one-dimensional combinatorial central limit theorem is obtained using Stein’s method of exchangeable pairs.
Introduction {#intro_section}
------------
Let $\mathbbm{X}=\lbrace X_{i,j}:i,j\in[n]\rbrace$ be an $n\times n$ array of independent $\mathbbm{R}$-valued random variables, where $n\geq 2$, $\mathbbm{E}X_{i,j}=c_{ij}$, $\text{Var} X_{i,j}=\sigma_{ij}^2\geq 0$ and $\mathbbm{E}|X_{i,j}|^3<\infty$. Suppose that $c_{i\cdot}=c_{\cdot j}=0$ where $c_{i\cdot}=\sum_{j=1}^n\frac{c_{ij}}{n}=\mathbbm{E}X_{i\pi(i)}$, $c_{\cdot j}=\sum_{i=1}^n\frac{c_{ij}}{n}$. Let $\pi$ be a uniform random permutation of $[n]$, independent of $\mathbbm{X}$ and for $$\label{s_n}
s_n^2=\frac{1}{n}\sum_{i,j=1}^n \sigma_{ij}^2+\frac{1}{n-1}\sum_{i,j=1}^n c_{ij}^2.$$ let $$\mathbf{Y}_n(t)=\frac{1}{s_n}\sum_{i=1}^{\lfloor nt\cdot\rfloor}X_{i\pi(i)}=\frac{1}{s_n}\sum_{i=1}^nX_{i\pi(i)}\mathbbm{1}_{[i/n,1]}(t),\quad t\in[0,1].$$
We note that $s_n^2=\text{Var}\left[\sum_{i=1}^nX_{i\pi(i)}\right]$ by the first part of [@chen2015 Theorem 1.1]. The process $\mathbf{Y}_n$ is similar to the process $Y$ considered in [@functional_combinatorial] and defined by (1.4) therein with the most important difference being that we allow the $X_{i,j}$’s to be random, whereas the authors in [@functional_combinatorial] assumed them to be deterministic. Bounds on the distance between one-dimensional distributions of $\mathbf{Y}_n$ and a normal distribution have been obtained via Stein’s method in [@chen2015 Theorem 1.1].
Exchangeable pair setup {#ex_section}
-----------------------
Select uniformly at random two different indices $I,J\in [n]$ and let: $$\mathbf{Y}_n'=\mathbf{Y}_n-\frac{1}{s_n}X_{I\pi(I)}\mathbbm{1}_{[I/n,1]}-\frac{1}{s_n}X_{J\pi(J)}\mathbbm{1}_{[J/n,1]}+\frac{1}{s_n}X_{I\pi(J)}\mathbbm{1}_{[I/n,1]}+\frac{1}{s_n}X_{J\pi(I)}\mathbbm{1}_{[J/n,1]}.$$ Note that $(\mathbf{Y}_n,\mathbf{Y}_n')$ is an exchangeable pair and that for all $f\in M$: $$\begin{aligned}
&\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)\left[\mathbf{Y}_n-\mathbf{Y}_n'\right]\right\rbrace\\
=&\frac{1}{s_n}\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)\left[X_{I\pi(I)}\mathbbm{1}_{[I/n,1]}+X_{J\pi(J)}\mathbbm{1}_{[J/n,1]}-X_{I\pi(J)}\mathbbm{1}_{[I/n,1]}-X_{J\pi(I)}\mathbbm{1}_{[J/n,1]}\right]\right\rbrace\\
=&\frac{1}{n(n-1)s_n}\sum_{i, j=1}^n\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)\left[X_{i\pi(i)}\mathbbm{1}_{[i/n,1]}+X_{j\pi(j)}\mathbbm{1}_{[j/n,1]}\right.\right.\\
&\left.\left.-X_{i\pi(j)}\mathbbm{1}_{[i/n,1]}-X_{j\pi(i)}\mathbbm{1}_{[j/n,1]}\right]\right\rbrace\\
=&\frac{2}{n-1}Df(\mathbf{Y}_n)[\mathbf{Y}_n]-\frac{2}{n(n-1)s_n}\sum_{i,j=1}^n\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)\left[X_{i,\pi(j)}\mathbbm{1}_{[i/n,1]}\right]. \end{aligned}$$
Therefore: $$\begin{aligned}
\label{ex_condition}
\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)[\mathbf{Y}_n-\mathbf{Y}_n']\right\rbrace=\frac{2}{n-1}Df(\mathbf{Y}_n)\left[\mathbf{Y}_n-\frac{1}{ns_n}\sum_{i,j=1}^n\mathbbm{E}^{\mathbf{Y}_n}[X_{i,\pi(j)}]\mathbbm{1}_{[i/n]}\right].\end{aligned}$$ So condition (\[condition\]) is satisfied with $$\Lambda_n=\frac{n-1}{4}\quad\text{and}\quad R_f=\frac{1}{ns_n}\sum_{i,j=1}^nDf(\mathbf{Y}_n)\left[\mathbbm{E}^{\mathbf{Y}_n}[X_{i,\pi(j)}]\mathbbm{1}_{[i/n]}\right].$$
Pre-limiting process {#section_pre_lim}
--------------------
Now let $\hat{Z}_i=\frac{1}{\sqrt{n-1}}\sum_{l=1}^nX_{il}''\left(Z_{il}-\frac{1}{n}\sum_{j=1}^nZ_{jl}\right)$, for $\mathbbm{X}''=\lbrace X_{ij}'':i,j\in[n]\rbrace$ being an independent copy of of $\mathbbm{X}$ and $Z_{il}$’s i.i.d. standard normal, independent of all the $X_{il}$’s and $X_{il}''$’s. Then, let $$\label{pre_lim_an}
\mathbf{D}_n(t)=\frac{1}{s_n}\sum_{i=1}^{\lfloor nt\rfloor}\hat{Z}_i,\quad t\in[0,1].$$ We will compare the distribution of $\mathbf{Y}_n$ with the distribution of $\mathbf{D}_n$. $\mathbf{D}_n$ is a conceptually easy process with the same covariance structure as $\mathbf{Y}_n$. It is constructed in a way similar to the process in [@functional_combinatorial (3.13)]. Note that $\hat{Z}_i$ has mean $0$ for all $i$ and $$\begin{aligned}
\mathbbm{E}\hat{Z}_i^2=&\frac{1}{n-1}\sum_{l=1}^n\mathbbm{E}\left[X_{il}^2\right]\mathbbm{E}\left[\left(Z_{il}-\frac{1}{n}\sum_{j=1}^nZ_{jl}\right)^2\right]\nonumber\\
&+\frac{1}{n-1}\sum_{1\leq l\neq k\leq n}\mathbbm{E}\left[X_{il}X_{ik}\right]\mathbbm{E}\left[\left(Z_{il}-\frac{1}{n}\sum_{j=1}^nZ_{jl}\right)\left(Z_{ik}-\frac{1}{n}\sum_{j=1}^nZ_{jk}\right)\right]\nonumber\\
=&\frac{1}{n-1}\sum_{l=1}^n\mathbbm{E}\left[X_{il}^2\right]\left(1-\frac{2}{n}+\frac{1}{n}\right)\nonumber\\
=&\frac{1}{n}\sum_{l=1}^n\mathbbm{E}X_{il}^2\nonumber\\
=&\frac{1}{2n^2}\left(2(n-1)\sum_{l=1}^n\mathbbm{E}X_{il}^2+2\sum_{i=1}^n\mathbbm{E}X_{ir}^2\right)\nonumber\\
=&\frac{1}{2n^2}\left(\sum_{1\leq k\neq l\leq n} \mathbbm{E}\left[\left(X_{ik}-X_{il}\right)^2\right]+2\sum_{1\leq k\neq l\leq n}\mathbbm{E}X_{ik}\mathbbm{E}X_{il}+2\sum_{r=1}^n\mathbbm{E}X_{ir}^2\right)\nonumber\\
=&\frac{1}{2n^2}\left(\sum_{1\leq k\neq l\leq n} \mathbbm{E}\left[\left(X_{ik}-X_{il}\right)^2\right]+2\sum_{r=1}^n\sigma_{ir}^2\right)\label{e_zi}\end{aligned}$$ as $c_{i\cdot}=0$, and, for $i\neq j$, $$\begin{aligned}
\mathbbm{E}\hat{Z}_i\hat{Z}_j=&\frac{1}{n-1}\sum_{k,l=1}^n\mathbbm{E}(X_{ik}X_{jl})\mathbbm{E}\left[\left(Z_{ik}-\frac{1}{n}\sum_{r=1}^nZ_{rk}\right)\left(Z_{jl}-\frac{1}{n}\sum_{r=1}^nZ_{rl}\right)\right]\nonumber\\
=&-\frac{1}{n(n-1)}\sum_{k=1}^nc_{ik}c_{jk}\nonumber\\
=&\frac{1}{2n^2(n-1)}\left(2\sum_{k=1}^n\left(-\mathbbm{E}X_{ik}\right)\mathbbm{E}X_{jk}-2(n-1)\sum_{k=1}^n\mathbbm{E}X_{ik}\mathbbm{E}X_{jk}\right)\nonumber\\
=&\frac{1}{2n^2(n-1)}\left(2\sum_{1\leq k\neq l\leq n}\mathbbm{E}X_{il}\mathbbm{E}X_{jk}-2\sum_{1\leq k\neq l\leq n}\mathbbm{E}X_{ik}\mathbbm{E}X_{jk}\right)\nonumber\\
=&\frac{1}{2n^2(n-1)}\sum_{1\leq k\neq l\leq n}\mathbbm{E}(X_{ik}-X_{il})(X_{jl}-X_{jk}).\label{e_zi_zj}\end{aligned}$$
Pre-limiting approximation
--------------------------
We have the following theorem, comparing the distribution of $\mathbf{Y}_n$ and $\mathbf{D}_n$:
\[combi\_pre\_lim\] For $\mathbf{Y}_n$ defined in Subsection \[intro\_section\], $\mathbf{D}_n$ defined in Subsection \[section\_pre\_lim\] and any $g\in M^1$, as defined in (\[m\_1\]), $$\begin{aligned}
&\left|\mathbbm{E}g(\mathbf{Y}_n)-\mathbbm{E}g(\mathbf{D}_n)\right|\\
\leq&\frac{\|g\|_{M^1}}{n^3(n-1)s_n^3}\sum_{1\leq i,j,k,l,u\leq n}\left\lbrace \vphantom{\sum_{i=1}^n}3\mathbbm{E}|X_{ik}|^3+5\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|^2+7\mathbbm{E}|X_{ik}|^2\mathbbm{E}|X_{jl}|\right.\nonumber\\
&+5\mathbbm{E}|X_{ik}|^2\mathbbm{E}|X_{jk}|+16\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|\mathbbm{E}|X_{jl}|+2\mathbbm{E}|X_{iu}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|\nonumber\\
&+4\mathbbm{E}|X_{iu}|\mathbbm{E}|X_{il}|\mathbbm{E}|X_{jk}|+6\mathbbm{E}|X_{uk}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{jl}|+2\mathbbm{E}|X_{uk}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{jk}|\\
&\left.+\frac{1}{n}\left(2\mathbbm{E}\left|X_{ik}\right|+2\mathbbm{E}\left|X_{j,l}\right|+2\mathbbm{E}|X_{uk}|+2\mathbbm{E}|X_{ul}|\right)\sum_{r=1}^n\left(\mathbbm{E}|X_{ir}|^2+|c_{ir}c_{jr}|\right)\right\rbrace\\
&+\frac{2\|g\|_{M^1}}{\sqrt{n}}+\frac{4\|g\|_{M^1}}{3ns_n^2}\sum_{i,j=1}^n\sigma_{i,j}^2.\end{aligned}$$
The first long sum in the bound corresponds to $\epsilon_1$ and (to a large extent) $\epsilon_2$ of Theorem \[theorem1\]. It represents the usual Berry-Esseen third moment estimate arising as a result of applying Taylor’s theorem. Term $\frac{2\|g\|_{M^1}}{\sqrt{n}} $ also comes from the estimation of $\epsilon_2$. The last term corresponds to $\epsilon_3$.
Assuming that $s_n=O(\sqrt{n})$, we obtain that the bound in Theorem \[combi\_pre\_lim\] is of order $\frac{1}{\sqrt{n}}$.
If we assume that $\mathbbm{E}|X_{ik}|^3\leq \beta_3$ for all $i,k=1,\cdots, n$ then the bound simplifies in the following way $$\begin{aligned}
&\left|\mathbbm{E}g(\mathbf{Y}_n)-\mathbbm{E}g(\mathbf{D}_n)\right|\\
\leq&\|g\|_{M^1}\left(\frac{58\beta_3n^2}{(n-1)s_n^3}+\frac{8\beta_3^{1/3}}{n(n-1)s_n^3}\sum_{i,j,r=1}^n|c_{ir}c_{jr}|+\frac{2}{\sqrt{n}}+\frac{4}{3ns_n^2}\sum_{i,j=1}^n\sigma_{i,j}^2\right).\end{aligned}$$
We will use Theorem \[theorem1\] to prove Theorem \[combi\_pre\_lim\]. In the proof, in **Step 1**, we justify why Theorem \[theorem1\] may indeed be used in this case. In other words, we check that $\mathbf{D}_n$ of (\[pre\_lim\_an\]) satisfies the conditions $\mathbf{D}_n$ of Theorem (\[theorem1\]) is supposed to satisfy and that the exchangeable-pair condition for $\mathbf{Y}_n$ holds. In **Step 2** we bound terms $\epsilon_1$ and $\epsilon_3$ coming from Theorem \[theorem1\]. This is relatively straightforward due to the $\mathbf{Y}_n$ and $\mathbf{Y}_n'$ of Subsection \[ex\_section\] being constructed in such a way that they are close to each other and $R_f$ of the same subsection being small. Then, in **Step 3**, we treat the remaining term using a strategy analogous to that of the proof of [@functional_combinatorial Theorem 2.1]. The strategy is based on Taylor’s expansions and considering copies of $\mathbf{Y}_n$ which are independent of some of the summands in $\mathbf{Y}_n$. Finally, we combine the estimates obtained in the previous steps to obtain the assertion.
We adopt the notation of Subsections \[intro\_section\], \[ex\_section\] and \[section\_pre\_lim\]. Furthermore, we fix a function $g\in M^1$, as defined in (\[m\_1\]) and let $f=\phi_n(g)$, a solution to the Stein equation for $\mathbf{D}_n$, as defined in (\[phi\]).
**Step 1.** We note that $\mathbf{D}_n$ can be expressed in the following way: $$\mathbf{D}_n=\sum_{i,l=1}^n\left(Z_{il}-\frac{1}{n}\sum_{j=1}^nZ_{jl}\right)J_{i,l},\quad\text{where}\quad J_{i,l}(t)=\frac{X_{il}''}{s_n\sqrt{n-1}}\mathbbm{1}_{[i/n,1]}(t),$$ which, together with (\[ex\_condition\]), lets us apply Theorem \[theorem1\].
**Step 2.** For the first term in Theorem \[theorem1\], for any $g\in M^1$: $$\epsilon_1=\frac{\|g\|_{M^1}}{6}\mathbbm{E}\|(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\|\|\mathbf{Y}_n-\mathbf{Y}_n'\|^2\leq \frac{(n-1)\|g\|_{M^1}}{24}\mathbbm{E}\|\mathbf{Y}_n-\mathbf{Y}_n'\|^3.$$ We note that: $$\begin{aligned}
\mathbbm{E}\|\mathbf{Y}_n-\mathbf{Y}_n'\|^3&\leq\frac{8}{s_n^3}\left(\mathbbm{E}|X_{I\pi(I)}|^3+\mathbbm{E}|X_{J\pi(J)}|^3+\mathbbm{E}|X_{I\pi(J)}|^3+\mathbbm{E}|X_{J\pi(I)}|^3\right)\nonumber\\
&=\frac{8}{n(n-1)s_n^3}\sum_{i\neq j}\left(\mathbbm{E}|X_{i\pi(i)}|^3+\mathbbm{E}|X_{j\pi(j)}|^3+\mathbbm{E}|X_{i\pi(j)}|^3+\mathbbm{E}|X_{j\pi(i)}|^3\right)\nonumber\\
&=\frac{16}{n(n-1)s_n^3}\sum_{i\neq j}\left(\mathbbm{E}|X_{i\pi(i)}|^3+\mathbbm{E}|X_{i\pi(j)}|^3\right)\nonumber\\
&=\frac{32}{n^2s_n^3}\sum_{i,j=1}^n\mathbbm{E}|X_{ij}|^3.\end{aligned}$$ Hence, $$\label{44.2}
\epsilon_1\leq \frac{4\|g\|_{M^1}}{3ns_n^3}\sum_{i,j=1}^n\mathbbm{E}|X_{ij}|^3.$$ Furthermore, by Proposition \[prop12.7\]: $$\begin{aligned}
\epsilon_3=\left|\frac{1}{ns_n}\sum_{i,j=1}^n\mathbbm{E}Df(\mathbf{Y}_n)\left[X_{i,\pi(j)}\mathbbm{1}_{[i/n,1]}\right]\right|=&\left|\frac{1}{ns_n}\sum_{i,j=1}^n\mathbbm{E}Df(\mathbf{Y}_n)\left[X_{i,j}\mathbbm{1}_{[i/n,1]}\right]\right|\nonumber\\
\leq&\|g\|_{M^1}\frac{1}{ns_n}\mathbbm{E}\left\|\sum_{i,j=1}^n X_{i,j}\mathbbm{1}_{[i/n,1]}\right\|\nonumber\\
\leq&\frac{2\|g\|_{M^1}}{ns_n}\sqrt{\mathbbm{E}\left|\sum_{i,j=1}^n X_{i,j}\right|^2}\nonumber\\
\leq&\frac{2\|g\|_{M^1}}{ns_n}\sqrt{\sum_{i,j=1}^n\sigma_{i,j}^2}\nonumber\\
\leq&\frac{2\|g\|_{M^1}}{\sqrt{n}},\label{44.3}\end{aligned}$$ where we have used Doob’s $L^2$ inequality in the second inequality and (\[s\_n\]) in the last one.
**Step 3.** Now define a new permutation $\pi_{ijkl}$ coupled with $\pi$ such that: $$\mathcal{L}(\pi_{ijkl})=\mathcal{L}(\pi|\pi(i)=k,\pi(j)=l),$$ where $\mathcal{L}(\cdot)$ denotes the law. As noted in [@chen2015], we can construct it in the following way. For $\tau_{ij}$ denoting the transposition of $i,j$: $$\pi_{ijkl}=\begin{cases}
\pi,&\text{if }l=\pi(j),k=\pi(i)\\
\pi\cdot\tau_{\pi^{-1}(k),i},&\text{if }l=\pi(j),k\neq \pi(i)\\
\pi\cdot\tau_{\pi^{-1}(l),j},&\text{if }l\neq\pi(j),k=\pi(i)\\
\pi\cdot\tau_{\pi^{-1}(l),i}\cdot\tau_{\pi^{-1}(k),j}\cdot\tau_{ij},&\text{if }l\neq\pi(j),k\neq\pi(i).
\end{cases}$$ We also let $$\mathbf{Y}_{n,ijkl}=\frac{1}{s_n}\sum_{i'=1}^nX_{i'\pi_{ijkl}(i')}\mathbbm{1}_{[i'/n,1]}.$$ Then $\mathcal{L}(\mathbf{Y}_{n,ijkl})=\mathcal{L}(\mathbf{Y}_n|\pi(i)=k,\pi(j)=l)$ (recalling that $\mathcal{L}(\cdot)$ denotes the law). Also, for each choice of $i\neq j$, $k\neq l$ let $\mathbbm{X}^{ijkl}:=\left\lbrace X_{i'j'}^{ijkl}:i',j'\in[n]\right\rbrace$ be the same as $\mathbbm{X}:=\lbrace X_{ij};i,j\in[n]\rbrace$ except that $\lbrace X_{ik},X_{il},X_{jk},X_{jl}\rbrace$ has been replaced by an independent copy $\lbrace X_{ik}',X_{il}',X_{jk}',X_{jl}'\rbrace$. Then let $$\mathbf{Y}_n^{ijkl}=\frac{1}{s_n}\sum_{i'=1}^nX_{i'\pi(i')}^{ijkl}\mathbbm{1}_{[i'/n,1]}$$ and note that $\mathbf{Y}_n^{ijkl}$ is independent of $\lbrace X_{ik},X_{il},X_{jk},X_{jl}\rbrace$ and $\mathcal{L}(\mathbf{Y}_n^{ijkl})=\mathcal{L}(\mathbf{Y}_n)$ (where $\mathcal{L}$ denotes the law).
Now, by Lemma \[lemma1\_app\], proved in the appendix, for $\epsilon_2$ of Theorem \[theorem1\], $$\begin{aligned}
\epsilon_2=&\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbf{D}_n,\mathbf{D}_n]\right|\nonumber\\
\leq & A+B\label{44.4}\end{aligned}$$ where $$\begin{aligned}
A=&\left|\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left[\frac{(X_{ik}-X_{il})^2}{2n}-\frac{\hat{Z}_i^2}{n-1}\right]\right.\right.\nonumber\\
&\phantom{\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}}\cdot\left.\left(D^2f(\mathbf{Y}_{n,ijkl})-D^2f\left(\mathbf{Y}_{n}^{ijkl}\right)\right)\left[\mathbbm{1}_{[i/n,1]}\mathbbm{1}_{[i/n,1]}\right]\vphantom{\left[\frac{1^2}{2^2}\right]}\right\rbrace\nonumber\\
&+\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left[\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}-\hat{Z}_i\hat{Z}_j\right]\right.\nonumber\\
&\left.\left.\hphantom{\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}}\cdot\left(D^2f(\mathbf{Y}_{n,ijkl})-D^2f\left(\mathbf{Y}_{n}^{ijkl}\right)\right)\left[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}\right]\vphantom{\left[\frac{1^2}{2^2}\right]}\right\rbrace\vphantom{\frac{1}{2}\underset{2}{\sum_{2}}}\right|\label{a_def},\\
B=&\left|\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left[\frac{(X_{ik}-X_{il})^2}{2n}-\frac{\hat{Z}_i^2}{n-1}\right]D^2f\left(\mathbf{Y}_{n}^{ijkl}\right)\left[\mathbbm{1}_{[i/n,1]}\mathbbm{1}_{[i/n,1]}\right]\right\rbrace\right.\nonumber\\
&\left.+\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left[\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}-\hat{Z}_i\hat{Z}_j\right]\right.\right.\nonumber\\
&\phantom{\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}}\left.\left.\cdot D^2f\left(\mathbf{Y}_{n}^{ijkl}\right)\left[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}\right]\vphantom{\left[\frac{1^2}{2^2}\right]}\right\rbrace\vphantom{\frac{1^2}{2}\underset{2}{\sum_{2}}}\right|.\nonumber\end{aligned}$$ Recalling that $\mathbf{Y}_n^{ijkl}$ is independent of $\lbrace X_{ik},X_{il},X_{jk},X_{jl}\rbrace$ and $\mathcal{L}(\mathbf{Y}_n^{ijkl})=\mathcal{L}(\mathbf{Y}_n)$, $$\begin{aligned}
B=&\left|\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left[\frac{(X_{ik}-X_{il})^2}{2n}-\frac{\hat{Z}_i^2}{n-1}\right]\mathbbm{E}\left\lbrace D^2f\left(\mathbf{Y}_{n}\right)\left[\mathbbm{1}_{[i/n,1]}\mathbbm{1}_{[i/n,1]}\right]\right\rbrace\right.\nonumber\\
&+\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left[\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}-\hat{Z}_i\hat{Z}_j\right]\nonumber\\
&\hphantom{\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}}\left.\cdot\mathbbm{E}\left\lbrace D^2f\left(\mathbf{Y}_{n}\right)\left[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}\right]\vphantom{\frac{1}{2}}\right\rbrace\vphantom{\frac{1^2}{2^2}\underset{2}{\sum_2}}\right|\nonumber\\
\leq&\frac{\|g\|_{M^1}}{n^2(n-1)s_n^2}\sum_{1\leq i\neq j\leq n}\sum_{r=1}^n\sigma^2_{ir}\nonumber\\
=&\frac{\|g\|_{M^1}}{n^2s_n^2}\sum_{i,j=1}^n\sigma_{i,j}^2,\label{44.5}\end{aligned}$$ where the inequality follows by (\[e\_zi\]), (\[e\_zi\_zj\]) and Proposition \[prop12.7\]. Furthermore, by Lemma \[lemma2\_app\], proved in the appendix, $$\begin{aligned}
A\leq&\frac{\|g\|_{M^1}}{n^3(n-1)s_n^3}\sum_{1\leq i,j,k,l,u\leq n}\left\lbrace\vphantom{\sum_1^2}\mathbbm{E}|X_{ik}|^3+5\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|^2+7\mathbbm{E}|X_{ik}|^2\mathbbm{E}|X_{jl}|\right.\nonumber\\
&+5\mathbbm{E}|X_{ik}|^2\mathbbm{E}|X_{jk}|+16\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|\mathbbm{E}|X_{jl}|+2\mathbbm{E}|X_{iu}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|\nonumber\\
&+4\mathbbm{E}|X_{iu}|\mathbbm{E}|X_{il}|\mathbbm{E}|X_{jk}|+6\mathbbm{E}|X_{uk}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{jl}|+2\mathbbm{E}|X_{uk}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{jk}|\nonumber\\
&\left.+\frac{1}{n}\left(2\mathbbm{E}\left|X_{ik}\right|+2\mathbbm{E}\left|X_{j,l}\right|+2\mathbbm{E}|X_{uk}|+2\mathbbm{E}|X_{ul}|\right)\cdot\sum_{r=1}^n\left(\mathbbm{E}|X_{ir}|^2+|c_{ir}c_{jr}|\right)\right\rbrace.\label{a_est}\end{aligned}$$ We now use (\[44.2\]),(\[44.3\]),(\[44.4\]),(\[44.5\]),(\[a\_est\]) to obtain the assertion.
Convergence to a continuous Gaussian process
--------------------------------------------
\[conv\_cont\_theorem\] Let $\mathbbm{X}$ and $\mathbf{Y}_n$ be as defined in Subsection \[intro\_section\] and suppose that for all $u,t\in[0,1]$: $$\label{assumption1}
\frac{1}{s_n^2(n-1)}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{j=1}^{\lfloor nu\rfloor}\sum_{k=1}^n\mathbbm{E}X_{ik}X_{jk}\left(\delta_{i,j}-\frac{1}{n}\right)\xrightarrow{n\to\infty}\sigma(u,t)$$ and $$\label{assumption2}
\frac{1}{s_n^2}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{j=1}^{\lfloor nu\rfloor}\sum_{l=1}^n\mathbbm{E}X_{il}X_{jl}\xrightarrow{n\to\infty}\sigma^{(2)}(u,t)$$ pointwise for some functions $\sigma,\sigma^{(2)}:[0,1]^2\to\mathbbm{R}_+$. Suppose furthermore that: $$\label{assumption3}
\sup_{n\in\mathbbm{N}}\frac{1}{n^2s_n^4}\sum_{l=1}^n\sum_{i=1}^n\text{Var}\left[X_{il}^2\right]<\infty.$$ and: $$\label{assumption4}
\frac{1}{s_n^2(n-1)}\sum_{i=1}^{\lfloor nt\rfloor}\left(\sum_{l=1}^nX_{il}''Z_{il}\right)^2\xrightarrow{P} c(t)$$ pointwise for some function $c:[0,1]\to\mathbbm{R}_+$ and: $$\label{assumption5}
\lim_{n\to\infty}\frac{1}{s_n\sqrt{n-1}}\mathbbm{E}\left[\sup_{i=1,\cdots,n}|X_{il}''Z_{il}|\right]=0.$$ Then $\left(\mathbf{Y}_n(t),t\in[0,1]\right)$ converges weakly in the uniform topology to a continuous Gaussian process $\left(\mathbf{Z}(t),t\in[0,1]\right)$ with the covariance function $\sigma$.
Assumption (\[assumption2\]) could also say that $$\frac{1}{s_n^2}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{j=1}^{\lfloor nu\rfloor}\sum_{l=1}^n\mathbbm{E}X_{il}X_{jl}$$ simply converges pointwise rather than giving the limit a name. However, we will use $\sigma^{(2)}$ in the proof so it is convenient to use it in the formulation of the Theorem as well.
Assumption (\[assumption4\]) is necessary for the limiting process in Theorem \[conv\_cont\_theorem\] to be continuous. It essentially corresponds to the the assumption that the quadratic variation of the following process $$\mathbf{D}_n^{(1)}(t)=\frac{1}{s_n\sqrt{n-1}}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{l=1}^nX_{il}''Z_{il}$$ converges to the function $c$ pointwise in probability, which then implies the weak convergence of the process $\mathbf{D}_n^{(1)}$ to a continuous process. While it is relatively easy to show that $\mathbf{D}_n^{(2)}=\mathbf{D}_n-\mathbf{D}_n^{(1)}$ converges to a continuous limit, we had to explicitly add this assumption to ensure that $\mathbf{D}_n$ does as well.
The proof of Theorem \[conv\_cont\_theorem\] will be similar to the proof of [@functional_combinatorial Theorem 3.3]. The pre-limiting approximand $\mathbf{D}_n$, defined in Subsection \[section\_pre\_lim\], will be expressed as a sum of two parts. In **Steps 1** and **2** we prove that each of those parts is C-tight (i.e. they are tight and for each of them any convergent subsequence converges to a process with continuous sample paths). In **Step 3** we show that the assumptions of Theorem \[conv\_cont\_theorem\] trivially imply the convergence of the covariance function of $\mathbf{D}_n$, which together with C-tightness implies the convergence of $\mathbf{D}_n$ to a continuous process. Theorem \[theorem\_pre\_limiting\] will then be combined with Proposition \[prop\_m\] to show convergence of $\mathbf{Y}_n$ to the same limiting process. Finally, the combinatorial central limit theorem for random arrays, proved in [@chen_ho] and analysed in [@chen2015], will imply that $\mathbf{Z}$ is Gaussian.
We will use the notation of Subsections \[intro\_section\] and \[section\_pre\_lim\].
**Step 1.** Note that $\mathbf{D}_n=\mathbf{D}_n^{(1)}+\mathbf{D}_n^{(2)}$, where: $$\mathbf{D}_n^{(1)}(t)=\frac{1}{s_n\sqrt{n-1}}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{l=1}^nX_{il}''Z_{il},\quad \mathbf{D}_n^{(2)}(t)=\frac{1}{s_n\sqrt{n-1}}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{l=1}^nX_{il}''\bar{Z}_l$$ for $\bar{Z}_l=\frac{1}{n}\sum_{j=1}^nZ_{jl}$.
Now, note that, by (\[assumption4\]): $$\left< \mathbf{D}_n^{(1)}\right>_t\xrightarrow{P}c(t)$$ pointwise, where $\left<\cdot\right>$ denotes quadratic variation. Therefore, by [@ethier Chapter 7, Theorem 1.4] and using (\[assumption5\]), we obtain that $\mathbf{D}_n^{(1)}$ converges weakly in the Skorokhod topology on $D[0,1]$ to a continuous Gaussian process with independent increments.
We now note that the Skorokhod space equipped with the metric (topologically equivalent to the Skorokhod metric) with respect to which it is complete is also universally measurable by the discussion at the beginning of [@dudley_book Chapter 11.5]. Since it is also separable and $\mathbf{D}_n^{(1)}\Rightarrow \mathbf{Z}_1$, for some continuous process $\mathbf{Z}_1$, in the Skorokhod topology, [@dudley_book Theorem 11.5.3] implies that $(\mathbf{D}_n^{(1)})_{n\geq 1}$ is C-tight.
**Step 2.** Also, note that for $u>t$ s.t. $\lfloor nu\rfloor\geq \lfloor nt\rfloor +1$, $$\begin{aligned}
\mathbbm{E}\left[\left.\left|\mathbf{D}_n^{(2)}(u)-\mathbf{D}_n^{(2)}(t)\right|^2\right|X_{il}'',i,l\in[n]\right]=&\frac{1}{n(n-1)s_n^2}\sum_{l=1}^n\left(\sum_{i=\lfloor nt\rfloor+1}^{\lfloor nu\rfloor}X_{il}\right)^2\\
\leq&\frac{\lfloor nu\rfloor -\lfloor nt\rfloor}{n(n-1)s_n^2}\sum_{l=1}^n\sum_{i=\lfloor nt\rfloor+1}^{\lfloor nu\rfloor}X_{il}^2\end{aligned}$$ and $$\mathbbm{E}\left[\left.\left|\mathbf{D}_n^{(2)}(u)-\mathbf{D}_n^{(2)}(t)\right|^2\right|X_{il}'',i,l\in[n]\right]=0,\quad\text{for }u>t\text{ s.t. }\lfloor nu\rfloor=\lfloor nt\rfloor.$$ Since $\left(\mathbf{D}_n^{(2)}|X_{il}'',i,l\in[n]\right)$ is Gaussian for $u$, such that $\lfloor nu\rfloor \geq \lfloor nt\rfloor +1$, $$\begin{aligned}
&\mathbbm{E}\left|\mathbf{D}_n^{(2)}(u)-\mathbf{D}_n^{(2)}(t)\right|^4\nonumber\\
=&3\mathbbm{E}\left\lbrace\left(\mathbbm{E}\left[\left.\left|\mathbf{D}_n^{(2)}(u)-\mathbf{D}_n^{(2)}(t)\right|^2\right|X_{il}'',i,l\in[n]\right]\right)^2\right\rbrace\nonumber\\
\leq&3\left(\frac{\lfloor nu\rfloor -\lfloor nt\rfloor}{n(n-1)s_n^2}\right)^2\mathbbm{E}\left(\sum_{l=1}^n\sum_{i=\lfloor nt\rfloor+1}^{\lfloor nu\rfloor}X_{il}^2\right)^2\nonumber\\
=&3\left(\frac{\lfloor nu\rfloor -\lfloor nt\rfloor}{n(n-1)s_n^2}\right)^2\left[\left(\sum_{l=1}^n\sum_{i=\lfloor nt\rfloor+1}^{\lfloor nu\rfloor}\mathbbm{E}X_{il}^2\right)^2+\sum_{l=1}^n\sum_{i=\lfloor nt\rfloor+1}^{\lfloor nu\rfloor}\left(\mathbbm{E}X_{il}^4-\left(\mathbbm{E}X_{il}^2\right)^2\right)\right]\nonumber\\
\leq&C\left(\frac{\lfloor nu\rfloor -\lfloor nt\rfloor}{(n-1)}\right)^2\label{4.1}\end{aligned}$$ for some constant $C$, by (\[assumption3\]). Now, note that: $$\text{Cov}\left(\mathbf{D}_n^{(2)}(t),\mathbf{D}_n^{(2)}(u)\right)=\frac{1}{s_n^2}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{j=1}^{\lfloor nu\rfloor}\sum_{l=1}^n\mathbbm{E}X_{il}X_{jl}\xrightarrow{n\to\infty}\sigma^{(2)}(t,u),$$ by (\[assumption2\]). Consider a mean zero Gaussian process $\mathbf{Z}_2$ with covariance function $\mathbbm{E}\mathbf{Z}_2(t)\mathbf{Z}_2(u)=\sigma^{(2)}(t,u)$. The finite dimensional distributions of $\mathbf{D}_n^{(2)}$ converge to those of $\mathbf{Z}_2$. We can now construct $\mathbf{D}_n^{(2)}$ and $\mathbf{Z}_2$ on the same probability space and use Skorokhod’s representation theorem, Fatou’s lemma and (\[4.1\]) to conclude that: $$\mathbbm{E}\left(\left|\mathbf{Z}_{2}(u)-\mathbf{Z}_2(t)\right|^4\right)\leq \lim_{n\to\infty}\mathbbm{E}\left(\left|\mathbf{D}_n^{(2)}(u)-\mathbf{D}_n^{(2)}(t)\right|^4\right)\leq C(u-t)^2.$$ By [@billingsley1 Theorem 12.4], we can assume that $\mathbf{Z}_2\in C[0,1]$. Now, note that for $0\leq t\leq v\leq u\leq 1$: $$\begin{aligned}
&\mathbbm{E}\left|\mathbf{D}_n^{(2)}(v)-\mathbf{D}_n^{(2)}(t)\right|^2\left|\mathbf{D}_n^{(2)}(v)-\mathbf{D}_n^{(2)}(u)\right|^2\\
\leq& \sqrt{\mathbbm{E}\left|\mathbf{D}_n^{(2)}(v)-\mathbf{D}_n^{(2)}(t)\right|^4\mathbbm{E}\left|\mathbf{D}_n^{(2)}(v)-\mathbf{D}_n^{(2)}(u)\right|^4}\\
\stackrel{(\ref{4.1})}\leq& C \frac{(\lfloor nv\rfloor -\lfloor nt\rfloor)(\lfloor nu\rfloor-\lfloor nv\rfloor)}{(n-1)^2}\\
\leq&\bar{C}(u-t)^2;\end{aligned}$$ for some constant $\bar{C}$. Therefore, by [@billingsley1 Theorem 15.6], $\mathbf{D}_n^{(2)}\Rightarrow \mathbf{Z}_2$ in the Skorokhod and uniform topologies and so, by [@dudley_book Theorem 11.5.3], $\mathbf{D}_n^{(2)}$ is C-tight.
**Step 3.** Since both $\mathbf{D}_n^{(1)}$ and $\mathbf{D}_n^{(2)}$ are C-tight, so is their difference $\mathbf{D}_n$. Now: $$\begin{aligned}
\text{Cov}(\mathbf{D}_n(t),\mathbf{D}_n(u))=&\frac{1}{s_n^2(n-1)}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{j=1}^{\lfloor nu\rfloor}\sum_{k,l=1}^n\mathbbm{E}\left\lbrace X_{ik}X_{jl}\left(Z_{ik}-\bar{Z}_k\right)\left(Z_{jl}-\bar{Z}_l\right)\right\rbrace\\
=&\frac{1}{s_n^2(n-1)}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{j=1}^{\lfloor nu\rfloor}\sum_{k=1}^n\mathbbm{E}\left\lbrace X_{ik}X_{jk}\left(Z_{ik}-\bar{Z}_k\right)\left(Z_{jk}-\bar{Z}_k\right)\right\rbrace\\
=&\frac{1}{s_n^2(n-1)}\sum_{i=1}^{\lfloor nt\rfloor}\sum_{j=1}^{\lfloor nu\rfloor}\sum_{k=1}^n\mathbbm{E}X_{ik}X_{jk}\left(\delta_{i,j}-\frac{1}{n}\right)\xrightarrow{n\to\infty}\sigma(u,t),\end{aligned}$$ by (\[assumption1\]) and we obtain that $\mathbf{D}_n$ converges to a random element $\mathbf{Z}\in C[0,1]$ with covariance function $\sigma$ in distribution with respect to the uniform and Skorokhod topologies.
Proposition \[prop\_m\] and Theorem \[combi\_pre\_lim\] therefore imply that $\left(\mathbf{Y}_n(t),t\in[0,1]\right)$ converges weakly to $\left(\mathbf{Z}(t),t\in[0,1]\right)$ in the uniform topology. Using, for example, [@chen2015 Theorem 1.1], we conclude that $\mathbf{Z}$ is a Gaussian process.
Edge and two-star counts in Bernoulli random graphs {#section6}
===================================================
In this section we consider a two-dimensional process whose first coordinate is a properly rescaled number of edges and the second one is a rescaled number of two-stars (i.e. subgraphs which are trees with one internal node and $2$ leaves) in a Bernoulli random graph with a fixed edge probability and $\lfloor nt\rfloor$ edges for $t\in[0,1]$. A similar setup has been considered in [@reinert_roellin1], where the authors established a bound on the distance between a three-dimensional vector consisting of a rescaled number of edges, a rescaled number of two-stars and a rescaled number of triangles in a $G(n,p)$ graph and a three-dimensional Gaussian vector. We first compare our process to a two-dimensional Gaussian pre-limiting Gaussian processes with paths in $D([0,1])$ and bound the distance between the two in Theorem \[theorem\_pre\_limiting\]. Then, in Theorem \[theorem\_continuous\], we bound the distance of our process from a continuous two-dimensional Gaussian process.
It is worth noting that the analysis of this section could easily be extended to one of a three-dimensional process whose coordinates represent the number of edges, the number of triangles and the number of two-stars in a $G(\lfloor nt\rfloor, p)$ graph. The only reason we do not do it here is that it would require some more involved algebraic computations and would make this section rather lengthy.
Introduction {#section1}
------------
Let us consider a Bernoulli random graph $G(n,p)$ on $n$ vertices with edge probabilities $p$.
Let $I_{i,j}=I_{j,i}$ be the Bernoulli$(p)$-indicator that edge $(i,j)$ is present in this graph. These indicators, for $(i,j)\in\lbrace 1,\cdots,n\rbrace^2$ are independent. We will look at a process representing at each $t\in[0,1]$ the re-scaled total number of edges in the graph formed out of the given Bernoulli random graph by considering only its first $\lfloor nt\rfloor$ vertices and the edges between them: $$\mathbf{T}_n(t)=\frac{\lfloor nt\rfloor-2}{2n^2}\sum_{i,j=1}^{\lfloor nt\rfloor} I_{i,j}=\frac{\lfloor nt\rfloor-2}{n^2}\sum_{1\leq i<j\leq \lfloor nt\rfloor}I_{i,j},$$ and at a process representing a re-scaled statistic related to the number of two-stars in the same graph: $$\mathbf{V}_n(t)=\frac{1}{2n^2}\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq \lfloor nt\rfloor}}I_{ij}I_{jk}=\frac{1}{n^2}\sum_{1\leq i<j<k\leq \lfloor nt\rfloor}\left(I_{i,j}I_{j,k}+I_{i,j}I_{i,k}+I_{j,k}I_{i,k}\right).$$
Let $\mathbf{Y}_n(t)=\left(\mathbf{T}_n(t)-\mathbbm{E}\mathbf{T}_n(t),\mathbf{V}_n(t)-\mathbbm{E}\mathbf{V}_n(t)\right)$ for $t\in[0,1]$.
Note that, for all $t\in[0,1]$, $\mathbbm{E}\mathbf{T}_n(t)=\frac{\lfloor nt\rfloor -2}{n^2}{\lfloor nt\rfloor \choose 2}p$ and $\mathbbm{E}\mathbf{V}_n(t)=\frac{3}{n^2}{\lfloor nt\rfloor \choose 3}p^2$. Furthermore, note that, by an argument similar to that of [@reinert_roellin1 Section 5], the covariance matrix of $\left(\mathbf{T}_n(t)-\mathbbm{E}\mathbf{T}_n(t),\mathbf{V}_n(t)-\mathbbm{E}\mathbf{V}_n(t)\right)$ is given by $$3\frac{(\lfloor nt\rfloor -2){\lfloor nt\rfloor \choose 3}}{n^4}p(1-p)\left(\begin{array}{cc}
1&2p\\
2p&4p^2 \end{array}\right).$$ Hence, the scaling ensures that the covariances are of the same order in $n$.
Exchangeable pair setup {#section2}
-----------------------
We now construct an exchangeable pair, as in [@reinert_roellin1], by picking $(I,J)$ according to $\mathbbm{P}[I=i,J=j]=\frac{1}{{n\choose 2}}$ for $1\leq i<j\leq n$. If $I=i,J=j$, we replace $I_{i,j}=I_{j,i}$ by an independent copy $I_{i,j}'=I_{j,i}'$ and put: $$\begin{aligned}
\mathbf{T}_n'(t)&=\mathbf{T}_n(t)-\frac{\lfloor nt\rfloor-2}{n^2}\left(I_{I,J}-I_{I,J}'\right)\mathbbm{1}_{[I/n,1]\cap[J/n,1]}(t)\\
\mathbf{V}_n'(t)&=\mathbf{V}_n(t)-\frac{1}{n^2}\sum_{k:k\neq I,J}\left(I_{I,J}-I_{I,J}'\right)\left(I_{J,k}+I_{I,k}\right)\mathbbm{1}_{[I/n,1]\cap[J/n,1]\cap[k/n,1]}(t).\end{aligned}$$ We also let $\mathbf{Y}_n'(t)=\left(\mathbf{T}_n'(t)-\mathbbm{E}\mathbf{T}_n(t),\mathbf{V}_n'(t)-\mathbbm{E}\mathbf{V}_n(t)\right)$ and note that, for $\mathbf{Y}_n=\left(\mathbf{Y}_n(t),t\in[0,1]\right)$ and $\mathbf{Y}_n'=\left(\mathbf{Y}_n'(t),t\in[0,1]\right)$, $(\mathbf{Y}_n,\mathbf{Y}_n')$ forms an exchangeable pair. Let $e_1=(1,0)$, $e_2=(0,1)$. We note that, for any $m=1,2$ and for any $f\in M$, as defined in Section \[section22\], $$\begin{aligned}
&\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)\left[\left(\mathbf{T}_n'-\mathbf{T}_n\right)e_m\right]\right\rbrace\\
=&\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)\left[\frac{\lfloor n\cdot\rfloor-2}{n^2}\left(I_{I,J}'-I_{I,J}\right)\mathbbm{1}_{[I/n,1]\cap[J/n,1]}e_m\right]\right\rbrace\\
=&\frac{2}{n^3(n-1)}\sum_{i<j}\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)\left[(\lfloor n\cdot\rfloor-2)\left(I_{i,j}'-I_{i,j}\right)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}e_m\right]|I=i,J=j\right\rbrace\\
=&-\frac{1}{{n\choose 2}}Df(\mathbf{Y}_n)[\mathbf{T}_ne_m]+\frac{2}{n^3(n-1)}p\sum_{i<j}Df(\mathbf{Y}_n)\left[(\lfloor n\cdot\rfloor-2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}e_m\right]\\
=&-\frac{1}{{n\choose 2}}Df(\mathbf{Y}_n)[\left(\mathbf{T}_n(\cdot)-\mathbbm{E}\mathbf{T}_n(\cdot)\right)e_m].\\\end{aligned}$$ Also: $$\begin{aligned}
&\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)[(\mathbf{V}_n-\mathbf{V}_n')e_m]\\
=&\frac{1}{n^2{n\choose 2}}\sum_{i<j}\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace\sum_{k:k\neq i,j}Df(\mathbf{Y}_n)\left[\left(I_{i,j}-I_{i,j}'\right)\left(I_{j,k}+I_{i,k}\right)\right.\right.\\
&\cdot\left.\left.\left.\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}e_m\right]\right|I=i,J=j\right\rbrace\\
=&\frac{2}{{n\choose 2}}Df(\mathbf{Y}_n)[\mathbf{V}_ne_m]\\
&-\frac{p}{n^2{n\choose 2}}\sum_{i<j}\sum_{k:k\neq i,j}\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)\left[\left(I_{j,k}+I_{i,k}\right)\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}e_m\right]\\
=&\frac{2}{{n\choose 2}}Df(\mathbf{Y}_n)[\mathbf{V}_ne_m]-\frac{p}{n^2{n\choose 2}}\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)\left[I_{i,j}\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}e_m\right]\\
=&\frac{2}{{n\choose 2}}Df(\mathbf{Y}_n)[\left(\mathbf{V}_n-\mathbbm{E}\mathbf{V}_n(\cdot)\right)e_m]\\
&-\frac{p}{n^2{n\choose 2}}\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)\left[(I_{i,j}-p)\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}e_m\right]\\
=&\frac{2}{{n\choose 2}}Df(\mathbf{Y}_n)[\left(\mathbf{V}_n-\mathbbm{E}\mathbf{V}_n(\cdot)\right)e_m]\\
&-\frac{2p}{{n\choose 2}}Df(\mathbf{Y}_n)\left[\frac{1}{\lfloor n\cdot\rfloor-2}\left(\mathbf{T}_n-\mathbbm{E}\mathbf{T}_n(\cdot)\right)e_m\left(\sum_{k=1}^n\mathbbm{1}_{[k/n,1]}-2\right)\right]\\
=&\frac{2}{{n\choose 2}}Df(\mathbf{Y}_n)[\left(\mathbf{V}_n-\mathbbm{E}\mathbf{V}_n(\cdot)\right)e_m]-\frac{2p}{{n\choose 2}}Df(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbbm{E}\mathbf{T}_n(\cdot))e_m\right].\end{aligned}$$ Therefore, for any $m=1,2$: $$\begin{aligned}
\text{A)}\quad &Df(\mathbf{Y}_n)\left[\left(\mathbf{T}_n-\mathbbm{E}\mathbf{T}_n\right)e_m\right]=\frac{n(n-1)}{2}\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')e_m\right]\right\rbrace\\
\text{B)}\quad &Df(\mathbf{Y}_n)\left[\left(\mathbf{V}_n-\mathbbm{E}\mathbf{V}_n\right)e_m\right]\\
=&\frac{n(n-1)}{4}\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)\left[(\mathbf{V}_n-\mathbf{V}_n')e_m\right]+pDf(\mathbf{Y}_n)\left[\left(\mathbf{T}_n-\mathbbm{E}\mathbf{T}_n\right)e_m\right]\right\rbrace\\
=&\frac{n(n-1)}{4}\mathbbm{E}^{\mathbf{Y}_n}\left\lbrace Df(\mathbf{Y}_n)\left[\left(2p(\mathbf{T}_n-\mathbf{T}_n')+\mathbf{V}_n-\mathbf{V}_n'\right)e_m\right]\right\rbrace\end{aligned}$$ and so: $$Df(\mathbf{Y}_n)[\mathbf{Y}_n]=2\mathbbm{E}^{\mathbf{Y}_n}Df(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\right],$$ where: $$\label{eq_lambda}
\Lambda_n=\frac{n(n-1)}{8}\left(\begin{array}{ccc}
2&2p\\
0&1
\end{array}\right).$$ Therefore, condition (\[condition\]) is satisfied with $\Lambda_n$ of (\[eq\_lambda\]) and $R_f=0$.
A pre-limiting process {#section3}
----------------------
Let $\mathbf{D}_n=(\mathbf{D}_n^{(1)},\mathbf{D}_n^{(2)})$, where $\mathbf{D}_n^{(2)}=\mathbf{D}_n^{(2,1)}+\mathbf{D}_n^{(2,2)}$, be defined in the following way: $$\begin{aligned}
&\mathbf{D}_n^{(1)}(t)=\left(\lfloor nt\rfloor-2\right)\sum_{i,j=1}^{\lfloor nt\rfloor}Z_{i,j}^{(1)},\quad t\in[0,1]\\
&\mathbf{D}_n^{(2,1)}(t)=\left(\lfloor nt\rfloor-2\right)\sum_{i,j=1}^{\lfloor nt\rfloor}Z_{i,j}^{(2,1)},\quad t\in[0,1]\\
&\mathbf{D}_n^{(2,2)}(t)=\sum_{i,j,k=1}^{\lfloor nt\rfloor}Z_{i,j,k}^{(2,2)},\quad t\in[0,1]\end{aligned}$$ where $Z_{i,i}^{(1)}=0$ for all $i$, $Z_{i,i}^{(1,2)}=0$ for all $i$ and $Z_{i,j,k}^{(2,2)}=0$ if $i=j$ or $i=k$ of $j=k$. Furthermore, assume that the collection $\lbrace Z^{(1)}_{i,j}: i,j\in [n], i\neq j\rbrace\cup\lbrace Z^{(1,2)}_{i,j}: i,j\in [n], i\neq j\rbrace\cup\lbrace Z^{(2,2)}_{i,j,k}: i,j,k\in [n], i\neq j\neq k\neq i\rbrace$ is jointly centred Gaussian with the following covariance structure: $$\begin{aligned}
&\mathbbm{E}Z_{ij}^{(1)}Z_{kl}^{(1)}=\begin{cases}
\frac{p(1-p)}{2n^4},&i=k,j=l,i\neq j\\
0,&\text{otherwise,}\end{cases}\\
&\mathbbm{E}Z_{i,j}^{(1)}Z_{k,l}^{(2,1)}=\begin{cases}
\frac{p^2(1-p)}{4n^4},&i=k,j=l,i\neq j\\
0,&\text{otherwise,}
\end{cases}\\
&\mathbbm{E}Z_{i,j,k}^{(2,2)}Z_{l,m}^{(1)}=\begin{cases}
\frac{3p^2(1-p)}{4n^4},&i=l,j=m,i\neq j\neq k\neq i\\
0,&\text{otherwise,}
\end{cases}\\
&\mathbbm{E}Z_{i,j,k}^{(2,2)}Z_{l,m}^{(2,1)}=\begin{cases}
\frac{p^3(1-p)}{2n^4},&i=l,j=m,i\neq j\neq k\neq i\\
0,&\text{otherwise,}
\end{cases}\\
&\mathbbm{E}Z_{i,j,k}^{(2,2)}Z_{r,s,t}^{(2,2)}=\begin{cases}
\frac{p^2(1-p^2)}{2n^4},&i=r,j=s,k=t, i\neq j\neq k\neq i\\
\frac{p^3(1-p)}{n^4},&i=r,j=s,k\neq t, i\neq j\neq k\neq i, i\neq j\neq t\neq i\\
0,&\text{otherwise,}
\end{cases}\\
&\mathbbm{E}Z_{i,j}^{(2,1)}Z_{k,l}^{(2,1)}=\begin{cases}
\frac{1}{n^5},&i=k,j=l, i\neq j\\
0,&\text{otherwise.}\end{cases}\end{aligned}$$ It will become clear in Remark \[remark\_reasons\] why we have chosen this covariance structure.
Distance from the pre-limiting process
--------------------------------------
We first give a theorem providing a bound on the distance between $\mathbf{Y}_n$ and the pre-limiting piecewise constant Gaussian process.
\[theorem\_pre\_limiting\] Let $\mathbf{Y}_n$ be defined as in Section \[section1\] and $\mathbf{D}_n$ be defined as in Section \[section3\]. Then, for any $g\in M^2$, as defined by (\[m\_2\]), $$\left|\mathbbm{E}g(\mathbf{Y}_n)-\mathbbm{E}g(\mathbf{D}_n)\right|\leq 12\|g\|_{M^2}n^{-1}.$$
In **Step 1** of the proof, which is based on Theorem \[theorem1\], we estimate term $\epsilon_1$ thereof. It involves bounding $\|\Lambda_n\|_2$ of (\[eq\_lambda\]) and the third moment of $\|\mathbf{Y}_n-\mathbf{Y}_n'\|$ for $\mathbf{Y}_n'$ constructed in Section \[section2\]. In **Step 2** we treat $\epsilon_2$, which requires involved calculations, based on Stein’s method, which are, to a large extent, postponed to the appendix. Term $\epsilon_3$ is equal to zero as $R_f$ of Section \[section2\] is equal to zero.
We adopt the notation of sections \[section1\], \[section2\], \[section3\]. We will apply Theorem \[theorem1\].
**Step 1.** First note that, for $\epsilon_1$ in Theorem \[theorem1\], $$\begin{aligned}
|(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n|\leq \|\Lambda_n\|_2|\mathbf{Y}_n-\mathbf{Y}_n'|,\end{aligned}$$ where $|\cdot|$ denotes the Euclidean norm in $\mathbbm{R}^2$ and $\|\cdot\|_2$ is the induced operator $2$-norm. Furthermore, for $\|\cdot\|_F$ denoting the Frobenius norm (which, for $\Theta\in\mathbbm{R}^{d_1\times d_2}$ is defined by $\|\Theta\|_F=\sqrt{\sum_{i=1}^{d_1}\sum_{j=1}^{d_2}|\Theta_{i,j}|}$), $$\begin{aligned}
\|\Lambda_n\|_2\leq \|\Lambda_n\|_F=\frac{n(n-1)}{8}\sqrt{2^2+(2p)^2+0^2+1^2}\leq \frac{3n(n-1)}{8}.\end{aligned}$$ Therefore: $$\begin{aligned}
&\mathbbm{E}\|(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n\|\|\mathbf{Y}_n-\mathbf{Y}_n'\|^2\nonumber\\
\leq&\frac{3n(n-1)}{8} \mathbbm{E}\|\mathbf{Y}_n-\mathbf{Y}_n'\|^3\nonumber\\
\leq& \frac{3n(n-1)}{8}\mathbbm{E}\left[\frac{(n-2)^2}{n^4}\left(I_{I,J}-I'_{I,J}\right)^2+\frac{1}{n^4}\left(\sum_{k:k\neq I,J}(I_{I,J}-I_{I,J}')\left(I_{J,k}+I_{I,k}\right)\right)^2\right]^{3/2}\nonumber\\
\leq&\frac{3n(n-1)}{8}\left[\frac{(n-2)^2}{n^4}+\frac{\left(2(n-2)\right)^2}{n^4}\right]^{3/2}\nonumber\\
\leq&\frac{5}{n},
\label{4.1.1.1}\end{aligned}$$ where the third inequality follows because $|I_{I,J}-I_{I,J}'|\leq 1$ and $|I_{J,k}+I_{I,k}|\leq 2$ for all $k$. Therefore, $$\epsilon_1\leq \frac{5\|g\|_{M^2}}{6n}.$$
**Step 2.** For $\epsilon_2$ in Theorem \[theorem1\], we wish to bound: $$\begin{aligned}
&\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(\mathbf{Y}_n-\mathbf{Y}_n'\right)\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]\right|\nonumber\\
=&\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(2(\mathbf{T}_n-\mathbf{T}_n'),2p(\mathbf{T}_n-\mathbf{T}_n')+(\mathbf{V}_n-\mathbf{V}_n')\right),\left(\mathbf{T}_n-\mathbf{T}_n',\mathbf{V}_n-\mathbf{V}_n'\right)\right]\right.\nonumber\\
&\left.-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]\right|\nonumber\\
\leq&S_1+S_2+S_3+S_4+S_5+S_6+S_7,\label{4_int}\end{aligned}$$ where: $$\begin{aligned}
S_1&=\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')(2,0),(\mathbf{T}_n-\mathbf{T}_n')(1,0)\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(\mathbf{D}_n^{(1)},0\right),\left(\mathbf{D}_n^{(1)},0\right)\right]\right|\nonumber\\
S_2&=\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')(0,2p),(\mathbf{T}_n-\mathbf{T}_n')(1,0)\right]-2\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(0,\mathbf{D}_n^{(2,1)}\right),\left(\mathbf{D}_n^{(1)},0\right)\right]\right|\nonumber\\
S_3&=\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')(2,0),(\mathbf{V}_n-\mathbf{V}_n')(0,1)\right]-\frac{4}{3}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(\mathbf{D}_n^{(1)},0\right),\left(0,\mathbf{D}_n^{(2,2)}\right)\right]\right|\nonumber\\
S_4&=\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')(0,2p),(\mathbf{V}_n-\mathbf{V}_n')(0,1)\right]-2\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(0,\mathbf{D}_n^{(2,1)}\right),\left(0,\mathbf{D}_n^{(2,2)}\right)\right]\right|\nonumber\\
S_5&=\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{V}_n-\mathbf{V}_n')(0,1),(\mathbf{T}_n-\mathbf{T}_n')(1,0)\right]-\frac{2}{3}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(0,\mathbf{D}_n^{(2,2)}\right),\left(\mathbf{D}_n^{(1)},0\right)\right]\right|\nonumber\\
S_6&=\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{V}_n-\mathbf{V}_n')(0,1),(\mathbf{V}_n-\mathbf{V}_n')(0,1)\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(0,\mathbf{D}_n^{(2,2)}\right),\left(0,\mathbf{D}_n^{(2,2)}\right)\right]\right|\nonumber\\
S_7&=\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(0,\mathbf{D}_n^{(2,1)}\right),\left(0,\mathbf{D}_n^{(2,1)}\right)\right]\right|\label{s1s2}. \end{aligned}$$ The following bounds are obtained in Lemma \[lemma8\_app\], in the appendix: $$\begin{aligned}
&S_1\leq \frac{\sqrt{5}\|g\|_{M^2}}{12n},\quad S_2\leq\frac{\sqrt{5}\|g\|_{M^2}}{12n},\quad S_3\leq\frac{\sqrt{178}\|g\|_{M^2}}{6n}, \quad S_4\leq\frac{\sqrt{178}\|g\|_{M^2}}{6n} \nonumber\\
&S_5\leq\frac{\sqrt{178}\|g\|_{M^2}}{12n}, \quad S_6\leq \frac{\sqrt{612}\|g\|_{M^2}}{6n}, \quad S_7\leq\frac{\|g\|_{M^2}}{n}.\label{s_est}\end{aligned}$$
Note that, by (\[4\_int\]) and (\[s\_est\]), $$\begin{aligned}
&\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\mathbf{D}_n,\mathbf{D}_n\right]\right|\nonumber\\
=&\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')(2,2p)+(\mathbf{V}_n-\mathbf{V}_n')(0,1),(\mathbf{T}_n-\mathbf{T}_n')(1,0)+(\mathbf{V}_n-\mathbf{V}_n')(0,1)\right]\right.\nonumber\\
\leq&11\|g\|_{M^2}n^{-1}.\label{4.8}\end{aligned}$$
Using Theorem \[theorem1\] together with (\[4.8\]) and (\[4.1.1.1\]) gives the desired result.
\[remark\_reasons\] The reasons for the covariance structure of $\mathbf{D}_n$ taking the particular form described in Section \[section3\] become clear when we look at (\[s1s2\]) and (\[s\_est\]). The processes we compare are two-dimensional. The $\mathbf{D}_n^{(1)}$-part of the pre-limiting process $\mathbf{D}_n$ corresponds to the contribution of $\mathbf{T}_n-\mathbf{T}_n'$ to the first coordinate in processes $(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n$ and $\mathbf{Y}_n-\mathbf{Y}_n'$. Similarly, $\mathbf{D}_n^{(2,1)}$ corresponds to the contribution of $\mathbf{T}_n-\mathbf{T}_n'$ to the second coordinate and $\mathbf{D}_n^{(2,2)}$ corresponds to the contribution of $\mathbf{V}_n-\mathbf{V}_n'$ to the second coordinate.
The covariances are chosen so that at any time points $s,t\in[0,1]$,\
$\text{Cov}\left(\mathbf{D}_n(s),\mathbf{D}_n(t)\right)$ is close to $\text{Cov}\left((\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n(s),(\mathbf{Y}_n-\mathbf{Y}_n')(t)\right)$. This makes the bounds in (\[s\_est\]) small. Specifically, the only contribution to $$\text{Cov}(\mathbf{D}_n(s),\mathbf{D}_n(t))-\text{Cov}\left((\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n(s),(\mathbf{Y}_n-\mathbf{Y}_n')(t)\right)$$ for $s,t\in[0,1]$ comes from the covariance of $\mathbf{D}_n^{(1)}$ and this is achieved by choosing specific values for $\text{Cov}\left(\mathbf{D}_n^{(2)}(s),\mathbf{D}_n^{(2)}(t)\right)$ and $\text{Cov}\left(\mathbf{D}_n^{(1)}(s),\mathbf{D}_n^{(2)}(t)\right)$ for $s,t\in[0,1]$.
The covariance structure of $\mathbf{D}_n^{(1)}$ is chosen so that $$\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(0,\mathbf{D}_n^{(2,1)}\right),\left(0,\mathbf{D}_n^{(2,1)}\right)\right]\right|$$ is small and this choice is made in an arbitrary way.
Distance from the continuous process
------------------------------------
We now establish a bound on the speed of convergence of $\mathbf{Y}_n$ to a continuous Gaussian process whose covariance is the limit of the covariance of $\mathbf{D}_n$. We do this by bounding the distance between $\mathbf{D}_n$ and the continuous process via the Brownian modulus of continuity and using Theorem \[theorem\_pre\_limiting\].
\[theorem\_continuous\] Let $\mathbf{Y}_n$ be defined as in Subsection \[section1\] and let $\mathbf{Z}=(\mathbf{Z}^{(1)},\mathbf{Z}^{(2)})$ be defined by: $$\begin{cases}
\mathbf{Z}^{(1)}(t)=\frac{\sqrt{p(1-p)}}{\sqrt{2+8p^2}}t\mathbf{B}_1(t^2)+\frac{p\sqrt{2p(1-p)}}{\sqrt{1+4p^2}}t\mathbf{B}_2(t^2),\\
\mathbf{Z}^{(2)}(t)=\frac{p\sqrt{2p(1-p)}}{\sqrt{1+4p^2}}t\mathbf{B}_1(t^2)+\frac{2p^2\sqrt{2p(1-p)}}{\sqrt{1+4p^2}}t\mathbf{B}_2(t^2)
\end{cases},$$ where $\mathbf{B}_1,\mathbf{B}_2$ are independent standard Brownian Motions. Then, for any $g\in M^2$: $$\left|\mathbbm{E}g(\mathbf{Y}_n)-\mathbbm{E}g(\mathbf{Z})\right|\leq \|g\|_{M^2}\left(913n^{-1/2}\sqrt{\log n}+112n^{-1/2}\right).$$
Theorem \[theorem\_continuous\], together with Proposition \[prop\_m\], implies that $\mathbf{Y}_n$ converges to $\mathbf{Z}$ in distribution with respect to the Skorokhod and uniform topologies.
In **Step 1** of the proof of Theorem \[theorem\_continuous\], we provide a coupling between $\mathbf{D}_n$ and i.i.d standard Brownian Motions. Using those Brownian Motions, we construct a process $\mathbf{Z}_n$ having the same distribution as $\mathbf{D}_n$. In **Step 2** we couple $\mathbf{Z}_n$ and $\mathbf{Z}$ and bound the first two moments of the supremum distance between them, using the Brownian modulus of continuity. In **Step 3** we use those bounds together with the Mean Value Theorem to obtain Theorem \[theorem\_continuous\].
\
**Step 1.** Let $\mathbf{B}_1$, $\mathbf{B}_2$, $\mathbf{B}_3$, $\mathbf{B}_4$, $\mathbf{B}_5$ be i.i.d. standard Brownian Motions and let $\mathbf{Z}_n=\left(\mathbf{Z}_n^{(1)},\mathbf{Z}_n^{(2)}\right)$ be defined by: $$\begin{aligned}
\text{A)}\quad \mathbf{Z}_n^{(1)}(t)=&\frac{(\lfloor nt\rfloor -2)\sqrt{p(1-p)}}{n^2\sqrt{2+8p^2}}\mathbf{B}_1\left(\lfloor nt\rfloor(\lfloor nt\rfloor -1)\right)\\
&+\frac{(\lfloor nt\rfloor -2)p\sqrt{2p(1-p)}}{n^2\sqrt{1+4p^2}}\mathbf{B}_2\left(\lfloor nt\rfloor(\lfloor nt\rfloor -1)\right);\\
\text{B)}\quad \mathbf{Z}_n^{(2)}(t)=&\frac{(\lfloor nt\rfloor -2)p\sqrt{2p(1-p)}}{n^2\sqrt{1+4p^2}}\mathbf{B}_1\left(\lfloor nt\rfloor(\lfloor nt\rfloor -1)\right)\\
&+\frac{(\lfloor nt\rfloor -2)2p^2\sqrt{2p(1-p)}}{n^2\sqrt{1+4p^2}}\mathbf{B}_2\left(\lfloor nt\rfloor(\lfloor nt\rfloor -1)\right)\\
&+\frac{\lfloor nt\rfloor -2}{n^{5/2}}\mathbf{B}_3\left(\lfloor nt\rfloor(\lfloor nt\rfloor-1)\right)+\frac{p(1-p)}{\sqrt{2}n^2}\mathbf{B}_4\left(\lfloor nt\rfloor^2(\lfloor nt\rfloor-1)\right)\\
&+\frac{\sqrt{2p^3(1-p)}}{n^2}\mathbf{B}_5(1).\end{aligned}$$ Now, note that $\left(\mathbf{D}_n^{(1)},\mathbf{D}_n^{(2)}\right)\stackrel{\mathcal{D}}=\left(\mathbf{Z}_n^{(1)},\mathbf{Z}_n^{(2)}\right)$. To see this, observe that for all $u,t\in[0,1]$, $$\begin{aligned}
\text{A)}\quad&\mathbbm{E}\mathbf{D}_n^{(1)}(t)\mathbf{D}_n^{(1)}(u)=(\lfloor nt\rfloor -2)(\lfloor nu\rfloor -2)\lfloor n(t\wedge u)\rfloor(\lfloor n(t\wedge u)\rfloor-1)\frac{p(1-p)}{2n^4}\nonumber\\
=&\mathbbm{E}\mathbf{Z}_n^{(1)}(t)\mathbf{Z}_n^{(1)}(u)\nonumber;\\
\text{B)}\quad&\mathbbm{E}\mathbf{D}_n^{(2)}(t)\mathbf{D}_n^{(2)}(u)=\mathbbm{E}\mathbf{Z}_n^{(2)}(t)\mathbf{Z}_n^{(2)}(u);\nonumber\\
\text{C)}\quad&\mathbbm{E}\mathbf{D}_n^{(1)}(t)\mathbf{D}_n^{(2)}(u)=(\lfloor nt\rfloor -2)(\lfloor nu\rfloor -2)\lfloor n(t\wedge u)\rfloor(\lfloor n(t\wedge u)\rfloor-1)\frac{p^2(1-p)}{n^4}\nonumber\\
=&\mathbbm{E}\mathbf{Z}_n^{(1)}(t)\mathbf{Z}_n^{(2)}(u),\label{cov_structure}\end{aligned}$$ where B) is proved in Lemma \[lemma9\_app\], in the appendix.
**Step 2.** We let $\mathbf{Z}$ and $\mathbf{Z}_n$ be coupled in such a way that $\mathbf{Z}$ is constructed as in Theorem \[theorem\_continuous\], using the same Brownian Motions $\mathbf{B}_1,\mathbf{B}_2$, as the ones used in the construction of $\mathbf{Z}_n$. In Lemma \[lemma10\_app\], proved in the appendix, we derive bounds for moments of the supremum distance between $\mathbf{Z}$ and $\mathbf{Z}_n$: $$\begin{aligned}
&\mathbbm{E}\left\|\mathbf{Z}_n-\mathbf{Z}\right\|\leq\frac{12}{n^{1/2}}+\frac{51\sqrt{\log n}}{\sqrt{n}};\nonumber\\
&\mathbbm{E}\left\|\mathbf{Z}_n-\mathbf{Z}\right\|^2\leq\frac{121}{n}+\frac{743\log n}{n};\nonumber\\
&\mathbbm{E}\|\mathbf{Z}\|^2\leq 5.\label{4.1.2.1}\end{aligned}$$
**Step 3.** We note that $\|Dg(w)\|\leq \|g\|_{M^{2}}(1+\|w\|)$ and therefore, by (\[4.1.2.1\]): $$\begin{aligned}
\left|\mathbbm{E}g(\mathbf{Z})-\mathbbm{E}g(\mathbf{D}_n)\right|\stackrel{\text{MVT}}\leq&\mathbbm{E}\left[\sup_{c\in[0,1]}\left\|Dg(\mathbf{Z}+c(\mathbf{Z}_n-\mathbf{Z}))\right\|\|\mathbf{Z}-\mathbf{Z}_n\|\right]\\
\leq&\|g\|_{M^2}\mathbbm{E}\left[\sup_{c\in[0,1]}\left(1+\|\mathbf{Z}+c(\mathbf{Z}_n-\mathbf{Z})\|\right)\|\mathbf{Z}-\mathbf{Z}_n\|\right]\\
\leq&\|g\|_{M^{2}}\mathbbm{E}\left[\|\mathbf{Z}-\mathbf{Z}_n\|+\|\mathbf{Z}\|\|\mathbf{Z}-\mathbf{Z}_n\|+\|\mathbf{Z}-\mathbf{Z}_n\|^2\right]\\
\leq&\|g\|_{M^{2}}\left[\mathbbm{E}\|\mathbf{Z}-\mathbf{Z}_n\|+\sqrt{\mathbbm{E}\|\mathbf{Z}\|^2\mathbbm{E}\|\mathbf{Z}-\mathbf{Z}_n\|^2}+\mathbbm{E}\|\mathbf{Z}-\mathbf{Z}_n\|^2\right]\\
\leq&\|g\|_{M^2}\left(901n^{-1/2}+112n^{-1/2}\sqrt{\log n}\right),\end{aligned}$$ which, together with Theorem \[theorem\_pre\_limiting\] gives the desired result.
The representation of $\mathbf{Z}$ in terms of two independent Brownian Motions comes from a careful analysis of the limiting covariance of $\mathbf{D}_n$. Indeed, (\[cov\_structure\]) provides an explicit derivation of the covariance, which converges to the covariance of $\mathbf{Z}$.
Acknowledgements {#acknowledgements .unnumbered}
================
The author would like to thank Gesine Reinert for many helpful discussions and comments on the early versions of this work. The author is also grateful to Andrew Barbour, Christian D[ö]{}bler, Ivan Nourdin, Giovanni Peccati and Yvik Swan for many interesting discussions.
Appendix - technical details of the proofs of Theorems \[combi\_pre\_lim\], \[theorem\_pre\_limiting\] and \[theorem\_continuous\]
==================================================================================================================================
Technical details of the proof of Theorem \[combi\_pre\_lim\]
-------------------------------------------------------------
\[lemma1\_app\] In the setup of Theorem \[theorem\_pre\_limiting\] and for $\epsilon_2$ defined by Theorem \[theorem1\], $$\begin{aligned}
\epsilon_2=&\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbf{D}_n,\mathbf{D}_n]\right|\nonumber\\
\leq& A+B,\end{aligned}$$ for $$\begin{aligned}
A=&\left|\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left[\frac{(X_{ik}-X_{il})^2}{2n}-\frac{\hat{Z}_i^2}{n-1}\right]\right.\right.\nonumber\\
&\phantom{\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}}\cdot\left.\left(D^2f(Y_{n,ijkl})-D^2f\left(Y_{n}^{ijkl}\right)\right)\left[\mathbbm{1}_{[i/n,1]}\mathbbm{1}_{[i/n,1]}\right]\vphantom{\left[\frac{1^2}{2^2}\right]}\right\rbrace\nonumber\\
&+\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left[\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}-\hat{Z}_i\hat{Z}_j\right]\right.\nonumber\\
&\left.\left.\hphantom{\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}}\cdot\left(D^2f(Y_{n,ijkl})-D^2f\left(Y_{n}^{ijkl}\right)\right)\left[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}\right]\vphantom{\left[\frac{1^2}{2^2}\right]}\right\rbrace\vphantom{\frac{1}{2}\underset{2}{\sum_{2}}}\right|\nonumber,\\
B=&\left|\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left[\frac{(X_{ik}-X_{il})^2}{2n}-\frac{\hat{Z}_i^2}{n-1}\right]D^2f\left(Y_{n}^{ijkl}\right)\left[\mathbbm{1}_{[i/n,1]}\mathbbm{1}_{[i/n,1]}\right]\right\rbrace\right.\nonumber\\
&\left.+\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left[\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}-\hat{Z}_i\hat{Z}_j\right]\right.\right.\nonumber\\
&\phantom{\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}}\left.\left.\cdot D^2f\left(Y_{n}^{ijkl}\right)\left[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}\right]\vphantom{\left[\frac{1^2}{2^2}\right]}\right\rbrace\vphantom{\frac{1^2}{2}\underset{2}{\sum_{2}}}\right|.\nonumber\end{aligned}$$
Note that $$\begin{aligned}
\epsilon_2=&\left|\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{Y}_n-\mathbf{Y}_n')\Lambda_n,\mathbf{Y}_n-\mathbf{Y}_n'\right]-\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbf{D}_n,\mathbf{D}_n]\right|\nonumber\\
=&\left|\frac{n-1}{4}\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbf{Y}_n-\mathbf{Y}_n',\mathbf{Y}_n-\mathbf{Y}_n']-\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbf{D}_n,\mathbf{D}_n]\right|\label{eps222}\end{aligned}$$ and $$\begin{aligned}
&\frac{n-1}{4}\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbf{Y}_n-\mathbf{Y}_n',\mathbf{Y}_n-\mathbf{Y}_n']-\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbf{D}_n,\mathbf{D}_n]\nonumber\\
=&\frac{1}{2ns_n^2}\sum_{i,j=1}^n\mathbbm{E}\left\lbrace(X_{i\pi(i)}-X_{i\pi(j)})^2D^2f(\mathbf{Y}_n)\left[\mathbbm{1}_{[i/n,1]}\mathbbm{1}_{[i/n,1]}\right]\right\rbrace\nonumber\\
&+\frac{1}{2ns_n^2}\sum_{i,j=1}^n\mathbbm{E}\left\lbrace(X_{i\pi(i)}-X_{i\pi(j)})(X_{j\pi(j)}-X_{j\pi(i)})D^2f(\mathbf{Y}_n)\left[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}\right]\right\rbrace\nonumber\\
& -\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbf{D}_n,\mathbf{D}_n]\nonumber\\
=&\frac{1}{2n^2(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace(X_{ik}-X_{il})^2\left.\cdot D^2f(\mathbf{Y}_n)\left[\mathbbm{1}_{[i/n,1]}\mathbbm{1}_{[i/n,1]}\right]\right|\pi(i)=k,\pi(j)=l\right\rbrace\nonumber\\
&+\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left[\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}\right]\right.\nonumber\\
&\phantom{\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}}\cdot\left.D^2f(\mathbf{Y}_n)\left[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}\right]\left.\vphantom{\frac{1}{2}}\right|\pi(i)=k,\pi(j)=l\vphantom{\frac{1}{2}}\right\rbrace\nonumber\\
&-\frac{1}{s_n^2}\sum_{1\leq i\neq j\leq n}\mathbbm{E}[\hat{Z}_i\hat{Z}_j]\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}]\nonumber\\
&-\frac{1}{(n-1)s_n^2}\sum_{1\leq i\neq j\leq n}\mathbbm{E}[\hat{Z}_i^2]\mathbbm{E}D^2f(\mathbf{Y}_n)[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[i/n,1]}]\nonumber\\
=&\frac{1}{2n^2(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace (X_{ik}-X_{il})^2 D^2f(Y_{n,ijkl})\left[\mathbbm{1}_{[i/n,1]}\mathbbm{1}_{[i/n,1]}\right]\right\rbrace\nonumber\\
&+\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}D^2f(Y_{n,ijkl})\left[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}\right]\right\rbrace\nonumber\\
&-\frac{1}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}[\hat{Z}_i\hat{Z}_j]\mathbbm{E}D^2f(Y_{n,ijkl})[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[j/n,1]}]\nonumber\\
&-\frac{1}{n(n-1)^2s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}[\hat{Z}_i^2]\mathbbm{E}D^2f(Y_{n,ijkl})[\mathbbm{1}_{[i/n,1]},\mathbbm{1}_{[i/n,1]}].\label{eps22}\end{aligned}$$ Now, the lemma follows by taking the absolute value in (\[eps22\]) and combining it with (\[eps222\]).
\[lemma2\_app\] For $A$ of (\[a\_def\]), $$\begin{aligned}
A\leq&\frac{\|g\|_{M^1}}{n^3(n-1)s_n^3}\sum_{1\leq i,j,k,l,u\leq n}\left\lbrace\vphantom{\sum_1^2}\mathbbm{E}|X_{ik}|^3+5\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|^2+7\mathbbm{E}|X_{ik}|^2\mathbbm{E}|X_{jl}|\right.\nonumber\\
&+5\mathbbm{E}|X_{ik}|^2\mathbbm{E}|X_{jk}|+16\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|\mathbbm{E}|X_{jl}|+2\mathbbm{E}|X_{iu}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|\nonumber\\
&+4\mathbbm{E}|X_{iu}|\mathbbm{E}|X_{il}|\mathbbm{E}|X_{jk}|+6\mathbbm{E}|X_{uk}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{jl}|+2\mathbbm{E}|X_{uk}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{jk}|\nonumber\\
&\left.+\frac{1}{n}\left(2\mathbbm{E}\left|X_{ik}\right|+2\mathbbm{E}\left|X_{j,l}\right|+2\mathbbm{E}|X_{uk}|+2\mathbbm{E}|X_{ul}|\right)\cdot\sum_{r=1}^n\left(\mathbbm{E}|X_{ir}|^2+|c_{ir}c_{jr}|\right)\right\rbrace.\nonumber\end{aligned}$$
Let us adopt the notation of the proof of Theorem \[combi\_pre\_lim\]. Define index sets $\mathcal{I}=\lbrace i,j,\pi^{-1}(k),\pi^{-1}(l)\rbrace$ and $\mathcal{J}=\lbrace k,l,\pi(i),\pi(j)\rbrace$. Then, letting $\mathbf{S}=\frac{1}{s_n}\sum_{i'\not\in\mathcal{I}}X_{i'\pi(i')}\mathbbm{1}_{[i'/n,1]}$, we can write: $$\mathbf{Y}_{n,ijkl}=\mathbf{S}+\frac{1}{s_n}\sum_{i'\in\mathcal{I}}X_{i'\pi_{ijkl}(i')}\mathbbm{1}_{[i'/n,1]},\qquad \mathbf{Y}_n^{ijkl}=\mathbf{S}+\frac{1}{s_n}\sum_{i'\in\mathcal{I}}X_{i'\pi(i')}^{ijkl}\mathbbm{1}_{[i'/n,1]}.$$ Since $\mathbf{S}$ depends only on the components of $\mathbbm{X}$ outside the square $\mathcal{I}\times\mathcal{J}$ and $\lbrace \pi(i):i\not\in\mathcal{I}\rbrace$, $\mathbf{S}$ is independent of: $$\left\lbrace X_{il},X_{jk},X_{ik},X_{jl},\sum_{i'\in\mathcal{I}}X_{i'\pi_{ijkl}(i')},\sum_{i'\in\mathcal{I}}X_{i'\pi(i')}^{ijkl}\right\rbrace,$$ given $\pi^{-1}(k), \pi^{-1}(l),\pi(i),\pi(j)$.
Note that, by Proposition \[prop12.7\], $$\begin{aligned}
A\leq&\frac{\|g\|_{M^1}}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left\|Y_{n,ijkl}-\mathbf{Y}_n^{ijkl}\right\|\left(\left|\frac{(X_{ik}-X_{il})^2}{2n}-\frac{\mathbbm{E}\hat{Z}_i^2}{n-1}\right|\right.\right.\nonumber\\
&\hphantom{\frac{\|g\|_{M^1}}{n(n-1)s_n^2}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\leq}\left.\left.+\left|\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}-\mathbbm{E}(\hat{Z}_i\hat{Z}_j)\right|\right)\right\rbrace\nonumber\\
\leq&\frac{\|g\|_{M^1}}{n(n-1)s_n^3}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\sum_{i'\in\mathcal{I}}\mathbbm{E}\left\lbrace\vphantom{\left|\frac{1^2}{1^2}\right|}\left|X_{i',\pi_{ijkl}(i')}-X_{i'\pi(i')}^{ijkl}\right|\right.\nonumber\\
&\left.\cdot\left(\left|\frac{(X_{ik}-X_{il})^2}{2n}-\frac{\mathbbm{E}\hat{Z}_i^2}{n-1}\right|+\left|\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}-\mathbbm{E}(\hat{Z}_i\hat{Z}_j)\right|\right)\right\rbrace\nonumber\\
\leq& \frac{\|g\|_{M^1}}{n(n-1)s_n^3}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\vphantom{\frac{1^2}{2^2}}\left(\left|X_{ik}-X^{ijkl}_{i,\pi(i)}\right|+\left|X_{j,l}-X^{ijkl}_{j,\pi(j)}\right|+\left|X_{i,k}-X_{\pi^{-1}(k),k}^{ijkl}\right|\right.\right.\nonumber\\
&\left.\left.+\left|X_{j,l}-X_{\pi^{-1}(l),l}^{ijkl}\right|\right)\left(\left|\frac{(X_{ik}-X_{il})^2}{2n}-\frac{\mathbbm{E}\hat{Z}_i^2}{n-1}\right|+\left|\frac{(X_{ik}-X_{il})(X_{jl}-X_{jk})}{2n}-\mathbbm{E}(\hat{Z}_i\hat{Z}_j)\right|\right)\right\rbrace\nonumber\\
\leq&\frac{\|g\|_{M^1}}{2n(n-1)^2s_n^3}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left(2\left|X_{ik}\right|+\left|X^{ijkl}_{i,\pi(i)}\right|+2\left|X_{j,l}\right|+\left|X^{ijkl}_{j,\pi(j)}\right|+\left|X_{\pi^{-1}(k),k}^{ijkl}\right|\right.\right.\nonumber\\
&\left.+\left|X_{\pi^{-1}(l),l}^{ijkl}\right|\right)\left(\left|X_{ik}\right|^2+\left|X_{il}\right|^2+2\left|X_{ik}X_{il}\right|+2\left|\hat{Z}_i\right|^2+\left|X_{ik}X_{jl}\right|+\left|X_{ik}X_{jk}\right|\right.\nonumber\\
&\left.\left.+\left|X_{il}X_{jl}\right|+\left|X_{il}X_{jk}\right|+2(n-1)\left|\mathbbm{E}(\hat{Z}_i\hat{Z}_j)\right|\right)\right\rbrace\nonumber\\
\leq&\frac{\|g\|_{M^1}}{2n^2(n-1)s_n^3}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace\left(\left|X_{ik}\right|+\left|X_{j,l}\right|\right)\left(\left|X_{ik}\right|^2+\left|X_{il}\right|^2+2\left|X_{ik}X_{il}\right|+\frac{2}{n}\sum_{r=1}^n\mathbbm{E}|X_{ir}|^2\right.\right.\nonumber\\
&\left.\left.+\left|X_{ik}X_{jl}\right|+\left|X_{ik}X_{jk}\right|+\left|X_{il}X_{jl}\right|+\left|X_{il}X_{jk}\right|+\frac{2}{n}\sum_{r=1}^n|c_{ir}c_{jr}|\right)\right\rbrace\nonumber\\
&+\frac{\|g\|_{M^1}}{n^3(n-1)s_n^3}\underset{i\neq j,k\neq l}{\sum_{1\leq i,j,k,l,u\leq n}}\left(\mathbbm{E}|X_{i,u}|+\mathbbm{E}|X_{j,u}|+\mathbbm{E}|X_{uk}|+\mathbbm{E}|X_{u,l}|\right)\mathbbm{E}\left\lbrace\vphantom{\frac{1}{2}\sum_1^2}\left|X_{ik}\right|^2+\left|X_{il}\right|^2\right.\nonumber\\
&\left.+2\left|X_{ik}X_{il}\right|+\frac{1}{n}\sum_{r=1}^n\mathbbm{E}|X_{ir}|^2+\left|X_{ik}X_{jl}\right|+\left|X_{ik}X_{jk}\right|+\left|X_{il}X_{jl}\right|+\left|X_{il}X_{jk}\right|+\frac{1}{n}\sum_{r=1}^n|c_{ir}c_{jr}|\right\rbrace\nonumber\\
\leq&\frac{\|g\|_{M^1}}{n^3(n-1)s_n^3}\sum_{1\leq i,j,k,l,u\leq n}\left\lbrace\vphantom{\sum_1^2}\mathbbm{E}|X_{ik}|^3+5\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|^2+7\mathbbm{E}|X_{ik}|^2\mathbbm{E}|X_{jl}|\right.\nonumber\\
&+5\mathbbm{E}|X_{ik}|^2\mathbbm{E}|X_{jk}|+16\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|\mathbbm{E}|X_{jl}|+2\mathbbm{E}|X_{iu}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{il}|\nonumber\\
&+4\mathbbm{E}|X_{iu}|\mathbbm{E}|X_{il}|\mathbbm{E}|X_{jk}|+6\mathbbm{E}|X_{uk}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{jl}|+2\mathbbm{E}|X_{uk}|\mathbbm{E}|X_{ik}|\mathbbm{E}|X_{jk}|\nonumber\\
&\left.+\frac{1}{n}\left(2\mathbbm{E}\left|X_{ik}\right|+2\mathbbm{E}\left|X_{j,l}\right|+2\mathbbm{E}|X_{uk}|+2\mathbbm{E}|X_{ul}|\right)\cdot\sum_{r=1}^n\left(\mathbbm{E}|X_{ir}|^2+|c_{ir}c_{jr}|\right)\right\rbrace.\nonumber\end{aligned}$$ which finishes the proof.
Technical details of the proof of Theorem \[theorem\_pre\_limiting\]
--------------------------------------------------------------------
\[lemma8\_app\] For $S_i,i=1,\cdots,7$ of (\[s1s2\]), we have the following estimates: $$\begin{aligned}
&S_1\leq \frac{\sqrt{5}\|g\|_{M^2}}{12n},\quad S_2\leq\frac{\sqrt{5}\|g\|_{M^2}}{12n},\quad S_3\leq\frac{\sqrt{178}\|g\|_{M^2}}{6n}, \quad S_4\leq\frac{\sqrt{178}\|g\|_{M^2}}{6n} \nonumber\\
&S_5\leq\frac{\sqrt{178}\|g\|_{M^2}}{12n}, \quad S_6\leq \frac{\sqrt{612}\|g\|_{M^2}}{6n}, \quad S_7\leq\frac{\|g\|_{M^2}}{n}.\end{aligned}$$
For $S_1$, for fixed $i,j\in\lbrace 1,\cdots, n\rbrace$, let $\mathbf{Y}_n^{ij}$ be equal to $\mathbf{Y}_n$ except for the fact that $I_{ij}$ is replaced by an independent copy, i.e. for all $t\in [0,1]$ let: $$\begin{aligned}
\mathbf{T}_n^{ij}(t)&=\mathbf{T}_n(t)-\frac{\lfloor nt\rfloor-2}{n^2}\left(I_{ij}-I_{ij}'\right)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(t)\\
\mathbf{V}_n^{ij}(t)&=\mathbf{V}_n(t)-\frac{1}{n^2}\sum_{k:k\neq i,j}\left(I_{ij}-I_{ij}'\right)\left(I_{jk}+I_{ik}\right)\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(t)\end{aligned}$$ and let $\mathbf{Y}_n^{ij}(t)=\left(\mathbf{T}_n^{ij}(t)-\mathbbm{E}\mathbf{T}_n(t),\mathbf{V}_n^{ij}(t)-\mathbbm{E}\mathbf{V}_n(t)\right)$.
By noting that the mean zero $Z_i^{(1)}$ and $Z_j^{(1)}$ are independent for $i\neq j$, we obtain: $$\begin{aligned}
S_1=&\left|\vphantom{\sum_1^1}\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')(2,0),(\mathbf{T}_n-\mathbf{T}_n')(1,0)\right]\right.\nonumber\\
&\left.-\sum_{j,k=1}^n\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\sum_{i=1}^{n}Z_{i,k}^{(1)}(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[k/n,1]},\right.\right.\nonumber\\
&\phantom{-\sum_{j,k=1}^n\mathbbm{E}D^2f(Y_n)\left[\right]}\left.\left.\sum_{i=1}^{n}Z_{i,j}^{(1)}(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}\right]\right|\nonumber\\
=&\left|\frac{1}{4n^4}\sum_{1\leq i\neq j\leq n}\mathbbm{E}\left\lbrace\left(I_{i,j}-2pI_{i,j}+p\right)\right.\right.\nonumber\\
&\phantom{\,\,\frac{1}{4n^4}\sum_{1\leq i\neq j\leq n}}\left.\cdot D^2f(\mathbf{Y}_n)\left[(\lfloor n\cdot \rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(1,0),(\lfloor n\cdot \rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(1,0)\right]\right\rbrace\nonumber\\
&-\sum_{i,j=1}^n\left\lbrace\mathbbm{E}\left(Z_{i,j}^{(1)}\right)^2\right.\nonumber\\
&\left.\left.\hphantom{-\sum_{i,j=1}^n}\cdot\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[j/n,1]},(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}\right]\vphantom{\left(Z^{1}_2\right)^2}\right\rbrace\vphantom{\frac{1}{4n^2}\sum_{i}}\right|\nonumber\\
=&\left|\sum_{1\leq i\neq j\leq n}\mathbbm{E}\left\lbrace \left(\frac{1}{4n^4}(I_{i,j}-2pI_{i,j}+p)-\mathbbm{E}\left(Z_{i,j}^{(1)}\right)^2\right)\right.\right.\nonumber\\
&\left.\left.\hphantom{\sum_{1\leq i\neq j\leq n}\mathbbm{E}}\cdot D^2f(\mathbf{Y}_n)\left[(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[j/n,1]},(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}\right]\vphantom{\frac{1}{4n^2}}\right\rbrace\vphantom{\sum_1^2}\right|\nonumber\\
=&\left|\sum_{1\leq i\neq j\leq n}\mathbbm{E}\left\lbrace \frac{1}{4n^4}(I_{i,j}-2pI_{i,j}+p)\right.\right.\nonumber\\
&\left.\left.\cdot\left(D^2f(\mathbf{Y}_n)-D^2f(\mathbf{Y}_n^{ij})\right)\left[(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[j/n,1]},(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}\right]\vphantom{\frac{1}{n^2}}\right\rbrace\vphantom{\sum_1^2}\right|\nonumber\\
\leq&\frac{\|g\|_{M^2}}{12n^2}\sum_{1\leq i\neq j\leq n}\mathbbm{E}\left|(I_{i,j}-2pI_{i,j}+p)\right|\left\|\mathbf{Y}_n-\mathbf{Y}_n^{ij}\right\|\label{eq_star},\end{aligned}$$ where (\[eq\_star\]) follows from Proposition \[prop12.7\]. Now, $$\left\|\mathbf{Y}_n-\mathbf{Y}_n^{ij}\right\|\leq\frac{1}{n^2}\sqrt{(\lfloor n\cdot\rfloor -2)^2(I_{ij}-I_{ij}')^2+\left(\sum_{k:k\neq i,j}|I_{ij}-I_{ij}'|(I_{jk}+I_{ik})\right)^2}$$ and so, by (\[eq\_star\]), $$\begin{aligned}
S_1\leq&\frac{\|g\|_{M^2}}{12n^4}\sum_{1\leq i\neq j\leq n}\mathbbm{E}\left\lbrace\vphantom{\sqrt{(n-2)^2(I_{ij}-I_{ij}')^2+\left(\sum_{k\neq i,j}|I_{ij}-I_{ij}'|(I_{jk}+I_{ik})\right)^2}}\left|I_{i,j}-2pI_{i,j}+p\right|\right.\nonumber\\
&\left.\hphantom{\frac{\|g\|_{M^2}}{12n^4}\sum_{1\leq i\neq j\leq n}\mathbbm{E}}\cdot\sqrt{(n-2)^2(I_{ij}-I_{ij}')^2+\left(\sum_{k\neq i,j}|I_{ij}-I_{ij}'|(I_{jk}+I_{ik})\right)^2}\right\rbrace\nonumber\\
\leq&\frac{\|g\|_{M^2}}{12n^3}\sum_{1\leq i\neq j\leq n}\mathbbm{E}\left\lbrace\left|I_{i,j}-2pI_{i,j}+p\right|\cdot\sqrt{(I_{ij}-I_{ij}')^2+\left(|I_{ij}-I_{ij}'|(I_{jk}+I_{ik})\right)^2}\right\rbrace\nonumber\\
\leq&\frac{\sqrt{5}\|g\|_{M^2}}{12n},\label{4.1}\end{aligned}$$ where the last inequality holds because $|I_{ij}-2pI_{ij}+p|\leq 1$, $|I_{ij}-I_{ij}'|\leq 1$ and $I_{jk}+I_{ik}\leq 2$ for all $k\in\lbrace 1,\cdots,n\rbrace$.
Similarly, for $S_2$: $$\begin{aligned}
S_2=&\left|\vphantom{\left[\sum_1^1\right]}\frac{n(n-1)}{8}\mathbbm{E}\left\lbrace D^2f(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')(0,2p),(\mathbf{T}_n-\mathbf{T}_n')(1,0)\right]\right\rbrace\right.\nonumber\\
&-2\sum_{j,k=1}^n\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\sum_{i=1}^{n}Z_{i,k}^{(2,1)}(\lfloor n\cdot \rfloor -2)\mathbbm{1}_{[i/n,1]\cap[k/n,1]}(0,1),\right.\nonumber\\
&\left.\left.\hphantom{-2\sum_{j,k=1}^n\mathbbm{E}D^2f(\mathbf{Y}_n)}\sum_{i=1}^{n}Z_{i,j}^{(1)}(\lfloor n\cdot \rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(1,0)\right]\right|\nonumber\\
=&\left|\frac{p}{4n^4}\sum_{1\leq i\neq j\leq n}\mathbbm{E}\left\lbrace\left(I_{i,j}-2pI_{i,j}+p\right)\right.\right.\nonumber\\
&\cdot \left.D^2f(\mathbf{Y}_n)\left[(\lfloor n\cdot \rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(0,1),(\lfloor n\cdot \rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(1,0)\right]\right\rbrace\nonumber\\
&-\sum_{1\leq i\neq j\leq n}\left\lbrace\mathbbm{E}\left(Z_{i,j}^{(1)}Z_{i,j}^{(2,1)}\right)\right.\nonumber\\
&\left.\left.\cdot\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\lfloor n\cdot \rfloor -2)(0,1)\mathbbm{1}_{[i/n,1]\cap[j/n,1]},(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}\right]\vphantom{\left(Z^1_i\right)}\right\rbrace\vphantom{\frac{p}{4n^2}\sum_{1\leq}}\right|\nonumber\\
\leq&\frac{\sqrt{5}p\|g\|_{M^2}}{12n}\nonumber\\
\leq& \frac{\sqrt{5}\|g\|_{M^2}}{12n}.\label{4.2}\end{aligned}$$ For $S_3$, let $\mathbf{Y}_n^{ijk}$ equal to $\mathbf{Y}_n$ except that $I_{ij},I_{jk},I_{ik}$ are replaced by $I_{ij}'$, $I_{jk}'$, $I_{ik}'$, i.e. for all $t\in[0,1]$ let $$\begin{aligned}
\mathbf{T}_n^{ijk}(t)=&\mathbf{T}_n(t)-\frac{\lfloor nt\rfloor -2}{n^2}\left[(I_{ij}-I_{ij}')\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(t)\right.\nonumber\\
&\left.+(I_{jk}-I_{jk}')\mathbbm{1}_{[j/n,1]\cap[k/n,1]}(t)+(I_{ik}-I_{ik}')\mathbbm{1}_{[i/n,1]\cap[k/n,1]}(t)\right]\nonumber\\
\mathbf{V}_n^{ijk}(t)=&\mathbf{V}_n(t)-\frac{1}{n^2}\sum_{l:l\neq i,j,k}\left[\left(I_{ij}-I_{ij}'\right)\left(I_{jl}+I_{il}\right)\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[l/n,1]}(t)\right.\nonumber\\
&+\left(I_{jk}-I_{jk}'\right)\left(I_{jl}+I_{kl}\right)\mathbbm{1}_{[k/n,1]\cap[j/n,1]\cap[l/n,1]}(t)\nonumber\\
&\left.+\left(I_{ik}-I_{ik}'\right)\left(I_{jl}+I_{il}\right)\mathbbm{1}_{[i/n,1]\cap[k/n,1]\cap[l/n,1]}(t)\right]\nonumber\\
&-\frac{1}{n^2}\left[(I_{ij}I_{jk}-I_{ij}'I_{jk}')+(I_{ij}I_{ik}-I_{ij}'I_{ik}')+(I_{ik}I_{jk}-I_{ik}'I_{jk}')\right]\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(t).\label{eq_ijk}\end{aligned}$$ Let $\mathbf{Y}_n^{ijk}(t)=\left(\mathbf{T}_n^{ijk}(t)-\mathbbm{E}\mathbf{T}_n(t),\mathbf{V}_n^{ijk}(t)-\mathbbm{E}\mathbf{V}_n(t)\right)$ for all $t\in[0,1]$. Note that $$\begin{aligned}
S_3=&\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')(2,0),(\mathbf{V}_n-\mathbf{V}_n')(0,1)\right]\right.\nonumber\\
&\left.-\frac{4}{3}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\sum_{i,j=1}^{n}Z_{i,j}^{(1)}(\lfloor n\cdot \rfloor -2)(1,0)\mathbbm{1}_{[i/n,1]\cap[j/n,1]},\sum_{i,j,k=1}^{n}Z_{i,j,l}^{(2,2)}(0,1)\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[l/n,1]}\right]\right|\nonumber\\
=&\left|\frac{1}{4n^4}\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}\mathbbm{E}\left.\lbrace(I_{ij}-I_{ij}')^2(I_{jk}+I_{ik})\right.\right.\nonumber\\
&\left. \hphantom{\frac{1}{4n^4}\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}\mathbbm{E}}\left.\cdot D^2f(\mathbf{Y}_n)\left[(\lfloor n\cdot\rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(1,0),\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(0,1)\right]\right\rbrace\right.\nonumber\\
&\left.-\frac{4}{3}\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}\mathbbm{E}\left\lbrace Z_{i,j}^{(1)}Z_{i,j,k}^{(2,2)}D^2f(\mathbf{Y}_n)\left[(\lfloor n\cdot \rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(1,0),\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(0,1)\right]\right\rbrace\right|\nonumber\\
=&\left|\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}\mathbbm{E}\left\lbrace\left(\frac{1}{4n^4}(I_{ij}-2pI_{ij}+p)(I_{jk}+I_{ik})-\frac{4}{3}\mathbbm{E}Z_{i,j}^{(1)}Z_{i,j,k}^{(2,2)}\right)\right.\right.\nonumber\\
&\left.\left.\hphantom{\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}\mathbbm{E}}\cdot D^2f(\mathbf{Y}_n)\left[(\lfloor n\cdot \rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(1,0),\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(0,1)\right]\vphantom{\left(\frac{1}{2}\right)}\right\rbrace\vphantom{\frac{1}{2}\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}}\right|\nonumber\\
=&\left|\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}\mathbbm{E}\left\lbrace\left(\frac{1}{4n^4}(I_{ij}-2pI_{ij}+p)(I_{jk}+I_{ik})\right)\right.\right.\nonumber\\
&\left.\left.\cdot\left(D^2f(\mathbf{Y}_n)-D^2f(\mathbf{Y}_n^{ijk})\right)\left[(\lfloor n\cdot \rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(1,0),\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(0,1)\right]\vphantom{\left(\frac{1}{2}\right)}\right\rbrace\vphantom{\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}}\right|\nonumber\\
\leq&\frac{\|g\|_{M^2}}{12n^3}\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq n}}\mathbbm{E}\left(I_{ij}-2pI_{ij}+p\right)\left(I_{jk}+I_{ik}\right)\left\|\mathbf{Y}_n-\mathbf{Y}_n^{ijk}\right\|.\label{eq4.3}\end{aligned}$$ Now, by (\[eq\_ijk\]), we note that: $$\begin{aligned}
\|\mathbf{Y}_n-\mathbf{Y}_n^{ijk}\|\leq&\frac{1}{n^2}\left\lbrace(n-2)^2(|I_{ij}-I_{ij}'|+|I_{jk}-I_{jk}'|+|I_{ik}-I_{ik}'|)^2\right.\\
&+\left[\sum_{l:l\neq i,j,k}\left(|I_{ij}-I'_{ij}|(I_{jl}+I_{il})+|I_{jk}-I_{jk}'|(I_{jl}+I_{kl})\right.\right.\\
&\left.\left.+|I_{ik}-I_{ik}'|(I_{jl}+I_{il})+|I_{ik}-I_{ik}'|(I_{jl}+I_{il})\right)\right.\\
&\left.\left.+|I_{ij}I_{jk}-I_{ij}'I_{jk}'|+|I_{ij}I_{ik}-I_{ij}'I_{ik}'|+|I_{ij}I_{jk}-I_{ij}'I_{jk}'| \right]^2\right\rbrace^{1/2}\\
\leq&\frac{1}{n^2}\sqrt{ 9(n-2)^2+(8(n-3)+3)^2}\\
=&\frac{\sqrt{73n^2-372n+477}}{n^2},\end{aligned}$$ where the second inequality follows from the fact that for all $a,b,c\in\lbrace 1,\cdots, n\rbrace$, $|I_{ab}-I_{ab}'|\leq 1$, $(I_{ab}+I_{bc})\leq 2$ and $|I_{ab}I_{bc}-I_{ab}'I_{bc}'|\leq 1$. Also, $(I_{jk}+I_{ik})\leq 2$ and $I_{ij}-2pI_{ij}+p\leq 1$. Therefore, by (\[eq4.3\]): $$\begin{aligned}
S_3\leq&\frac{\|g\|_Mn(n-1)(n-2)\sqrt{73n^2-372n+477}}{6n^5}\nonumber\\
\leq &\frac{\sqrt{178}\|g\|_{M^2}}{6n}.\label{4.3}\end{aligned}$$ Similarly, $$\begin{aligned}
S_4\leq \frac{\sqrt{178}\|g\|_Mp}{6n}\leq\frac{\sqrt{178}\|g\|_{M^2}}{6n}.\label{4.4}\end{aligned}$$ and, for $S_5$: $$\begin{aligned}
S_5=&\frac{1}{2}\left|\frac{n(n-1)}{8}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[(\mathbf{T}_n-\mathbf{T}_n')(2,0),(\mathbf{V}_n-\mathbf{V}_n')(0,1)\right]-\frac{4}{3}\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\left(\mathbf{D}_n^{(1)},0\right),\left(0,\mathbf{D}_n^{(2,2)}\right)\right]\right|\nonumber\\
\leq&\frac{\sqrt{178}\|g\|_{M^2}}{12n}.\label{4.5}\end{aligned}$$
Now, for $S_6$, let $\mathbf{Y}_n^{ijkl}$ be equal to $\mathbf{Y}_n$ except that $I_{ij},I_{ik},I_{il},I_{jk},I_{jl},I_{kl}$ are replaced with independent copies $I_{ij}',I_{ik}',I_{il}',I_{jk}',I_{jl}',I_{kl}'$, i.e. for all $t\in[0,1]$ let $$\begin{aligned}
\mathbf{T}_n^{ijkl}(t)=&\mathbf{T}_n(t)-\frac{\lfloor nt\rfloor -2}{n^2}\left[(I_{ij}-I_{ij}')\mathbbm{1}_{[i/n,1]\cap[j/n,1]}(t)+(I_{ik}-I_{ik}')\mathbbm{1}_{[i/n,1]\cap[k/n,1]}(t)\right.\nonumber\\
&+(I_{il}-I_{il}')\mathbbm{1}_{[i/n,1]\cap[l/n,1]}(t)+(I_{jk}-I_{jk}')\mathbbm{1}_{[j/n,1]\cap[k/n,1]}(t)\nonumber\\
&\left.+(I_{jl}-I_{jl}')\mathbbm{1}_{[j/n,1]\cap[l/n,1]}(t)+(I_{kl}-I_{kl}')\mathbbm{1}_{[k/n,1]\cap[l/n,1]}(t)\right]\nonumber\\
\mathbf{V}_n^{ijkl}(t)=&\mathbf{V}_n(t)-\frac{1}{n^2}\sum_{m:m\neq i,j,k,l}\left[\left(I_{ij}-I_{ij}'\right)\left(I_{im}+I_{jm}\right)\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[m/n,1]}(t)\right.\nonumber\\
&+\left(I_{ik}-I_{ik}'\right)\left(I_{im}+I_{km}\right)\mathbbm{1}_{[i/n,1]\cap[k/n,1]\cap[m/n,1]}(t)\nonumber\\
&+\left(I_{il}-I_{il}'\right)\left(I_{im}+I_{lm}\right)\mathbbm{1}_{[i/n,1]\cap[l/n,1]\cap[m/n,1]}(t)\nonumber\\
&+\left(I_{jk}-I_{jk}'\right)\left(I_{jm}+I_{km}\right)\mathbbm{1}_{[j/n,1]\cap[k/n,1]\cap[m/n,1]}(t)\nonumber\\
&+\left(I_{jl}-I_{jl}'\right)\left(I_{jm}+I_{lm}\right)\mathbbm{1}_{[j/n,1]\cap[l/n,1]\cap[m/n,1]}(t)\nonumber\\
&\left.+\left(I_{kl}-I_{ll}'\right)\left(I_{km}+I_{lm}\right)\mathbbm{1}_{[k/n,1]\cap[l/n,1]\cap[m/n,1]}(t)\right]\nonumber\\
&-\frac{1}{n^2}\left[(I_{ij}I_{jk}-I_{ij}'I_{jk}')+(I_{ij}I_{ik}-I_{ij}'I_{ik}')+(I_{ik}I_{jk}-I_{ij}'I_{jk}')\right]\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(t)\nonumber\\
&-\frac{1}{n^2}\left[(I_{ij}I_{jl}-I_{ij}'I_{jl}')+(I_{ij}I_{il}-I_{ij}'I_{il}')+(I_{il}I_{jl}-I_{ij}'I_{jl}')\right]\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[l/n,1]}(t)\nonumber\\
&-\frac{1}{n^2}\left[(I_{ik}I_{kl}-I_{ik}'I_{kl}')+(I_{ik}I_{il}-I_{ik}'I_{il}')+(I_{il}I_{kl}-I_{ik}'I_{kl}')\right]\mathbbm{1}_{[i/n,1]\cap[k/n,1]\cap[l/n,1]}(t)\nonumber\\
&-\frac{1}{n^2}\left[(I_{jk}I_{jl}-I_{jk}'I_{jl}')+(I_{jl}I_{kl}-I_{jl}'I_{kl}')+(I_{kl}I_{jk}-I_{kl}'I_{jk}')\right]\mathbbm{1}_{[j/n,1]\cap[k/n,1]\cap[l/n,1]}(t)
\label{eq_ijkl}\end{aligned}$$ and for all $t\in[0,1]$ let $\mathbf{Y}_n^{ijkl}(t)=\left(\mathbf{T}_n^{ijkl}(t)-\mathbbm{E}\mathbf{T}_n,\mathbf{V}_n^{ijkl}(t)-\mathbbm{E}\mathbf{V}_n(t)\right).$ Note that: $$\begin{aligned}
S_6\leq& \left|\frac{1}{8n^4}\sum_{1\leq i\neq j\leq n}\sum_{k\neq i,j}\sum_{l\neq i,j}\mathbbm{E}\left\lbrace(I_{ij}-I_{ij}')^2(I_{jk}+I_{ik})(I_{jl}+I_{il})\right.\right.\nonumber\\
&\left.\left.\cdot D^2f(\mathbf{Y}_n)\left[\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(0,1),\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[l/n,1]}(0,1)\right]\right\rbrace\right.\nonumber\\
&-\left.\mathbbm{E}D^2f(\mathbf{Y}_n)\left[\sum_{i,j,k=1}^nZ_{i,j,k}^{(2,2)}\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(0,1),\sum_{i,j,k=1}^nZ_{i,j,k}^{(2,2)}\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(0,1)\right]\right|\nonumber\\
\leq&\left|\sum_{1\leq i\neq j\leq n}\sum_{k\neq i,j}\sum_{l\neq i,j}\mathbbm{E}\left\lbrace\left(\frac{1}{8n^4}(I_{ij}-I_{ij}')^2(I_{jk}+I_{ik})(I_{jl}+I_{il})-Z_{ijk}^{(2,2)}Z_{ijl}^{(2,2)}\right)\right.\right.\nonumber\\
&\left.\left.\cdot D^2f(\mathbf{Y}_n)\left[\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(0,1),\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[l/n,1]}(0,1)\right]\vphantom{\left(\frac{1}{2}\right)}\right\rbrace\vphantom{\sum_1}\right|\nonumber\\
=&\left|\sum_{1\leq i\neq j\leq n}\sum_{k\neq i,j}\sum_{l\neq i,j}\frac{1}{8n^4}\mathbbm{E}\left\lbrace(I_{ij}-I_{ij}')^2(I_{jk}+I_{ik})(I_{jl}+I_{il})\right.\right.\nonumber\\
&\left.\left.\cdot \left(D^2f(\mathbf{Y}_n)-D^2f(\mathbf{Y}_n^{ijkl})\right)\left[\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[k/n,1]}(0,1),\mathbbm{1}_{[i/n,1]\cap[j/n,1]\cap[l/n,1]}(0,1)\right]\right\rbrace\vphantom{\sum_i\frac{1}{2}}\right|\nonumber\\
\leq& \frac{\|g\|_{M^2}}{24n^4}\underset{i,j,k,l\text{ distinct}}{\sum_{1\leq i,j,k,l\leq n}}\mathbbm{E}\left\lbrace(I_{ij}-2pI_{ij}+p)(I_{jk}+I_{ik})(I_{jl}+I_{il})\|\mathbf{Y}_n-\mathbf{Y}_n^{ijkl}\|\right\rbrace.\label{6.11}\end{aligned}$$ Now, by (\[eq\_ijkl\]), note that: $$\begin{aligned}
&\|\mathbf{Y}_n-\mathbf{Y}_n^{ijkl}\|\\
\leq&\frac{1}{n^2}\left\lbrace\vphantom{\sum_{m:m\neq i,j,k,l}}(n-2)^2\left(|I_{ij}-I_{ij}'|+|I_{ik}-I_{ik}'|+|I_{il}-I_{i}'|+|I_{jk}-I_{jk}'|+|I_{jl}-I_{jl}'|+|I_{kl}-I_{kl}'|\right)^2\right.\\
&+\left[\sum_{m:m\neq i,j,k,l}\left[\left|I_{ij}-I_{ij}'\right|\left(I_{im}+I_{jm}\right)+\left|I_{ik}-I_{ik}'\right|\left(I_{im}+I_{km}\right)+\left|I_{il}-I_{il}'\right|\left(I_{im}+I_{lm}\right)\right.\right.\\
&\left.\hphantom{\sum_{m:m\neq i,j,k,l}}+\left|I_{jk}-I_{jk}'\right|\left(I_{jm}+I_{km}\right)+\left|I_{jl}-I_{jl}'\right|\left(I_{jm}+I_{lm}\right)+\left|I_{kl}-I_{ll}'\right|\left(I_{km}+I_{lm}\right)\right]\\
&+|I_{ij}I_{jk}-I_{ij}'I_{jk}'|+|I_{ij}I_{ik}-I_{ij}'I_{ik}'|+|I_{ik}I_{jk}-I_{ij}'I_{jk}'|+|I_{ij}I_{jl}-I_{ij}'I_{jl}'|\\
&+|I_{ij}I_{il}-I_{ij}'I_{il}'|+|I_{il}I_{jl}-I_{ij}'I_{jl}'|+|I_{ik}I_{kl}-I_{ik}'I_{kl}'|+|I_{ik}I_{il}-I_{ik}'I_{il}'|\\
&+|I_{il}I_{kl}-I_{ik}'I_{kl}'|\left.\left.+|I_{jk}I_{jl}-I_{jk}'I_{jl}'|+|I_{jl}I_{kl}-I_{jl}'I_{kl}'|+|I_{kl}I_{jk}-I_{kl}'I_{jk}'|\vphantom{\sum_{m:m\neq i,j,k,l}}\right]^2 \right\rbrace^{1/2}\\
\leq&\frac{\sqrt{36(n-2)^2+\left(12(n-4)+12\right)^2}}{n^2}\\
=&\frac{\sqrt{180n^2-1008n+1440}}{n^2}.\end{aligned}$$ Therefore, by (\[6.11\]): $$\begin{aligned}
S_7\leq&\frac{\|g\|_{M^2}\cdot 4\sqrt{180n^2-1008n+1440}}{24n^2}\leq \frac{\sqrt{612}\|g\|_{M^2}}{6n}.\label{4.6}\end{aligned}$$ Furthermore, for $S_7$, note that: $$\begin{aligned}
S_7=&\left|\sum_{i,j=1}^n\mathbbm{E}\left(Z_{i,j}^{(2,1)}\right)^2D^2f(\mathbf{Y}_n)\left[\left(0,(\lfloor n\cdot\rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}\right),\left(0,(\lfloor n\cdot\rfloor -2)\mathbbm{1}_{[i/n,1]\cap[j/n,1]}\right)\right]\right|\nonumber\\
\leq&\frac{\|g\|_{M^2}}{n}.\label{4.7}\end{aligned}$$ The result now follows by (\[4.1\]), (\[4.2\]), (\[4.3\]), (\[4.4\]), (\[4.5\]), (\[4.6\]), (\[4.7\]).
Technical details of the proof of Theorem \[theorem\_continuous\]
-----------------------------------------------------------------
\[lemma9\_app\] Using the notation of **Step 1** of the proof of Theorem \[theorem\_continuous\], for all $u,t\in[0,1]$, $$\mathbbm{E}\mathbf{D}_n^{(2)}(t)\mathbf{D}_n^{(2)}(u)=\mathbbm{E}\mathbf{Z}_n^{(2)}(t)\mathbf{Z}_n^{(2)}(u).$$
Note that $$\begin{aligned}
&\mathbbm{E}\mathbf{D}_n^{(2)}(t)\mathbf{D}_n^{(2)}(u)\nonumber\\
=&\mathbbm{E}\mathbf{D}_n^{(2,1)}(t)\mathbf{D}_n^{(2,1)}(u)+\mathbbm{E}\mathbf{D}_n^{(2,1)}(t)\mathbf{D}_n^{(2,2)}(u)+\mathbbm{E}\mathbf{D}_n^{(2,2)}(t)\mathbf{D}_n^{(2,1)}(u)+\mathbbm{E}\mathbf{D}_n^{(2,2)}(t)\mathbf{D}_n^{(2,2)}(u)\nonumber\\
=&(\lfloor nt\rfloor-2)(\lfloor nu\rfloor -2)\sum_{1\leq i,j\leq \lfloor n(t\wedge u)\rfloor}\mathbbm{E}\left[\left(Z_{ij}^{(2,1)}\right)^2\right]\nonumber\\
&+(\lfloor nt\rfloor -2)\underset{i\neq j}{\sum_{1\leq i,j\leq \lfloor n(t\wedge u)\rfloor}}\underset{k\neq i, k\neq j}{\sum_{1\leq k\leq \lfloor nu\rfloor}}\mathbbm{E}Z^{(2,1)}_{i,j}Z^{(2,2)}_{i,j,k}\nonumber\\
&+(\lfloor nu\rfloor -2)\underset{i\neq j}{\sum_{1\leq i,j\leq \lfloor n(t\wedge u)\rfloor}}\underset{k\neq i, k\neq j}{\sum_{1\leq k\leq \lfloor nt\rfloor}}\mathbbm{E}Z^{(2,1)}_{i,j}Z^{(2,2)}_{i,j,k}\nonumber\\
&+\underset{i,j,k\text{ distinct}}{\sum_{1\leq i,j,k\leq \lfloor n(u\wedge t)\rfloor}}\mathbbm{E}\left[\left(Z_{i,j,k}^{(2,2)}\right)^2\right]\nonumber\\
&+\underset{i,j,k,l\text{ distinct}}{\underset{1\leq k\leq \lfloor nu\rfloor,1\leq l\leq \lfloor nt\rfloor}{\sum_{1\leq i,j\leq \lfloor n(u\wedge t)\rfloor}}}\mathbbm{E}Z_{i,j,k}^{(2,2)}Z_{i,j,l}^{(2,2)}\nonumber\\
=&\frac{(\lfloor nt\rfloor -2)(\lfloor nu\rfloor -2)\lfloor n(t\wedge u)\rfloor(\lfloor n(t\wedge u)\rfloor-1)}{n^5}\nonumber\\
&+(\lfloor nt\rfloor-2)(\lfloor nu\rfloor-2)\lfloor n(t\wedge u)\rfloor(\lfloor n(t\wedge u)\rfloor-1)\frac{p^3(1-p)}{n^4}\nonumber\\
&+\lfloor n(t\wedge u)\rfloor(\lfloor n(t\wedge u)\rfloor-1)(\lfloor n(t\wedge u)\rfloor-2)\frac{p^2(1-p^2)}{2n^4}\nonumber\\
&+\lfloor n(t\wedge u)\rfloor(\lfloor n(t\wedge u)\rfloor-1)(\lfloor n(u\wedge t)\rfloor -2)(\lfloor n(u\vee t)\rfloor -3)\frac{p^3(1-p)}{n^4}\nonumber\\
=&(\lfloor nt\rfloor-2)(\lfloor nu\rfloor-2)\lfloor n(t\wedge u)\rfloor(\lfloor n(t\wedge u)\rfloor-1)\frac{2p^3(1-p)}{n^4}\nonumber\\
&+\lfloor n(t\wedge u)\rfloor(\lfloor n(t\wedge u)\rfloor-1)\nonumber\\
&\hphantom{\lfloor n(t\wedge u)\rfloor}\cdot\left(\frac{(\lfloor nt\rfloor-2)(\lfloor nu\rfloor-2)}{n^5}+\frac{\lfloor n(t\wedge u)\rfloor p^2(1-p)^2}{2n^4}+\frac{2p^3(1-p)}{n^4}\right)\nonumber\\
=&\mathbbm{E}\mathbf{Z}_n^{(2)}(t)\mathbf{Z}_n^{(2)}(u)\nonumber,\end{aligned}$$ which finishes the proof.
\[lemma10\_app\] Using the notation of **Step 2** of the proof of Theorem \[theorem\_continuous\], $$\begin{aligned}
&\mathbbm{E}\left\|\mathbf{Z}_n-\mathbf{Z}\right\|\leq\frac{12}{n^{1/2}}+\frac{51\sqrt{\log n}}{\sqrt{n}}\\
&\mathbbm{E}\left\|\mathbf{Z}_n-\mathbf{Z}\right\|^2\leq\frac{121}{n}+\frac{743\log n}{n}\\
&\mathbbm{E}\|\mathbf{Z}\|^2\leq 5.\end{aligned}$$
Note the following
1. By Doob’s $L^2$ inequality, $$\begin{aligned}
\text{A)}\quad&\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\mathbf{B}_3\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)\right|\right]\leq 2\sqrt{\mathbbm{E}\left[\left|\mathbf{B}_3\left(\frac{n(n -1)}{n^2}\right)\right|^2\right]}\leq 2\nonumber\\
\text{B)}\quad&\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\mathbf{B}_4\left(\frac{\lfloor nt\rfloor^2(\lfloor nt\rfloor -1)}{n^3}\right)\right|\right]\leq 2\sqrt{\mathbbm{E}\left[\left|\mathbf{B}_4\left(\frac{n^2(n -1)}{n^3}\right)\right|\right]}\leq 2.\label{second_in}\end{aligned}$$
2. By Doob’s $L^2$ inequality, $$\label{fourth_in_1}
\mathbbm{E}\left[\sup_{t\in[0,1]}|\mathbf{B}_1(t^2)|\right]\leq 2\quad\text{and}\quad\left|\frac{\lfloor nt\rfloor-2}{n}-t\right|\leq \frac{3}{n} \quad\text{ for all }t\in[0,1]$$
3. Using [@ito_processes Lemma 3] and the fact that $$\left|\frac{\lfloor nt\rfloor(\lfloor nt\rfloor-1)}{n^2}-t^2\right|\leq \left|\frac{(nt-\lfloor nt\rfloor)(nt+\lfloor nt\rfloor)}{n^2}\right|+\frac{1}{n^2}\leq \frac{3}{n},$$ we obtain $$\label{fourth_in_2}
\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\mathbf{B}_1\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-\mathbf{B}_1(t^2)\right|\right]\leq \frac{30\sqrt{3\log\left(\frac{2n}{3}\right)}}{n^{1/2}\sqrt{\pi\log(2)}}.$$
Now, can bound $\mathbbm{E}\left\|\mathbf{Z}_n-\mathbf{Z}\right\|$ in the following way: $$\begin{aligned}
&\mathbbm{E}\left\|\mathbf{Z}_n-\mathbf{Z}\right\|\nonumber\\
\leq&\frac{\sqrt{p(1-p)}}{\sqrt{2+8p^2}}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_1\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_1(t^2)\right|\right]\nonumber\\
&+\frac{p\sqrt{2p(1-p)}}{\sqrt{1+4p^2}}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_2\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_2(t^2)\right|\right]\nonumber\\
&+\frac{p\sqrt{2p(1-p)}}{\sqrt{1+4p^2}}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_1\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_1(t^2)\right|\right]\nonumber\\
&+\frac{2p^2\sqrt{2p(1-p)}}{\sqrt{1+4p^2}}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_2\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_2(t^2)\right|\right]\nonumber\\
&+\frac{1}{n^{1/2}}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_3\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)\right|\right]\nonumber\\
&+\frac{p(1-p)}{\sqrt{2}n^{1/2}}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\mathbf{B}_4\left(\frac{\lfloor nt\rfloor^2(\lfloor nt\rfloor -1)}{n^3}\right)\right|\right]+\frac{\sqrt{2p^3(1-p)}}{n^2}\mathbbm{E}|\mathbf{B}_5(1)|\nonumber\\
\stackrel{(\ref{second_in})}\leq& \frac{(1+4p+4p^2)\sqrt{p(1-p)}}{\sqrt{2+8p^2}}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_1\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_1(t^2)\right|\right]\nonumber\\
&+\frac{2}{n^{1/2}}+\frac{\sqrt{2}p(1-p)}{n^{1/2}}+\frac{2\sqrt{p^3(1-p)}}{\sqrt{\pi}n^2}\nonumber\\
\leq&\frac{(1+4p+4p^2)\sqrt{p(1-p)}}{\sqrt{2+8p^2}}\left(\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\left(\frac{\lfloor nt\rfloor -2}{n}-t\right)\mathbf{B}_1(t^2)\right|\right]\right.\nonumber\\
&\left.+\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\mathbf{B}_1\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-\mathbf{B}_1(t^2)\right|\right]\right)+\frac{2+\sqrt{2}p(1-p)}{n^{1/2}}+\frac{2\sqrt{p^3(1-p)}}{\sqrt{\pi}n^2}\nonumber\\
\stackrel{(\ref{fourth_in_1}),(\ref{fourth_in_2})}\leq&\frac{(1+4p+4p^2)\sqrt{p(1-p)}}{\sqrt{2+8p^2}}\left(\frac{6}{n}+\frac{30\sqrt{3\log n}}{n^{1/2}\sqrt{\pi\log(2)}}\right)+\frac{2+\sqrt{2}p(1-p)}{n^{1/2}}+\frac{2\sqrt{p^3(1-p)}}{\sqrt{\pi}n^2}\nonumber\\
\leq&\frac{12}{n^{1/2}}+\frac{51\sqrt{\log n}}{\sqrt{n}}.\end{aligned}$$
Similarly, using Doob’s $L^2$ inequality and [@ito_processes Lemma 3], $$\begin{aligned}
&\mathbbm{E}\|\mathbf{Z}_n-\mathbf{Z}\|^2\nonumber\\
\leq&2\frac{p(1-p)}{2+8p^2}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_1\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_1(t^2)\right|^2\right]\nonumber\\
&+2\frac{2p^3(1-p)}{1+4p^2}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_2\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_2(t^2)\right|^2\right]\nonumber\\
&+5\frac{2p^3(1-p)}{1+4p^2}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_1\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_1(t^2)\right|^2\right]\nonumber\\
&+5\frac{8p^5(1-p)}{1+4p^2}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_2\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_2(t^2)\right|^2\right]\nonumber\\
&+\frac{5}{n}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_3\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)\right|^2\right]\nonumber\\
&+\frac{5p^2(1-p)^2}{2n}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\mathbf{B}_4\left(\frac{\lfloor nt\rfloor^2(\lfloor nt\rfloor -1)}{n^3}\right)\right|^2\right]+\frac{2p^3(1-p)}{n^4}\mathbbm{E}|\mathbf{B}_5(1)|^2\nonumber\\
\leq& \frac{p(1-p)(1+14p^2+40p^4)}{1+4p^2}\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\frac{\lfloor nt\rfloor -2}{n}\mathbf{B}_1\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-t\mathbf{B}_1(t^2)\right|^2\right]\nonumber\\
&+\frac{20}{n}+\frac{10p^2(1-p)^2}{n}+\frac{2p^3(1-p)}{n^4}\nonumber\\
\leq& \frac{p(1-p)(1+14p^2+40p^4)}{1+4p^2}\left(\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\left(\frac{\lfloor nt\rfloor -2}{n}-t\right)\mathbf{B}_1(t^2)\right|^2\right]\right.\nonumber\\
&\left.+\mathbbm{E}\left[\sup_{t\in[0,1]}\left|\mathbf{B}_1\left(\frac{\lfloor nt\rfloor(\lfloor nt\rfloor -1)}{n^2}\right)-\mathbf{B}_1(t^2)\right|^2\right]\right)+\frac{20+10p^2(1-p)^2}{n}+\frac{2p^3(1-p)}{n^4}\nonumber\\
\leq&\frac{p(1-p)(1+14p^2+40p^4)}{1+4p^2}\left(\frac{36}{n^2}+\frac{270\log n}{n\log 2}\right)+\frac{20+10p^2(1-p)^2}{n}+\frac{2p^3(1-p)}{n^4}\nonumber\\
\leq&\frac{121}{n}+\frac{743\log n}{n}.\end{aligned}$$ Furthermore, by Doob’s $L^2$ inequality, $$\begin{aligned}
\mathbbm{E}\|\mathbf{Z}\|^2\leq&\mathbbm{E}\left[\sup_{t\in[0,1]}\left(\frac{\sqrt{p(1-p)}}{\sqrt{2+8p^2}}t\mathbf{B}_1(t^2)+\frac{p\sqrt{2p(1-p)}}{\sqrt{1+4p^2}}t\mathbf{B}_2(t^2)\right)^2\right]\nonumber\\
&+\mathbbm{E}\left[\sup_{t\in[0,1]}\left(\frac{p\sqrt{2p(1-p)}}{\sqrt{1+4p^2}}t\mathbf{B}_1(t^2)+\frac{2p^2\sqrt{2p(1-p)}}{\sqrt{1+4p^2}}t\mathbf{B}_2(t^2)\right)^2\right]\nonumber\\
\leq&\frac{p(1-p)(1+8p^2+16p^4)}{1+4p^2}\mathbbm{E}\left[\sup_{t\in[0,1]}|\mathbf{B}_1(t^2)|^2\right]\nonumber\\
\leq&\frac{4p(1-p)(1+8p^2+16p^4)}{1+4p^2}\leq 5.\end{aligned}$$ This finishes the proof.
|
Bonneville-la-Louvet is a commune. It is found in the region Basse-Normandie in the Calvados department in the northwest of France.
Communes in Calvados |
<?php
/**
* @package Functional-php
* @author Lars Strojny <lstrojny@php.net>
* @copyright 2011-2017 Lars Strojny
* @license https://opensource.org/licenses/MIT MIT
* @link https://github.com/lstrojny/functional-php
*/
namespace Functional\Tests;
use ArrayObject;
use Functional\Exceptions\InvalidArgumentException;
use PHPUnit\Framework\Constraint\Constraint;
use stdClass;
use function Functional\ary;
use function Functional\filter;
use function Functional\pluck;
use function Functional\value_to_key;
use function preg_match;
use function random_bytes;
use function stream_context_create;
use const NAN;
use const PHP_VERSION_ID;
class ValueToKeyTest extends AbstractTestCase
{
const OBJECT_REF_REGEX = '@^\[i:0;~%s:(?<hash>[^\[:]+)(:\d+)?(\[.*])?\]$@';
public static function getSimpleTypeExpectations(): array
{
$binary = random_bytes(10);
return [
'Nothing' => [[], '[]'],
'NULL' => [[null], '[i:0;~N;]'],
'null string' => [['null'], '[i:0;~s:4:"null";]'],
'string' => [['string'], '[i:0;~s:6:"string";]'],
'integers' => [[12, 123], '[i:0;~i:12;:i:1;~i:123;]'],
'funky integers' => [[INF, NAN], '[i:0;~d:INF;:i:1;~d:NAN;]'],
'integer & float' => [[12, 123.10], '[i:0;~i:12;:i:1;~d:123.1;]'],
'array of string' => [[['foo', 'bar']], '[i:0;~[i:0;~s:3:"foo";:i:1;~s:3:"bar";]]'],
'nested array of strings (1)' => [
[['foo', 'bar', ['foo', 'bar']]],
'[i:0;~[i:0;~s:3:"foo";:i:1;~s:3:"bar";:i:2;~[i:0;~s:3:"foo";:i:1;~s:3:"bar";]]]',
],
'nested array of strings (variation)' => [
[['foo', 'bar', ['foo', ['bar']]]],
'[i:0;~[i:0;~s:3:"foo";:i:1;~s:3:"bar";:i:2;~[i:0;~s:3:"foo";:i:1;~[i:0;~s:3:"bar";]]]]',
],
'multiple nested arrays of strings' => [
[['foo', 'bar', ['foo', ['bar'], 'baz']]],
'[i:0;~[i:0;~s:3:"foo";:i:1;~s:3:"bar";:i:2;~[i:0;~s:3:"foo";:i:1;~[i:0;~s:3:"bar";]:i:2;~s:3:"baz";]]]',
],
'multiple nested arrays of strings (variation)' => [
[['foo', 'bar', ['foo', ['bar', 'baz']]]],
'[i:0;~[i:0;~s:3:"foo";:i:1;~s:3:"bar";:i:2;~[i:0;~s:3:"foo";:i:1;~[i:0;~s:3:"bar";:i:1;~s:3:"baz";]]]]',
],
'hashes' => [[['foo' => 'bar']], '[i:0;~[s:3:"foo";~s:3:"bar";]]'],
[[$binary], '[i:0;~s:10:"' . $binary . '";]'],
[[new stdClass()], self::matchesRegularExpression(self::createObjectRefRegex('stdClass'))],
[[new ArrayObject()], self::matchesRegularExpression(self::createObjectRefRegex('ArrayObject'))],
];
}
/** @dataProvider getSimpleTypeExpectations */
public function testValueToRefOnSimpleTypes(array $input, $constraint)
{
$ref = value_to_key(...$input);
self::assertThat($ref, $constraint instanceof Constraint ? $constraint : self::identicalTo($constraint));
$hash[$ref] = 'value';
self::assertSame('value', $hash[$ref], 'Ref can be used as an array key');
}
public function testExpectationsAreNonIdentical()
{
$strings = filter(pluck(self::getSimpleTypeExpectations(), 1), ary('is_string', 1));
while ($string = array_pop($strings)) {
foreach ($strings as $otherString) {
if ($string === $otherString) {
self::fail($string);
}
}
}
self::assertTrue(true, 'All expectations are different');
}
public static function getErrorCases()
{
return [
[stream_context_create()],
[[stream_context_create()]],
[['key' => stream_context_create()]],
[new ArrayObject(['key' => stream_context_create()])],
];
}
/** @dataProvider getErrorCases */
public function testResourcesAreForbidden($value)
{
$this->expectException(InvalidArgumentException::class);
value_to_key($value);
}
public function testObjectReferencesWithStdClass()
{
$key1 = value_to_key(new stdClass());
$key2 = value_to_key(new stdClass());
self::assertNotSame($key1, $key2);
self::assertSame(
1,
preg_match(self::createObjectRefRegex('stdClass'), $key1, $key1Matches),
'Can extract object hash from key1'
);
self::assertSame(
1,
preg_match(self::createObjectRefRegex('stdClass'), $key2, $key2Matches),
'Can extract object hash from key2'
);
if (PHP_VERSION_ID >= 70400) {
self::assertSame($key1Matches['hash'], $key2Matches['hash'], 'Object hashes match');
self::assertSame('[i:0;~stdClass:' . $key1Matches['hash'] . ':0]', $key1, 'Object versions do not match');
self::assertSame('[i:0;~stdClass:' . $key1Matches['hash'] . ':1]', $key2, 'Object versions do not match');
} else {
self::assertNotSame($key1Matches['hash'], $key2Matches['hash'], 'Object hashes should not match');
}
}
public function testObjectReferencesWithArrayObject()
{
$key1 = value_to_key(new ArrayObject());
$key2 = value_to_key(new ArrayObject(['foo' => 'bar']));
self::assertNotSame($key1, $key2);
self::assertSame(
1,
preg_match(self::createObjectRefRegex('ArrayObject'), $key1, $key1Matches),
'Can extract object hash from key1'
);
self::assertSame(
1,
preg_match(self::createObjectRefRegex('ArrayObject'), $key2, $key2Matches),
'Can extract object hash from key2'
);
if (PHP_VERSION_ID >= 70400) {
self::assertSame($key1Matches['hash'], $key2Matches['hash'], 'Object hashes match');
self::assertSame('[i:0;~ArrayObject:' . $key1Matches['hash'] . ':2[]]', $key1, 'Object versions do not match');
self::assertSame('[i:0;~ArrayObject:' . $key1Matches['hash'] . ':3[s:3:"foo";~s:3:"bar";]]', $key2, 'Object versions do not match');
} else {
self::assertNotSame($key1Matches['hash'], $key2Matches['hash'], 'Object hashes don’t match');
}
}
private static function createObjectRefRegex(string $class = '.*'): string
{
return sprintf(self::OBJECT_REF_REGEX, $class);
}
}
|
Alfred Cotton Bedford (November 5, 1863 - September 21, 1925) was president of the Standard Oil Company of New Jersey starting on December 22, 1916.
Biography
Bedford was born on November 5, 1863 in Brooklyn, New York City. He married Edith Kinsman Clark on January 8, 1890. He was promoted from treasurer to president of the Standard Oil Company of New Jersey starting on December 22, 1916. He was made chairman of the board on November 15, 1917.
He was made a Commandant of the Legion in 1922. Bedford died on September 21, 1925 leaving an estate of $3,000,000. He was buried in Green-Wood Cemetery in Brooklyn. |
Being in it Together
Katherine Phelps August 1998
I read stories and I write stories. Recently, I have been finding myself
enjoying stories less than I wish I could. This is because of a growing
frustration with so few stories that involve females as an equal component
of the human race. In part I believe this may just be a lack of awareness
of how stories have been traditionally told and how they may be different.
I have found writers, both men and women, who are more than willing to
redress the imbalance. For those who want to broaden the scope of their
storytelling I have written this wish list:
I would like to see more stories about girls and women.
I would like to see more stories about empowered girls and women.
I would like to see stories that portray female empowerment as normal and not exceptional.
I would like to see stories where females are portrayed as equally active and capable as the males.
I would like to see stories where males are portrayed as sometines passive and
in need of help from others, which would include the help of females.
I would like to see stories where female protagonists have both females
and males assisting them in their adventures, rather than solely a
female who can accomplish things because she has the help of a group of
males.
In stories about groups of people I would like to see a balance of
females and males, rather than the females being outnumbered by the
males.
In stories about protagonists meeting a group of people,
whether it is a planetary council, a team of workers, or the villain's
minions, I would like to see that group be an even blend of females and
males.
I would like to see females and males portrayed as human beings,
each of whom are uniquely individual, rather than as two separate species
with defining characteristics.
I would like to see females portrayed as
working in the broadest possible diversity of employment.
I would like
to see more females portrayed in positions of responsibility, and this
is portrayed as normal and not exceptional.
I would like to see stories
where women are defined by the content of their character, not their sexuality
or physical appearance.
I would like to see stories that can envision the
future as containing something other than a hierarchy.
I would like to see stories that portray women as having contributed to
the past.
I would like to see the concepts of archetype and archetypical stories
dropped. The insistence that old fairytales such as Sleeping
Beauty or Cinderella contain some sort of cosmically
validated wisdom is a form of cultural conservatism that keeps women
locked into roles of disempowerment. Within this context an archetype
is a sanctified stereotype.
I would like to see more stories that go beyond showing women
as victims of men.
I would like to see more stories where women retain their identity and
sense of empowerment when they are in relationship with a man.
I would like to see more stories where a relationship is seen as an
equal partnership entered into and continuing out of love, choice and
commitment rather than obligation.
I would like to see more stories where it is understood that it is
everybody's choice who they enter into a relationship with, and that
it is senseless to fight over the attentions of a potential partner.
I would like to see a diversity of couple relationships portrayed,
whether they are old, young, old and young, same gender, different gender,
involving people with special needs, people of different races, etc.
I would like to see more stories about couples facing challenges together.
I would like to see stories where marriage or childbirth are not portrayed
as the sole high points in a woman's life, but part of many wonderful moments
that we all pass through during a lifetime.
I would like to see stories where child care is portrayed as equally
the responsibility of both parents.
I would like to see more stories where both parents are involved in a child's
life.
I would like to see more stories where parents are more actively
concerned with their child(ren)'s life.
I would like to see sexuality portrayed
as a normal part of human being, not something separate and abnormal.
I would like to see sexuality portrayed as part of the lives of people of
all colours, shapes and sizes, and experienced throughout adulthood.
I would like to see more stories that actually go into detail about what
fun, loving and mature sexuality is like.
I would like to see more stories that portray what a fun, loving and
mature on-going relationship is like.
I would like to see stories that address the issues of childhood sexuality:
what sex is, what children experience of their sexuality even at a young
age, and what their rights concerning their bodies are.
I would like to see more stories where people of many races and cultures
all participate in each other's worlds, rather than living in separate
mono-cultures.
I would like to see stories go beyond mere tokenism, such
as one token strong female or one token person of colour.
I would like to see a balance of stories where the lead protagonist is
female and/or non-white and/or non-heterosexual and s(he) may happen to
have a friend who is a white, anglo-saxon, protestant male.
I would like to see stories where people can be portrayed as different,
but still of equal value.
I would like to further suggest that we need to encourage a wider diversity
of people to express themselves.
We need to encourage people to write more inclusively.
We need to encourage editors and publishers to be bolder in
selecting a wider diversity of stories for publication.
We also need to encourage people to read more broadly.
It is legitimate to want to write from your own perspective and your
own experience. It is also important to remember that our lives are
interconnected, and in fact interdependent upon many other people's
lives and all that exists on this planet. Respect for all things and
recognition of all beings makes our chances of survival greater. It
also opens us to richer and more fulfilling lives. |
Vlaamse Vervoersmaatschappij De Lijn (English: Flemish transport company De Lijn), usually known as De Lijn (, "The Line"), is a company run by the Flemish government in Belgium.
They provide public transportation with about 2240 buses and 399 trams. De Lijn was founded in 1991. They were made after the public transportation companies of Antwerp and Ghent fused with the Flemish part of the NMVB (Nationale Maatschappij van Buurtspoorwegen, or the "National Company of Neighborhood Railways").
Operations
De Lijn operates:
Antwerp Tramway
Ghent Tramway
Belgian coast tram, a line along the whole Belgian coast, between De Panne and Knokke.
Only 1/2 of the buses with the logo of De Lijn on them are actually owned by De Lijn. The other half are buses owned by private companies, such as Keolis. These companies get paid to drive the services of De Lijn. |
Q:
Oracle XML Parsing Vs Java XML Parsing
I have a situation to choose between parsing XML documents in Oracle PL/SQL and parsing them in Java. The system receives the XML documents on a message queue and so the XML documents are not on the file system, unless I write them to the filesystem after reading from queue. And, the intent of parsing is to insert/update records in a bunch of database tables.
Which one is a better option from a performance stand-point?
A:
I'd say Java as if you wanted to horizontally scale (ie. add more servers) then the licence costs of Oracle might prevent this.
Adding another App server just to parse XML with Java is cheap by comparison.
Also (flamebait) DBAs are grumpy.
A:
It's really a competition between PL/SQL and many possible Java parsers. It's very likely that some of the Java parsers beat PL/SQL on performance.
Some other reasons to go with a Java parser:
License costs will be much less.
You're not chained to a particular database.
Your solution has more deployment options.
However if you need to extract information from the XML and insert it into an Oracle database, the advantage might go to PL/SQL. In this case it might be worthwhile to prototype both approaches and see. Also consider the development time needed for each: if the number of bytes of XML coming into your system is relatively small, just pick the solution that's fastest to implement.
|
Jairus Cassius Fairchild (December 27, 1801-October 24, 1862) was an American politician and businessman.
Biography
Fairchild was born in Granville, New York. He moved to Hudson, Ohio and became a merchant. Later he would move to Franklin Mills, Ohio for a short time. While there he operated a tannery before moving to Cleveland around 1834. He then moved to Milwaukee, Wisconsin in 1845 and then to Madison, Wisconsin. Fairchild had a business working with cranberries and the lumber industry. He was also president of a railroad. From 1848 to 1852, Fairchild was the first State Treasurer of the State of Wisconsin. In 1856 he was elected the first Mayor of the city of Madison, Wisconsin. Two of his sons Cassius, and Lucius were also active in Wisconsin politics. |
Find space for pop up shops
Glasgow
This Scottish city is big on space and full of creativity.
Perched on the River Clyde is Scotland’s biggest city. Glasgow is actually the third largest city in the UK, with a population of 600,000 people. Here you’re walking through one of the Industrial Revolution’s pivotal districts. With a rich history in engineering, textiles and shipbuilding still evident wherever you wander.
Today, Glasgow is also famous for its arts and culture scene. With the School of Art, Zaha Hadid’s award-winning Riverside Museum, and Kelvingrove Art Gallery & Museum all making waves. Visitors also flock to Hampden Park for a taste of football history.
And with plenty of space and a curious population, it’s no surprise Glasgow has the nation’s second highest retail spend after London. Check out the Style Mile hotspots of Princes Square and Buchanan Street for cool shops and big brand names. Or head to the West End, for acclaimed vintage and antique boutiques. |
Gallup, Inc. is an American analytics and advisory company based in Washington, D.C. Founded by George Gallup in 1935, the company became known for its public opinion polls conducted worldwide. |
Inside Penang's providers sector, the greatest amount of employment was recorded from the retail, accommodation, and foods and beverages (File&B) sub-sectors, clearly depicting the affect of tourist arrivals on assistance-associated industries.[216] Because the inscription of George Town as being a UNESCO Environment Heritage Internet site, an rising trend could be the acquisition of heritage shophouses inside the zone by overseas investors, In particular from Singapore and Hong Kong.
Available in just a thirty-moment travel from Georgetown, Many of these tranquil locales are located alongside the northern Portion of Penang, with a couple of alongside the western, south and southwest coastline.
Parkroyal might be deemed a home absent from home because of the personal provider and cosy guestrooms – but provided that Browse A lot more...
Do Be aware that it’s not a suitable place for swimming because of standard fishing boats bobbling while in the waters. Gertak Sanggul is available in just a fifteen-moment scenic push from Bayan Lepas or by using the Immediate Penang Bus #308.
Suitable camping floor and amenities furnished by the authorities make camping a luxurious. Hen watching really should not be missed below. The all-natural swimming swimming pools provide a fantastic place for family members outings and nature camps.
As a consequence of its secluded locale, there aren’t a lot of recreational routines other than swimming and picnicking through the beach. Nevertheless, it’s a good location to unwind and escape from the busier locales in Penang.
Readers also flock to Gertak Sanggul for its new seafood and Hai Boey Seafood Cafe is one of the better eateries on Penang Island. Open day-to-day from seventeen:30 onwards, couples can get pleasure from a passionate dinner within the beach when the tiny ones can love swings and hammocks hanging in the trees.
This also marked the beginning of George City's drop, which lasted up on the early 2000s.[84] As being the Malaysian federal federal government continued to acquire Kuala Lumpur and nearby Port Klang by managing investments in conversation, transport, instruction and wellbeing, Penang began to put up with significant brain drain as youthful Penangites began emigrating for improved click work options.
Situated alongside The attractive shorelines of Penang, PARKROYAL Penang vacation resort is perfect for unforgettable honeymoons, fun loved ones getaways and company workshops. Talk to our welcoming PARKROYAL people for tips on dealing with link the very best on the island.
Centuries of improvement have brought a mixture of architectural models to George Town, each historical and modern day. The oldest part of town centre is usually a UNESCO Entire world Heritage Web page, while outdoors the UNESCO zone lies the modern cityscape, with skyscrapers, residential large-rises, Workplace blocks and browsing malls crafted all over the city.
We also give you a Young ones’ Club, an outdoor recreation location, in addition to a kids’s swimming pool with a synthetic beach. Take pleasure in area and international flavors for breakfast, lunch and supper inside our lively cafe, Makan Kitchen area. Grab a clean salad or sandwich from your Foodstore, and sip fruity cocktails inside our peaceful The Bar.
Eighty Japanese fighters and bombers had flown about Georgetown unopposed... A huge number of people today had stuffed the streets to watch the spectacle, which turned to tragedy if the bombs began to tumble.
The island's expatriates have also introduced a host of other celebrations from their countries of origin. Bon Odori is celebrated on a yearly basis within the Esplanade by the Japanese, while St.
Until eventually 2001, the Hire Control Act prevented urban advancement from threatening the existence of pre-war homes in the centre of George Town, by prohibiting landlords from arbitrarily raising rentals and thus allowing for the lower-profits teams to reside in these residences.[eighty] Its eventual repeal drastically changed the landscape of Penang's demographic sample and financial exercise - it triggered right away appreciation of house and housing costs, forcing out tenants of numerous generations out of their houses to the city outskirts, although accelerating the development of new townships in hitherto sparsely populated areas url of Penang.
Distinctive EventsBring the heat of DoubleTree by Hilton™ to any celebration with resources that enable you to strategy, book and revel in.Prepare a Distinctive party
Batu Ferringhi — about the north Coastline with white sandy beaches, high-class hotels and places to eat, a favorite spot for the two locals and guests with tons of h2o sport pursuits.
For individuals who wish to go page snorkelling in Pulau Kendi, it’s hugely advisable to do so with a seasoned diver. As these are Dwell corals with loads of colourful fish, it is vital not to break their fragile ecology through your stop by in this article.
Normal wedding day arch at the entrance and decorations alongside the walkway and floral decoration for all tables
George City is household to several of the oldest educational institutions in Malaysia, rendering it a pioneer while in the nation's education technique. Under British rule, missionary educational institutions had been arrange across George Town.
Be aware that you have at hand more than the exact fare, as the driver does not have modify (obviously you pays additional and resign the alter).
The first method of transportation in George City was the horse hackney carriage, which was well-known in between the late 18th century and 1935, once penang hotel near beach the rickshaw received reputation.
The best sectors in Penang's financial state are providers and producing. The key component of Penang's production sector, in particular, is definitely the Bayan Lepas No cost Industrial Zone, in which several multi-countrywide electronics and engineering firms have put in place factories since the seventies.
The most effective ways to sight see is always to stroll all over Georgetown; but wear light clothing, start off early each morning, and placed on a good amount of Solar-block during the daytime. When crossing the roadways, make sure to look each techniques, even over a just one-way Avenue.
These are generally Along with George Town's standing like a gastronomic haven, with CNN positioning the town as considered one of Asia's greatest Avenue foods towns.[12]
Expertise Penang's unique heritage by enjoying the area society and well-known cuisine while Checking out generations-previous Read Far more»
A small stall near the entrance sells clean fruit juice and fruit dishes. You can even enjoy an awesome look at on the north-western coastline from the island.
The Penang Hop On Hop Off buses services [forty five] gives value for revenue - RM45 for the 24 hour pass if you intend to be out and about from the island, masking most vacationer sights. By trishaw[edit]
Jogging out of your time to determine & do everything? See this rapid and useful tour manual which will assist you to to determine the top Go through More...
1st Avenue Penang, [two]. A compact and relatively new shopping mall located in the heart of Georgetown together Jalan Magazine, 1st Avenue Shopping center spreads over 7 retail concentrations with outfits, electronics along with a cinema on the highest ground. edit
Look out for guys who grope folks around the bus (it transpires to equally male and ladies!). Inside the event this transpires, get off the bus to a reasonably populated, perfectly lit Avenue, while in the celebration the perpetrator could decide to follow you. You can certainly look enable from other locals or maybe the 'Polis' (police).
Penang's superior time is around Christmas, New Year's Day, and Chinese New Year (Look at the lunar calendar; it could slide on the top of January or early to mid February), in the event the east Coastline of Malaysia is drenched and hordes of Sunlight-in search of travelers descend around the island. Accommodation tends to be packed, and priced appropriately. Get in[edit]
In the cosmopolitan sights of Kuala Lumpur towards the large richness on the Borneo rainforest and cultural sights of Penang into the myths and legends of mysterious Langkawi, these tours are sure to spellbind and amaze you!
Watersports are on the agenda For most guests, although the waters are a tad too murky for scuba diving as well as a little bit too tranquil for surfing or more Serious pursuits. You could try out jet skis and hotels in batu ferringhi penang parasailing in the vicinity of the majority of the hotels together Batu Feringhi Beach front.
Among the finest tips on how to sight see is to wander about Georgetown; but wear mild dresses, get started early each morning, and put on loads of Solar-block during the daytime. When crossing the roadways, make sure to glimpse the two methods, even on a one particular-way Avenue.
Assistance is obtainable to your Perhentian Islands for a hundred thirty-a hundred url and fifty RM, boat bundled. There are various organizations throughout with the bus depot in Hat Yai, so You should not take the 1st rate you're presented. It should be not more than three hundred BHT Although they'll try to show you normally! By boat[edit]
Do be cautious of purse-snatchers - specially when wearing jewellery and/or carrying bags. Some of these felons exercise the art of 'ride-by' grabbing handbags which may result in significant injuries to the target.
The most populous condition in Malaysia, just off Johor’s east coast is sixty four on the country’s most attractive volcanic islands Go through Additional...
Below we checklist down our top rated 10 picks of the greatest hotels Batu Ferringhi provides - They vary from passionate, honeymoon-acceptable resorts that blend website in wonderfully Together with the encompassing Group, to family vacation rentals perfect for massive family members.
I could truly feel my coronary heart beating fast and I had been perspiring. Colin looked at me and reported, “You looked as For those who have seen a ghost!”
I will certainly be contacting on Golfasian inside the near long run to book For extra lessons And that i have been spreading optimistic messages to all shut good friends on Golfasian’s pleasant and Qualified team and without doubt they'll also shortly be in touch along with you.
foongpc said... nic, oh I like 'The Shining' by Stephen King - truly good story! Hotels are certainly scary destination to be cos a lot of people love to dedicate suicides in there.
goolooloo reported... which is why i never ever dare to stay at hotel place by itself! yr story generating my pee Virtually stream out!
Placing a single's underwear at The pinnacle of your mattress allows as well. Sleeping while in the nude also allows. If you do any of these, you will not be disturbed.
Your vacation is protected – a lot of the flights and flight-inclusive holidays on this Web-site are economically safeguarded via the ATOL plan. But ATOL protection would not apply to all holiday and vacation providers stated on this Site. Please question us to confirm what security may possibly implement to the scheduling.
If you don't receive an ATOL Certificate then the booking won't be ATOL shielded. holidays penang If you are doing get an ATOL Certificate but every one of the portions of your journey usually are not detailed on it, Individuals parts will not be ATOL protected. Please see our reserving ailments for data or To learn more about fiscal safety as well as the ATOL Certification go to the ATOL Web site at
I stayed in one Penang Hotel in advance of. I checked in early morning.. Went into your area to get ready for bed when there was a sounds on the window.
Boy, was I Incorrect! Both equally Colin and I had been rapid asleep when someone banged on our door. I swiftly acquired nearly my feet and requested who’s there. It absolutely was Kye Li. I quickly opened the door. She was crying.
Discover the entire world by rail. Experience legendary rail journeys and tailormade holidays by teach all around the world.
Mouth watering delicacies within the site Bellevue resort that is found at the hilltop. The cost is rather aggressive. What's more, it gives home in case you'll like to remain for a night.
Babette said... I almost never had nightmares but I continue to recall the one particular I'd After i was a child. visit Quite Terrifying! If I experience any unnatural occurences in a resort room, you guess I am going to ask being moved to another place.
My to start with endeavor into the planet of blogging. This is where I weblog on everything I like, And that i signify anything!
Yeah, Steve Work opportunities is battling a rare form of pancreatic most cancers. While he underwent operation to remove an islet mobile tumor from his pancreas in 2003.
Following a tiring working day walking all over Georgetown, we went for evening meal and after that came back again to your hotel to retire for your night time. I went around to the ladies’ home and chit chat for quite a while ahead of likely again to my area to rest. There was no sign to arrange me for what would come about the subsequent working day.
foongpc stated... cashmere, gosh! That's scary! Jogs my memory of Individuals vampires attempting to get into your home with the window in the Motion picture Salem's Whole lot.
TZ reported... Aiyo.... i utilized to vacation a great deal ... Anytime i scent in different ways within the resort home... i will request a room improve... I could not see but i could scent :p
Sensational New York is among the most renowned city on the globe and no matter if you should store ‘til you fall, benefit from the renowned galleries and museums or expertise the...
Purchase your local currency on the internet and have it sent directly to your private home by the next organization working day, 0% Fee, Absolutely free insured Special Shipping and delivery, Far better prices than on the airport or within the large Road.
foongpc said... molly, oh Do not Permit my ghost Tale along with other ghost tales prevent you from traveling! I believe providing you here remain in a hotel that is not way too operate down, and a area that's not in the much conclude corner, I think probability of encountering this stuff are pretty remote.
Later that working day, we searched for a temple and introduced Kye Li there. I don’t don't forget the location of the temple, but we received Kye Li a talisman or ‘fu’ in Chinese.
hyperX, I feel it's not great to mention the title with the lodge - not very honest to your lodge concerned. But depending on my hints and clues presented, probably you can type of guess? : )
nic explained... oh no.. this reminds me of 1408 as well as the Shining from Stephen King... hotel is indeed an incredibly Terrifying position... u page nv know what type of individuals have stayed in that space and slept on that bed prior to...
Sociable compact team tours all around the world, travelling on neighborhood transport and staying in holidays penang very simple accommodation as well as tenting below The celebrities!
Although searching our Web site It can save you holidays, tours, lodges etcetera which interest you for your TF Favourites by clicking about the icon. You could access your checklist of items listed here anytime that will help you discover them a lot quicker and you can even send the data to the friends and family to take a look at.
If a general public holiday falls on One more general public holiday break, the subsequent working day shall be substituted for a public getaway.
Kye Li experienced almost forgotten her ordeal by the time we went back on the hotel to rest that evening. I was pondering, possibly Along with the talisman she felt Substantially safer and wasn't apprehensive any more.
Canopy Walk, which happens to be a suspension bridge hanging in excess of the treetops. There is absolutely no entrance cost and it's opened seven days each week. You'll want to walk up the hill if you want to see it. |
Monika Herceg (born 1990, in Sisak) is a Croatian poet, playwright, editor, feminist and activist. She is from the small village Pecki near Petrinja, Croatia. She was awarded multiple literature prizes. She is known for being a prominent young poet of the new generation and the most awarded young author in recent Croatian history, sometimes called a "literary sensation". She explores the topics of poverty, domestic violence, immigration, and class and gender inequalities.
Biography
She grew up in small village Pecki, near Petrinja, where she studied Physics, first at University of Zagreb and then at the University of Rijeka. She currently lives, works as an editor and raises two kids in Zagreb.
"No one among our contemporary authors laughs like Monika Herceg; nor writes more sorrowful poems," writes Miljenko Jergovic, a Croatian novelist and essayist. The latter statement is especially true when it comes to Herceg's debut poetry collection Initial Coordinates. The poems in the book portray the lives of women in rural Croatia throughout the twentieth century, whose stories of poverty and struggle are recounted in the voices of Herceg's family members.
"There were no books in our house, and paper was only used to light the fire," Monika recalls. However, during her education in the Croatian town of Petrinja, her teachers soon recognized her talent and provided her the support her family could not. Herceg began writing poetry while working several jobs, all taken on to finance her study of physics.
Work and career
In 2017, she won Goran for her book Pocetne koordinate(Initial Coordinates), the most important award for young authors in Croatia. As a result, the book was published in 2018 and, after that, she won the Kvirin Award, Fran Galovic Slavic award and the international award Mostovi Struge.
Initial Coordinates details Herceg's return to the roots of her family and to those earliest, often traumatic, memories that have haunted her throughout her life.
Her second book, Lovostaj (The Closed Season) (Jesenski i Turk, 2019.), was also a success: the manuscript won the Na vrh jezika award for the best unpublished poetry volume in 2018 and was published in 2019. Her third book, Vrijeme prije jezika (Time Before the Tongue) (Fraktura, 2020 ) won the Zvonko Milkovic award.
At the international level, she won the second prize of the International Poetry Competition Castello di Duino that took place in Italy in 2016 and in 2018, she was granted the Bridges of Struga award during the Mostovi Struge festival in Macedonia for best debut of a young author. In 2021 she won the Fierce Women award for her activism.
Her works have been translated in more than fifteen languages and they were published by some well-known magazines. She is part of Versopolis, an online platform dedicated to the promotion of young European authors. Her trilingual poetry books have been published in Lithuania and Austria. Another selection of her works have been published in French as Ciel sous tension, L'Ollave, 2019.
Her stories were also awarded with several regional and national awards, such as the Biber award and the Lapis Histriae award.
Her drama script Gdje se kupuju njeznosti (Where to Buy Tenderness) was awarded by the Croatian National Theatre in Zagreb. Her play took off in 2021 and was a success. She was awarded for other drama scripts and also was granted the Marin Drzic award the most, important drama script award in Croatia, for her drama Kill Yourself, Dear Dad,.
She is a member of the Croatia Writers Society and of the editorial board of their magazine.
Awards
2017 Goran award for young poets
2017 Castello di Duino
2017 Stevan Sremac award
2018 Kvirin award for young poets
2018 Fran Galovic award for the best book
2018 Slavic award for the best debut
2018 Na vrh jezika award
2018 Mostovi Struge international award for the best debut
2019 Lapis Histrie award for the best short story
2019 Biber award for the best short story
2020 Zvonko Milkovic award for the best book
2020 Price s Balkana award for the best short drama script
2020 National theatre in Zagreb award for the best drama script
2021 Marin Drzic drama script award
2021 National theatre in Mostar award for best drama scripts
2021 Fierce Woman award
Works
Pocetne koordinate (Initial Coordinates), Zagreb, 2018; SKUD Ivan Goran Kovacic and Beograd; Knjizevna radionica Rasic, 2019.
Lovostaj (Closed season), Zagreb: Jesenski i Turk, 2019 and Beograd; Kontrast, 2020.
Vrijeme prije jezika (Time Before the Tongue), Zagreb: Fraktura, 2020 and Beograd; Kontrast, 2021.
Gdje se kupuju njeznosti (2020.) (Where to Buy Tenderness), drama script
Mrtve ne treba micati (2020.) (Dead should not be moved), short drama script
Ubij se, tata (2020), (Kill yourself, dear Dad), drama script
Zakopana cuda (2020.) (Buried miracles), drama script
TRANSLATIONS
Ciel sous tension, trans. Martina Kramer, Paris: L'Ollave, 2019.Poetinis Druskininku ruduo, Vilnius: 2019.Wo Lyrik zuhause ist, trans. Jelena Dabic Austrija, 2020.
Pocetni koordinati, trans. Doko Zdraveski, PNV, Skopje, 2020.
Lovostoj., trans. Doko Zdraveski, PNV, Skopje, 2021.
OU LES TENDRESSES S'ACHETENT-ELLES, Nicolas Raljevic, Paris: Prozor Editions, 2021.
Initial Coordinates, USA, Sandorf Passage, 2022. |
/* *****************************************************************************
* Copyright (c) 2007-2015 Alexis Naveros.
*
* Ecere Corporation has unlimited/unrestricted rights.
* *****************************************************************************/
#ifndef MMHASH_H
#define MMHASH_H
/*
#define MM_HASH_DEBUG_STATISTICS
*/
enum
{
MM_HASH_ENTRYCMP_INVALID,
MM_HASH_ENTRYCMP_FOUND,
MM_HASH_ENTRYCMP_SKIP
};
enum
{
MM_HASH_ENTRYLIST_BREAK,
MM_HASH_ENTRYLIST_CONTINUE
};
typedef struct
{
/* Clear the entry so that entryvalid() returns zero */
void (*clearentry)( void *entry );
/* Returns non-zero if the entry is valid and existing */
int (*entryvalid)( const void *entry );
/* Return key for an arbitrary set of user-defined data */
uint32_t (*entrykey)( const void *entry );
/* Return MM_HASH_ENTRYCMP* to stop or continue the search */
int (*entrycmp)( const void *entry, const void *entryref );
/* Return MM_HASH_ENTRYLIST* to stop or continue the search */
int (*entrylist)( void *opaque, const void *entry, const void *entryref );
/* Clear many entries at once */
void (*clearentries)( void *entries, unsigned int count );
} mmHashAccess;
/* Do not keep track of entry count, table will not be able to say when it needs to shrink or grow */
#define MM_HASH_FLAGS_NO_COUNT (0x1)
size_t mmHashRequiredSize( size_t entrysize, uint32_t hashbits, uint32_t pageshift );
void mmHashInit( void *hashtable, const mmHashAccess *access, size_t entrysize, uint32_t hashbits, uint32_t pageshift, uint32_t flags );
int mmHashGetStatus( void *hashtable, int *rethashbits );
void mmHashReset( void *hashtable, const mmHashAccess *access );
enum
{
MM_HASH_STATUS_MUSTGROW,
MM_HASH_STATUS_MUSTSHRINK,
MM_HASH_STATUS_NORMAL,
MM_HASH_STATUS_UNKNOWN
};
void *mmHashDirectFindEntry( void *hashtable, const mmHashAccess *access, const void *findentry );
void *mmHashLockFindEntry( void *hashtable, const mmHashAccess *access, void *findentry );
void mmHashDirectListEntry( void *hashtable, const mmHashAccess *access, void *listentry, void *opaque );
void mmHashLockListEntry( void *hashtable, const mmHashAccess *access, void *listentry, void *opaque );
int mmHashDirectReadEntry( void *hashtable, const mmHashAccess *access, void *readentry );
int mmHashLockReadEntry( void *hashtable, const mmHashAccess *access, void *readentry );
int mmHashDirectCallEntry( void *hashtable, const mmHashAccess *access, void *callentry, void (*callback)( void *opaque, void *entry, int newflag ), void *opaque, int addflag );
int mmHashLockCallEntry( void *hashtable, const mmHashAccess *access, void *callentry, void (*callback)( void *opaque, void *entry, int newflag ), void *opaque, int addflag );
/* The hash key for replaced entries must remain the same! */
int mmHashDirectReplaceEntry( void *hashtable, const mmHashAccess *access, void *replaceentry, int addflag );
int mmHashLockReplaceEntry( void *hashtable, const mmHashAccess *access, void *replaceentry, int addflag );
int mmHashDirectAddEntry( void *hashtable, const mmHashAccess *access, void *adddentry, int nodupflag );
int mmHashLockAddEntry( void *hashtable, const mmHashAccess *access, void *adddentry, int nodupflag );
int mmHashDirectAddEntry2( void *hashtable, const mmHashAccess *access, void *addentry, int nodupflag, void ** retEntry);
int mmHashDirectReadOrAddEntry( void *hashtable, const mmHashAccess *access, void *readaddentry, int *readflag );
int mmHashLockReadOrAddEntry( void *hashtable, const mmHashAccess *access, void *readaddentry, int *readflag );
int mmHashDirectDeleteEntry( void *hashtable, const mmHashAccess *access, void *deleteentry, int readflag );
int mmHashLockDeleteEntry( void *hashtable, const mmHashAccess *access, void *deleteentry, int readflag );
// NOTE: When setting dontmovestuff to 1, a resize must be done to repack!
int mmHashDirectDeleteEntry2( void *hashtable, const mmHashAccess *access, void *entry, int dontmovestuff);
void mmHashResize( void *newtable, void *oldtable, const mmHashAccess *access, uint32_t hashbits, uint32_t pageshift );
void mmHashResize2( void *newtable, void *oldtable, const mmHashAccess *access, uint32_t hashbits, uint32_t pageshift, void ** movedEntryPtr);
void mmHashListAll( void *hashtable, int (*list)( void *opaque, void *entry ), void *opaque );
void * mmHashGetNext( void *hashtable, void * entry, const mmHashAccess *access);
void * mmHashGetPrev( void *hashtable, void * entry, const mmHashAccess *access);
enum
{
MM_HASH_FAILURE,
MM_HASH_SUCCESS,
MM_HASH_TRYAGAIN,
MM_HASH_FOUND /* Internal, can not be returned by any public call */
};
////
typedef struct
{
uint32_t hashkey;
uint32_t pagestart;
uint32_t pagefinal;
void *next;
} mmHashLockRange;
typedef struct
{
void *hashtable;
void *rangelist;
int newcount;
} mmHashLock;
void mmHashLockInit( mmHashLock *hashlock, int newcount );
void mmHashLockAdd( void *hashtable, const mmHashAccess *access, void *entry, mmHashLock *hashlock, mmHashLockRange *lockrange );
void mmHashLockAcquire( void *hashtable, const mmHashAccess *access, mmHashLock *hashlock );
void mmHashLockRelease( void *hashtable, mmHashLock *hashlock );
void mmHashGlobalLockEnable( void *hashtable );
void mmHashGlobalLockDisable( void *hashtable );
////
void mmHashDirectDebugDuplicate( void *hashtable, const mmHashAccess *access, void (*callback)( void *opaque, void *entry0, void *entry1 ), void *opaque );
void mmHashDirectDebugPages( void *hashtable );
void mmHashDirectDebugContent( void *hashtable, void (*callback)( uint32_t hashkey, void *entry ) );
void mmHashStatistics( void *hashtable, long *accesscount, long *collisioncount, long *relocationcount, long *entrycount, long *entrycountmax, long *hashsizemax );
unsigned int mmHashGetCount( void *hashtable);
#endif
|
GB or Gb could mean:
Sarin
Great Britain, or the United Kingdom (ISO code GB)
Gigabyte (GB) unit of measurement of bytes
Game Boy handheld video game console line |
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Src/stm32f0xx_hal.c
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal.h
fap_backplane\stm32f0xx_hal.o: ../Inc/stm32f0xx_hal_conf.h
fap_backplane\stm32f0xx_hal.o: ../Inc/main.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_rcc.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_def.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/CMSIS/Device/ST/STM32F0xx/Include/stm32f0xx.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/CMSIS/Device/ST/STM32F0xx/Include/stm32f072xb.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/CMSIS/Include/core_cm0.h
fap_backplane\stm32f0xx_hal.o: C:\Keil_v5\ARM\ARMCC\Bin\..\include\stdint.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/CMSIS/Include/core_cmInstr.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/CMSIS/Include/cmsis_armcc.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/CMSIS/Include/core_cmFunc.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/CMSIS/Device/ST/STM32F0xx/Include/system_stm32f0xx.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/Legacy/stm32_hal_legacy.h
fap_backplane\stm32f0xx_hal.o: C:\Keil_v5\ARM\ARMCC\Bin\..\include\stdio.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_rcc_ex.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_gpio.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_gpio_ex.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_dma.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_dma_ex.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_cortex.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_flash.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_flash_ex.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_i2c.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_i2c_ex.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_pcd.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_pcd_ex.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_pwr.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_pwr_ex.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_tim.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_tim_ex.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_uart.h
fap_backplane\stm32f0xx_hal.o: ../Drivers/STM32F0xx_HAL_Driver/Inc/stm32f0xx_hal_uart_ex.h
|
The Senate of the Republic, () constitutionally Chamber of Senators of the Honorable Congress of the Union (), is the upper house of Mexico's bicameral Congress. It currently consists of 128 members, who serve six-year terms.
Make-up
After a series of reforms during the 1990s, the Senate is made up of 128 senators:
Two for each of the 32 states elected under the principle of relative majority;
One for each of the 32 states assigned under the principle of first minority (i.e. awarded to the party who had won the second highest number of votes within the state or Federal District);
Thirty-two national senators-at-large, divided among the parties in proportion to their share of the national vote.
Notes |
describe('Frontpage', function() {
beforeEach(function(){
cy.visit('build/clean/index.html');
});
it('Has the "Marios" namespace in the main content', function() {
cy.get('.content.namespace').contains("Marios");
});
});
|
The blacktip reef shark (Carcharhinus melanopterus) is a species of shark, in the family Carcharhinidae. They live in the Indian and Pacific Oceans. They are found in shallow, inshore waters. They are usually . |
Korres Wild Rose Skin Care
KORRES Wild Rose range of beauty and skin products has been repeatedly recognized by awards in the US, Singapore, Canada, Poland and the UK. The Wild Rose 24 Hour Moisturising Cream won an award in The Allure A-List for Sephora Top-Selling Product 2009, and remains to be as popular around the world as when it was first launched. The simplicity and effectiveness of this cream makes it a perfect purchase for anyone with Normal/Dry skin, or Oily/Combination skin, looking for softness and radiance. Try with KORRES Wild Rose Exfoliating Cleanser 150ml (£18) for a truly wonderful daily experience! |
Banteux () is a commune in Nord in north France. In 2018, 346 people lived there. |
The proper synthesis and processing of proteins is critical to normal cellular function. The endoplasmic reticulum (ER) is an organelle found in all higher organisms, whose central role in cell function is to mediate protein synthesis. Humans afflicted with abnormal protein processing in the ER and a related organelle, the Golgi body, suffer from devastating developmental abnormalities and comprise a broad category of disease known as Congenital Disorders of Glycosylation (CDGs). The key aspect of protein processing in the ER and Golgi is the addition of sugars to newly synthesized proteins, called glycosylation. This proposal seeks to characterize fundamental aspects of protein glycosylation, specifically how abnormal glycosylation influences the generation of signals within a cell. These signals are generated as a result of abnormal protein synthesis, which results in ER stress. The activation of ER stress can result in cell suicide (apoptosis), adaptation to the stress, growth arrest, or stimulation of localized inflammation. Our long-term goals focus upon how cells activate apoptosis following ER stress. This proposed project will allow characterization of the molecules that carry this stress signal, and examine how this cell suicide is executed. The improper processing of proteins in the ER and Golgi causes mutations in a variety of genes, and the type of disease that results from such mutations depends upon the identity of the mutated protein. Cystic fibrosis patients suffer lung degeneration that is the result of ER stress-activated signals as a membrane protein is improperly glycosylated, and one type of inherited hypercholesterolemia (high cholesterol) is the result of ER-associated processing deficiencies of a signal receptor. The characterization of ER stress and its signaling mechanisms will offer vital insight into the cell biology of stressed cells, and will be valuable to our understanding of diseases that result from abnormal ER function/processing. |
Cejov is small village near Humpolec in the Pelhrimov District, Vysocina Region of the Czech Republic. 473 people live there and it has 7,98 km2.
Villages in Vysocina Region |
Beer: Ratings & Reviews
More User Reviews:
4.2/5rDev n/alook: 4 | smell: 4 | taste: 4.5 | feel: 4 | overall: 4
A: Poured a glowing deep orange color with good carbonation and a nice white cap
S: Aromatic with hints at citrus and flowers.
T: Nice flavor, starts with a nice biting citrus, floral. The beer was served rather warm for an APA and that wrecked the flavor a bit. I may be off but I thought it was 2 row or lighter specialty malt base. Perhaps Cent and Cascade on the hop bill. |
The following are cities in Western Sahara, listed by population. Due to an ongoing conflict over the territory, most are controlled by Morocco. The eastern and southern parts are controlled by the Sahrawi Arab Democratic Republic (SADR). |
/**
* @file parse.c
* @author Ambroz Bizjak <ambrop7@gmail.com>
*
* @section LICENSE
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions are met:
* 1. Redistributions of source code must retain the above copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. Neither the name of the author nor the
* names of its contributors may be used to endorse or promote products
* derived from this software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
* WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
* DISCLAIMED. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
* DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
* (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
* ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
* SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
*
* @section DESCRIPTION
*
* Synopsis:
* parse_number(string str)
* parse_hex_number(string str)
* parse_value(string str)
* parse_ipv4_addr(string str)
* parse_ipv6_addr(string str)
*
* Variables:
* succeeded - "true" or "false", reflecting success of the parsing
* (empty) - normalized parsed value (only if succeeded)
*
* Synopsis:
* parse_ipv4_cidr_addr(string str)
* parse_ipv6_cidr_addr(string str)
*
* Variables:
* succeeded - "true" or "false", reflecting success of the parsing
* (empty) - normalized CIDR notation address (only if succeeded)
* addr - normalized address without prefix (only if succeeded)
* prefix - normalized prefix without address (only if succeeded)
*/
#include <stdio.h>
#include <stdlib.h>
#include <inttypes.h>
#include <misc/parse_number.h>
#include <misc/ipaddr.h>
#include <misc/ipaddr6.h>
#include <ncd/NCDValParser.h>
#include <ncd/module_common.h>
#include <generated/blog_channel_ncd_parse.h>
struct instance {
NCDModuleInst *i;
NCDValMem mem;
NCDValRef value;
int succeeded;
};
struct ipv4_cidr_instance {
NCDModuleInst *i;
int succeeded;
struct ipv4_ifaddr ifaddr;
};
struct ipv6_cidr_instance {
NCDModuleInst *i;
int succeeded;
struct ipv6_ifaddr ifaddr;
};
enum {STRING_ADDR, STRING_PREFIX};
static const char *strings[] = {
"addr", "prefix", NULL
};
typedef int (*parse_func) (NCDModuleInst *i, MemRef str, NCDValMem *mem, NCDValRef *out);
static int parse_number (NCDModuleInst *i, MemRef str, NCDValMem *mem, NCDValRef *out)
{
uintmax_t n;
if (!parse_unsigned_integer(str, &n)) {
ModuleLog(i, BLOG_ERROR, "failed to parse number");
return 0;
}
*out = ncd_make_uintmax(mem, n);
if (NCDVal_IsInvalid(*out)) {
return 0;
}
return 1;
}
static int parse_hex_number (NCDModuleInst *i, MemRef str, NCDValMem *mem, NCDValRef *out)
{
uintmax_t n;
if (!parse_unsigned_hex_integer(str, &n)) {
ModuleLog(i, BLOG_ERROR, "failed to parse hex number");
return 0;
}
*out = ncd_make_uintmax(mem, n);
if (NCDVal_IsInvalid(*out)) {
return 0;
}
return 1;
}
static int parse_value (NCDModuleInst *i, MemRef str, NCDValMem *mem, NCDValRef *out)
{
if (!NCDValParser_Parse(str, mem, out)) {
ModuleLog(i, BLOG_ERROR, "failed to parse value");
return 0;
}
return 1;
}
static int parse_ipv4_addr (NCDModuleInst *i, MemRef str, NCDValMem *mem, NCDValRef *out)
{
uint32_t addr;
if (!ipaddr_parse_ipv4_addr(str, &addr)) {
ModuleLog(i, BLOG_ERROR, "failed to parse ipv4 addresss");
return 0;
}
char buf[IPADDR_PRINT_MAX];
ipaddr_print_addr(addr, buf);
*out = NCDVal_NewString(mem, buf);
if (NCDVal_IsInvalid(*out)) {
return 0;
}
return 1;
}
static int parse_ipv6_addr (NCDModuleInst *i, MemRef str, NCDValMem *mem, NCDValRef *out)
{
struct ipv6_addr addr;
if (!ipaddr6_parse_ipv6_addr(str, &addr)) {
ModuleLog(i, BLOG_ERROR, "failed to parse ipv6 addresss");
return 0;
}
char buf[IPADDR6_PRINT_MAX];
ipaddr6_print_addr(addr, buf);
*out = NCDVal_NewString(mem, buf);
if (NCDVal_IsInvalid(*out)) {
return 0;
}
return 1;
}
static void new_templ (void *vo, NCDModuleInst *i, const struct NCDModuleInst_new_params *params, parse_func pfunc)
{
struct instance *o = vo;
o->i = i;
// read arguments
NCDValRef str_arg;
if (!NCDVal_ListRead(params->args, 1, &str_arg)) {
ModuleLog(i, BLOG_ERROR, "wrong arity");
goto fail0;
}
if (!NCDVal_IsString(str_arg)) {
ModuleLog(o->i, BLOG_ERROR, "wrong type");
goto fail0;
}
// init mem
NCDValMem_Init(&o->mem, i->params->iparams->string_index);
// parse
o->succeeded = pfunc(i, NCDVal_StringMemRef(str_arg), &o->mem, &o->value);
// signal up
NCDModuleInst_Backend_Up(i);
return;
fail0:
NCDModuleInst_Backend_DeadError(i);
}
static void func_die (void *vo)
{
struct instance *o = vo;
// free mem
NCDValMem_Free(&o->mem);
NCDModuleInst_Backend_Dead(o->i);
}
static int func_getvar2 (void *vo, NCD_string_id_t name, NCDValMem *mem, NCDValRef *out)
{
struct instance *o = vo;
if (name == NCD_STRING_SUCCEEDED) {
*out = ncd_make_boolean(mem, o->succeeded);
return 1;
}
if (o->succeeded && name == NCD_STRING_EMPTY) {
*out = NCDVal_NewCopy(mem, o->value);
return 1;
}
return 0;
}
static void func_new_parse_number (void *vo, NCDModuleInst *i, const struct NCDModuleInst_new_params *params)
{
new_templ(vo, i, params, parse_number);
}
static void func_new_parse_hex_number (void *vo, NCDModuleInst *i, const struct NCDModuleInst_new_params *params)
{
new_templ(vo, i, params, parse_hex_number);
}
static void func_new_parse_value (void *vo, NCDModuleInst *i, const struct NCDModuleInst_new_params *params)
{
new_templ(vo, i, params, parse_value);
}
static void func_new_parse_ipv4_addr (void *vo, NCDModuleInst *i, const struct NCDModuleInst_new_params *params)
{
new_templ(vo, i, params, parse_ipv4_addr);
}
static void func_new_parse_ipv6_addr (void *vo, NCDModuleInst *i, const struct NCDModuleInst_new_params *params)
{
new_templ(vo, i, params, parse_ipv6_addr);
}
static void ipv4_cidr_addr_func_new (void *vo, NCDModuleInst *i, const struct NCDModuleInst_new_params *params)
{
struct ipv4_cidr_instance *o = vo;
o->i = i;
NCDValRef str_arg;
if (!NCDVal_ListRead(params->args, 1, &str_arg)) {
ModuleLog(i, BLOG_ERROR, "wrong arity");
goto fail0;
}
if (!NCDVal_IsString(str_arg)) {
ModuleLog(o->i, BLOG_ERROR, "wrong type");
goto fail0;
}
o->succeeded = ipaddr_parse_ipv4_ifaddr(NCDVal_StringMemRef(str_arg), &o->ifaddr);
NCDModuleInst_Backend_Up(i);
return;
fail0:
NCDModuleInst_Backend_DeadError(i);
}
static int ipv4_cidr_addr_func_getvar2 (void *vo, NCD_string_id_t name, NCDValMem *mem, NCDValRef *out)
{
struct ipv4_cidr_instance *o = vo;
if (name == NCD_STRING_SUCCEEDED) {
*out = ncd_make_boolean(mem, o->succeeded);
return 1;
}
if (!o->succeeded) {
return 0;
}
char str[IPADDR_PRINT_MAX];
if (name == NCD_STRING_EMPTY) {
ipaddr_print_ifaddr(o->ifaddr, str);
}
else if (name == ModuleString(o->i, STRING_ADDR)) {
ipaddr_print_addr(o->ifaddr.addr, str);
}
else if (name == ModuleString(o->i, STRING_PREFIX)) {
sprintf(str, "%d", o->ifaddr.prefix);
}
else {
return 0;
}
*out = NCDVal_NewString(mem, str);
return 1;
}
static void ipv6_cidr_addr_func_new (void *vo, NCDModuleInst *i, const struct NCDModuleInst_new_params *params)
{
struct ipv6_cidr_instance *o = vo;
o->i = i;
NCDValRef str_arg;
if (!NCDVal_ListRead(params->args, 1, &str_arg)) {
ModuleLog(i, BLOG_ERROR, "wrong arity");
goto fail0;
}
if (!NCDVal_IsString(str_arg)) {
ModuleLog(o->i, BLOG_ERROR, "wrong type");
goto fail0;
}
o->succeeded = ipaddr6_parse_ipv6_ifaddr(NCDVal_StringMemRef(str_arg), &o->ifaddr);
NCDModuleInst_Backend_Up(i);
return;
fail0:
NCDModuleInst_Backend_DeadError(i);
}
static int ipv6_cidr_addr_func_getvar2 (void *vo, NCD_string_id_t name, NCDValMem *mem, NCDValRef *out)
{
struct ipv6_cidr_instance *o = vo;
if (name == NCD_STRING_SUCCEEDED) {
*out = ncd_make_boolean(mem, o->succeeded);
return 1;
}
if (!o->succeeded) {
return 0;
}
char str[IPADDR6_PRINT_MAX];
if (name == NCD_STRING_EMPTY) {
ipaddr6_print_ifaddr(o->ifaddr, str);
}
else if (name == ModuleString(o->i, STRING_ADDR)) {
ipaddr6_print_addr(o->ifaddr.addr, str);
}
else if (name == ModuleString(o->i, STRING_PREFIX)) {
sprintf(str, "%d", o->ifaddr.prefix);
}
else {
return 0;
}
*out = NCDVal_NewString(mem, str);
return 1;
}
static struct NCDModule modules[] = {
{
.type = "parse_number",
.func_new2 = func_new_parse_number,
.func_die = func_die,
.func_getvar2 = func_getvar2,
.alloc_size = sizeof(struct instance)
}, {
.type = "parse_hex_number",
.func_new2 = func_new_parse_hex_number,
.func_die = func_die,
.func_getvar2 = func_getvar2,
.alloc_size = sizeof(struct instance)
}, {
.type = "parse_value",
.func_new2 = func_new_parse_value,
.func_die = func_die,
.func_getvar2 = func_getvar2,
.alloc_size = sizeof(struct instance)
}, {
.type = "parse_ipv4_addr",
.func_new2 = func_new_parse_ipv4_addr,
.func_die = func_die,
.func_getvar2 = func_getvar2,
.alloc_size = sizeof(struct instance)
}, {
.type = "parse_ipv6_addr",
.func_new2 = func_new_parse_ipv6_addr,
.func_die = func_die,
.func_getvar2 = func_getvar2,
.alloc_size = sizeof(struct instance)
}, {
.type = "parse_ipv4_cidr_addr",
.func_new2 = ipv4_cidr_addr_func_new,
.func_getvar2 = ipv4_cidr_addr_func_getvar2,
.alloc_size = sizeof(struct ipv4_cidr_instance)
}, {
.type = "parse_ipv6_cidr_addr",
.func_new2 = ipv6_cidr_addr_func_new,
.func_getvar2 = ipv6_cidr_addr_func_getvar2,
.alloc_size = sizeof(struct ipv6_cidr_instance)
}, {
.type = NULL
}
};
const struct NCDModuleGroup ncdmodule_parse = {
.modules = modules,
.strings = strings
};
|
The first lady of Florida is the informal title and role held by the hostess of the Florida Governor's Mansion and usually the wife of the governor of Florida, during the governor's term in office.
Casey DeSantis is the current first lady of Florida, in role since January 2019 as the wife of Governor Ron DeSantis.
Origins and Role
The first lady is not elected by the citizens of Florida, there are no official jobs she is officially required to perform and she is not paid for being the first lady, but she is often involved in political campaigns, managements of the Governor's Mansion, and participating in social causes and accompanying the governor at official and ceremonial occasions and events.
Causes and Initiatives
Casey DeSantis launched four major initiatives during her as term as the first lady of the state such as, Hope Florida, Florida Cancer Connect, Resiliency Florida, Hope Healing for Florida and The Facts. Your Future.
List of first ladies of Florida
Casey DeSantis (2019-present)
Ann Scott (2011-2019)
Carole Crist (2007-2011)
Columba Bush (1999-2007)
Rhea Chiles (1991-1998)
Margie Mixson (1987)
Adele Khoury Graham (1979-1987)
Donna Lou Harper Askew (1971-1978)
Erika Mattfeld Kirk (1967-1970)
Mildred Carlyon Burns (1965-1967)
Julia Burnett Bryant (1961-1964)
Mary Call Darby Collins (1955-1960)
Thelma Brinson Johns (September 28, 1953-1954)
Olie Brown McCarty (1953-September 28, 1953)
Barbara Manning Warren (1949-1952)
Mary Rebecca Harwood Caldwell (1945-1949)
Mary Agnes Groover Holland (1941-1944)
Mildred Victoria Thompson Cone (1937-1942)
Alice May Agee Sholtz (1933-1936)
Nell Ray Carlton (1929-1932)
Lottie Wilt Pepper Martin (1925-1928)
Maude Randell Hardee (1921-1925)
Alice May Campbell Catts (1917-1920)
Virginia Darby Trammel (1913-1916)
Rhoda Elizabeth Waller Gibbes, mother of governor Albert Gilchrist who was a bachelor (1909-1912)
Annie Isabell Douglass (1905-1908)
May Mann Jennings (1901-1904)
Mary C. Davis Bloxham (1897-1900)
Mary Eugenia Spencer Mitchell (1893-1896)
Floride Lydia Pearson Fleming (1889-1892)
Wathen Herbert Taylor Perry (1885-1888)
Mary C. Davis Bloxham (1881-1884)
Ameila Dickens Drew (1877-1881)
Marcellus Lovejoy Stearns was a bachelor (March 1874-1876)
Catherine Smith Campbell Hart (1873-March 18, 1874)
Chloe Merrick Reed (1868-1872)
Philoclea Alson Walker (December 20, 1865-July 4, 1868)
Harriett Newell Marvin (July 13, 1865-December 20, 1865)
Elizabeth S. Coleman Allison (April 1, 1865-May 19, 1865)
Caroline Howze Milton (October 7, 1861-April 1, 1865)
Martha Starke Peay Perry (October 5, 1857-October 7, 1861)
Mary M. Scott Broome (October 3, 1853-October 5, 1857)
Elizabeth Simpson Brown (October 1, 1849-October 3, 1853)
William Dunn Moseley was a widower (June 25, 1845-October 1, 1849)
Territorial period
Elizabeth Foort Branch (August 11, 1844-June 25, 1845)
Mary Letitia Kirkman Call (March 19, 1841-August 11, 1844)
Mary Marth Smith Reid (December 2, 1839-March 19, 1841)
Mary Letitia Kirkman Call (March 16, 1836-December 2, 1839)
Peggy O'Neale Timberlake Eaton (April 24, 1834-March 16, 1836)
Nancy Hines Duval (April 17, 1822-April 24, 1834)
Rachel Donelson Jackson (March 10, 1821-November 12, 1821) |
microRNA-206 is required for osteoarthritis development through its effect on apoptosis and autophagy of articular chondrocytes via modulating the phosphoinositide 3-kinase/protein kinase B-mTOR pathway by targeting insulin-like growth factor-1.
microRNA (miR) has been shown to be involved in the treatment of diseases such as osteoarthritis (OA). This study aims to investigate the role of miR-206 in regulating insulin-like growth factor-1 (IGF-1) in chondrocyte autophagy and apoptosis in an OA rat model via the phosphoinositide 3-kinase (P13K)/protein kinase B (AKT)-mechanistic target of rapamycin (mTOR) signaling pathway. Wistar rats were used to establish the OA rat model, followed by the observation of histopathological changes, Mankin score, and the detection of IGF-1-positive expression and tissue apoptosis. The underlying regulatory mechanisms of miR-206 were analyzed in concert with treatment by an miR-206 mimic, an miR-206 inhibitor, or small interfering RNA against IGF-1 in chondrocytes isolated from OA rats. Then, the expression of miR-206, IGF-1, and related factors in the signaling pathway, cell cycle, and apoptosis, as well as inflammatory factors, were determined. Subsequently, chondrocyte proliferation, cell cycle distribution, apoptosis, autophagy, and autolysosome were measured. OA articular cartilage tissue exhibited a higher Mankin score, promoted cell apoptotic rate, increased expression of IGF-1, Beclin1, light chain 3 (LC3), Unc-51-like autophagy activating kinase 1 (ULK1), autophagy-related 5 (Atg5), caspase-3, and Bax, yet exhibited decreased expression of miR-206, P13K, AKT, mTOR, and Bcl-2. Besides, miR-206 downregulated the expression of IGF-1 and activated the P13K/AKT signaling pathway. Moreover, miR-206 overexpression and IGF-1 silencing inhibited the interleukins levels (IL-6, IL-17, and IL-18), cell apoptotic rate, the formation of autolysosome, and cell autophagy while promoting the expression of IL-1β and cell proliferation. The findings from our study provide a basis for the efficient treatment of OA by investigating the inhibitory effects of miR-206 on autophagy and apoptosis of articular cartilage in OA via activating the IGF-1-mediated PI3K/AKT-mTOR signaling pathway. |
Our Revolution: A Future to Believe In is a book by U.S. Senator of Vermont, Bernie Sanders. It was published by Thomas Dunne Books in 2016.
It was released on November 15, 2016, a week after the election of Donald Trump. The book was written in the context of Sanders's 2016 presidential campaign and aimed to explain some of its rationale.
In the book, Sanders sets out his position on climate change, free college tuition, income inequality, close the gender wage gap and to defeat Donald Trump while campaigning for Hillary Clinton during the last three months leading to the 2016 presidential election. |
Wednesday, September 17, 2014
Egg Harbor City Man Indicted for Murder in Connection with Fatal Shooting in Galloway
MAYS LANDING– An Egg Harbor City man was indicted for murder today in connection with the fatal shooting of a Bergen County man in Galloway in 2010, Atlantic County Prosecutor Jim McClain announced.
Rafael J. Olmo, 31, of the 400 block Philadelphia Ave, Egg Harbor City, was indicted by an Atlantic County Grand Jury this afternoon for murder and related charges for the 2010 shooting death in Galloway Twp. of Leandro A. Rodriguez, 36, of Hackensack, NJ.
On the afternoon of December 2, 2010, Galloway Township police responded to the report of a dead body discovered in the backyard of an unoccupied residence on the 500 block of South Berlin Avenue in Galloway Township, an apparent victim of gunshot wounds.
The victim was subsequently identified as Rodriguez, and the autopsy performed the next day determined that the death was a homicide, caused by two gunshots to the face.
A 2 1⁄2 year investigation by the Atlantic County Prosecutor’s Office Major Crimes Unit and the Galloway Township Police Department resulted in the authorization of charges on July 12, 2012 by County Prosecutor Jim McClain for murder and weapons offenses.
Olmo—who is currently in federal custody on another matter—was indicted today on five (5) criminal counts:
Murder, a crime of the 1st degree,
Felony Murder—1st degree,
Possession of a Weapon for Unlawful Purposes—2nd degree,
Unlawful Possession of a Weapon, without a permit to carry—2nd degree, and
Possession of a Weapon by a Convicted Person—a 2nd degree crime.
A conviction for murder carries a potential penalty of incarceration in New Jersey State prison for 30 years to life. The potential penalty for a 2nd degree conviction is 5 to 10 years of imprisonment.
Chief Assistant Prosecutor John Maher represents the State in the case.
These charges are an accusation and not proof of guilt. In all criminal cases, a charged defendant is presumed innocent unless and until proven guilty.
Anyone with information involving serious crimes is asked to call the Atlantic County Prosecutor’s Office at 609-909-7800 or go to the Prosecutor’s Office Web site at http://www.acpo.org/tips.html and provide information by filling out the form anonymously on the Submit a Tip page. People can also call Crime Stoppers at 609-652-1234 or 1-800-658-8477 (TIPS) or visit the Crime Stoppers Website at http://www.crimestoppersatlantic.com/. Crime Stoppers offers cash rewards for information leading to the arrest and indictment of those who commit crimes in Atlantic County. |
Sixty-nine is a number. It comes between sixty-eight and seventy, and is an odd number. It is divisible by 1, 3, 23, and 69.
Integers |
Fabio Mendouca Carvalho
Fabio Mendouca Carvalho (born 28 July 1993) is a Swiss footballer who played for FC Lausanne-Sport as a defender or midfielder.
He then played for FC Le Mont Ls in the Swiss Challenge League in the 2016-2017 season. After the club's relegation due to financial issues, he signed for FC Stade-Lausanne Ouchy in the Swiss Promotion League.
Football career
On 14 March 2015, Carvalho made his professional debut with Lausanne in a 2014–15 Swiss Challenge League match against FC Winterthur.
He has won the Challenge League Championship with Lausanne-Sport in 2015-2016
References
External links
Category:1995 births
Category:Living people
Category:Swiss footballers
Category:Association football defenders
Category:Swiss Challenge League players
Category:FC Lausanne-Sport players
Category:Place of birth missing (living people) |
Charles Shane Robinson (born July 2, 1964) is an American professional wrestling referee. He is currently working with the WWE where he has been working 2001.
Robinson started out as a photographer for Pro Wrestling Federation (PWF) in 1995.
World Championship Wrestling
On September 15, 1997, He refereed a tryout dark match between Chris Taylor and Kendall Windham before WCW Monday Nitro at Independence Arena in Charlotte, NC. A week later, he was signed by World Championship Wrestling (WCW).
His first appearance for WCW was at the WCW TV tapings at Universal Studios in Orlando, Florida. He turned heel, refereed Four Horsemen matches and aligned himself with Ric Flair. During his heel run, he favored the Horsemen in matches he refereed which annoyed Randy Savage. Savage, who was suspended by Flair (then-WCW President), proposed a match between Robinson and Savage's girlfriend Gorgeous George where if George defeated Robinson, Savage would be reinstated. The match took place on May 9, 1999 at Slamboree 1999. Robinson (dubbed "Little Naitch") copied Flair's signature strut, "wooo!" catchphrase and even wore a robe similar to Flair's. Robinson would lose the match after George hit him with a diving elbow drop.
World Wrestling Federation/Entertainment/WWE
When the World Wrestling Federation bought WCW in March 2001, they hired Robinson. Robinson was a part of The Alliance. The first match that he refereed in the WWF was on July 2, 2001. Even though he was a part of the Alliance, he was mainly a fair and impartial referee. On the July 1, 2004 episode of SmackDown!, he was forced to wrestle Luther Reigns by then-General Manager Kurt Angle. The match was quickly stopped by Charlie Haas however.
On April 18, 2014, while he was traveling with the WWE in Saudi Arabia, he suffered a freak accident after he nearly lost his thumb when he deeply cut it while helping to set up the wrestling ring. He received 6 stitches from a nearby WWE medic. |
/*
* Copyright (c) Facebook, Inc. and its affiliates.
*
* This source code is licensed under the MIT license found in the
* LICENSE file in the root directory of this source tree.
*/
package com.facebook.react;
import android.app.Application;
import androidx.annotation.Nullable;
import com.facebook.infer.annotation.Assertions;
import com.facebook.react.bridge.JSIModulePackage;
import com.facebook.react.bridge.JavaScriptExecutorFactory;
import com.facebook.react.bridge.ReactMarker;
import com.facebook.react.bridge.ReactMarkerConstants;
import com.facebook.react.common.LifecycleState;
import com.facebook.react.devsupport.RedBoxHandler;
import com.facebook.react.uimanager.UIImplementationProvider;
import java.util.List;
/**
* Simple class that holds an instance of {@link ReactInstanceManager}. This can be used in your
* {@link Application class} (see {@link ReactApplication}), or as a static field.
*/
public abstract class ReactNativeHost {
private final Application mApplication;
private @Nullable ReactInstanceManager mReactInstanceManager;
protected ReactNativeHost(Application application) {
mApplication = application;
}
/** Get the current {@link ReactInstanceManager} instance, or create one. */
public ReactInstanceManager getReactInstanceManager() {
if (mReactInstanceManager == null) {
ReactMarker.logMarker(ReactMarkerConstants.GET_REACT_INSTANCE_MANAGER_START);
mReactInstanceManager = createReactInstanceManager();
ReactMarker.logMarker(ReactMarkerConstants.GET_REACT_INSTANCE_MANAGER_END);
}
return mReactInstanceManager;
}
/**
* Get whether this holder contains a {@link ReactInstanceManager} instance, or not. I.e. if
* {@link #getReactInstanceManager()} has been called at least once since this object was created
* or {@link #clear()} was called.
*/
public boolean hasInstance() {
return mReactInstanceManager != null;
}
/**
* Destroy the current instance and release the internal reference to it, allowing it to be GCed.
*/
public void clear() {
if (mReactInstanceManager != null) {
mReactInstanceManager.destroy();
mReactInstanceManager = null;
}
}
protected ReactInstanceManager createReactInstanceManager() {
ReactMarker.logMarker(ReactMarkerConstants.BUILD_REACT_INSTANCE_MANAGER_START);
ReactInstanceManagerBuilder builder =
ReactInstanceManager.builder()
.setApplication(mApplication)
.setJSMainModulePath(getJSMainModuleName())
.setUseDeveloperSupport(getUseDeveloperSupport())
.setRedBoxHandler(getRedBoxHandler())
.setJavaScriptExecutorFactory(getJavaScriptExecutorFactory())
.setUIImplementationProvider(getUIImplementationProvider())
.setJSIModulesPackage(getJSIModulePackage())
.setInitialLifecycleState(LifecycleState.BEFORE_CREATE);
for (ReactPackage reactPackage : getPackages()) {
builder.addPackage(reactPackage);
}
String jsBundleFile = getJSBundleFile();
if (jsBundleFile != null) {
builder.setJSBundleFile(jsBundleFile);
} else {
builder.setBundleAssetName(Assertions.assertNotNull(getBundleAssetName()));
}
ReactInstanceManager reactInstanceManager = builder.build();
ReactMarker.logMarker(ReactMarkerConstants.BUILD_REACT_INSTANCE_MANAGER_END);
return reactInstanceManager;
}
/** Get the {@link RedBoxHandler} to send RedBox-related callbacks to. */
protected @Nullable RedBoxHandler getRedBoxHandler() {
return null;
}
/** Get the {@link JavaScriptExecutorFactory}. Override this to use a custom Executor. */
protected @Nullable JavaScriptExecutorFactory getJavaScriptExecutorFactory() {
return null;
}
protected final Application getApplication() {
return mApplication;
}
/**
* Get the {@link UIImplementationProvider} to use. Override this method if you want to use a
* custom UI implementation.
*
* <p>Note: this is very advanced functionality, in 99% of cases you don't need to override this.
*/
protected UIImplementationProvider getUIImplementationProvider() {
return new UIImplementationProvider();
}
protected @Nullable JSIModulePackage getJSIModulePackage() {
return null;
}
/**
* Returns the name of the main module. Determines the URL used to fetch the JS bundle from the
* packager server. It is only used when dev support is enabled. This is the first file to be
* executed once the {@link ReactInstanceManager} is created. e.g. "index.android"
*/
protected String getJSMainModuleName() {
return "index.android";
}
/**
* Returns a custom path of the bundle file. This is used in cases the bundle should be loaded
* from a custom path. By default it is loaded from Android assets, from a path specified by
* {@link getBundleAssetName}. e.g. "file://sdcard/myapp_cache/index.android.bundle"
*/
protected @Nullable String getJSBundleFile() {
return null;
}
/**
* Returns the name of the bundle in assets. If this is null, and no file path is specified for
* the bundle, the app will only work with {@code getUseDeveloperSupport} enabled and will always
* try to load the JS bundle from the packager server. e.g. "index.android.bundle"
*/
protected @Nullable String getBundleAssetName() {
return "index.android.bundle";
}
/** Returns whether dev mode should be enabled. This enables e.g. the dev menu. */
public abstract boolean getUseDeveloperSupport();
/**
* Returns a list of {@link ReactPackage} used by the app. You'll most likely want to return at
* least the {@code MainReactPackage}. If your app uses additional views or modules besides the
* default ones, you'll want to include more packages here.
*/
protected abstract List<ReactPackage> getPackages();
}
|
Black Hawk County is a county in the northeastern part of U.S. state of Iowa. As of the 2020 census, the population was 131,144, making it Iowa's fifth-most populous county. The county seat is Waterloo. The county was founded on February 17, 1843 and named after Black Hawk, a Sauk leader during the 1832 Black Hawk War. |
I am trying to swap out an incandescent light for an LED light on my electric scooter. I've managed to remove the old incandescent light (right in figure) from its holster. When I replace it with the LED (left) light that I recently purchased, the LED doesn't light up, while the incandescent light does. The holster is designed such that the bulbs can be inserted in one direction only.
The incandescent light is rated at 12V, while the LED says from 9-84V if I'm not reading it wrongly. Does anyone have any suggestion on why the incandescent one works, while the LED one doesn't?
Since the LED's are diodes, do you think the guy who soldered the incandescent holder might have just not-cared about which was positive and which was negative and therefore gotten the negative and positive terminals switched?
Same issue, the incandescent on scooters has a live from the battery or 12v transformer to the earth pin and the switches swap the lower pins to earth. The dirty way to change this is swap the earth and main pins over on the headlight plug giving you normal lighting,but no full beam, other than that you need to rewrire the switch that may also cause problems to the rear light/brake light. Or a switching relay to swap poles.
Intelligence is distributed nearly evenly, with only the occasional concentration in one person. The total quantity of Intelligence is a constant: as more people come into being, fewer and fewer get a sufficient amount for themselves.
Some say this has already reached homeopathic levels.
So what I did was measure the voltage at the connector that the incandescent holster plugs into. There are 3 wires there and I found 12V between two of them, so I fashioned an electrical connector from some thick wire I had and inserted it into the 2 appropriate holes in the connector that is running inside the scooter, apparently to the controller.
That worked, but I wasn't really bright enough, so I got a second LED light and mounted it in front of the dash. I wanted to connect it in parallel with the existing make-shift connector and this is where it started to get a bit messy as I didn't have everything I needed to make the connection. I tried wrapping the new LED's wires around the appropriate part of the thick wires that I had inserted into the connector. The second LED lit up too which was great, but I was in a bit of a rush and didn't secure the electrical connection very well.
Later that evening both LED's went out and when I measure the voltage at the connector at home, there was now no voltage across them. I suspect that during the ride, some of the wires must have short circuited and burned something out in the controller.
A little while later, my bike started behaving very strangely. It turns on with a key just like a normal scooter. However, my bike was turning on by itself even when the key wasn't inserted. When the bike was on, it would not respond to the throttle, but periodically jerk and stop, jerk and stop. When I tried to push the bike home, it was somehow applying something akin to a regenerative brake, even though my bike doesn't have regenerative braking. So it was basically impossible to push my bike anywhere (because of this magnetic braking effect) and it wasn't responding to the throttle. I was stuck for a while wondering what I should do.
I was lucky that I had taken off some of the plastic covering the insides of the bike, that I hadn't bothered to put back yet (as I'm still tinkering inside the bike), and I could just reach in and disconnect the battery. After doing that, I could push the bike. Then gingerly reconnecting my battery, I found that the bike's controller had reset to a sane state, akin to rebooting my computer (controller) and I could ride the bike home.
I was quite concerned about the bike after that and I went down and checked on it several times that evening and into the night with a volt meter. Luckily, it wasn't doing anything bad to my battery, but the burn-out of the connector for the lamp stayed dead. The rest of the bike seems to be functioning fine though after the reset.
Well, I learned that the light on my bike is connected to the controller and short-circuiting probably did something weird to my controller, putting it in a kind of unexpected state. Resetting the controller by disconnecting power seems to put it back into a sane state. Right now my plan is to run a wire from my battery through a separate switch to the lights taking the controller out of the control loop, and to use proper XT60 connectors instead.
So... I've now connected up the above LED to my battery through a switch. The battery is 60V nominal, but can be as high as 71V when freshly charged. The LED is rated from 9V to 80V.
I also have a Volt/ammeter connected on my bike and I can measure that this LED is drawing 1.7A or more than 100W! To me, that is a ridiculously high power draw for the LED. Does anyone know how these cheap LED's are able to operate over such a wide voltage range and why the power drawn is so much?
The LED has a pretty large heat sink, so I suspect there's just a simple resistor in there turning a lot of the current into heat... If anyone one has some insight on what's in there, would appreciate hearing your thoughts.
So... I've now connected up the above LED to my battery through a switch. The battery is 60V nominal, but can be as high as 71V when freshly charged. The LED is rated from 9V to 80V.
I also have a Volt/ammeter connected on my bike and I can measure that this LED is drawing 1.7A or more than 100W! To me, that is a ridiculously high power draw for the LED. Does anyone know how these cheap LED's are able to operate over such a wide voltage range and why the power drawn is so much?
The LED has a pretty large heat sink, so I suspect there's just a simple resistor in there turning a lot of the current into heat... If anyone one has some insight on what's in there, would appreciate hearing your thoughts.
Sounds like the LED is using a linear regulator to regulate current (a terrible way to do it.)
I'd recommend getting a better light, like one of the ebikes.ca lights. They use 1-4 watts and operate with an input up to 75 volts. |
Traveller's Tales is a British video game developer and subsidiary of TT Games. The company was founded in 1989 by Jon Burton and Andy Ingram. The company was originally a small company, focused on its own games. It became much bigger after they developed games for larger companies such as Sega and Disney Interactive Studios. In 2004, development on Lego Star Wars: The Video Game began with Giant Interactive Entertainment, the exclusive rights holder to Lego video games. Traveller's Tales bought the company in 2005, and the two became one, known as TT Games.
Video game companies of the United Kingdom |
Torsional pendulum preliminary experiment 2 essay
A torsional pendulum is a flat disk, suspended horizontally by a wire attached at the top of the fixed support when the disk is tuned through a small angle, the wire is twisted on being released the disk performs torsional oscillations about the axis performs torsional oscillations about the axis of the support. A torsional pendulum, or torsional oscillator, consists of a disk-like mass suspended from a the values of i laboratory/software torsion is a twisting force that causes shear stress on the section. Experiment 4 - structural analysis 1 lab report torsion test microstructure study of ferrous and non ferrous alloys under various compositions and heat treatment conditions lab report. Theory: if simple harmonic motion applies, which i am assuming it does as shown in the equations above, also there is a clear similarity between the time period for a torsional pendulum and for a mass spring system which is simple harmonic motion, as shown in these 2 equations.
In a structural component due to axial loading, torsion, and bending acting individually or in consider the torsional mass-spring-damper system in fig2 department of the army torsional pendulum, support for hanging the pendulum, regular circular body. Pendulum experiment lab report research question: how does the angle and length of a pendulum is effect the period/oscillation of a 1physics experiments for ph201 and ph202, (usa dept here is the list of labs which we will be doing in the 2011-2013 years. In this experiment you will make a simple pendulum consisting of a plumb bob and a jectile launcher, ballistic pendulum, springs, simple pendulum, calorimeter explain exactly what you measured and report the value(s. In our experiment, the applied relatively big and heavy phys- ical pendulum was built, not for a newest measure of the gravita- tional constant, but for the study of special gravitational effects en.
Coulomb balance alison hu physics department, the college of wooster, wooster, ohio 44691, usa used in this experiment the torsion balance in-volved two charged spheres, one of which was sus-pended as one sphere was brought closer to the suspended sphere, the charges caused the sus. Hi can you explain why a mobile mass is pushed towards a hidden light and goes back to original position when light is turned off the mobile mass is at the end of a torsional pendulum suspended by trifilar small copper wire and is completely enclosed in a box. Surface tension page 2 film inside the loop of thread is punctured, the thread springs out into a circular shape 11 to become familiar with torsion tests of rods with solid circular at the heart of the apparatus is a torsion balance placed on a turntable.
Very high resolution micromechanical measurements on thin wires in torsion w ali1,2, dj dunstan1a and aj bushby3 1school of physics and astronomy, queen mary university of london, london e1 4ns, uk, 2government college university, lahore, pakistan 2 school of engineering and materials science, queen mary university of london, london e1 4ns, uk. A large torsion pendulum illustrates simple harmonic motion are you looking for torsional pendulum experiment viva questions with answers a) the modulus of rigidity, g b) the shear stress at the limit of proportionality, τ. The aim of this experiment was to measure newton's gravitational constant, g using a torsion pendulum 1 dof torsion experiment for matlab /simulink users one of many interchangeable experiment modules from tecquipment's modern, flexible 2h combined loading: torsion t ap.
This experiment will endeavour to establish the torsional elastic constant (the rotational equivalent of the spring constant) of a particular type of torsion pendulum known as the maxwell pendulum measurements for the period of such a pendulum will also enable the determination of the. To determine the acceleration of free fall - sample essay – = constant and the gradient of the line analysis of preliminary experiment from our experiment we came across five problems:- 1 5 metres of thread 3 2 pieces of slated wood 4 pendulum / bob 5 stool 6 stop watch 7 2 metre sticks 8 protractor 9 card and felt pen method. The trouton experiment, e = mc 2, and a slice of minkowski space-time 1 the forgotten precursor to the trouton-noble experiment trouton’s torsion pendulum was designed to detect these jolts not surprisingly from a modern relativistic point of view, trouton found lorentz’s analysis of the trouton experiment, a negative result in.
Torsional pendulum preliminary experiment 2 essay
Mechanical resonance free and forced shm of a torsional pendulum - laura imperatori - scientific essay - physics - mechanics - publish your bachelor's or master's thesis, dissertation, term paper or essay. A narrative type of essay refers to a written trusted essay writing service knows for sure how to be a student is a delicate torsion balance an experiment was conducted to investigate the effects of resonance on an oscillating torsion pendulum and to determine the q factor for the abnormal laboratory values. A torsional pendulum is formed by taking a meter stick of mass 200 kg, and attaching to its center a wire with its upper end clamped, the vertical wire supports the stick as the stick turns in a horizontal plane. The pendulum functions as a figure of newton’s 2 nd law, which affirms that for each force there is an equivalent and opposite feedback the basic experiments demonstrate another of newton’s laws, that is, bodies in motion continue to move unless acted on by another force.
The purpose of the torsion pendulum experiment is to determine the torsion constant for a given wire torsional plant operation the pc for this experiment should already be venturi meter and orifice plate lab report.
Essay illegitimate science a personal story bruce maccabee 6962 eyler valley flint road, sabillasville, md 21 780 solar eclipses saxl claimed that the period of a torsional pendulum inside a grounded faraday cage was observed to increase during an eclipse the this is not a formal report on my experiment, but more of a retrospective.
Torsion pendulum is independent of the amplitude of the motion pendulums (or pendula if we are being exact) of the lab, you should begin by documenting your work into a lab report. As a result, the fundamental frequency due to the l=2 and m=1 term caused by the attitude of the torsion pendulum brings in about 9 ppm in order to reduce the influence of the fundamental frequency to less than 1 ppm, the requirement of the attitude of the pendulum should be better than 03 mrad. - pendulum investigation introduction in this investigation, i will try to attempt an experiment that will measure the time taken for a pendulum to oscillate for one complete swing i will also explore and investigate the numerous variables that might effect the time taken to oscillate. The residual twist angle of the torsion pendulum the preliminary apparatus is shown in figure 2, and a detailed description of the apparatus in the formal experiment, the torsion fibre. |
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