texts
sequence | meta
dict | scores
sequence | avg_score
float64 0
0.08
| num_sents
int64 5
5
|
|---|---|---|---|---|
[
"One man’s unrelenting struggle to convert a community that was poaching migratory birds in the hundreds of thousands to one that became conservators and protectors. ",
"A tale of extreme dedication, suffering and sacrifice.",
"\n\nThe community residing in small fishing villages on the shores of Lake Chilka in Odisha had for long poached thousands of migratory birds as they came in from Central and North Asia to spend the winter months. ",
"The birds were being trapped brutally and sold across Odisha, trains made unscheduled stops to pick cages filled with exotic birds, local officials accepted them as bribes and the people began to believe that they had magical powers to cure diseases. ",
"By the 1980’s a strong mafia had established itself controlling the trade.",
"\n\nOne man decided to end all this. ",
"Over 2 decades he kept up his struggle and campaign to protect these foreign guests. ",
"He was beaten, tortured , framed and jailed – yet did not give up. ",
"Today, the same community are protectors and conservators. ",
"Bombay Natural History Society estimated that over the 20 year period the migratory bird population has increased nearly 30 times.",
"\n\nOne of the greatest tales of conservation and protection is waiting to be told. ",
"This is what legends are made of."
] | {
"pile_set_name": "Pile-CC"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0000591715976331361,
0,
0
] | 0.000005 | 5 |
[
"Q:\n\nHTMLAgilityPack - Remove Node with out stripping the inner text\n\nMy html content is \n<a href=\"#asdf\">asdf</a>\n<H5 align=\"left\"><A href=\"#d570525d497.htm#toc\">Table \nof Contents</A><br></H5>\n\nI'm using HTML Agility Pack to load the html. ",
"I want to find <a> nodes and remove the node without removing its inner text as mentioned below \nasdf\n<H5 align=\"left\">Table \nof Contents<br></H5>\n\nI'm using below code,\nvar htmlDocument = new HtmlDocument();\nhtmlDocument.",
"LoadHtml(htmlPage);\nvar Nodes = htmlDocument.",
"DocumentNode.",
"SelectNodes(\"//a\");\nforeach (var Node in Nodes)\n{\n Node.",
"InnerText.",
"Trim();\n}\n\nIt's not working. ",
"Something wrong with the code?",
"\n\nA:\n\nRemove the node from parent while keeping the grand children\nforeach (var Node in Nodes)\n{\n Node.",
"ParentNode.",
"RemoveChild(Node, true); //<-- keepGrandChildren\n}\n\nvar newhtml = htmlDocument.",
"DocumentNode.",
"OuterHtml;\n\noutput:\nasdf\n<h5 align=\"left\">Table \nof Contents<br></h5>\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0.000020108990729755272,
0,
0.00591715976331361,
0.0002872737719046251,
0.01,
0,
0,
0.00008899964400142399,
0,
0,
0.00591715976331361,
0.00039674667724657806
] | 0.001741 | 5 |
[
"Q:\n\nCommunity ads broken?",
"\n\nI noticed a blank ad, and clicked on the Stats link to see this: \n\nSomething seems broken. ",
"I note that the Community Promotion Ads meta question is fine, all the images are there.",
"\n\nA:\n\nArgh. ",
"This issue popped on a few other sites as well but it's difficult to spot every instance. ",
"We're rolling out a fix to clean this up. ",
"\nThank you for bringing this to our attention!",
"\n::high five::\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0.00012913223140495868,
0,
0,
0,
0,
0
] | 0.000016 | 5 |
[
"URBANA – Following two reports of job scams within the past couple weeks, the Division of Public Safety is hoping to remind students and others to be judicious when looking for employment.",
"\n\nA U. of I. student reported on June 15 that she had been the victim of deceptive practices after applying on a U. of I. online job board for a job that does not exist. ",
"The student said she became suspicious the job was not legitimate and called police after being asked to wire $150 from her account to another.",
"\n\nIn the second incident, a U. of I. student reported on June 26 that she had been the victim of deceptive practices after applying on a U. of I. online job board for an office position. ",
"The student said she became suspicious the job was not legitimate after being asked to send $250 from her account to someone in Nigeria.",
"\n\nJob-seekers should never accept any job from someone who wants to send or receive a check or cash before the applicant is hired or actually working. ",
"This goes for all cases, whether the job is listed on a public board or through a service offered by the University of Illinois at Urbana-Champaign.",
"\n\nSome other commonalities between recent reports of deceptive practices exist:\n\nFraudulent employers have sought some sort of assistant.",
"\n\nApplicants are asked to set up a Yahoo! ",
"Messenger account to communicate with the fraudulent employer.",
"\n\nApplicants are asked to complete a series of menial tasks before asking the applicant to wire money to someone else’s account.",
"\n\nApplicants may be asked to buy supplies with a promise of reimbursement.",
"\n\nThe University’s Virtual Job Board is monitored for suspicious or fraudulent listings, but there may be some delay between the time the job is posted and the time it is vetted and deleted by University staff.",
"\n\nAnyone who believes they have been the victim of deceptive practices or fraud should contact the University of Illinois Police Department at 217-333-1216.",
"\n\nThe FBI also fields claims of Internet crime at www.ic3.gov. ",
"This does not take the place of a police report – it is offered only as an additional resource to report and track Internet crime.",
"\n\nTechnology Services also offers a phishing resource page."
] | {
"pile_set_name": "OpenWebText2"
} | [
0.000028293345405160706,
0,
0,
0,
0,
0,
0.00004565376186997809,
0,
0.0005668934240362812,
0,
0,
0,
0.000022675736961451248,
0.000041091387245233394,
0.0005039052658100277,
0,
0
] | 0.000071 | 5 |
[
"Niall Cameron\n\nNiall Cameron (born 1979) is a Scottish table tennis player from Elgin, Scotland.",
"\n\nHe represented Scotland in the 2002 Commonwealth Games in Manchester and the 2014 Commonwealth Games in Glasgow. ",
"He is currently ranked 4th in Scotland.",
"\n\n4x Scottish Men's Doubles Champion\n4x Scottish Mixed Doubles Champion\nCommonwealth Championships Team Bronze (2013)\nBritish Premier League Winner (2011)\n\nExternal links\n Go Scotland 2014 Commonwealth Games web page\n\nReferences\n\nCategory:Living people\nCategory:1979 births\nCategory:Scottish table tennis players\nCategory:Table tennis players at the 2002 Commonwealth Games\nCategory:Table tennis players at the 2014 Commonwealth Games\nCategory:British male table tennis players"
] | {
"pile_set_name": "Wikipedia (en)"
} | [
0.00021701388888888888,
0,
0,
0.000017580176592873877
] | 0.000059 | 5 |
[
"/*-----------------------------------------------------------------------\n/ PFF - Low level disk interface modlue include file (C)ChaN, 2014\n/-----------------------------------------------------------------------*/\n/* Changes for Teacup see pff.c. */",
"\n\n#include \"sd.h\"\n\n#ifdef SD\n\n#ifndef _DISKIO_DEFINED\n#define _DISKIO_DEFINED\n\n#ifdef __cplusplus\nextern \"C\" {\n#endif\n\n#include \"pff_conf.h\"\n\n\n/* Status of Disk Functions */\ntypedef BYTE DSTATUS;\n\n\n/* Results of Disk Functions */\ntypedef enum {\n RES_OK = 0, /* 0: Function succeeded */\n RES_ERROR, /* 1: Disk error */\n RES_NOTRDY, /* 2: Not ready */\n RES_PARERR, /* 3: Invalid parameter */\n RES_EOL_FOUND, /* 4: Function succeeded and also found an EOL. */",
"\n} DRESULT;\n\n\n/*---------------------------------------*/\n/* Prototypes for disk control functions */\n\nDSTATUS disk_initialize (void);\n#if _USE_READ\n DRESULT disk_readp (BYTE* buffer, DWORD sector, UINT offset, UINT count);\n DRESULT disk_parsep (DWORD sector, UINT offset, UINT* count,\n uint8_t (*parser)(uint8_t));\n#endif\n#if _USE_WRITE\n DRESULT disk_writep (const BYTE* buffer, DWORD sc);\n#endif\n\n#define STA_NOINIT 0x01 /* Drive not initialized */\n#define STA_NODISK 0x02 /* No medium in the drive */\n\n#ifdef __cplusplus\n}\n#endif\n\n#endif /* _DISKIO_DEFINED */\n\n#endif /* SD */\n"
] | {
"pile_set_name": "Github"
} | [
0,
0.00002891797210655033,
0.000025847540864962106
] | 0.000018 | 5 |
[
"Tag Archives: Art\n\nSafeLaunch returns to Santa Ynez Airport Day with a Crazy Pilot, Paint and a Message on Saturday, May 21\n\nPilots and future pilots attending last year’s Santa Ynez Airport Day were stunned to see one pilot encourage kids to paint bright images all over his airplane! ",
"This Saturday, May 21 from 10am-3pm, he’ll be back.",
"\n\nAlmost every pilot who witnessed the throng of enthusiastic kids painting the white Cessna Skylane last year thought that he must be crazy. ",
"He may well be, but there is a mission and a method to his madness. ",
"It’s called SafeLaunch and it is the name of the nonprofit Ron Cuff co-founded with Janet Rowse, wife of Santa Barbara City Councilmember Randy Rowse.",
"\n\nSafeLaunch, the name that implies launching kids safely into adulthood without the burden of addiction was derived from the thousands of safe launches from aircraft carriers that Commander Cuff witnessed and participated in while serving as a Naval Aviator.",
"\n\nSafeLaunch is the nation’s one and only nonprofit of its kind, 100% dedicated to primary prevention. ",
"According to Cuff, “Parents need to know that addiction affects over 23 million Americans and that 90% of it starts in the teen years.” ",
"Janet Rowse emphasizes the scientifically-proven vulnerability of teens’ developing brains– “This brain disease is almost 100% preventable, so it isn’t good enough to hope that your child will make a good decision whenever an opportunity presents itself,” she says. “",
"Parents need information and tools to protect their children’s developing brains and futures, which is what SafeLaunch provides”.",
"\n\nRegardless of the “crazy pilot” moniker, Cuff can’t be dissuaded. “",
"Hey, I’ve got a blank canvas that flies, and we tell kids that painting a life free from addiction is the way to go. ",
"All they need is a destination, a flight plan and a clear head.”",
"\n\nWinged Dream Machine Helps Teach Addiction-free Lesson\n\nAn airplane-as-metaphor for “the vast possibilities that a life without addiction holds” is helping a California nonprofit steer youngsters away from early exposure to drug abuse.",
"\n\nSafeLaunch, of Santa Barbara, California, taps resources of education, art, and aviation to preempt the damage that drug or alcohol abuse can inflict on its most vulnerable prey: children.",
"\n\nWhen exposed to alcohol, tobacco, or other drugs, “children are up to six times more vulnerable to the brain disease of addiction than adults,” SafeLaunch says, citing information from addiction education organization Casa Columbia. ",
"That means all children. ",
"Forget about demographic or socioeconomic sub-categories, or common notions of at-risk populations. ",
"When it comes to the vulnerability of children to addiction, labels don’t apply.",
"\n\nAbout 90 percent of the time, addiction begins in the teen years, SafeLaunch says. ",
"By facing down addiction for what it is—”a preventable brain disease”—SafeLaunch believes addiction can be defeated.",
"\n\nIn 2012, teen photographers from the SafeLaunch Media $500 Contest met with people in recovery at the Santa Barbara Rescue Mission, and read their stories. ",
"Teen artists then artistically interpreted the portraits and the stories. ",
"The message is loud and clear: Avoid early first exposure to alcohol and drugs. ",
"As the poet-philosopher Noah BenShea says, “Addiction is a powerful teacher, but the tuition is your life.”",
"\n\n“All of the participants have played an important role in raising awareness of the increased risk that teens have to addiction,” SafeLaunch co-founder Janet Rowse said. “",
"The impact of the personal stories of the people in recovery who participated is evident in the art and photography by these talented students.”"
] | {
"pile_set_name": "Pile-CC"
} | [
0,
0,
0.00004959333465582226,
0,
0.00017777777777777779,
0.000029814701629373446,
0,
0.00005406574394463668,
0.000014027409558276873,
0.00006009254251547383,
0.00021003990758244068,
0,
0,
0,
0,
0.000018107741059302852,
0,
0,
0,
0.00013840830449826988,
0,
0.0000400576830636116,
0,
0,
0.00008734387282732115,
0.00003380205516495403,
0
] | 0.000034 | 5 |
[
"We couldn't find anything matching the term \"pupil hacks google maps to label school hell on earth\" on Gizmodo\n\nYou can try expanding your search to all G/O Media sites"
] | {
"pile_set_name": "OpenWebText2"
} | [
0.000035430839002267575
] | 0.000035 | 5 |
[
"Popular filters\n\nPulaski Rentals\n\n6\napartments\n\n“So cozy!” ",
"We stayed there in april - so maybe not the most usual time. ",
"But it was so cozy and lovely and clean and the beach was nearly deserted - it was beautiful, quiet and restful. ",
"The owner is right next door to answer any questions, but there's a\n\n“Perfect for our family!” ",
"I cannot say enough about how fantastic this lodge was!! ",
"The owner was extremely easy to communicate with, even had to change our dates at the last minute and was no problem. ",
"We had to be nearby for my mother-in-law's burial"
] | {
"pile_set_name": "Pile-CC"
} | [
0,
0,
0,
0,
0,
0,
0
] | 0 | 5 |
[
"113 F.3d 279\nUNITED STATES of America, Appellee,v.Thakhone KHOUNSAVANH, Defendant, Appellant.",
"\nNo. ",
"96-1244.",
"\nUnited States Court of Appeals,First Circuit.",
"\nHeard Feb. 5, 1997.Decided May 16, 1997.",
"\n\nJennifer Petersen, with whom Karl R.D. Suchecki and Petersen & Suchecki were on brief, Boston, MA, for appellant.",
"\nSheldon Whitehouse, United States Attorney, with whom Zechariah Chafee, Assistant United States Attorney, was on brief, for appellee.",
"\nBefore STAHL, Circuit Judge, BOWNES, Senior Circuit Judge, and LYNCH, Circuit Judge.",
"\nBOWNES, Senior Circuit Judge.",
"\n\n\n1\nDefendant Thakhone Khounsavanh appeals his conviction for Conspiracy to Distribute Cocaine Base and for Possession with Intent to Distribute Cocaine Base. ",
" See 21 U.S.C. §§ 841(a)(1), 846; 18 U.S.C. § 2. ",
" He contends that the district court erred in denying his motion to suppress the fruits of a search on the ground that the affidavit underlying the search warrant lacked sufficient information to support a finding of probable cause. ",
" We affirm.",
"\n\nThe Facts\n\n2\nOn May 23, 1995, Providence, Rhode Island police officers executed a search warrant for the first floor rear apartment at 676-678 Chalkstone Avenue, a three-family tenement building. ",
" The warrant was based on an affidavit submitted by Detective Freddy Rocha. ",
" According to the affidavit, a confidential informant had told Detective Rocha that two men were storing and selling crack cocaine in that apartment. ",
" The affidavit described the two men as \" 'Fat Boy' Alias John Doe ... an Asian Male, Unkn. ",
" Age. ",
"5'6\"' Tall and 170 Lbs. ",
"and 'Turtle' Alias John Doe. ",
"5'7\"' 130 Lbs.\" ",
"The informant also told the detective that he \"could make a purchase of cocaine from this subject.\" ",
" (The affidavit alternates several times between referring to the subjects in the singular and in the plural.)",
"\n\n\n3\nThe detective sought to corroborate the informant's story by taking him up on his offer to conduct a controlled buy of cocaine from the apartment under the officer's supervision. ",
" According to the affidavit, Detective Rocha \"drove to the Chalkstone Avenue area [and] searched the informant for contraband. ",
" Finding none the informant was given an amount of U.S. currency and directed to make a purchase of cocaine from 'Fat Boy' and 'Turtle' at 676-678 Chalkstone Ave.\" ",
"The detective watched the informant enter the building through the rear door and exit five minutes later through the same door. ",
" The detective met the informant at a pre-arranged location, where the informant handed him a quantity of suspected cocaine which he stated he had purchased from \"Fat Boy.\" ",
" Tests later revealed that the substance was indeed cocaine.",
"\n\n\n4\nThe detective then applied for a warrant to search the first floor rear apartment at 676-678 Chalkstone Avenue and/or the two men (\"Fat Boy\" and \"Turtle\"). ",
" The complaint for the warrant (which was sworn to before a state court judge) added to the affidavit's description the facts that \"Fat Boy\" was approximately twenty-five years old with \"short hair balding,\" and that \"Turtle\" was an Asian male with black short hair. ",
" The court issued the warrant, both as to the premises and as to the persons of \"Fat Boy\" and \"Turtle.\"",
"\n\n\n5\nThe police executed the warrant the same day. ",
" When the police entered the apartment, two men who approximately fit the informant's descriptions fled to a bedroom. ",
" Three other people were present in the apartment during the search but did not leave the room they had been in when the police arrived. ",
" One detective searched \"Fat Boy\" and found in his front pants pocket a plastic bag containing fourteen smaller bags of what tested out as crack cocaine. ",
" Another detective found, in the ceiling of the kitchen, a bag containing 650 smaller bags of crack cocaine. ",
" Another small bag of powder cocaine was found in the bedroom. ",
" In addition to the drugs, the police seized the wallets and identification of the two men who fled, one of whom is the defendant. ",
" They also found in the apartment and seized a pager, bagging material, and a gas bill on which the defendant's name appeared.",
"\n\n\n6\nThe defendant moved to suppress the fruits of the search. ",
" After hearing, the district court denied the motion. ",
" The defendant then entered a plea of guilty to Counts I and II of the indictment, and the government dismissed Count III. ",
" In his plea agreement, the defendant gave notice that he intended to appeal the denial of his suppression motion, pursuant to Fed.",
"R.Crim.",
"P. 11(a)(2).",
"\n\nStandard of Review\n\n7\nIn reviewing a denial of a suppression motion, the district court's ultimate legal conclusion, including the determination that a given set of facts constituted probable cause, is a question of law subject to de novo review. ",
" See Ornelas v. United States, --- U.S. ----, ----, 116 S.Ct. ",
"1657, 1659, 134 L.Ed.2d 911 (1996); United States v. Zayas-Diaz, 95 F.3d 105, 111 n. 6 (1st Cir.1996). ",
" The district court's findings (if any) of historical facts--\"the events which occurred leading up to the ... search,\" Ornelas, --- U.S. at ----, 116 S.Ct. ",
"at 1661--must be upheld unless they are clearly erroneous. ",
" See id. at ----, 116 S.Ct. ",
"at 1663; Zayas-Diaz, 95 F.3d at 111 n. 6. ",
"A reviewing court must \"give due weight to inferences drawn from those facts by resident judges and local law enforcement officers.\" ",
" Ornelas, --- U.S. at ----, 116 S.Ct. ",
"at 1663. ",
" But \"the decision whether these historical facts, viewed from the standpoint of an objectively reasonable police officer, amount to ... probable cause\" is a mixed question of law and fact which we review de novo. ",
" Id. at ----- -----, 116 S.Ct. ",
"at 1661-63.",
"\n\nAnalysis\n\n8\nThe Fourth Amendment states: \"The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated, and no Warrants shall issue, but upon probable cause, supported by Oath or affirmation, and particularly describing the place to be searched, and the persons or things to be seized.\" ",
" U.S. Const. ",
"amend. ",
" IV. ",
"There is a strong preference for the use of search warrants. ",
" See Ornelas, --- U.S. at ----, 116 S.Ct. ",
"at 1663; Payton v. New York, 445 U.S. 573, 586, 100 S.Ct. ",
"1371, 1380, 63 L.Ed.2d 639 (1980). ",
" While the warrant requirement may be dispensed with in certain exigent circumstances that are \"few in number and carefully delineated,\" United States v. United States Dist. ",
"Court, 407 U.S. 297, 318, 92 S.Ct. ",
"2125, 2137, 32 L.Ed.2d 752 (1972), the probable cause requirement is rigorously adhered to. ",
" See Arizona v. Hicks, 480 U.S. 321, 326-27, 329, 107 S.Ct. ",
"1149, 1153-54, 1155, 94 L.Ed.2d 347 (1987). ",
" \"Probable cause exists when 'the affidavit upon which a warrant is founded demonstrates in some trustworthy fashion the likelihood that an offense has been committed and that there is sound reason to believe that a particular search will turn up evidence of it' \" or that the search will turn up contraband. ",
" United States v. Schaefer, 87 F.3d 562, 565 (1st Cir.1996) (quoting United States v. Aguirre, 839 F.2d 854, 857-58 (1st Cir.1988)).",
"\n\n\n9\nThe standard we apply in determining the sufficiency of an affidavit is whether the \"totality of the circumstances\" stated in the affidavit demonstrates probable cause to search either the premises or the person.1 See Illinois v. Gates, 462 U.S. 213, 238, 103 S.Ct. ",
"2317, 2332, 76 L.Ed.2d 527 (1983). ",
" \"[P]robable cause need not be tantamount to proof beyond a reasonable doubt.... Probability is the touchstone.\" ",
" Aguirre, 839 F.2d at 857 (internal quotation marks and citations omitted). ",
" See Gates, 462 U.S. at 244 n. 13, 103 S.Ct. ",
"at 2335 n. 13 (\"[P]robable cause requires only a probability or substantial chance of criminal activity, not an actual showing of such activity.\"). ",
" To establish probable cause for a premises search, the information available in the affidavit must show \"a fair probability that contraband or evidence of a crime will be found in a particular place.\" ",
" Id. at 238, 103 S.Ct. ",
"at 2332. ",
" An affidavit supporting a request for a search warrant must give the magistrate a \"substantial basis\" upon which to conclude that there is such a \"fair probability.\" ",
" Gates, 462 U.S. at 238-39, 103 S.Ct. ",
"at 2332-33. ",
" The facts must be judged against an objective standard: \"would the facts available to the officer at the moment of ... the search 'warrant a [person] of reasonable caution in the belief' that the action taken was appropriate?\" ",
" Terry v. Ohio, 392 U.S. 1, 21-22, 88 S.Ct. ",
"1868, 1880, 20 L.Ed.2d 889 (1968).",
"\n\n\n10\nIn many cases, as here, part of the basis for probable cause derives from information that the police have obtained from an informant. ",
" Prior to Gates, the Court had developed a two-pronged test for such a case: when the warrant affidavit rests on hearsay--an informant's report--the affidavit must inform the magistrate \"of some of the underlying circumstances from which the informant concluded that the narcotics were where he claimed they were [the basis of knowledge prong], and some of the underlying circumstances from which the officer concluded that the informant ... was 'credible' or his information 'reliable' [the veracity prong].\" ",
" Aguilar v. Texas, 378 U.S. 108, 114, 84 S.Ct. ",
"1509, 1514, 12 L.Ed.2d 723 (1964); Spinelli v. United States, 393 U.S. 410, 416, 89 S.Ct. ",
"584, 589, 21 L.Ed.2d 637 (1969). ",
" Gates abandoned the notion that \"these elements should be understood as entirely separate and independent requirements to be rigidly exacted in every case\" before a probable cause determination may be sustained. ",
" Gates, 462 U.S. at 230, 103 S.Ct. ",
"at 2328. ",
" Gates replaced the two-pronged framework of Aguilar and Spinelli with the totality of the circumstances test.",
"\n\n\n11\nWhile eschewing a rigid adherence to each of the Aguilar-Spinelli factors, Gates maintained the relevancy of the considerations set forth in those cases. ",
" The Gates Court surely did not intend that its totality test would \"threaten[ ] to 'obliterate one of the most fundamental distinctions between our form of government, where officers are under the law, and the police-state where they are the law.' \" ",
" Gates, 462 U.S. at 291, 103 S.Ct. ",
"at 2360 (Brennan, J., dissenting) (quoting Johnson v. United States, 333 U.S. 10, 17, 68 S.Ct. ",
"367, 370, 92 L.Ed. ",
"436 (1948)). ",
" Nor did Gates intend for trial and appellate courts to abdicate their responsibility to uphold the Fourth Amendment's probable cause requirement. ",
" See Hicks, 480 U.S. 321, 107 S.Ct. ",
"1149, 94 L.Ed.2d 347. ",
" We have never read Gates as a total abandonment of standards and rules of law in determining whether the state may intrude on a citizen's privacy. ",
" Nor does Gates mean that reviewing courts are writing on a clean slate when we confront the question of when an informant's information rises to the level of probable cause. ",
" The Gates Court agreed that the Aguilar and Spinelli factors, including \"an informant's 'veracity,' 'reliability' and 'basis of knowledge' are all highly relevant in determining the value of his report.\" ",
" Gates, 462 U.S. at 230, 103 S.Ct. ",
"at 2328; see Schaefer, 87 F.3d at 566 (the Aguilar and Spinelli factors are \"highly relevant,\" even after Gates ).",
"\n\n\n12\nWe have recently offered a non-exhaustive list of possible factors that a magistrate or reviewing court will consider:\n\n\n13\nAmong others, the factors that may contribute to a \"probable cause\" determination include whether an affidavit supports the probable \" 'veracity' or 'basis of knowledge' of persons supplying hearsay information\"; whether informant statements are self-authenticating; whether some or all the informant's factual statements were corroborated wherever reasonable and practicable (e.g., through police surveillance); and whether a law-enforcement affiant included a professional assessment of the probable significance of the facts related by the informant, based on experience or expertise. ",
" None of these factors is indispensable; thus, stronger evidence on one or more factors may compensate for a weaker or deficient showing on another.",
"\n\n\n14\nZayas-Diaz, 95 F.3d at 111 (citations and footnote omitted).",
"\n\n\n15\nThe risk that the informant is lying or in error need not be wholly eliminated. ",
" Rather, what is needed is that \"the probability of a lying or inaccurate informer has been sufficiently reduced by corroborative facts and observations.\" ",
" 2 W. LaFave, Search and Seizure: A Treatise on the Fourth Amendment 168 (3d ed. ",
" 1996) (\"LaFave\") (quotation omitted). ",
" The judgment to be made is: when does verification of part of the informant's story make it sufficiently likely that the crucial part of the informant's story (i.e., allegations that criminal activity has occurred and that evidence pertaining thereto will be found in the location to be searched) is true, such as would \" 'warrant a [person] of reasonable caution in the belief' that [a search would be] appropriate,\" based upon what the informant has said? ",
" See Terry, 392 U.S. at 21-22, 88 S.Ct. ",
"at 1880.",
"\n\n\n16\nIn analyzing whether there is sufficient corroboration, in verifying the reliability of the informant or in demonstrating an adequate basis for knowledge, it is not particularly probative for the informant to supply a lot of details about irrelevant facts that other people could easily know about and that are not incriminating, such as describing all the furniture in an apartment or the defendant's routine activities. ",
" Such details do not demonstrate that the informant has a legitimate basis for knowing about the defendant's allegedly criminal activity which, after all, is what the affidavit must establish. ",
" \"At best, [such] details merit the conclusion that the informant has been in the premises in question [or knows the defendant's daily routine], but since a direct statement to that effect by the informant would not carry the day, it can hardly be enough that this particular conclusion is reached by inference from the statement of detail.\" ",
" 2 LaFave at 160 (footnote omitted). ",
" Unless such details, combined with other circumstances, would in some way generate suspicion that criminal conduct has occurred or that contraband or evidence exists on the premises or on the person to be searched, they would not warrant a prudent police officer in the belief that a search would be appropriate. ",
" Cf. ",
"Alabama v. White, 496 U.S. 325, 332, 110 S.Ct. ",
"2412, 2417, 110 L.Ed.2d 301 (1990) (where anonymous caller told police a woman would leave a certain apartment building at a particular time and get into a particularly described car and drive to a certain motel, and where surveilling officers observed such behavior, these facts constitute a \"close case\" to establish merely reasonable suspicion to make a Terry stop).",
"\n\n\n17\nIn the instant case, the defendant challenges two distinct aspects of the search: whether the police had probable cause to obtain a warrant to search the apartment; and whether the police were justified in searching the defendant when they did. ",
" We will analyze each of these aspects separately. ",
" We conclude that the warrant was based upon sufficient facts to establish probable cause to search the premises; then when that search was executed, additional information came to light which provided probable cause to search the person of the defendant.",
"\n\n\n18\nThe government argues that a controlled buy, observed by the officer, is per se sufficient to establish probable cause to search the apartment. ",
" We disagree. ",
" A per se rule is not appropriate in the context of protecting precious Fourth Amendment freedoms. ",
" Fourth Amendment rights \"are not mere second-class rights but belong in the catalog of indispensable freedoms. ",
" Among deprivations of rights, none is so effective in cowing a population, crushing the spirit of the individual and putting terror in every heart. ",
" Uncontrolled search and seizure is one of the first and most effective weapons in the arsenal of every arbitrary government.\" ",
" Brinegar v. United States, 338 U.S. 160, 180, 69 S.Ct. ",
"1302, 1313, 93 L.Ed. ",
"1879 (1949) (Jackson, J., dissenting). ",
" \"But the right to be secure against searches and seizures is one of the most difficult to protect. ",
" Since the officers are themselves the chief invaders, there is no enforcement outside of court.... Courts can protect the innocent against such invasions only indirectly and through the medium of excluding evidence obtained against those who frequently are guilty.\" ",
" Id. at 181, 69 S.Ct. ",
"at 1313. ",
" As Justice Scalia has written for the Court, \"there is nothing new in the realization that the Constitution sometimes insulates the criminality of a few in order to protect the privacy of us all.\" ",
" Hicks, 480 U.S. at 329, 107 S.Ct. ",
"at 1155.",
"\n\n\n19\nMoreover, a probable cause determination is fundamentally a fact-specific inquiry. ",
" No one factor possesses talismanic powers. ",
" Because of the importance of Fourth Amendment freedoms to every American, and because of the factspecific nature of the probable cause inquiry, we reject the government's contention that a controlled buy should be per se sufficient to establish probable cause. ",
" See United States v. Caggiano, 899 F.2d 99, 102 (1st Cir.1990) (a determination of probable cause \"cannot be based on hard certainties and rigid rules\"); cf. ",
" Richards v. Wisconsin, --- U.S. ----, ----, 117 S.Ct. ",
"1416, 1421, 137 L.Ed.2d 615 (1997) (rejecting a per se exception to the knock-and-announce element of Fourth Amendment's reasonableness requirement for felony drug investigations). ",
" We hold instead that every case must be evaluated \"on its own facts and circumstances,\" Ker v. California, 374 U.S. 23, 33, 83 S.Ct. ",
"1623, 1630, 10 L.Ed.2d 726 (1963) (internal quotation marks omitted), with due consideration to the totality of all the circumstances in that particular case, Gates, 462 U.S. at 238, 103 S.Ct. ",
"at 2332. ",
" See also Ornelas, --- U.S. at ----, 116 S.Ct. ",
"at 1661. ",
" \"[T]he fact that [a controlled buy] may frequently present circumstances warranting [a finding of probable cause] cannot remove from the neutral scrutiny of [a magistrate and] a reviewing court the [existence of probable cause] in a particular case. ",
" Instead, in each case, it is the duty of a court confronted with the question to determine whether the facts and circumstances of the particular [affidavit in support of a warrant application] justified\" the issuance of the warrant. ",
" Richards, --- U.S. at ----, 117 S.Ct. ",
"at 1421. ",
" Accordingly, we hold that magistrates and reviewing courts must carefully review every warrant application on its own merit, to determine whether all the facts and circumstances of that case are sufficient to establish probable cause to conduct a search.",
"\n\n\n20\nWe do agree, however, that, taking into account the totality of circumstances in the instant case, the government had established probable cause for the search of the first floor rear apartment at 676-678 Chalkstone Avenue. ",
" According to the officer's affidavit, the informant had told him that he knew \"Fat Boy\" and \"Turtle\" were storing and selling drugs in the apartment in question; the informant had offered to make a purchase from those individuals in that apartment (knowing that, if he was lying, he would be found out relatively quickly); and the informant in fact went to the apartment without crack cocaine, after having been patted down, and emerged several minutes later with crack, explaining that he had purchased the crack from \"Fat Boy.",
"\"2 While all these facts did not corroborate each other with certainty, the combination of facts \" 'reduced the chances of a reckless or prevaricating tale,' [and] thus provid[ed] 'a substantial basis for crediting the hearsay.' \" ",
" Gates, 462 U.S. at 244-45, 103 S.Ct. ",
"at 2335 (quoting Jones v. United States, 362 U.S. 257, 269, 271, 80 S.Ct. ",
"725, 736, 4 L.Ed.2d 697 (1960)). ",
" Taken together, these facts were sufficient to give the magistrate a \"substantial basis\" upon which to conclude that there was a \"fair probability that contraband or evidence of a crime [would] be found\" in the apartment. ",
" See Gates, 462 U.S. at 238, 103 S.Ct. ",
"at 2332.",
"\n\n\n21\nThis case contains almost the exact same fact pattern as in United States v. Garcia, 983 F.2d 1160 (1st Cir.1993). ",
" In Garcia, the defendant had moved to suppress evidence seized during the search of an apartment in a three-family building, on the ground that the affidavit underlying the search warrant upon which the search team relied failed to demonstrate probable cause for the search.",
"\n\n\n22\nThat affidavit, in essence, stated: that [the affiant, a police detective] had reason to believe that a large-scale drug operation was being conducted out of the second floor apartment of 93-95 Gallatin Street; that he met with a reliable confidential informant who told him that two Hispanic persons were storing and selling drugs; that the informant had seen large amounts of cocaine in the apartment; and that, to corroborate this information, [the detective] executed a \"controlled buy\" through the informant. ",
" The affidavit fully described the \"controlled buy.\"",
"\n\n\n23\nId. at 1166. ",
" In Garcia, as here, the controlled buy was less than ideal: the detective was able to watch the informant enter and leave the building through its front door, but did not follow the informant into the building and thus was unable to verify with certainty which apartment was the source of the drugs (or even whether the drugs had been secreted elsewhere in the building, as the defendant had hypothesized). ",
" Id. at 1166-67. ",
" In addition, Garcia shared another anomaly with the instant case: when the informant handed the drugs to the officer, he reported that he had purchased the drugs from \"the Hispanic male [singular] who resided in the second floor apartment,\" even though the informant had previously told him that there were two Hispanic persons involved in the drug-selling operation. ",
" Id. at 1167.",
"\n\n\n24\nWe found that the state court judge issuing the warrant and the district judge reviewing it \"drew a reasonable inference of probable cause that there was drug trafficking in the second floor apartment of 93-95 Gallatin Street.\" ",
" Id. Likewise, in the instant case, the affidavit contained sufficient information to lead a reasonable person to believe that crack cocaine was being stored in and sold from the first floor rear apartment at 676-678 Chalkstone Avenue, also a three-story tenement building.",
"\n\n\n25\nThe present case is controlled by Garcia even though the affidavit there contained one fact that the present affidavit did not: the detective in Garcia described the informant as \"reliable.\" ",
" This is a distinction without a real difference. ",
" A bald assertion of reliability, with no allegations regarding the basis for the officer's belief that the informant is reliable--such as convictions obtained as a result of information supplied in the past by the informant--is \"entitled to only slight weight.\" ",
" United States v. Foree, 43 F.3d 1572, 1576 (11th Cir.1995) (internal quotation marks omitted); see Gates, 462 U.S. at 239, 103 S.Ct. ",
"at 2332-33 (\"An officer's statement that 'affiants have received reliable information from a credible person and do believe' that heroin is stored in a home, is likewise inadequate.\"). ",
" Even though the informant's past performance may be considered in evaluating the credibility or reliability of the informant, a mere allegation that the informant is \"credible\" or \"reliable\" does not permit the judicial officer to assume that any such past performance actually took place or that the performance was of a nature to merit such a characterization of the informant.",
"\n\n\n26\nThus, it is of only \"slight\" moment that this case lacks the conclusory assertion of reliability that was present in Garcia. ",
" The more important facts are the similarities between the two cases: an informant who alleges that drugs are being stored and sold in a particular apartment, who offered to make a controlled buy and who did make a controlled buy from the same apartment. ",
" The corroboration of the informant's story did not consist merely of corroborating some innocent facts that any number of people might know. ",
" This was corroboration of the very criminal activity which the police were investigating, and of the existence of contraband or evidence on the premises to be searched. ",
" As such, it supports a finding of probable cause in a way that facts about furniture or routine activities do not.",
"\n\n\n27\nTo be sure, the controlled buy in this case was, as the defendant claims, not free of problems. ",
" Compare United States v. Cruz Jimenez, 894 F.2d 1, 3 (1st Cir.1990) (informant, searched first, had cocaine when she exited defendant's motel room; that, plus what police overheard from body recorder she wore during transaction, confirmed that she obtained drugs from defendant). ",
" But as noted, in Garcia, 983 F.2d at 1166-67, we upheld a probable cause determination where the facts, including the imperfections of the controlled buy, were remarkably similar to those here.3\n\n\n28\nThe defendant further argues that the search warrant was inadequate because of a few minor discrepancies or errors in some facts in the affidavit and in the officer's testimony about the name of the street from which he was conducting surveillance during the controlled buy. ",
" We disagree. ",
" The magistrate \"may reasonably choose to ... disregard petty inconsistencies\" in informants' statements. ",
" Schaefer, 87 F.3d at 567 (quoted in Zayas-Diaz, 95 F.3d at 115-16).",
"\n\n\n29\nWe turn now to the defendant's claim that the affidavit contained insufficient information to form the basis for probable cause to search the person of this defendant. ",
" This is a separate issue from the existence of probable cause to search the premises which we have discussed supra. ",
" Probable cause to search a person \"must be supported by probable cause particularized with respect to that person.\" ",
" Ybarra v. Illinois, 444 U.S. 85, 91, 100 S.Ct. ",
"338, 342, 62 L.Ed.2d 238 (1979); United States v. Sepulveda, 102 F.3d 1313, 1315 (1st Cir.1996). ",
" \"[A] person's mere propinquity to others independently suspected of criminal activity does not, without more, give rise to probable cause to search that person.\" ",
" Ybarra, 444 U.S. at 91, 100 S.Ct. ",
"at 342; Sepulveda, 102 F.3d at 1315. ",
" The factors discussed supra, while providing probable cause to believe that the premises contained contraband or evidence of a crime, do not alone provide a sufficient basis for the police to have searched this defendant's person (on which they found his identification which, coupled with the gas bill they had found in the apartment, tied him to the premises).",
"\n\n\n30\nThe government argues that the \"specificity and detail\" of the informant's descriptions of \"Fat Boy\" and \"Turtle\" are so \"precise\" that they are \"self-authenticating,\" an additional factor that would support issuing a warrant to search the person of this defendant (citing Zayas-Diaz, 95 F.3d at 111). ",
" We disagree. ",
" It is true that there may be cases where an informant provides such a wealth of detail, with such a high degree of specificity that it is unlikely that the informant is inventing these assertions, and his veracity is supported through the very specificity and detail of his statement. ",
" See id.; United States v. Caggiano, 899 F.2d 99, 102-03 (1st Cir.1990). ",
" In the instant case, however, the so-called \"precision\" in the affidavit--\" 'Turtle' Alias John Doe. ",
"5'7\"' 130 Lbs.",
"\"--is not nearly enough to make the informant's statement self-authenticating. ",
" This is true even if we accept the government's invitation to consider as well the additional assertions contained in the complaint attached to the affidavit: that \"Turtle\" was an Asian male with black short hair.4\n\n\n31\nNor does the controlled buy in this case offer a corroborative cure for the affidavit's deficiencies. ",
" The controlled buy--during which the informant said he had bought drugs from \"Fat Boy,\" not from this defendant--was sufficient to cure the lack of probable cause to search the premises but was inadequate to cure the lack of probable cause to believe that a search of the defendant's person would likely turn up contraband or evidence of a crime.",
"\n\n\n32\nNevertheless, once the officers entered the apartment legally pursuant to the legal search warrant for the premises, they observed two men fleeing who (approximately) fit those admittedly sketchy descriptions. ",
" This flight, coupled with the controlled buy monitored by the detective and the informant's description (including height and weight) of two alleged drug traffickers selling drugs out of that apartment, was sufficient to establish probable cause to search the defendant's person, without a warrant.5 Thus, even though the affidavit was insufficient to sustain a warrant to search the person of this defendant, the affidavit was sufficient to sustain a warrant to search the apartment, and once the police entered the apartment legally, the defendant's suspicious behavior (coupled with the informant's report and the controlled buy) was sufficient to establish probable cause to search the defendant for contraband or evidence of a crime.",
"\n\nConclusion\n\n33\nWe cannot say that the affidavit here lacked probable cause sufficient to justify a search of the first floor rear apartment at 676-678 Chalkstone Avenue. ",
" Nevertheless, we urge police officers to include in their affidavits as much information as they can legally gather on which to base a finding of reliability and basis for the informant's knowledge. ",
" And we will require magistrates and reviewing courts to scrutinize affidavits such as this one carefully.",
"\n\n\n34\nAs we said in the context of Rule 11, \"[t]he more meticulously [a legal rule] is adhered to, the more it tends to discourage, or at least to enable more expeditious disposition of\" a defendant's attacks on asserted violations of the rule. ",
" United States v. Martinez-Martinez, 69 F.3d 1215, 1225-26 (1st Cir.1995) , cert. ",
"denied, --- U.S. ----, 116 S.Ct. ",
"1343, 134 L.Ed.2d 492 (1996) (quoting United States v. Cotal-Crespo, 47 F.3d 1, 8 (1st Cir.), ",
"cert. ",
"denied, --- U.S. ----, 116 S.Ct. ",
"94, 133 L.Ed.2d 49 (1995), in turn quoting McCarthy v. United States, 394 U.S. 459, 465, 89 S.Ct. ",
"1166, 1170, 22 L.Ed.2d 418 (1969)). ",
" Therefore, \"[a]lthough we conclude that the [probable cause determination] in this case was adequate, we are nevertheless compelled to remind district courts [and police and magistrates] that, for the sake of judicial economy and fundamental fairness, the best way to ensure that\" the Fourth Amendment's probable cause requirement is complied with is to meticulously comply with it. ",
" Martinez-Martinez, 69 F.3d at 1225-26 (quoting Cotal-Crespo, 47 F.3d at 8); see Richards, --- U.S. at ----, 117 S.Ct. ",
"at 1421 (emphasizing importance of neutral scrutiny of police behavior by a reviewing court to ensure compliance with Fourth Amendment in particular case).",
"\n\n\n35\nAffirmed.",
"\n\n\n\n1\n \"The issuing magistrate ordinarily considers only the facts set forth in supporting affidavits accompanying the warrant application.\" ",
" Zayas-Diaz, 95 F.3d at 111\n\n\n2\n The complaint contained additional facts but those were not part of the affidavit. ",
" See infra at 20 & n. 4\n\n\n3\n The government contends that, even if the affidavit did not contain sufficient corroboration to establish probable cause to search, suppression is not appropriate because of the Leon good faith exception. ",
" See United States v. Leon, 468 U.S. 897, 104 S.Ct. ",
"3405, 82 L.Ed.2d 677 (1984). ",
" \"This good faith exception, however, is grounded in an objective standard of reasonableness. ",
" As a result, an officer is required to have a 'reasonable knowledge of what the law prohibits.' \" ",
" United States v. Fuccillo, 808 F.2d 173, 177 (1st Cir.), ",
"cert. ",
"denied, 482 U.S. 905, 107 S.Ct. ",
"2481, 96 L.Ed.2d 374 (1987) (quoting Leon, 468 U.S. at 919 n. 20, 104 S.Ct. ",
"at 3419 n. 20). ",
" \"Suppression is still an appropriate remedy when 'the officers were ... reckless in preparing their affidavit....' \" Fuccillo, 808 F.2d at 178 (quoting Leon, 468 U.S. at 926, 104 S.Ct. ",
"at 3422). ",
" In Fuccillo, we held that the officers \"were reckless in not including in the affidavit information which was known or easily accessible to them.\" ",
" Id. at 178. ",
" There, the officers \"simply did not 'take every step that could reasonably be expected of them.' \" ",
" Id. (quoting Massachusetts v. Sheppard, 468 U.S. 981, 989, 104 S.Ct. ",
"3424, 3428, 82 L.Ed.2d 737 (1984)). ",
" In this case, it is an open question whether this objective standard of reasonableness was met. ",
" We need not reach this question, however, since we determine the evidence is admissible, in any event, on other grounds\n\n\n4\n The latter details were not included in the affidavit itself, and \"[t]he issuing magistrate ordinarily considers only the facts set forth in supporting affidavits accompanying the warrant application.\" ",
" Zayas-Diaz, 95 F.3d at 111. ",
" The magistrate may also consider testimony given before him or her, if the testimony was sworn to and made a part of the affidavit. ",
" See Fed.",
"R.Crim.",
"P. 41(c). ",
" We need not decide whether the complaint accompanying the affidavit in this case should be considered as part of the affidavit, because we hold infra that the police had probable cause to search the defendant's person regardless of how we would decide this issue\n\n\n5\n The warrantless aspect of the search of the defendant's person was justified by exigent circumstances in this case: two individuals who met an informant's descriptions of drug dealers fled from police officers as they executed a search warrant, during the investigation of a crime involving drugs that could easily be disposed of. ",
" See McCabe v. Life-Line Ambulance Serv., ",
"77 F.3d 540, 545 (1st Cir.1996); United States v. Wihbey, 75 F.3d 761, 766 (1st Cir.1996)\n\n\n"
] | {
"pile_set_name": "FreeLaw"
} | [
0.00011562030292519367,
0,
0,
0.000945179584120983,
0,
0.0003024574669187146,
0.00011138338159946535,
0.0008304498269896194,
0.0022222222222222222,
0.0000390625,
0,
0,
0,
0,
0.00017313019390581717,
0.000044444444444444447,
0.00011814744801512288,
0,
0,
0.0011890606420927466,
0,
0,
0,
0,
0.000062000124000248,
0.000037180249851279,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00006609822195782934,
0.00005827166249053085,
0,
0,
0,
0,
0.00009245562130177516,
0.000041091387245233394,
0,
0,
0.0005408328826392645,
0,
0,
0,
0,
0,
0,
0,
0.00510204081632653,
0,
0,
0,
0,
0.0002872737719046251,
0,
0,
0,
0,
0,
0,
0,
0.0001147842056932966,
0.00001351643598615917,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0005165289256198347,
0,
0,
0.0000038296421965295784,
0,
0,
0,
0,
0,
0,
0.00008264462809917355,
0.0000390625,
0,
0,
0.00011080332409972299,
0,
0,
0,
0,
0,
0,
0,
0.00007138607971445568,
0,
0.00007561436672967865,
0,
0,
0.0002295684113865932,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0004526935264825713,
0.000007344246884203259,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00031887755102040814,
0,
0.0006574621959237343,
0,
0,
0,
0,
0.000050503775157193,
0,
0,
0,
0,
0,
0,
0,
0.000030524098775983637,
0,
0,
0,
0.00043402777777777775,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00018261504747991235,
0,
0,
0,
0,
0.00006830134553650708,
0.000013223140495867768,
0,
0,
0,
0.0000059488399762046405,
0,
0.0000072652770613407345,
0,
0,
0,
0.00005101520253035405,
0,
0,
0.00005486968449931413,
0,
0,
0.00005827166249053085,
0,
0,
0,
0,
0,
0.000012574820180071425,
0,
0,
0,
0.00021626297577854672,
0,
0,
0,
0,
0,
0,
0,
0.0006925207756232687,
0,
0.00001054140664530275,
0,
0,
0,
0.00009611687812379854,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.000148720999405116,
0,
0.00011317338162064282,
0,
0,
0.00010412328196584755,
0,
0,
0.00020833333333333335,
0,
0,
0,
0,
0,
0.00036982248520710064,
0,
0,
0,
0,
0,
0,
0.00017313019390581717,
0,
0.000028596757127741712,
0,
0,
0,
0,
0.0002040816326530612,
0,
0,
0,
0.0011890606420927466,
0,
0,
0,
0,
0,
0,
0.00011562030292519367
] | 0.000074 | 5 |
[
"#region License\n/*\n * Ext.cs\n *\n * Some parts of this code are derived from Mono (http://www.mono-project.com):\n * - GetStatusDescription is derived from HttpListenerResponse.cs (System.",
"Net)\n * - IsPredefinedScheme is derived from Uri.cs (System)\n * - MaybeUri is derived from Uri.cs (System)\n *\n * The MIT License\n *\n * Copyright (c) 2001 Garrett Rooney\n * Copyright (c) 2003 Ian MacLean\n * Copyright (c) 2003 Ben Maurer\n * Copyright (c) 2003, 2005, 2009 Novell, Inc. (http://www.novell.com)\n * Copyright (c) 2009 Stephane Delcroix\n * Copyright (c) 2010-2016 sta.blockhead\n *\n * Permission is hereby granted, free of charge, to any person obtaining a copy\n * of this software and associated documentation files (the \"Software\"), to deal\n * in the Software without restriction, including without limitation the rights\n * to use, copy, modify, merge, publish, distribute, sublicense, and/or sell\n * copies of the Software, and to permit persons to whom the Software is\n * furnished to do so, subject to the following conditions:\n *\n * The above copyright notice and this permission notice shall be included in\n * all copies or substantial portions of the Software.",
"\n *\n * THE SOFTWARE IS PROVIDED \"AS IS\", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR\n * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,\n * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. ",
"IN NO EVENT SHALL THE\n * AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER\n * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,\n * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN\n * THE SOFTWARE.",
"\n */\n#endregion\n\n#region Contributors\n/*\n * Contributors:\n * - Liryna <liryna.stark@gmail.com>\n * - Nikola Kovacevic <nikolak@outlook.com>\n * - Chris Swiedler\n */\n#endregion\n\nusing System;\nusing System.",
"Collections.",
"Generic;\nusing System.",
"Collections.",
"Specialized;\nusing System.",
"IO;\nusing System.",
"IO.Compression;\nusing System.",
"Net.",
"Sockets;\nusing System.",
"Security.",
"Cryptography.",
"X509Certificates;\nusing System.",
"Text;\nusing WebSocketSharp.",
"Net;\nusing WebSocketSharp.",
"Net.",
"WebSockets;\nusing WebSocketSharp.",
"Server;\n\nnamespace WebSocketSharp\n{\n /// <summary>\n /// Provides a set of static methods for websocket-sharp.",
"\n /// </summary>\n public static class Ext\n {\n #region Private Fields\n\n private static readonly byte[] _last = new byte[] { 0x00 };\n private static readonly int _retry = 5;\n private const string _tspecials = \"()<>@,;:\\\\\\\"/[]?={} \\t\";\n\n #endregion\n\n #region Private Methods\n\n private static byte[] compress (this byte[] data)\n {\n if (data.",
"LongLength == 0)\n //return new byte[] { 0x00, 0x00, 0x00, 0xff, 0xff };\n return data;\n\n using (var input = new MemoryStream (data))\n return input.compressToArray ();\n }\n\n private static MemoryStream compress (this Stream stream)\n {\n var output = new MemoryStream ();\n if (stream.",
"Length == 0)\n return output;\n\n stream.",
"Position = 0;\n using (var ds = new DeflateStream (output, CompressionMode.",
"Compress, true)) {\n stream.",
"CopyTo (ds, 1024);\n ds.",
"Close (); // BFINAL set to 1.",
"\n output.",
"Write (_last, 0, 1);\n output.",
"Position = 0;\n\n return output;\n }\n }\n\n private static byte[] compressToArray (this Stream stream)\n {\n using (var output = stream.compress ()) {\n output.",
"Close ();\n return output.",
"ToArray ();\n }\n }\n\n private static byte[] decompress (this byte[] data)\n {\n if (data.",
"LongLength == 0)\n return data;\n\n using (var input = new MemoryStream (data))\n return input.decompressToArray ();\n }\n\n private static MemoryStream decompress (this Stream stream)\n {\n var output = new MemoryStream ();\n if (stream.",
"Length == 0)\n return output;\n\n stream.",
"Position = 0;\n using (var ds = new DeflateStream (stream, CompressionMode.",
"Decompress, true)) {\n ds.",
"CopyTo (output, 1024);\n output.",
"Position = 0;\n\n return output;\n }\n }\n\n private static byte[] decompressToArray (this Stream stream)\n {\n using (var output = stream.decompress ()) {\n output.",
"Close ();\n return output.",
"ToArray ();\n }\n }\n\n private static void times (this ulong n, Action action)\n {\n for (ulong i = 0; i < n; i++)\n action ();\n }\n\n #endregion\n\n #region Internal Methods\n\n internal static byte[] Append (this ushort code, string reason)\n {\n var ret = code.",
"InternalToByteArray (ByteOrder.",
"Big);\n if (reason !",
"= null && reason.",
"Length > 0) {\n var buff = new List<byte> (ret);\n buff.",
"AddRange (Encoding.",
"UTF8.GetBytes (reason));\n ret = buff.",
"ToArray ();\n }\n\n return ret;\n }\n\n internal static string CheckIfAvailable (\n this ServerState state, bool ready, bool start, bool shutting)\n {\n return (!",
"ready && (state == ServerState.",
"Ready || state == ServerState.",
"Stop)) ||\n (!",
"start && state == ServerState.",
"Start) ||\n (!",
"shutting && state == ServerState.",
"ShuttingDown)\n ? \"",
"This operation isn't available in: \" + state.",
"ToString ().ToLower ()\n : null;\n }\n\n internal static string CheckIfAvailable (\n this WebSocketState state, bool connecting, bool open, bool closing, bool closed)\n {\n return (!",
"connecting && state == WebSocketState.",
"Connecting) ||\n (!",
"open && state == WebSocketState.",
"Open) ||\n (!",
"closing && state == WebSocketState.",
"Closing) ||\n (!",
"closed && state == WebSocketState.",
"Closed)\n ? \"",
"This operation isn't available in: \" + state.",
"ToString ().ToLower ()\n : null;\n }\n\n internal static string CheckIfValidProtocols (this string[] protocols)\n {\n return protocols.",
"Contains (\n protocol => protocol == null || protocol.",
"Length == 0 || !",
"protocol.",
"IsToken ())\n ? \"",
"Contains an invalid value.\"",
"\n : protocols.",
"ContainsTwice ()\n ? \"",
"Contains a value twice.\"",
"\n : null;\n }\n\n internal static string CheckIfValidServicePath (this string path)\n {\n return path == null || path.",
"Length == 0\n ? \"'",
"path' is null or empty.\"",
"\n : path[0] !",
"= '/'\n ? \"'",
"path' isn't an absolute path.\"",
"\n : path.",
"IndexOfAny (new[] { '?', '#' }) ",
"> -1\n ? \"'",
"path' includes either or both query and fragment components.\"",
"\n : null;\n }\n\n internal static string CheckIfValidSessionID (this string id)\n {\n return id == null || id.",
"Length == 0 ? \"'",
"id' is null or empty.\" : ",
"null;\n }\n\n internal static string CheckIfValidWaitTime (this TimeSpan time)\n {\n return time <= TimeSpan.",
"Zero ? \"",
"A wait time is zero or less.\" : ",
"null;\n }\n\n internal static bool CheckWaitTime (this TimeSpan time, out string message)\n {\n message = null;\n\n if (time <= TimeSpan.",
"Zero) {\n message = \"A wait time is zero or less.\";",
"\n return false;\n }\n\n return true;\n }\n\n internal static void Close (this HttpListenerResponse response, HttpStatusCode code)\n {\n response.",
"StatusCode = (int) code;\n response.",
"OutputStream.",
"Close ();\n }\n\n internal static void CloseWithAuthChallenge (\n this HttpListenerResponse response, string challenge)\n {\n response.",
"Headers.",
"InternalSet (\"WWW-Authenticate\", challenge, true);\n response.",
"Close (HttpStatusCode.",
"Unauthorized);\n }\n\n internal static byte[] Compress (this byte[] data, CompressionMethod method)\n {\n return method == CompressionMethod.",
"Deflate\n ? ",
"data.compress ()\n : data;\n }\n\n internal static Stream Compress (this Stream stream, CompressionMethod method)\n {\n return method == CompressionMethod.",
"Deflate\n ? ",
"stream.compress ()\n : stream;\n }\n\n internal static byte[] CompressToArray (this Stream stream, CompressionMethod method)\n {\n return method == CompressionMethod.",
"Deflate\n ? ",
"stream.compressToArray ()\n : stream.",
"ToByteArray ();\n }\n\n internal static bool Contains<T> (this IEnumerable<T> source, Func<T, bool> condition)\n {\n foreach (T elm in source)\n if (condition (elm))\n return true;\n\n return false;\n }\n\n internal static bool ContainsTwice (this string[] values)\n {\n var len = values.",
"Length;\n\n Func<int, bool> contains = null;\n contains = idx => {\n if (idx < len - 1) {\n for (var i = idx + 1; i < len; i++)\n if (values[i] == values[idx])\n return true;\n\n return contains (++idx);\n }\n\n return false;\n };\n\n return contains (0);\n }\n\n internal static T[] Copy<T> (this T[] source, long length)\n {\n var dest = new T[length];\n Array.",
"Copy (source, 0, dest, 0, length);\n\n return dest;\n }\n\n internal static void CopyTo (this Stream source, Stream destination, int bufferLength)\n {\n var buff = new byte[bufferLength];\n var nread = 0;\n while ((nread = source.",
"Read (buff, 0, bufferLength)) > 0)\n destination.",
"Write (buff, 0, nread);\n }\n\n internal static void CopyToAsync (\n this Stream source,\n Stream destination,\n int bufferLength,\n Action completed,\n Action<Exception> error)\n {\n var buff = new byte[bufferLength];\n\n AsyncCallback callback = null;\n callback = ar => {\n try {\n var nread = source.",
"EndRead (ar);\n if (nread <= 0) {\n if (completed !",
"= null)\n completed ();\n\n return;\n }\n\n destination.",
"Write (buff, 0, nread);\n source.",
"BeginRead (buff, 0, bufferLength, callback, null);\n }\n catch (Exception ex) {\n if (error !",
"= null)\n error (ex);\n }\n };\n\n try {\n source.",
"BeginRead (buff, 0, bufferLength, callback, null);\n }\n catch (Exception ex) {\n if (error !",
"= null)\n error (ex);\n }\n }\n\n internal static byte[] Decompress (this byte[] data, CompressionMethod method)\n {\n return method == CompressionMethod.",
"Deflate\n ? ",
"data.decompress ()\n : data;\n }\n\n internal static Stream Decompress (this Stream stream, CompressionMethod method)\n {\n return method == CompressionMethod.",
"Deflate\n ? ",
"stream.decompress ()\n : stream;\n }\n\n internal static byte[] DecompressToArray (this Stream stream, CompressionMethod method)\n {\n return method == CompressionMethod.",
"Deflate\n ? ",
"stream.decompressToArray ()\n : stream.",
"ToByteArray ();\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"int\"/> equals the specified <see cref=\"char\"/>,\n /// and invokes the specified <c>Action<int></c> delegate at the same time.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"value\"/> equals <paramref name=\"c\"/>;\n /// otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"value\">\n /// An <see cref=\"int\"/> to compare.",
"\n /// </param>\n /// <param name=\"c\">\n /// A <see cref=\"char\"/> to compare.",
"\n /// </param>\n /// <param name=\"action\">\n /// An <c>Action<int></c> delegate that references the method(s) called\n /// at the same time as comparing. ",
"An <see cref=\"int\"/> parameter to pass to\n /// the method(s) is <paramref name=\"value\"/>.",
"\n /// </param>\n internal static bool EqualsWith (this int value, char c, Action<int> action)\n {\n action (value);\n return value == c - 0;\n }\n\n /// <summary>\n /// Gets the absolute path from the specified <see cref=\"Uri\"/>.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"string\"/> that represents the absolute path if it's successfully found;\n /// otherwise, <see langword=\"null\"/>.",
"\n /// </returns>\n /// <param name=\"uri\">\n /// A <see cref=\"Uri\"/> that represents the URI to get the absolute path from.",
"\n /// </param>\n internal static string GetAbsolutePath (this Uri uri)\n {\n if (uri.",
"IsAbsoluteUri)\n return uri.",
"AbsolutePath;\n\n var original = uri.",
"OriginalString;\n if (original[0] !",
"= '/')\n return null;\n\n var idx = original.",
"IndexOfAny (new[] { '?', '#' });",
"\n return idx > 0 ? ",
"original.",
"Substring (0, idx) : original;\n }\n\n internal static string GetMessage (this CloseStatusCode code)\n {\n return code == CloseStatusCode.",
"ProtocolError\n ? \"",
"A WebSocket protocol error has occurred.\"",
"\n : code == CloseStatusCode.",
"UnsupportedData\n ? \"",
"Unsupported data has been received.\"",
"\n : code == CloseStatusCode.",
"Abnormal\n ? \"",
"An exception has occurred.\"",
"\n : code == CloseStatusCode.",
"InvalidData\n ? \"",
"Invalid data has been received.\"",
"\n : code == CloseStatusCode.",
"PolicyViolation\n ? \"",
"A policy violation has occurred.\"",
"\n : code == CloseStatusCode.",
"TooBig\n ? \"",
"A too big message has been received.\"",
"\n : code == CloseStatusCode.",
"MandatoryExtension\n ? \"",
"WebSocket client didn't receive expected extension(s).\"",
"\n : code == CloseStatusCode.",
"ServerError\n ? \"",
"WebSocket server got an internal error.\"",
"\n : code == CloseStatusCode.",
"TlsHandshakeFailure\n ? \"",
"An error has occurred during a TLS handshake.\"",
"\n : String.",
"Empty;\n }\n\n /// <summary>\n /// Gets the name from the specified <see cref=\"string\"/> that contains a pair of name and\n /// value separated by a separator character.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"string\"/> that represents the name if any; otherwise, <c>null</c>.",
"\n /// </returns>\n /// <param name=\"nameAndValue\">\n /// A <see cref=\"string\"/> that contains a pair of name and value separated by\n /// a separator character.",
"\n /// </param>\n /// <param name=\"separator\">\n /// A <see cref=\"char\"/> that represents the separator character.",
"\n /// </param>\n internal static string GetName (this string nameAndValue, char separator)\n {\n var idx = nameAndValue.",
"IndexOf (separator);\n return idx > 0 ? ",
"nameAndValue.",
"Substring (0, idx).Trim () : null;\n }\n\n /// <summary>\n /// Gets the value from the specified <see cref=\"string\"/> that contains a pair of name and\n /// value separated by a separator character.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"string\"/> that represents the value if any; otherwise, <c>null</c>.",
"\n /// </returns>\n /// <param name=\"nameAndValue\">\n /// A <see cref=\"string\"/> that contains a pair of name and value separated by\n /// a separator character.",
"\n /// </param>\n /// <param name=\"separator\">\n /// A <see cref=\"char\"/> that represents the separator character.",
"\n /// </param>\n internal static string GetValue (this string nameAndValue, char separator)\n {\n var idx = nameAndValue.",
"IndexOf (separator);\n return idx > -1 && idx < nameAndValue.",
"Length - 1\n ? ",
"nameAndValue.",
"Substring (idx + 1).Trim ()\n : null;\n }\n\n internal static string GetValue (this string nameAndValue, char separator, bool unquote)\n {\n var idx = nameAndValue.",
"IndexOf (separator);\n if (idx < 0 || idx == nameAndValue.",
"Length - 1)\n return null;\n\n var val = nameAndValue.",
"Substring (idx + 1).Trim ();\n return unquote ? ",
"val.",
"Unquote () : val;\n }\n\n internal static TcpListenerWebSocketContext GetWebSocketContext (\n this TcpClient tcpClient,\n string protocol,\n bool secure,\n ServerSslConfiguration sslConfig,\n Logger logger)\n {\n return new TcpListenerWebSocketContext (tcpClient, protocol, secure, sslConfig, logger);\n }\n\n internal static byte[] InternalToByteArray (this ushort value, ByteOrder order)\n {\n var bytes = BitConverter.",
"GetBytes (value);\n if (!",
"order.",
"IsHostOrder ())\n Array.",
"Reverse (bytes);\n\n return bytes;\n }\n\n internal static byte[] InternalToByteArray (this ulong value, ByteOrder order)\n {\n var bytes = BitConverter.",
"GetBytes (value);\n if (!",
"order.",
"IsHostOrder ())\n Array.",
"Reverse (bytes);\n\n return bytes;\n }\n\n internal static bool IsCompressionExtension (this string value, CompressionMethod method)\n {\n return value.",
"StartsWith (method.",
"ToExtensionString ());\n }\n\n internal static bool IsControl (this byte opcode)\n {\n return opcode > 0x7 && opcode < 0x10;\n }\n\n internal static bool IsControl (this Opcode opcode)\n {\n return opcode >= Opcode.",
"Close;\n }\n\n internal static bool IsData (this byte opcode)\n {\n return opcode == 0x1 || opcode == 0x2;\n }\n\n internal static bool IsData (this Opcode opcode)\n {\n return opcode == Opcode.",
"Text || opcode == Opcode.",
"Binary;\n }\n\n internal static bool IsPortNumber (this int value)\n {\n return value > 0 && value < 65536;\n }\n\n internal static bool IsReserved (this ushort code)\n {\n return code == (ushort) CloseStatusCode.",
"Undefined ||\n code == (ushort) CloseStatusCode.",
"NoStatus ||\n code == (ushort) CloseStatusCode.",
"Abnormal ||\n code == (ushort) CloseStatusCode.",
"TlsHandshakeFailure;\n }\n\n internal static bool IsReserved (this CloseStatusCode code)\n {\n return code == CloseStatusCode.",
"Undefined ||\n code == CloseStatusCode.",
"NoStatus ||\n code == CloseStatusCode.",
"Abnormal ||\n code == CloseStatusCode.",
"TlsHandshakeFailure;\n }\n\n internal static bool IsSupported (this byte opcode)\n {\n return Enum.",
"IsDefined (typeof (Opcode), opcode);\n }\n\n internal static bool IsText (this string value)\n {\n var len = value.",
"Length;\n for (var i = 0; i < len; i++) {\n var c = value[i];\n if (c < 0x20 && !\"",
"\\r\\n\\t\".",
"Contains (c))\n return false;\n\n if (c == 0x7f)\n return false;\n\n if (c == '\\n' && ++i < len) {\n c = value[i];\n if (!\" ",
"\\t\".",
"Contains (c))\n return false;\n }\n }\n\n return true;\n }\n\n internal static bool IsToken (this string value)\n {\n foreach (var c in value)\n if (c < 0x20 || c >= 0x7f || _tspecials.",
"Contains (c))\n return false;\n\n return true;\n }\n\n internal static string Quote (this string value)\n {\n return String.",
"Format (\"\\\"{0}\\\"\", value.",
"Replace (\"\\\"\", \"\\\\\\\"\"));\n }\n\n internal static byte[] ReadBytes (this Stream stream, int length)\n {\n var buff = new byte[length];\n var offset = 0;\n try {\n var nread = 0;\n while (length > 0) {\n nread = stream.",
"Read (buff, offset, length);\n if (nread == 0)\n break;\n\n offset += nread;\n length -= nread;\n }\n }\n catch {\n }\n\n return buff.",
"SubArray (0, offset);\n }\n\n internal static byte[] ReadBytes (this Stream stream, long length, int bufferLength)\n {\n using (var dest = new MemoryStream ()) {\n try {\n var buff = new byte[bufferLength];\n var nread = 0;\n while (length > 0) {\n if (length < bufferLength)\n bufferLength = (int) length;\n\n nread = stream.",
"Read (buff, 0, bufferLength);\n if (nread == 0)\n break;\n\n dest.",
"Write (buff, 0, nread);\n length -= nread;\n }\n }\n catch {\n }\n\n dest.",
"Close ();\n return dest.",
"ToArray ();\n }\n }\n\n internal static void ReadBytesAsync (\n this Stream stream, int length, Action<byte[]> completed, Action<Exception> error\n )\n {\n var buff = new byte[length];\n var offset = 0;\n var retry = 0;\n\n AsyncCallback callback = null;\n callback =\n ar => {\n try {\n var nread = stream.",
"EndRead (ar);\n if (nread == 0 && retry < _retry) {\n retry++;\n stream.",
"BeginRead (buff, offset, length, callback, null);\n\n return;\n }\n\n if (nread == 0 || nread == length) {\n if (completed !",
"= null)\n completed (buff.",
"SubArray (0, offset + nread));\n\n return;\n }\n\n retry = 0;\n\n offset += nread;\n length -= nread;\n\n stream.",
"BeginRead (buff, offset, length, callback, null);\n }\n catch (Exception ex) {\n if (error !",
"= null)\n error (ex);\n }\n };\n\n try {\n stream.",
"BeginRead (buff, offset, length, callback, null);\n }\n catch (Exception ex) {\n if (error !",
"= null)\n error (ex);\n }\n }\n\n internal static void ReadBytesAsync (\n this Stream stream,\n long length,\n int bufferLength,\n Action<byte[]> completed,\n Action<Exception> error\n )\n {\n var dest = new MemoryStream ();\n var buff = new byte[bufferLength];\n var retry = 0;\n\n Action<long> read = null;\n read =\n len => {\n if (len < bufferLength)\n bufferLength = (int) len;\n\n stream.",
"BeginRead (\n buff,\n 0,\n bufferLength,\n ar => {\n try {\n var nread = stream.",
"EndRead (ar);\n if (nread > 0)\n dest.",
"Write (buff, 0, nread);\n\n if (nread == 0 && retry < _retry) {\n retry++;\n read (len);\n\n return;\n }\n\n if (nread == 0 || nread == len) {\n if (completed !",
"= null) {\n dest.",
"Close ();\n completed (dest.",
"ToArray ());\n }\n\n dest.",
"Dispose ();\n return;\n }\n\n retry = 0;\n read (len - nread);\n }\n catch (Exception ex) {\n dest.",
"Dispose ();\n if (error !",
"= null)\n error (ex);\n }\n },\n null\n );\n };\n\n try {\n read (length);\n }\n catch (Exception ex) {\n dest.",
"Dispose ();\n if (error !",
"= null)\n error (ex);\n }\n }\n\n internal static string RemovePrefix (this string value, params string[] prefixes)\n {\n var idx = 0;\n foreach (var prefix in prefixes) {\n if (value.",
"StartsWith (prefix)) {\n idx = prefix.",
"Length;\n break;\n }\n }\n\n return idx > 0 ? ",
"value.",
"Substring (idx) : value;\n }\n\n internal static T[] Reverse<T> (this T[] array)\n {\n var len = array.",
"Length;\n var reverse = new T[len];\n\n var end = len - 1;\n for (var i = 0; i <= end; i++)\n reverse[i] = array[end - i];\n\n return reverse;\n }\n\n internal static IEnumerable<string> SplitHeaderValue (\n this string value, params char[] separators)\n {\n var len = value.",
"Length;\n var seps = new string (separators);\n\n var buff = new StringBuilder (32);\n var escaped = false;\n var quoted = false;\n\n for (var i = 0; i < len; i++) {\n var c = value[i];\n if (c == '\"') {\n if (escaped)\n escaped = !",
"escaped;\n else\n quoted = !",
"quoted;\n }\n else if (c == '\\\\') {\n if (i < len - 1 && value[i + 1] == '\"')\n escaped = true;\n }\n else if (seps.",
"Contains (c)) {\n if (!",
"quoted) {\n yield return buff.",
"ToString ();\n buff.",
"Length = 0;\n\n continue;\n }\n }\n else {\n }\n\n buff.",
"Append (c);\n }\n\n if (buff.",
"Length > 0)\n yield return buff.",
"ToString ();\n }\n\n internal static byte[] ToByteArray (this Stream stream)\n {\n using (var output = new MemoryStream ()) {\n stream.",
"Position = 0;\n stream.",
"CopyTo (output, 1024);\n output.",
"Close ();\n\n return output.",
"ToArray ();\n }\n }\n\n internal static CompressionMethod ToCompressionMethod (this string value)\n {\n foreach (CompressionMethod method in Enum.",
"GetValues (typeof (CompressionMethod)))\n if (method.",
"ToExtensionString () == value)\n return method;\n\n return CompressionMethod.",
"None;\n }\n\n internal static string ToExtensionString (\n this CompressionMethod method, params string[] parameters)\n {\n if (method == CompressionMethod.",
"None)\n return String.",
"Empty;\n\n var m = String.",
"Format (\"permessage-{0}\", method.",
"ToString ().ToLower ());\n if (parameters == null || parameters.",
"Length == 0)\n return m;\n\n return String.",
"Format (\"{0}; {1}\", m, parameters.",
"ToString (\"; \"));\n }\n\n internal static System.",
"Net.",
"IPAddress ToIPAddress (this string hostnameOrAddress)\n {\n System.",
"Net.",
"IPAddress addr;\n if (System.",
"Net.",
"IPAddress.",
"TryParse (hostnameOrAddress, out addr))\n return addr;\n\n try {\n return System.",
"Net.",
"Dns.",
"GetHostAddresses (hostnameOrAddress)[0];\n }\n catch {\n return null;\n }\n }\n\n internal static List<TSource> ToList<TSource> (this IEnumerable<TSource> source)\n {\n return new List<TSource> (source);\n }\n\n internal static ushort ToUInt16 (this byte[] source, ByteOrder sourceOrder)\n {\n return BitConverter.",
"ToUInt16 (source.",
"ToHostOrder (sourceOrder), 0);\n }\n\n internal static ulong ToUInt64 (this byte[] source, ByteOrder sourceOrder)\n {\n return BitConverter.",
"ToUInt64 (source.",
"ToHostOrder (sourceOrder), 0);\n }\n\n internal static string TrimEndSlash (this string value)\n {\n value = value.",
"TrimEnd ('/');\n return value.",
"Length > 0 ? ",
"value : \"/\";\n }\n\n /// <summary>\n /// Tries to create a <see cref=\"Uri\"/> for WebSocket with\n /// the specified <paramref name=\"uriString\"/>.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if a <see cref=\"Uri\"/> is successfully created; otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"uriString\">\n /// A <see cref=\"string\"/> that represents a WebSocket URL to try.",
"\n /// </param>\n /// <param name=\"result\">\n /// When this method returns, a <see cref=\"Uri\"/> that represents a WebSocket URL,\n /// or <see langword=\"null\"/> if <paramref name=\"uriString\"/> is invalid.",
"\n /// </param>\n /// <param name=\"message\">\n /// When this method returns, a <see cref=\"string\"/> that represents an error message,\n /// or <see cref=\"String.",
"Empty\"/> if <paramref name=\"uriString\"/> is valid.",
"\n /// </param>\n internal static bool TryCreateWebSocketUri (\n this string uriString, out Uri result, out string message)\n {\n result = null;\n\n var uri = uriString.",
"ToUri ();\n if (uri == null) {\n message = \"An invalid URI string: \" + uriString;\n return false;\n }\n\n if (!",
"uri.",
"IsAbsoluteUri) {\n message = \"Not an absolute URI: \" + uriString;\n return false;\n }\n\n var schm = uri.",
"Scheme;\n if (!(",
"schm == \"ws\" || schm == \"wss\")) {\n message = \"The scheme part isn't 'ws' or 'wss': \" + uriString;\n return false;\n }\n\n if (uri.",
"Fragment.",
"Length > 0) {\n message = \"Includes the fragment component: \" + uriString;\n return false;\n }\n\n var port = uri.",
"Port;\n if (port == 0) {\n message = \"The port part is zero: \" + uriString;\n return false;\n }\n\n result = port !",
"= -1\n ? ",
"uri\n : new Uri (\n String.",
"Format (\n \"{0}://{1}:{2}{3}\",\n schm,\n uri.",
"Host,\n schm == \"ws\" ? ",
"80 : 443,\n uri.",
"PathAndQuery));\n\n message = String.",
"Empty;\n return true;\n }\n\n internal static string Unquote (this string value)\n {\n var start = value.",
"IndexOf ('\"');\n if (start < 0)\n return value;\n\n var end = value.",
"LastIndexOf ('\"');\n var len = end - start - 1;\n\n return len < 0\n ? ",
"value\n : len == 0\n ? ",
"String.",
"Empty\n : value.",
"Substring (start + 1, len).Replace (\"\\\\\\\"\", \"\\\"\");\n }\n\n internal static string UTF8Decode (this byte[] bytes)\n {\n try {\n return Encoding.",
"UTF8.GetString (bytes);\n }\n catch {\n return null;\n }\n }\n\n internal static byte[] UTF8Encode (this string s)\n {\n return Encoding.",
"UTF8.GetBytes (s);\n }\n\n internal static void WriteBytes (this Stream stream, byte[] bytes, int bufferLength)\n {\n using (var input = new MemoryStream (bytes))\n input.",
"CopyTo (stream, bufferLength);\n }\n\n internal static void WriteBytesAsync (\n this Stream stream, byte[] bytes, int bufferLength, Action completed, Action<Exception> error)\n {\n var input = new MemoryStream (bytes);\n input.",
"CopyToAsync (\n stream,\n bufferLength,\n () => {\n if (completed !",
"= null)\n completed ();\n\n input.",
"Dispose ();\n },\n ex => {\n input.",
"Dispose ();\n if (error !",
"= null)\n error (ex);\n });\n }\n\n #endregion\n\n #region Public Methods\n\n /// <summary>\n /// Determines whether the specified <see cref=\"string\"/> contains any of characters in\n /// the specified array of <see cref=\"char\"/>.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"value\"/> contains any of <paramref name=\"chars\"/>;\n /// otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"value\">\n /// A <see cref=\"string\"/> to test.",
"\n /// </param>\n /// <param name=\"chars\">\n /// An array of <see cref=\"char\"/> that contains characters to find.",
"\n /// </param>\n public static bool Contains (this string value, params char[] chars)\n {\n return chars == null || chars.",
"Length == 0\n ? ",
"true\n : value == null || value.",
"Length == 0\n ? ",
"false\n : value.",
"IndexOfAny (chars) > -1;\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"NameValueCollection\"/> contains\n /// the entry with the specified <paramref name=\"name\"/>.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"collection\"/> contains the entry with\n /// <paramref name=\"name\"/>; otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"collection\">\n /// A <see cref=\"NameValueCollection\"/> to test.",
"\n /// </param>\n /// <param name=\"name\">\n /// A <see cref=\"string\"/> that represents the key of the entry to find.",
"\n /// </param>\n public static bool Contains (this NameValueCollection collection, string name)\n {\n return collection !",
"= null && collection.",
"Count > 0 ? ",
"collection[name] !",
"= null : false;\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"NameValueCollection\"/> contains the entry with\n /// the specified both <paramref name=\"name\"/> and <paramref name=\"value\"/>.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"collection\"/> contains the entry with both\n /// <paramref name=\"name\"/> and <paramref name=\"value\"/>; otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"collection\">\n /// A <see cref=\"NameValueCollection\"/> to test.",
"\n /// </param>\n /// <param name=\"name\">\n /// A <see cref=\"string\"/> that represents the key of the entry to find.",
"\n /// </param>\n /// <param name=\"value\">\n /// A <see cref=\"string\"/> that represents the value of the entry to find.",
"\n /// </param>\n public static bool Contains (this NameValueCollection collection, string name, string value)\n {\n if (collection == null || collection.",
"Count == 0)\n return false;\n\n var vals = collection[name];\n if (vals == null)\n return false;\n\n foreach (var val in vals.",
"Split (','))\n if (val.",
"Trim ().Equals (value, StringComparison.",
"OrdinalIgnoreCase))\n return true;\n\n return false;\n }\n\n /// <summary>\n /// Emits the specified <see cref=\"EventHandler\"/> delegate if it isn't <see langword=\"null\"/>.",
"\n /// </summary>\n /// <param name=\"eventHandler\">\n /// A <see cref=\"EventHandler\"/> to emit.",
"\n /// </param>\n /// <param name=\"sender\">\n /// An <see cref=\"object\"/> from which emits this <paramref name=\"eventHandler\"/>.",
"\n /// </param>\n /// <param name=\"e\">\n /// A <see cref=\"EventArgs\"/> that contains no event data.",
"\n /// </param>\n public static void Emit (this EventHandler eventHandler, object sender, EventArgs e)\n {\n if (eventHandler !",
"= null)\n eventHandler (sender, e);\n }\n\n /// <summary>\n /// Emits the specified <c>EventHandler<TEventArgs></c> delegate if it isn't\n /// <see langword=\"null\"/>.",
"\n /// </summary>\n /// <param name=\"eventHandler\">\n /// An <c>EventHandler<TEventArgs></c> to emit.",
"\n /// </param>\n /// <param name=\"sender\">\n /// An <see cref=\"object\"/> from which emits this <paramref name=\"eventHandler\"/>.",
"\n /// </param>\n /// <param name=\"e\">\n /// A <c>TEventArgs</c> that represents the event data.",
"\n /// </param>\n /// <typeparam name=\"TEventArgs\">\n /// The type of the event data generated by the event.",
"\n /// </typeparam>\n public static void Emit<TEventArgs> (\n this EventHandler<TEventArgs> eventHandler, object sender, TEventArgs e)\n where TEventArgs : EventArgs\n {\n if (eventHandler !",
"= null)\n eventHandler (sender, e);\n }\n\n /// <summary>\n /// Gets the collection of the HTTP cookies from the specified HTTP <paramref name=\"headers\"/>.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"CookieCollection\"/> that receives a collection of the HTTP cookies.",
"\n /// </returns>\n /// <param name=\"headers\">\n /// A <see cref=\"NameValueCollection\"/> that contains a collection of the HTTP headers.",
"\n /// </param>\n /// <param name=\"response\">\n /// <c>true</c> if <paramref name=\"headers\"/> is a collection of the response headers;\n /// otherwise, <c>false</c>.",
"\n /// </param>\n public static CookieCollection GetCookies (this NameValueCollection headers, bool response)\n {\n var name = response ? \"",
"Set-Cookie\" : \"Cookie\";\n return headers !",
"= null && headers.",
"Contains (name)\n ? ",
"CookieCollection.",
"Parse (headers[name], response)\n : new CookieCollection ();\n }\n\n /// <summary>\n /// Gets the description of the specified HTTP status <paramref name=\"code\"/>.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"string\"/> that represents the description of the HTTP status code.",
"\n /// </returns>\n /// <param name=\"code\">\n /// One of <see cref=\"HttpStatusCode\"/> enum values, indicates the HTTP status code.",
"\n /// </param>\n public static string GetDescription (this HttpStatusCode code)\n {\n return ((int) code).GetStatusDescription ();\n }\n\n /// <summary>\n /// Gets the description of the specified HTTP status <paramref name=\"code\"/>.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"string\"/> that represents the description of the HTTP status code.",
"\n /// </returns>\n /// <param name=\"code\">\n /// An <see cref=\"int\"/> that represents the HTTP status code.",
"\n /// </param>\n public static string GetStatusDescription (this int code)\n {\n switch (code) {\n case 100: return \"Continue\";\n case 101: return \"Switching Protocols\";\n case 102: return \"Processing\";\n case 200: return \"OK\";\n case 201: return \"Created\";\n case 202: return \"Accepted\";\n case 203: return \"Non-Authoritative Information\";\n case 204: return \"No Content\";\n case 205: return \"Reset Content\";\n case 206: return \"Partial Content\";\n case 207: return \"Multi-Status\";\n case 300: return \"Multiple Choices\";\n case 301: return \"Moved Permanently\";\n case 302: return \"Found\";\n case 303: return \"See Other\";\n case 304: return \"Not Modified\";\n case 305: return \"Use Proxy\";\n case 307: return \"Temporary Redirect\";\n case 400: return \"Bad Request\";\n case 401: return \"Unauthorized\";\n case 402: return \"Payment Required\";\n case 403: return \"Forbidden\";\n case 404: return \"Not Found\";\n case 405: return \"Method Not Allowed\";\n case 406: return \"Not Acceptable\";\n case 407: return \"Proxy Authentication Required\";\n case 408: return \"Request Timeout\";\n case 409: return \"Conflict\";\n case 410: return \"Gone\";\n case 411: return \"Length Required\";\n case 412: return \"Precondition Failed\";\n case 413: return \"Request Entity Too Large\";\n case 414: return \"Request-Uri Too Long\";\n case 415: return \"Unsupported Media Type\";\n case 416: return \"Requested Range Not Satisfiable\";\n case 417: return \"Expectation Failed\";\n case 422: return \"Unprocessable Entity\";\n case 423: return \"Locked\";\n case 424: return \"Failed Dependency\";\n case 500: return \"Internal Server Error\";\n case 501: return \"Not Implemented\";\n case 502: return \"Bad Gateway\";\n case 503: return \"Service Unavailable\";\n case 504: return \"Gateway Timeout\";\n case 505: return \"Http Version Not Supported\";\n case 507: return \"Insufficient Storage\";\n }\n\n return String.",
"Empty;\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"ushort\"/> is in the allowable range of\n /// the WebSocket close status code.",
"\n /// </summary>\n /// <remarks>\n /// Not allowable ranges are the following:\n /// <list type=\"bullet\">\n /// <item>\n /// <term>\n /// Numbers in the range 0-999 are not used.",
"\n /// </term>\n /// </item>\n /// <item>\n /// <term>\n /// Numbers greater than 4999 are out of the reserved close status code ranges.",
"\n /// </term>\n /// </item>\n /// </list>\n /// </remarks>\n /// <returns>\n /// <c>true</c> if <paramref name=\"value\"/> is in the allowable range of the WebSocket\n /// close status code; otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"value\">\n /// A <see cref=\"ushort\"/> to test.",
"\n /// </param>\n public static bool IsCloseStatusCode (this ushort value)\n {\n return value > 999 && value < 5000;\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"string\"/> is enclosed in the specified\n /// <see cref=\"char\"/>.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"value\"/> is enclosed in <paramref name=\"c\"/>;\n /// otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"value\">\n /// A <see cref=\"string\"/> to test.",
"\n /// </param>\n /// <param name=\"c\">\n /// A <see cref=\"char\"/> that represents the character to find.",
"\n /// </param>\n public static bool IsEnclosedIn (this string value, char c)\n {\n return value !",
"= null &&\n value.",
"Length > 1 &&\n value[0] == c &&\n value[value.",
"Length - 1] == c;\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"ByteOrder\"/> is host (this computer\n /// architecture) byte order.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"order\"/> is host byte order; otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"order\">\n /// One of the <see cref=\"ByteOrder\"/> enum values, to test.",
"\n /// </param>\n public static bool IsHostOrder (this ByteOrder order)\n {\n // true: !(",
"true ^ true) or !(",
"false ^ false)\n // false: !(",
"true ^ false) or !(",
"false ^ true)\n return !(",
"BitConverter.",
"IsLittleEndian ^ (order == ByteOrder.",
"Little));\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"System.",
"Net.",
"IPAddress\"/> represents\n /// a local IP address.",
"\n /// </summary>\n /// <remarks>\n /// This local means NOT REMOTE for the current host.",
"\n /// </remarks>\n /// <returns>\n /// <c>true</c> if <paramref name=\"address\"/> represents a local IP address;\n /// otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"address\">\n /// A <see cref=\"System.",
"Net.",
"IPAddress\"/> to test.",
"\n /// </param>\n public static bool IsLocal (this System.",
"Net.",
"IPAddress address)\n {\n if (address == null)\n return false;\n\n if (address.",
"Equals (System.",
"Net.",
"IPAddress.",
"Any))\n return true;\n\n if (address.",
"Equals (System.",
"Net.",
"IPAddress.",
"Loopback))\n return true;\n\n if (Socket.",
"OSSupportsIPv6) {\n if (address.",
"Equals (System.",
"Net.",
"IPAddress.",
"IPv6Any))\n return true;\n\n if (address.",
"Equals (System.",
"Net.",
"IPAddress.",
"IPv6Loopback))\n return true;\n }\n\n var host = System.",
"Net.",
"Dns.",
"GetHostName ();\n var addrs = System.",
"Net.",
"Dns.",
"GetHostAddresses (host);\n foreach (var addr in addrs) {\n if (address.",
"Equals (addr))\n return true;\n }\n\n return false;\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"string\"/> is <see langword=\"null\"/> or empty.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"value\"/> is <see langword=\"null\"/> or empty;\n /// otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"value\">\n /// A <see cref=\"string\"/> to test.",
"\n /// </param>\n public static bool IsNullOrEmpty (this string value)\n {\n return value == null || value.",
"Length == 0;\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"string\"/> is a predefined scheme.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"value\"/> is a predefined scheme; otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"value\">\n /// A <see cref=\"string\"/> to test.",
"\n /// </param>\n public static bool IsPredefinedScheme (this string value)\n {\n if (value == null || value.",
"Length < 2)\n return false;\n\n var c = value[0];\n if (c == 'h')\n return value == \"http\" || value == \"https\";\n\n if (c == 'w')\n return value == \"ws\" || value == \"wss\";\n\n if (c == 'f')\n return value == \"file\" || value == \"ftp\";\n\n if (c == 'n') {\n c = value[1];\n return c == 'e'\n ? ",
"value == \"news\" || value == \"net.pipe\" || value == \"net.tcp\"\n : value == \"nntp\";\n }\n\n return (c == 'g' && value == \"gopher\") || (c == 'm' && value == \"mailto\");\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"HttpListenerRequest\"/> is\n /// an HTTP Upgrade request to switch to the specified <paramref name=\"protocol\"/>.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"request\"/> is an HTTP Upgrade request to switch to\n /// <paramref name=\"protocol\"/>; otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"request\">\n /// A <see cref=\"HttpListenerRequest\"/> that represents the HTTP request.",
"\n /// </param>\n /// <param name=\"protocol\">\n /// A <see cref=\"string\"/> that represents the protocol name.",
"\n /// </param>\n /// <exception cref=\"ArgumentNullException\">\n /// <para>\n /// <paramref name=\"request\"/> is <see langword=\"null\"/>.",
"\n /// </para>\n /// <para>\n /// -or-\n /// </para>\n /// <para>\n /// <paramref name=\"protocol\"/> is <see langword=\"null\"/>.",
"\n /// </para>\n /// </exception>\n /// <exception cref=\"ArgumentException\">\n /// <paramref name=\"protocol\"/> is empty.",
"\n /// </exception>\n public static bool IsUpgradeTo (this HttpListenerRequest request, string protocol)\n {\n if (request == null)\n throw new ArgumentNullException (\"request\");\n\n if (protocol == null)\n throw new ArgumentNullException (\"protocol\");\n\n if (protocol.",
"Length == 0)\n throw new ArgumentException (\"An empty string.\", \"",
"protocol\");\n\n return request.",
"Headers.",
"Contains (\"Upgrade\", protocol) &&\n request.",
"Headers.",
"Contains (\"Connection\", \"Upgrade\");\n }\n\n /// <summary>\n /// Determines whether the specified <see cref=\"string\"/> is a URI string.",
"\n /// </summary>\n /// <returns>\n /// <c>true</c> if <paramref name=\"value\"/> may be a URI string; otherwise, <c>false</c>.",
"\n /// </returns>\n /// <param name=\"value\">\n /// A <see cref=\"string\"/> to test.",
"\n /// </param>\n public static bool MaybeUri (this string value)\n {\n if (value == null || value.",
"Length == 0)\n return false;\n\n var idx = value.",
"IndexOf (':');\n if (idx == -1)\n return false;\n\n if (idx >= 10)\n return false;\n\n return value.",
"Substring (0, idx).IsPredefinedScheme ();\n }\n\n /// <summary>\n /// Retrieves a sub-array from the specified <paramref name=\"array\"/>. ",
"A sub-array starts at\n /// the specified element position in <paramref name=\"array\"/>.",
"\n /// </summary>\n /// <returns>\n /// An array of T that receives a sub-array, or an empty array of T if any problems with\n /// the parameters.",
"\n /// </returns>\n /// <param name=\"array\">\n /// An array of T from which to retrieve a sub-array.",
"\n /// </param>\n /// <param name=\"startIndex\">\n /// An <see cref=\"int\"/> that represents the zero-based starting position of\n /// a sub-array in <paramref name=\"array\"/>.",
"\n /// </param>\n /// <param name=\"length\">\n /// An <see cref=\"int\"/> that represents the number of elements to retrieve.",
"\n /// </param>\n /// <typeparam name=\"T\">\n /// The type of elements in <paramref name=\"array\"/>.",
"\n /// </typeparam>\n public static T[] SubArray<T> (this T[] array, int startIndex, int length)\n {\n int len;\n if (array == null || (len = array.",
"Length) == 0)\n return new T[0];\n\n if (startIndex < 0 || length <= 0 || startIndex + length > len)\n return new T[0];\n\n if (startIndex == 0 && length == len)\n return array;\n\n var subArray = new T[length];\n Array.",
"Copy (array, startIndex, subArray, 0, length);\n\n return subArray;\n }\n\n /// <summary>\n /// Retrieves a sub-array from the specified <paramref name=\"array\"/>. ",
"A sub-array starts at\n /// the specified element position in <paramref name=\"array\"/>.",
"\n /// </summary>\n /// <returns>\n /// An array of T that receives a sub-array, or an empty array of T if any problems with\n /// the parameters.",
"\n /// </returns>\n /// <param name=\"array\">\n /// An array of T from which to retrieve a sub-array.",
"\n /// </param>\n /// <param name=\"startIndex\">\n /// A <see cref=\"long\"/> that represents the zero-based starting position of\n /// a sub-array in <paramref name=\"array\"/>.",
"\n /// </param>\n /// <param name=\"length\">\n /// A <see cref=\"long\"/> that represents the number of elements to retrieve.",
"\n /// </param>\n /// <typeparam name=\"T\">\n /// The type of elements in <paramref name=\"array\"/>.",
"\n /// </typeparam>\n public static T[] SubArray<T> (this T[] array, long startIndex, long length)\n {\n long len;\n if (array == null || (len = array.",
"LongLength) == 0)\n return new T[0];\n\n if (startIndex < 0 || length <= 0 || startIndex + length > len)\n return new T[0];\n\n if (startIndex == 0 && length == len)\n return array;\n\n var subArray = new T[length];\n Array.",
"Copy (array, startIndex, subArray, 0, length);\n\n return subArray;\n }\n\n /// <summary>\n /// Executes the specified <see cref=\"Action\"/> delegate <paramref name=\"n\"/> times.",
"\n /// </summary>\n /// <param name=\"n\">\n /// An <see cref=\"int\"/> is the number of times to execute.",
"\n /// </param>\n /// <param name=\"action\">\n /// An <see cref=\"Action\"/> delegate that references the method(s) to execute.",
"\n /// </param>\n public static void Times (this int n, Action action)\n {\n if (n > 0 && action !",
"= null)\n ((ulong) n).times (action);\n }\n\n /// <summary>\n /// Executes the specified <see cref=\"Action\"/> delegate <paramref name=\"n\"/> times.",
"\n /// </summary>\n /// <param name=\"n\">\n /// A <see cref=\"long\"/> is the number of times to execute.",
"\n /// </param>\n /// <param name=\"action\">\n /// An <see cref=\"Action\"/> delegate that references the method(s) to execute.",
"\n /// </param>\n public static void Times (this long n, Action action)\n {\n if (n > 0 && action !",
"= null)\n ((ulong) n).times (action);\n }\n\n /// <summary>\n /// Executes the specified <see cref=\"Action\"/> delegate <paramref name=\"n\"/> times.",
"\n /// </summary>\n /// <param name=\"n\">\n /// A <see cref=\"uint\"/> is the number of times to execute.",
"\n /// </param>\n /// <param name=\"action\">\n /// An <see cref=\"Action\"/> delegate that references the method(s) to execute.",
"\n /// </param>\n public static void Times (this uint n, Action action)\n {\n if (n > 0 && action !",
"= null)\n ((ulong) n).times (action);\n }\n\n /// <summary>\n /// Executes the specified <see cref=\"Action\"/> delegate <paramref name=\"n\"/> times.",
"\n /// </summary>\n /// <param name=\"n\">\n /// A <see cref=\"ulong\"/> is the number of times to execute.",
"\n /// </param>\n /// <param name=\"action\">\n /// An <see cref=\"Action\"/> delegate that references the method(s) to execute.",
"\n /// </param>\n public static void Times (this ulong n, Action action)\n {\n if (n > 0 && action !",
"= null)\n n.times (action);\n }\n\n /// <summary>\n /// Executes the specified <c>Action<int></c> delegate <paramref name=\"n\"/> times.",
"\n /// </summary>\n /// <param name=\"n\">\n /// An <see cref=\"int\"/> is the number of times to execute.",
"\n /// </param>\n /// <param name=\"action\">\n /// An <c>Action<int></c> delegate that references the method(s) to execute.",
"\n /// An <see cref=\"int\"/> parameter to pass to the method(s) is the zero-based count of\n /// iteration.",
"\n /// </param>\n public static void Times (this int n, Action<int> action)\n {\n if (n > 0 && action !",
"= null)\n for (int i = 0; i < n; i++)\n action (i);\n }\n\n /// <summary>\n /// Executes the specified <c>Action<long></c> delegate <paramref name=\"n\"/> times.",
"\n /// </summary>\n /// <param name=\"n\">\n /// A <see cref=\"long\"/> is the number of times to execute.",
"\n /// </param>\n /// <param name=\"action\">\n /// An <c>Action<long></c> delegate that references the method(s) to execute.",
"\n /// A <see cref=\"long\"/> parameter to pass to the method(s) is the zero-based count of\n /// iteration.",
"\n /// </param>\n public static void Times (this long n, Action<long> action)\n {\n if (n > 0 && action !",
"= null)\n for (long i = 0; i < n; i++)\n action (i);\n }\n\n /// <summary>\n /// Executes the specified <c>Action<uint></c> delegate <paramref name=\"n\"/> times.",
"\n /// </summary>\n /// <param name=\"n\">\n /// A <see cref=\"uint\"/> is the number of times to execute.",
"\n /// </param>\n /// <param name=\"action\">\n /// An <c>Action<uint></c> delegate that references the method(s) to execute.",
"\n /// A <see cref=\"uint\"/> parameter to pass to the method(s) is the zero-based count of\n /// iteration.",
"\n /// </param>\n public static void Times (this uint n, Action<uint> action)\n {\n if (n > 0 && action !",
"= null)\n for (uint i = 0; i < n; i++)\n action (i);\n }\n\n /// <summary>\n /// Executes the specified <c>Action<ulong></c> delegate <paramref name=\"n\"/> times.",
"\n /// </summary>\n /// <param name=\"n\">\n /// A <see cref=\"ulong\"/> is the number of times to execute.",
"\n /// </param>\n /// <param name=\"action\">\n /// An <c>Action<ulong></c> delegate that references the method(s) to execute.",
"\n /// A <see cref=\"ulong\"/> parameter to pass to this method(s) is the zero-based count of\n /// iteration.",
"\n /// </param>\n public static void Times (this ulong n, Action<ulong> action)\n {\n if (n > 0 && action !",
"= null)\n for (ulong i = 0; i < n; i++)\n action (i);\n }\n\n /// <summary>\n /// Converts the specified array of <see cref=\"byte\"/> to the specified type data.",
"\n /// </summary>\n /// <returns>\n /// A T converted from <paramref name=\"source\"/>, or a default value of\n /// T if <paramref name=\"source\"/> is an empty array of <see cref=\"byte\"/> or\n /// if the type of T isn't <see cref=\"bool\"/>, <see cref=\"char\"/>, <see cref=\"double\"/>,\n /// <see cref=\"float\"/>, <see cref=\"int\"/>, <see cref=\"long\"/>, <see cref=\"short\"/>,\n /// <see cref=\"uint\"/>, <see cref=\"ulong\"/>, or <see cref=\"ushort\"/>.",
"\n /// </returns>\n /// <param name=\"source\">\n /// An array of <see cref=\"byte\"/> to convert.",
"\n /// </param>\n /// <param name=\"sourceOrder\">\n /// One of the <see cref=\"ByteOrder\"/> enum values, specifies the byte order of\n /// <paramref name=\"source\"/>.",
"\n /// </param>\n /// <typeparam name=\"T\">\n /// The type of the return. ",
"The T must be a value type.",
"\n /// </typeparam>\n /// <exception cref=\"ArgumentNullException\">\n /// <paramref name=\"source\"/> is <see langword=\"null\"/>.",
"\n /// </exception>\n public static T To<T> (this byte[] source, ByteOrder sourceOrder)\n where T : struct\n {\n if (source == null)\n throw new ArgumentNullException (\"source\");\n\n if (source.",
"Length == 0)\n return default (T);\n\n var type = typeof (T);\n var buff = source.",
"ToHostOrder (sourceOrder);\n\n return type == typeof (Boolean)\n ? (",
"T)(object) BitConverter.",
"ToBoolean (buff, 0)\n : type == typeof (Char)\n ? (",
"T)(object) BitConverter.",
"ToChar (buff, 0)\n : type == typeof (Double)\n ? (",
"T)(object) BitConverter.",
"ToDouble (buff, 0)\n : type == typeof (Int16)\n ? (",
"T)(object) BitConverter.",
"ToInt16 (buff, 0)\n : type == typeof (Int32)\n ? (",
"T)(object) BitConverter.",
"ToInt32 (buff, 0)\n : type == typeof (Int64)\n ? (",
"T)(object) BitConverter.",
"ToInt64 (buff, 0)\n : type == typeof (Single)\n ? (",
"T)(object) BitConverter.",
"ToSingle (buff, 0)\n : type == typeof (UInt16)\n ? (",
"T)(object) BitConverter.",
"ToUInt16 (buff, 0)\n : type == typeof (UInt32)\n ? (",
"T)(object) BitConverter.",
"ToUInt32 (buff, 0)\n : type == typeof (UInt64)\n ? (",
"T)(object) BitConverter.",
"ToUInt64 (buff, 0)\n : default (T);\n }\n\n /// <summary>\n /// Converts the specified <paramref name=\"value\"/> to an array of <see cref=\"byte\"/>.",
"\n /// </summary>\n /// <returns>\n /// An array of <see cref=\"byte\"/> converted from <paramref name=\"value\"/>.",
"\n /// </returns>\n /// <param name=\"value\">\n /// A T to convert.",
"\n /// </param>\n /// <param name=\"order\">\n /// One of the <see cref=\"ByteOrder\"/> enum values, specifies the byte order of the return.",
"\n /// </param>\n /// <typeparam name=\"T\">\n /// The type of <paramref name=\"value\"/>. ",
"The T must be a value type.",
"\n /// </typeparam>\n public static byte[] ToByteArray<T> (this T value, ByteOrder order)\n where T : struct\n {\n var type = typeof (T);\n var bytes = type == typeof (Boolean)\n ? ",
"BitConverter.",
"GetBytes ((Boolean)(object) value)\n : type == typeof (Byte)\n ? ",
"new byte[] { (Byte)(object) value }\n : type == typeof (Char)\n ? ",
"BitConverter.",
"GetBytes ((Char)(object) value)\n : type == typeof (Double)\n ? ",
"BitConverter.",
"GetBytes ((Double)(object) value)\n : type == typeof (Int16)\n ? ",
"BitConverter.",
"GetBytes ((Int16)(object) value)\n : type == typeof (Int32)\n ? ",
"BitConverter.",
"GetBytes ((Int32)(object) value)\n : type == typeof (Int64)\n ? ",
"BitConverter.",
"GetBytes ((Int64)(object) value)\n : type == typeof (Single)\n ? ",
"BitConverter.",
"GetBytes ((Single)(object) value)\n : type == typeof (UInt16)\n ? ",
"BitConverter.",
"GetBytes ((UInt16)(object) value)\n : type == typeof (UInt32)\n ? ",
"BitConverter.",
"GetBytes ((UInt32)(object) value)\n : type == typeof (UInt64)\n ? ",
"BitConverter.",
"GetBytes ((UInt64)(object) value)\n : WebSocket.",
"EmptyBytes;\n\n if (bytes.",
"Length > 1 && !",
"order.",
"IsHostOrder ())\n Array.",
"Reverse (bytes);\n\n return bytes;\n }\n\n /// <summary>\n /// Converts the order of the specified array of <see cref=\"byte\"/> to the host byte order.",
"\n /// </summary>\n /// <returns>\n /// An array of <see cref=\"byte\"/> converted from <paramref name=\"source\"/>.",
"\n /// </returns>\n /// <param name=\"source\">\n /// An array of <see cref=\"byte\"/> to convert.",
"\n /// </param>\n /// <param name=\"sourceOrder\">\n /// One of the <see cref=\"ByteOrder\"/> enum values, specifies the byte order of\n /// <paramref name=\"source\"/>.",
"\n /// </param>\n /// <exception cref=\"ArgumentNullException\">\n /// <paramref name=\"source\"/> is <see langword=\"null\"/>.",
"\n /// </exception>\n public static byte[] ToHostOrder (this byte[] source, ByteOrder sourceOrder)\n {\n if (source == null)\n throw new ArgumentNullException (\"source\");\n\n return source.",
"Length > 1 && !",
"sourceOrder.",
"IsHostOrder () ? ",
"source.",
"Reverse () : source;\n }\n\n /// <summary>\n /// Converts the specified <paramref name=\"array\"/> to a <see cref=\"string\"/> that\n /// concatenates the each element of <paramref name=\"array\"/> across the specified\n /// <paramref name=\"separator\"/>.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"string\"/> converted from <paramref name=\"array\"/>,\n /// or <see cref=\"String.",
"Empty\"/> if <paramref name=\"array\"/> is empty.",
"\n /// </returns>\n /// <param name=\"array\">\n /// An array of T to convert.",
"\n /// </param>\n /// <param name=\"separator\">\n /// A <see cref=\"string\"/> that represents the separator string.",
"\n /// </param>\n /// <typeparam name=\"T\">\n /// The type of elements in <paramref name=\"array\"/>.",
"\n /// </typeparam>\n /// <exception cref=\"ArgumentNullException\">\n /// <paramref name=\"array\"/> is <see langword=\"null\"/>.",
"\n /// </exception>\n public static string ToString<T> (this T[] array, string separator)\n {\n if (array == null)\n throw new ArgumentNullException (\"array\");\n\n var len = array.",
"Length;\n if (len == 0)\n return String.",
"Empty;\n\n if (separator == null)\n separator = String.",
"Empty;\n\n var buff = new StringBuilder (64);\n (len - 1).Times (i => buff.",
"AppendFormat (\"{0}{1}\", array[i].ToString (), separator));\n\n buff.",
"Append (array[len - 1].ToString ());\n return buff.",
"ToString ();\n }\n\n /// <summary>\n /// Converts the specified <see cref=\"string\"/> to a <see cref=\"Uri\"/>.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"Uri\"/> converted from <paramref name=\"uriString\"/>,\n /// or <see langword=\"null\"/> if <paramref name=\"uriString\"/> isn't successfully converted.",
"\n /// </returns>\n /// <param name=\"uriString\">\n /// A <see cref=\"string\"/> to convert.",
"\n /// </param>\n public static Uri ToUri (this string uriString)\n {\n Uri ret;\n Uri.",
"TryCreate (\n uriString, uriString.",
"MaybeUri () ? ",
"UriKind.",
"Absolute : UriKind.",
"Relative, out ret);\n\n return ret;\n }\n\n /// <summary>\n /// URL-decodes the specified <see cref=\"string\"/>.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"string\"/> that receives the decoded string,\n /// or the <paramref name=\"value\"/> if it's <see langword=\"null\"/> or empty.",
"\n /// </returns>\n /// <param name=\"value\">\n /// A <see cref=\"string\"/> to decode.",
"\n /// </param>\n public static string UrlDecode (this string value)\n {\n return value !",
"= null && value.",
"Length > 0 ? ",
"HttpUtility.",
"UrlDecode (value) : value;\n }\n\n /// <summary>\n /// URL-encodes the specified <see cref=\"string\"/>.",
"\n /// </summary>\n /// <returns>\n /// A <see cref=\"string\"/> that receives the encoded string,\n /// or <paramref name=\"value\"/> if it's <see langword=\"null\"/> or empty.",
"\n /// </returns>\n /// <param name=\"value\">\n /// A <see cref=\"string\"/> to encode.",
"\n /// </param>\n public static string UrlEncode (this string value)\n {\n return value !",
"= null && value.",
"Length > 0 ? ",
"HttpUtility.",
"UrlEncode (value) : value;\n }\n\n /// <summary>\n /// Writes and sends the specified <paramref name=\"content\"/> data with the specified\n /// <see cref=\"HttpListenerResponse\"/>.",
"\n /// </summary>\n /// <param name=\"response\">\n /// A <see cref=\"HttpListenerResponse\"/> that represents the HTTP response used to\n /// send the content data.",
"\n /// </param>\n /// <param name=\"content\">\n /// An array of <see cref=\"byte\"/> that represents the content data to send.",
"\n /// </param>\n /// <exception cref=\"ArgumentNullException\">\n /// <para>\n /// <paramref name=\"response\"/> is <see langword=\"null\"/>.",
"\n /// </para>\n /// <para>\n /// -or-\n /// </para>\n /// <para>\n /// <paramref name=\"content\"/> is <see langword=\"null\"/>.",
"\n /// </para>\n /// </exception>\n public static void WriteContent (this HttpListenerResponse response, byte[] content)\n {\n if (response == null)\n throw new ArgumentNullException (\"response\");\n\n if (content == null)\n throw new ArgumentNullException (\"content\");\n\n var len = content.",
"LongLength;\n if (len == 0) {\n response.",
"Close ();\n return;\n }\n\n response.",
"ContentLength64 = len;\n var output = response.",
"OutputStream;\n if (len <= Int32.MaxValue)\n output.",
"Write (content, 0, (int) len);\n else\n output.",
"WriteBytes (content, 1024);\n\n output.",
"Close ();\n }\n\n #endregion\n }\n}\n"
] | {
"pile_set_name": "Github"
} | [
0.00008671522719389525,
0.000008381096855098169,
0.000021633315305570577,
0.000013717421124828532,
0.0000980296049406921,
0,
0.004132231404958678,
0,
0.002958579881656805,
0.006920415224913495,
0.0011890606420927466,
0,
0.002066115702479339,
0,
0,
0.0020811654526534857,
0.0013717421124828531,
0.0014792899408284025,
0,
0.0018365472910927456,
0.00016232448664881097,
0.000013705764644609523,
0.000028577960676726108,
0,
0.0001602307322544464,
0,
0,
0,
0,
0,
0,
0,
0,
0.00002826615410707219,
0,
0.0003204614645088928,
0,
0,
0,
0,
0.000022826880934989044,
0.0010405827263267429,
0,
0.0034602076124567475,
0.00021626297577854672,
0.00554016620498615,
0,
0.00003018959062915107,
0.0020811654526534857,
0.0011111111111111111,
0,
0.0011111111111111111,
0,
0.0018365472910927456,
0,
0,
0,
0.0006925207756232687,
0,
0.0009765625,
0,
0.0008163265306122448,
0,
0.0008650519031141869,
0,
0,
0,
0,
0,
0,
0.0012755102040816326,
0,
0,
0,
0,
0.0000502992807202857,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00008888888888888889,
0,
0.0000979591836734694,
0,
0.000057810151462596836,
0,
0,
0.000028755187915153024,
0.000005072640207775343,
0.000016,
0,
0,
0.00021003990758244068,
0,
0,
0,
0,
0,
0.00006530612244897959,
0,
0.00009363003651571424,
0,
0.000055401662049861494,
0,
0,
0.000019578667084344897,
0.00004627701420704336,
0,
0,
0,
0,
0.00003225754423315753,
0,
0.00012018508503094766,
0.00010850694444444444,
0.0008650519031141869,
0,
0.0006574621959237343,
0,
0,
0,
0,
0.00004627701420704336,
0.0011111111111111111,
0.000594883997620464,
0,
0.0008650519031141869,
0,
0,
0,
0,
0,
0.0008650519031141869,
0.0009765625,
0,
0,
0,
0,
0,
0,
0,
0,
0.0003305785123966942,
0,
0,
0.000625,
0,
0,
0.0004725897920604915,
0,
0.00003228305785123967,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0000573921028466483,
0.0002366863905325444,
0,
0,
0.00002953686200378072,
0,
0,
0,
0,
0.000018986049999762676,
0.0011890606420927466,
0,
0.0011111111111111111,
0.00007346189164370983,
0.0011890606420927466,
0,
0.0011111111111111111,
0.000037180249851279,
0,
0,
0.00008899964400142399,
0.0016,
0.00001874027848053822,
0,
0.00029726516052318666,
0,
0.00005486968449931413,
0,
0.0004164931278633902,
0,
0.00008573388203017832,
0.0001951092611862643,
0.00010412328196584755,
0,
0,
0,
0.000020108990729755272,
0.000048225308641975306,
0,
0,
0,
0.000012753800632588513,
0,
0,
0,
0,
0.00017799928800284797,
0,
0.000625,
0.00003419855682090216,
0,
0,
0,
0.000004286528726172259,
0,
0.00021626297577854672,
0.000014457343607685523,
0,
0,
0,
0,
0,
0,
0,
0.000021633315305570577,
0.0004725897920604915,
0.0002227667631989307,
0,
0,
0,
0.000012755102040816325,
0,
0,
0,
0,
0,
0,
0,
0,
0.000044444444444444447,
0,
0,
0,
0.00011866619200189865,
0.0005745475438092502,
0.00012913223140495868,
0.00010503833899373271,
0,
0.0011890606420927466,
0,
0,
0,
0,
0.00036982248520710064,
0,
0.00018765246762994932,
0,
0.0018365472910927456,
0,
0.01,
0.00010850694444444444,
0,
0.0625,
0.00002448979591836735,
0,
0.00009008603216071348,
0,
0,
0.0008650519031141869,
0,
0.00008656509695290859,
0.0000591715976331361,
0.00006609822195782934,
0.00004449982200071199,
0,
0,
0,
0,
0.0625,
0.00013007284079084286,
0,
0.000044444444444444447,
0,
0,
0,
0.002066115702479339,
0.0003077870113881194,
0,
0.0005668934240362812,
0,
0,
0.00007181844297615628,
0,
0,
0,
0,
0.0011890606420927466,
0.0000400576830636116,
0.000037180249851279,
0.00008671522719389525,
0.00005038968019349637,
0,
0,
0,
0,
0.000015378700499807765,
0,
0,
0,
0.00005653230821414438,
0,
0,
0,
0,
0.000026298487836949376,
0,
0,
0,
0.0000573921028466483,
0.0022675736961451248,
0,
0,
0,
0,
0,
0,
0,
0.000037180249851279,
0,
0,
0.000625,
0,
0,
0,
0,
0.00015983803079546062,
0,
0,
0,
0,
0,
0.00006934171597633136,
0,
0,
0,
0,
0,
0,
0.0030864197530864196,
0,
0,
0.00003121001217190475,
0,
0,
0.000016128772116578765,
0,
0,
2.1553043332824682e-7,
0.00007527569724114569,
0,
0,
0,
0,
0,
0.00004162330905306972,
0,
0,
0,
0.0011890606420927466,
0,
0.000037180249851279,
0,
0,
0.0001020304050607081,
0,
0,
0,
0,
0.00591715976331361,
0.0007304601899196494,
0,
0,
0.0007689350249903883,
0.00011080332409972299,
0.00004385772553835358,
0,
0,
0,
0.0005202913631633714,
0,
0.00011562030292519367,
0,
0,
0.01,
0,
0,
0,
0.01,
0,
0.0006925207756232687,
0,
0,
0.01,
0,
0,
0,
0.01,
0.00019837333862328903,
0,
0.0625,
0.000594883997620464,
0,
0.0625,
0,
0,
0,
0,
0.00007305135510263716,
0,
0,
0,
0,
0,
0,
0,
0.00006103515625,
0,
0,
0,
0,
0.000011260754020089185,
0.00019837333862328903,
0,
0,
0.0003305785123966942,
0,
0.00005175715542673775,
0.00005827166249053085,
0,
0.00008416799932665601,
0,
0.00006718624025799517,
0,
0,
0,
0,
0,
0,
0,
0,
0.000015872763924382153,
0.00006839711364180432,
0,
0,
0,
0,
0,
0,
0,
0.000015378700499807765,
0.00005907372400756144,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00008416799932665601,
0,
0,
0,
0,
0,
0,
0,
0.00002953686200378072,
0,
0,
0,
0,
0.000029218407596785978,
0,
0,
0,
0,
0.000028905075731298418,
0.00008416799932665601,
0,
0.00007971938775510203,
0,
0.0000624200243438095,
0.000019665586698197158,
0.0001,
0,
0,
0,
0,
0.00002123638216993353,
0,
0,
0.001736111111111111,
0.00017777777777777779,
0.001736111111111111,
0,
0.001736111111111111,
0,
0.001736111111111111,
0,
0.001736111111111111,
0.0001234567901234568,
0.001736111111111111,
0,
0.001736111111111111,
0.0001,
0.001736111111111111,
0.00009245562130177516,
0.001736111111111111,
0.00008573388203017832,
0.001736111111111111,
0.0000617283950617284,
0.00007305135510263716,
0,
0,
0,
0,
0.000021633315305570577,
0.00591715976331361,
0.0001020304050607081,
0,
0.00591715976331361,
0.00008899964400142399,
0.00591715976331361,
0.00008116224332440549,
0.00591715976331361,
0.00007694675284702985,
0.00591715976331361,
0.00014363688595231256,
0.00591715976331361,
0.00006609822195782934,
0.00591715976331361,
0.00006103515625,
0.00591715976331361,
0.0000573921028466483,
0.00591715976331361,
0.00005406574394463668,
0.00591715976331361,
0.0002834467120181406,
0,
0,
0,
0.0011111111111111111,
0.0000400576830636116,
0.00007181844297615628,
0.0001,
0,
0,
0.00002311390532544379,
0,
0,
0.0034602076124567475,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.000297441998810232,
0.00019837333862328903,
0,
0.00007831466833737959,
0.000023564897728343855,
0,
0.0000980296049406921,
0.000594883997620464,
0,
0,
0,
0,
0,
0,
0.0001020304050607081,
0.00390625,
0,
0.006944444444444444,
0.00008734387282732115,
0,
0,
0.0001020304050607081,
0.00390625,
0,
0.006944444444444444,
0.000029218407596785978,
0,
0.00006009254251547383,
0,
0,
0.000009585062638384343,
0.00038446751249519417,
0,
0,
0.0002601456815816857,
0,
0.0005668934240362812,
0
] | 0.000789 | 5 |
[
"This is a call out meter. ",
" I think the best person to help you would be Kathy \nBenedict in Volume Management.",
"\n\nD\n\n\n \n\t\n\t\n\tFrom: Cynthia Hakemack 01/08/2001 03:43 PM\n\t\n\nTo: Daren J Farmer/HOU/ECT@ECT\ncc: Charles Howard/NA/Enron@ENRON, Charlene Richmond/HOU/ECT@ECT \nSubject: Copano P/L 01/00 - S93481\n\nDaren, I'm looking at S93481 for 01/00. ",
" 3,461 mmbtu was scheduled to Copano \nP/L in 02/00 and the counterparty was paid. ",
" In 05/00 the volumes were \nreversed from this deal. ",
" Would you be able to tell why they were reversed? ",
" \nI'm trying to determine if this is a valid recoverable item. ",
" Thanks."
] | {
"pile_set_name": "Enron Emails"
} | [
0,
0.0002903178980984178,
0.0000440392830404721,
0,
0,
0,
0,
0
] | 0.000042 | 5 |
[
"\n210 F.Supp.2d 813 (2002)\nIn the Matter of the EXTRADITION OF Serapio DIAZ MEDINA.",
"\nNo. ",
"4:02-133-MJ[1].",
"\nUnited States District Court, N.D. Texas, Fort Worth Division.",
"\nJuly 8, 2002.",
"\n*814 David Lee Jarvis, U.S. Attorney's Office, Fort Worth, Texas, for U.S.\nClaudia Montani, Federal Public Defender, Fort Worth, Texas, for defendant.",
"\n\nMEMORANDUM OPINION AND ORDER\nBLEIL, United States Magistrate Judge.",
"\nPending before the United States District Court for the Northern District of Texas is the matter of the extradition of Respondent Serapio Diaz Medina from the United States to face charges of aggravated homicide in Mexico. ",
"The court has conducted a hearing and provided the Government and Medina with the opportunity to brief issues related to Medina's opposition to extradition. ",
"Having reviewed the record and legal arguments presented by the parties, the court finds that the petition *815 for extradition should be granted for the following reasons:\n\nA. BACKGROUND\nMedina is the subject of an arrest warrant issued by a judge in Lagos de Moreno, State of Jalisco, Mexico and stands accused of fatally shooting a relative, Jose Diaz Limon, in Jalisco on June 24, 2000. ",
"On January 23, 2002, the United States Attorney, acting on behalf of the government of the United Mexican States (Mexico), filed a Complaint for the Provisional Arrest of Medina, with a View Towards Extradition. ",
"18 U.S.C. § 3184. ",
"See generally Extradition Treaty between the United States of America and the United Mexican States, May 4, 1978, art. ",
"11, U.S.-Mex., ",
"31 U.S.T. 5059 [hereinafter Extradition Treaty] (authorizing provisional arrest pending submission of a formal request for extradition). ",
"A provisional arrest warrant was issued on January 23, 2002, and executed on January 25, 2002. ",
"The court appointed counsel to represent Medina and ordered that Medina be detained pending an extradition hearing.",
"\nOn March 22, 2002, the Embassy of Mexico submitted Diplomatic Note No. ",
"2747 to the Secretary of State formally requesting Medina's extradition from the United States to Mexico. (",
"Gov't Ex. ",
"1). ",
"See Extradition Treaty, art. ",
"11, 31 U.S.T. 5059 (requiring formal extradition request within sixty days of fugitive's provisional arrest). ",
"An extradition hearing was held on May 30, 2002 before the undersigned United States Magistrate Judge in accordance with 18 U.S.C. § 3184.",
"\n\nB. STANDARDS FOR EXTRADITION\nExtradition is a self-contained body of law governed by the terms of the treaty between the United States and the country requesting extradition and by the provisions found in 18 U.S.C. §§ 3181-3196. ",
"Pamela B. Stuart, Treaty Traps How to Get Your Client Through the Maze of Extradition, 6-WTR CRIM.JUST. ",
"24, 28 (Winter 1992). ",
"Neither the Federal Rules of Criminal Procedure or Federal Rules of Evidence (except the rules governing privilege) apply to extradition proceedings. ",
"FED.R.CRIM.PROC. ",
"54(b)(5); FED.R.EVID. ",
"1101(d)(3).",
"\nThe substantive right of a foreign country to request return of a fugitive, and the duty of the United States to deliver the fugitive, depends entirely on existence of a treaty between the nations. ",
"In re United States, 713 F.2d 105, 107-08 (5th Cir.1983). ",
"The obligations imposed by treaties are to be liberally construed so as to give effect to the apparent intention of the parties. ",
"Factor v. Laubenheimer, 290 U.S. 276, 293-94, 54 S.Ct. ",
"191, 195-96, 78 L.Ed. ",
"315 (1933); Escobedo v. United States, 623 F.2d 1098, 1104 (5th Cir.1980).",
"\nThe controlling document in these proceedings is the extradition treaty between the United States of America and the United Mexican States, signed May 4, 1978 and effective January 25, 1980. ",
"A certified copy of this treaty has been submitted by the Government in support of its position. (",
"Gov't Ex. ",
"1). ",
"In conjunction with 18 U.S.C. § 3184, the Treaty imposes the following procedural requirements:\n1. ",
"The request for extradition must be made through diplomatic channels; and\n2. ",
"The request for extradition must contain a description of the offense for which extradition is requested and be accompanied by (a) a statement of facts, (b) the text of the legal provisions describing the essential elements of the offense, (c) the test of the legal provisions describing the punishment for the offense, (d) the test of the legal provisions relating to the time limit on the prosecution or execution of punishment of the offense, and (e) the *816 facts and personal information about the person sought to permit his identification, and if possible, information concerning his location.",
"\nExtradition Treaty, art. ",
"10, 31 U.S.T. 5059. ",
"When the request for extradition relates to a person who has not yet been convicted, the request must also be accompanied by a certified copy of the arrest warrant issued by a judge or other judicial officer of the country requesting extradition, and by\n[e]vidence which, in accordance with the laws of the requested Party, would justify the apprehension and commitment for trial of the person sought if the offense had been committed there.",
"\nId., art. ",
"10, para. ",
"3, 31 U.S.T. 5059. ",
"The request for extradition is to be processed in accordance with legislation of the requested Party. ",
"Id., art. ",
"13, 31 U.S.T. 5059.",
"\n\nC. DISCUSSION\n\n1. ",
"Extraditable Offense and Dual Criminality\nMexico seeks Medina's extradition on charges of aggravated homicide. ",
"Article 2 of the Treaty provides for extradition of any offense listed in the Appendix to the treaty and \"punishable in accordance with the laws of both Contracting Parties by deprivation of liberty the maximum of which shall not be less than one year.\" ",
"Extradition Treaty, art. ",
"2, para. ",
"1, 31 U.S.T. 5059. ",
"This principle of dual criminality requires that the act on which extradition is founded be considered a crime in both jurisdictions. ",
"Collins v. Loisel, 259 U.S. 309, 311-12, 42 S.Ct. ",
"469, 470, 66 L.Ed. ",
"956 (1922); In re Extradition of Lahoria, 932 F.Supp. ",
"802 (N.D.Tex.1996).",
"\nThe Appendix to the treaty between the United States and Mexico specifies murder as an extraditable offense. ",
"Extradition Treaty, app., ",
"31 U.S.T. 5059. ",
"See also C.P. JALISCO arts. ",
"213, 219 (defining aggravated homicide and providing a punishment range of twenty to thirty-five years' imprisonment). ",
"Murder is also a felony offense under both federal law and the laws of Texas and punishable by more than one year imprisonment.[2] 18 U.S.C. § 1111; TEX. ",
"PENAL CODE ANN. § ",
"19.02 (Vernon 1994).",
"\nAggravated homicide is an extraditable offense under Article 2 of the Extradition Treaty and the Appendix to the Extradition Treaty.",
"\n\n2. ",
"Identity of Fugitive\nMedina's identity as the person sought by Mexico and named in the Mexican arrest warrant is not contested.",
"\n\n3. ",
"Probable Cause\nMedina asserts that he has been grossly overcharged and is subject to a far greater penalty than the evidence would support.",
"\nExtradition shall be granted only if the evidence be found sufficient, according to the laws of the requested Party, either to justify the committal for trial of the person sought if the offense of which he has been accused had been committed in that place or to prove that he is the person convicted by the courts of the requesting Party.",
"\nExtradition Treaty, art. ",
"3, 31 U.S.T. 5059.",
"\nIn the United States, evidence that is sufficient to sustain the charges requires a showing of probable cause. ",
"See, e.g., Escobedo v. United States, 623 F.2d 1098, 1102 (5th Cir.1980); In re Extradition of Mainero, 990 F.Supp. ",
"1208, 1215-16 (S.D.Cal.1997); In re Extradition of Prushinowski, 574 F.Supp. ",
"1439, 1448 *817 (E.D.N.C.1983). ",
"Probable cause is the existence of reasonable grounds to believe the accused committed the offense charged, not convincing evidence of actual guilt. ",
"See Collins v. Loisel, 259 U.S. 309, 314-15, 42 S.Ct. ",
"469, 471, 66 L.Ed. ",
"956 (1922); Escobedo, 623 F.2d at 1102. ",
"See also Ntakirutimana v. Reno, 184 F.3d 419, 427 (5th Cir.1999).",
"\nMedina is charged with Aggravated Homicide, which the governing Jalisco criminal law defines in relevant part as follows:\nArticle 219. ",
"Bodily injuries and homicide are aggravated:\n1. ",
" When they are committed with premeditation, unfair advantage, treachery, or betrayal.",
"\nPremeditation exists when the perpetrator decides to commit a future crime, and chooses the means to do so.",
"\nUnfair advantage exists:\na). ",
" When the offender is obviously more skillful or stronger than the victim or when the victim is unarmed.",
"\nb). ",
" When the defendant is stronger due to the weapons he uses, to his greater skill in the handling of these weapons or due to the number of persons who accompany him.",
"\nc). ",
" When the defendant by any means, weakens the victim's defenses.",
"\nd). ",
" When the victim is defenseless or fallen and the offender is armed or on his feet; and\ne). ",
" When, due to any circumstances, the offender is in no danger of being killed or harmed by the victim when the offender is perpetrating the crime.",
"\nTreachery exists when someone is intentionally surprised, or abused by another.",
"\nBetrayal exists when there is breach of the trust or of the protection that had been promised either expressly or tacitly to the victim due to kinship, gratitude, friendship, employment relationship or any other circumstance that may inspire trust.",
"\nC.P. JALISCO art. ",
"219. (",
"Gov't Ex. ",
"2, Tab 19).",
"\nIn support of the request for Medina's extradition, the Government has submitted documentation that the Office of Attorney General for the State of Jalisco received a report on June 24, 2000 that Jose Diaz Limon had been shot and killed in the village of Las Papas. ",
"The report named Medina as the perpetrator. (",
"Gov't Ex. ",
"2, Tab 1). ",
"An investigation was initiated, including a review of the crime scene, an autopsy, and interviews with witnesses. (",
"Gov't Ex. ",
"2, Tabs 2-16). ",
"The deceased's father, Encarnacion Diaz, gave a statement that he was outside on the morning of the murder and had seen his son walking towards the bean fields. ",
"Upon hearing three or four gunshots, Diaz hurried towards the fields and found his son lying on the ground. ",
"Diaz also saw Serapio Medina running across the fields. (",
"Gov't Ex. ",
"2, Tab 4). ",
"Diaz stated that Serapio Medina had previously threatened to kill Limon over a land dispute and had blocked the road to deny the family access to the disputed property.",
"\nIn addition, Limon's mother and wife provided statements. ",
"Limon's mother, Maria Martinez, had seen Serapio Medina and his cousin early in the morning. (",
"Gov't Ex. ",
"2, Tab 4). ",
"A while later, her husband came home and told her that Medina had shot their son. ",
"Martinez checked on her son, who was not breathing, and saw Medina's cousin hiding nearby. ",
"Limon's common-law wife, Reyna Vazquez Ozuna, also testified that she had seen Medina and his cousin driving a herd of cattle across her husband's property that morning. (",
"Gov't Ex. ",
"2, Tab 5). ",
"Limon had left the house to check on his bean fields when Ozuna heard four shots. ",
"After learning that Limon was wounded, *818 Ozuna ran for help. ",
"She saw Medina driving a black pick-up truck at a high rate of speed. ",
"Ozuna stated that Medina was always armed and would show the gun to Limon and Ozuna whenever they passed by. (",
"Gov't Ex. ",
"2, Tab 5). ",
"In addition, Ozuna stated that her husband had received several death threats from Medina because his land bordered her husband's property.",
"\nMedina's brother-in-law, Martin Campos, was found at the crime scene and detained by police, but Medina could not be located. (",
"Gov't Ex. ",
"2, Tabs 1, 4). ",
"Campos testified that he was driving some cattle with Medina when Medina had to stop and open a gate. ",
"Limon approached and greeted Campos, but then turned to Medina and stated he was there to make Medina \"pay for the blows the police gave me because of you.\" (",
"Gov't Ex. ",
"2, Tab 11). ",
"Campos had turned his back on the men to tend to the cattle when he heard four gun shots. ",
"He saw Limon lying on the ground and Medina running away with a gun in his right hand. ",
"Campos did not see a firearm near Limon, and asserted he had been unaware that Medina was armed.",
"\nMedina's nephew Alonso Diaz was also taken into custody after he was identified as a person who drove Medina's wife and children into town after the shooting. ",
"Alonso Diaz stated that he gave them a ride because his mother had asked him to. ",
"His aunt and cousins were nervous and upset, but he did not know why and did not learn about the shooting until later that day. (",
"Gov't Ex. ",
"2, Tab 7).",
"\nThe prosecutor for Lagos de Moreno in the State of Jalisco petitioned for issuance of an arrest warrant for Medina for the commission of an aggravated homicide. (",
"Gov't Ex. ",
"2, Tab 17). ",
"An arrest warrant was issued on July 4, 2000 based on findings of premeditation because Medina was carrying a weapon, had a troubled history with the victim, and walked in an area where he would meet the victim; unfair advantage because Medina knew he was not in danger of being wounded or killed by his victim; and treachery because Medina took his victim by surprise. (",
"Gov't Ex. ",
"2, Tab 17).",
"\nMedina complains that the Mexican authorities have suppressed evidence and that the evidence does not support the aggravated offense with which he is charged. ",
"At the extradition hearing, Medina's son, Samuel Diaz, testified to a long-running family feud, which has included threats and poisoning livestock, over the rightful ownership of some property in Jalisco. ",
"Samuel Diaz also testified about Limon's violent tendencies and suspected drug trafficking activities. (",
"Extradition Hr'g at 9-12, 15). ",
"In addition, Medina has submitted the results of forensics tests performed in June 2000 on the right hand of Jose Diaz Limon and the left hand of Martin Campos. ",
"The tests were positive for residue indicating that both men had discharged a firearm. (",
"Def.",
"Ex.1). ",
"Medina complains that the Jalisco prosecutor, although he had a copy of this forensics report, did not include it in the information he submitted to obtain an arrest warrant. ",
"No ballistics tests have been provided to confirm the type of bullets removed from Limon's body or the caliber of the murder weapon. (",
"Extradition Hr'g at 56).",
"\nMedina also presents testimony from an expert witness who disputes the existence of premeditation because Limon was on Medina's property when he was shot and because Martin Campos' statements indicate that Limon actually approached Medina. (",
"Extradition Hr'g at 52-53). ",
"Medina's counsel also pointed out that during his initial interview Campos indicated that Limon shot at Medina, who pulled out his own gun. (",
"Gov't Ex. ",
"2, Tab 2; Extradition Hr'g at 54-55). ",
"Campos later provided statements contradicting his initial statement, *819 and asserted that his back was turned, that he was some distance from the other men, and that he did not see Limon with a weapon.",
"\nThe scope of the extradition hearing is circumscribed by a distinction between explanatory and contradictory evidence. ",
"Mainero, 990 F.Supp. ",
"at 1216. ",
"The accused may introduce evidence explaining or negating the existence of probable cause, but evidence related solely to a defense is properly excluded. ",
"Collins, 259 U.S. at 316, 42 S.Ct. ",
"at 472; Mainero, 990 F.Supp. ",
"at 1218. ",
"See also Stuart, Treaty Traps, 6-WTR CRIM.JUST. ",
"at 29. ",
"Matters of defense are not appropriate or relevant because the function of the hearing judge is to determine only whether there is competent evidence to justify holding the accused for trial, not whether the evidence is sufficient to sustain a conviction. ",
"Collins, 259 U.S. at 316, 42 S.Ct. ",
"at 472; Jimenez v. Aristeguieta, 311 F.2d 547, 556 (5th Cir.1962); Mainero, 990 F.Supp. ",
"at 1216; Prushinowski, 574 F.Supp. ",
"at 1446. ",
"See also Fernandez v. Phillips, 268 U.S. 311, 312, 45 S.Ct. ",
"541, 542, 69 L.Ed. ",
"970 (1925) (observing that competent evidence of reasonable grounds is not necessarily evidence competent to convict).",
"\nOther courts have likewise rejected complaints about the appropriateness of a particular charge, finding that a court does not have authority to alter prosecutorial choice during extradition proceedings, regardless of motives behind a particular selection, except to evaluate the charge for probable cause and dual criminality. ",
"Prushinowski, 574 F.Supp. ",
"at 1445-46. ",
"Objections in this vein are more legitimately matters of defense and not relevant to extradition proceedings. ",
"Id. at 1446.",
"\nMedina also contends that extradition is inappropriate because the evidence does not establish premeditation and unfair advantage and treachery, and that all three elements being in the arrest warrant must be shown. ",
"In support of this proposition, Medina adduced expert testimony to this effect at the hearing and later provided an affidavit from his expert witness affirming that all of the elements set out in the arrest warrant must be established. ",
"The Court notes that, at the extradition hearing, the court and counsel for the parties proceeded on the assumption that the offense of aggravated homicide required a probable cause showing as to all three of the foregoing elements. ",
"The court's comments on the record at the conclusion of that hearing reflect as much, indicating that because the court did not find sufficient evidence to establish the elements of unfair advantage and treachery, that the court did not believe that aggravated homicide had been shown. ",
"The court did indicate at the hearing that there was clear evidence of homicide and that there was probably evidence of premeditation.",
"\nHowever, the Mexican government, by and through the United States Attorney, has subsequently provided Mexican Supreme Court authority that the offense of aggravated homicide may be proved in the disjunctive and that any statements in the arrest warrant that suggest a conjunctive relationship among the elements are not binding on the prosecution. (",
"Gov't Supp. ",
"Mem.). ",
"See also Greene v. United States, 154 F. 401, 406 (5th Cir.1907) (noting that technical niceties will not defeat extradition or conviction). ",
"The statute on its face likewise reads in the disjunctive. ",
"See C.P. JALISCO art. ",
"219. (",
"Gov't Ex. ",
"2, Tab 19). ",
"This is also the most logical interpretation and application of Mexican law.",
"\nThere is probable cause to believe that the offense of aggravated homicide (with premeditation) occurred as that offense is defined under the relevant penal laws of the Mexican State of Jalisco, and there is probable cause to believe that *820 Medina was the perpetrator of that offense.",
"\n\n4. ",
"Rule of Speciality\nMedina, in asserting that he has been overcharged, also contends that he cannot be extradited on a lesser included offense not alleged in the charging instrument. ",
"The Government had suggested such a possibility during previous proceedings before the court.",
"\nIt is a longstanding practice and rule of extradition that a party shall not be delivered up by the government to be tried for any other offense than that charged in the extradition proceedings. ",
"United States v. Rauscher, 119 U.S. 407, 424, 7 S.Ct. ",
"234, 243, 30 L.Ed. ",
"425 (1886), cited in United States v. Alvarez-Machain, 504 U.S. 655, 112 S.Ct. ",
"2188, 119 L.Ed.2d 441 (1992). ",
"See also Greene v. United States, 154 F. 401, 404 (5th Cir.1907); Lahoria, 932 F.Supp. ",
"at 820; Prushinowski, 574 F.Supp. ",
"at 1446. ",
"Known as \"the rule of speciality,\" the doctrine has also been incorporated into the treaty between the United States and Mexico:\nA person extradited under the present Treaty shall not be detained, tried or punished in the territory of the requesting Party for an offense other than that for which extradition has been granted.[3]\nExtradition Treaty, art. ",
"17, para. ",
"1, 31 U.S.T. 5059. ",
"Medina thus argues there is no authority for extraditing him on a lesser or uncharged offense rather than the specific offense on which the request for extradition was based.",
"\nThe Government no longer advocates extraditing Medina on a lesser offense. ",
"Moreover, probable cause exists to support the charged offense of aggravated homicide. ",
"The issue of extradition for a lesser included offense has become purely an academic exercise and need not be determined in the present proceedings.",
"\n\n5. ",
"Extradition Defenses and Other Considerations\nThe Extradition Treaty also provides for certain defenses to extradition, including a refusal to extradite a person for purely political or purely military offenses, or when barred by a statute of limitations, or certain capital offenses. ",
"Extradition Treaty, arts. ",
"5-9, 31 U.S.T. 5059. ",
"Medina does not assert any of these defenses to extradition, nor does a review of the record suggest that these defenses are relevant to Medina's circumstances.",
"\nMedina does make a number of arguments about overreaching and abuse of process by the prosecuting authorities in Mexico. ",
"The duty to certify falls upon the extraditing judge, while the ultimate decision on extradition is the prerogative of the Secretary of State. ",
"In re United States, 713 F.2d at 109. ",
"Escobedo, 623 F.2d at 1106 (power to conduct foreign affairs). ",
"Assuming a judge has found in favor of extradition, the Secretary's discretionary decision is not generally subject to judicial review. ",
"Escobedo, 623 F.2d at 1105-06. ",
"And humanitarian concerns, i.e., risks of death, lack of due process in requesting state, etc., ",
"are all issues for the executive branch to determine. ",
"Escobedo, 623 F.2d at 1107; Mainero, 990 F.Supp. ",
"at 1229-30; Freedman v. United States, 437 F.Supp. ",
"1252, 1267 (N.D.Ga.1977).",
"\n\nD. CONCLUSION\nBased on the foregoing, the Court enters the following findings:\n1. ",
"The undersigned has subject matter jurisdiction and the authority to *821 hear these proceedings pursuant to 18 U.S.C. § 3184, and has personal jurisdiction over Respondent Serapio Medina.",
"\n2. ",
"A valid extradition treaty between the United States and Mexico has been in full force and effect at all times relevant to the present proceedings.",
"\n3. ",
"The requesting country has made a proper request through diplomatic channels invoking its rights under the extradition treaty.",
"\n4. ",
"Respondent Serapio Medina is the individual charged and sought by Mexican officials for the offense of aggravated homicide.",
"\n5. ",
"The charged offense of aggravated homicide is an extraditable offense under the terms of the extradition treaty between the United States and Mexico.",
"\n6. ",
"Probable cause exists to believe that an aggravated homicide occurred, and that Respondent Medina committed the offense of aggravated homicide for which he is charged and for which his extradition is sought.",
"\n7. ",
"The extradition request and exhibits from both the Government and Respondent were admitted into evidence during the hearing, and post-hearing briefs and submissions have been properly authenticated and admitted into evidence and as part of the record under the discretion of the Court.",
"\nIt is ORDERED that the request by the United Mexican States for extradition of Serapio Diaz Medina is GRANTED. ",
"This ruling will be certified to the Secretary of State, together with a copy of all evidence received in this proceeding, so that a warrant may issue upon the requisition of the proper authorities of the United Mexican States for the surrender of Serapio Diaz Medina according to the stipulations of the extradition treaty. ",
"This court shall also issue a warrant for the commitment of Medina, to be held until surrender to the proper authorities can be made.",
"\nIt is ORDERED that the United States Attorney shall prepare a certification consistent with this memorandum opinion and 18 U.S.C. § 3184 and submit an original and one copy of that certification to the Court within seven (7) days from the date of this opinion and order.[4]\nIt is further ORDERED that the Clerk of Court shall certify a copy of the transcript of the extradition hearing held May 30, 2002, to be forwarded, along with all documents filed in this matter, to the Secretary of State in the matter of the extradition of Serapio Diaz Medina.",
"\nNOTES\n[1] This case was initially filed under a Criminal Action Number, 4:02-CR-014-Y, but that action has since been closed and the case transferred to the docket of the United States Magistrate Judge as consistent with 18 U.S.C. § 3184.",
"\n[2] Dual criminality is generally measured by comparing the charged offense to conduct proscribed by federal law, the law of the asylum state, or the laws of a preponderance of states. ",
"In re Extradition of Prushinowski, 574 F.Supp. ",
"1439, 1446 (E.D.N.C.1983).",
"\n[3] The Treaty also provides limited exceptions to this rule. ",
"See Extradition Treaty, art. ",
"17, 31 U.S.T. 5059.",
"\n[4] The United States Attorney shall deliver one courtesy copy of the proposed certification order directly to the chambers of the United States Magistrate Judge.",
"\n"
] | {
"pile_set_name": "FreeLaw"
} | [
0,
0,
0,
0.0005039052658100277,
0,
0.00013157317661506075,
0.00021003990758244068,
0.00001992984693877551,
0,
0.00001962310555268477,
0.000022249911000355996,
0,
0,
0,
0,
0,
0,
0,
0.00008734387282732115,
0.01,
0,
0,
0,
0.00005250997689561017,
0,
0.00018491124260355032,
0,
0,
0,
0,
0,
0,
0,
0,
0.0003305785123966942,
0,
0,
0,
0,
0.01,
0,
0,
0,
0,
0,
0,
0.000005141890467449262,
0,
0,
0,
0.00009611687812379854,
0,
0,
0,
0.00008116224332440549,
0,
0,
0,
0,
0,
0.0004,
0,
0,
0.002770083102493075,
0,
0,
0,
0.0012755102040816326,
0,
0.000042165626581211,
0,
0,
0,
0,
0.000062000124000248,
0,
0.00005175715542673775,
0.000017301038062283735,
0,
0,
0,
0,
0,
0.0009765625,
0,
0.0003429355281207133,
0,
0.000625,
0.0002366863905325444,
0.00005406574394463668,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.01,
0,
0.000028054819116553746,
0,
0.01,
0,
0,
0.01,
0,
0.000038578758535550326,
0.00008573388203017832,
0.0003077870113881194,
0.01,
0,
0.00010629251700680272,
0.0002872737719046251,
0.00033952014486192844,
0.01,
0,
0,
0.00012075836251660429,
0.00006839711364180432,
0.01,
0,
0.000148720999405116,
0.00048828125,
0,
0.00008264462809917355,
0.01,
0,
0.00005175715542673775,
0.00006103515625,
0.01,
0,
0.00009611687812379854,
0.0000801153661272232,
0.01,
0,
0.0001234567901234568,
0.0001321178491214163,
0.00021701388888888888,
0.0000390625,
0.00015241579027587258,
0,
0.01,
0,
0,
0.01,
0,
0,
0.01,
0,
0.0000390625,
0.000023795359904818562,
0.00018491124260355032,
0,
0.00007715751707110065,
0,
0,
0,
0,
0.000055691690799732676,
0,
0.00006830134553650708,
0,
0.0001005985614405714,
0.01,
0,
0.00004805843906189927,
0,
0,
0,
0,
0,
0,
0,
0.0008680555555555555,
0,
0,
0,
0.00012913223140495868,
0.0008163265306122448,
0,
0.0002777777777777778,
0,
0,
0,
0,
0,
0,
0,
0.00002047460125714052,
0,
0.000018419937740610438,
0,
0,
0.000008163265306122448,
0.006944444444444444,
0,
0.0000502992807202857,
0,
0,
0,
0.01,
0,
0,
0.000012056327160493826,
0,
0,
0,
0,
0.0003429355281207133,
0,
0.0001602307322544464,
0,
0.0001321178491214163,
0.0008650519031141869,
0,
0.000007934933544931562,
0,
0,
0,
0,
0,
0,
0,
0.000024622960911049555,
0,
0,
0,
0,
0.000048902146804244705,
0.0006925207756232687,
0.00025195263290501383,
0,
0.0020811654526534857,
0,
0,
0.0004164931278633902,
0.00038446751249519417,
0,
0.0001417233560090703,
0.000028293345405160706,
0,
0,
0,
0,
0,
0.00006609822195782934,
0,
0,
0,
0,
0,
0.000012311480455524777,
0.00015943877551020407,
0.00001893491124260355,
0,
0.000013127494223902542,
0,
0,
0,
0.0014792899408284025,
0.000244140625,
0,
0,
0,
0
] | 0.00069 | 5 |
[
"Running, jogging and triathlons are in. ",
"Football, paintball and horseback riding are out. ",
"So are sports that can be enjoyed with a beer — or three.",
"\n\nThat’s the quick take on the latest survey from the Sport & Fitness Industry Association, released Monday. ",
"The group — a partnership of six industry associations — fielded nearly 20,000 surveys in January and February, asking Americans (both individuals and households) about their physical activity last year. ",
"Overall activity was flat, a turnaround from declines in recent years.",
"\n\nIndividual sports and activities, though, showed bigger changes, some of them dramatic. ",
"The number of people who participated at least once in adventure racing or a traditional triathlon increased by more than 25 percent last year compared with the year before. ",
"Meanwhile, nonmotorized scooter-riding and non-inline roller skating experienced big declines.",
"\n\nEven with such a big sample, year-by-year changes in individual sports may not mean much. ",
"I limited the analysis to activities with an estimate of at least 2 million participants last year, but that still means a change of 10 percent could be a difference of just a dozen or so respondents. ",
"And that’s when looking at total participants. ",
"The group also reports more regular participants, but that means an even smaller sample size. (",
"Also, as I noted when writing about this survey in a recent piece, the survey is fielded only in English, which could skew results for activities that are unusually popular or unpopular among U.S. residents who are less comfortable speaking to strangers in English.)",
"\n\nWe get a more reliable picture when looking at five-year trends.",
"\n\nTriathlon and adventure racing still top the gainers list. ",
"Kayaking, trail running and yoga are other solitary or noncompetitive endeavors increasing in popularity. ",
"Meanwhile, activities popular in bars or in other venues where beer often is sold — including pool, darts and bowling — are losing ground. ",
"So are all varieties of football — though touch football sustained the biggest percentage decline, suggesting concussion fears aren’t solely to blame.",
"\n\nTo sum up: We’re bowling alone — or together — less often, but running, paddling or posing more."
] | {
"pile_set_name": "OpenWebText2"
} | [
0,
0,
0,
0.00008416799932665601,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0.000004 | 5 |
[
"Q:\n\nInsert a picture into existing excel file\n\ni'm new to vb.net, and i want to open an existing excel file, and insert an image to a specific cell, such as 'C16' for exemple.",
"\nIt's been three days and i'm searching about this topic, but what i found was just creating a new excel file and insert a picture to it.",
"\nAnybody can help?",
"\n\nA:\n\nI've already found a solution:\nplease find it below\n workbook = APP.Workbooks.",
"Open(filepath)\n worksheet = workbook.",
"Worksheets(\"name of the excel sheet\")\n\n worksheet.",
"Visible = True\n Dim pic1 As String = \"picture path\"\n worksheet.",
"Range(\"I51:I51\").Select() \n\nI51 is the cell where i want my picture\n worksheet.",
"PageSetup.",
"Zoom = False\n worksheet.",
"PageSetup.",
"FitToPagesWide = 1\n worksheet.",
"PageSetup.",
"FitToPagesTall = 1\n Dim opicture1 As Object\n opicture1 = worksheet.",
"Pictures.",
"Insert(pic1)\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0.00003265306122448979,
0,
0,
0.00009425959091337542,
0,
0,
0,
0,
0.01,
0,
0.01,
0,
0.01,
0,
0,
0
] | 0.001883 | 5 |
[
"The best idea of KETER NOVEL Grey Bk STORAGE BOX $179 00 LANDERA Outdoor that can be used can be utilized as while seeing that a reference. ",
"Also see observe discover find some creative innovative ideas about pool storage box"
] | {
"pile_set_name": "Pile-CC"
} | [
0.0001020408163265306,
0
] | 0.000051 | 5 |
[
"Sunil Ambekar, national organising secretary of the RSS’s student wing ABVP. ",
"Sunil Ambekar, national organising secretary of the RSS’s student wing ABVP.",
"\n\nIn the backdrop of a pending data protection Bill that mandates increased data localisation, Sunil Ambekar, the national organising secretary of the RSS’s student wing ABVP, cautioned against the global “war on data” and encouraged citizens to embrace the “concept of external sovereignty that was established in Hindu philosophy”.",
"\n\nAmbekar was the keynote speaker at the Constitution Club for the launch of the book Data Sovereignty: The Pursuit of Supremacy, authored by Vinit Goenka — BJP’s IT Cell co-convener in 2014, who now works on IT solutions for Indian Railways — and co-authored by Lt Gen Vinod Kandare, who was the director of the General Defense Intelligence Agency, and other security and technology officials.",
"\n\nHe said, “Military attacks we can understand easily. ",
"But the silent proxy war on data is more difficult to understand. ",
"Similarly, the Naxal war and Naxalites we can understand but urban naxals are more difficult to understand… They say that they make the whole world a small village … but the power to attack has grown.”",
"\n\nHe said that centuries of foreign rule in India has taken away the country’s sovereignty and “pursuit of supremacy”, and the next frontier of this competition is over data.",
"\n\n“Chanakya said that until paradeentha (dependency) is not over, swaraja pura nahin hota hain (self-governance is not complete),” he told The Indian Express. “",
"Because of thousands of years of foreign rule, we have lost that pursuit of supremacy. ",
"We have thought that they are taking the data, no problem… We need to protect our borders and the same way we need to protect our data.”",
"\n\nMeanwhile, Vinit Goenka said that India missed the latest industrial revolution because the country was “a victim of external aggression”, and that external companies are again seeking the information of Indians.",
"\n\n📣 The Indian Express is now on Telegram. ",
"Click here to join our channel (@indianexpress) and stay updated with the latest headlines\n\nFor all the latest India News, download Indian Express App."
] | {
"pile_set_name": "OpenWebText2"
} | [
0.000337325012649688,
0.00034626038781163435,
0.00002705408110813516,
0.000045092633152103895,
0,
0,
0,
0,
0,
0,
0,
0.00002183596820683029,
0.0005408328826392645,
0.00013157317661506075
] | 0.000104 | 5 |
[
"theendusa Golf Equipment & Gear\n\nClub Grips\n\nBest Golf Club Grips 2016\n\nTag Archived of Best Club Grips 2018\n\nDiy Golf Net\n\n“The Ping-Pong stories everybody’s heard? ",
"All pretty much true. ",
"He’s really good and really competitive. ",
"But my favorite Phil story was probably last year in Boston. ",
"I was playing with Phil and Ian Poulter and none of us were hitting it really good but we were all getting it up and down a good bit.",
"\n\nCallaway Golf Shirts Clearance\n\nI was able to get him on the phone as we came off the course and Phil spoke with him for about 15 minutes. ",
"They chatted as if they were longtime friends talking about Phil’s strategy for the upcoming Tour events and where the exec liked to play golf.",
"\n\nYamaha G14 Golf Cart\n\nAnd he comes in and says ‘Hey mind if I sit with you?’ ",
"Yeah of course you know? ",
"So we’re talking and he’s talking about chipping and he says ‘It’s mind-boggling how many guys out here don’t know how to chip.’ [] ",
"And I’m sitting there thinking like Oh boy.",
"\n\n8x42 Binoculars\n\n“Walking to dinner with Phil one evening in Scotland a group of gentlemen came toward us and one of them shouted ‘Hey Phil remember me? ",
"I’m…’ — let’s just call him Charlie Golfer. ‘",
"We shook hands the last time the Open Championship was here.’",
"\n\nLeupold Rx 850i\n\n“Working at Callaway allowed me to get to know two icons of the game Arnold Palmer and Phil Mickelson. ",
"Phil has what Arnold had a certain swagger plus a twinkle in the eye. ",
"But the biggest thing is how much Phil loves golf. ",
"Arnold was the same way.",
"\n\nM24 Binoculars\n\nAs the pros roll into Carnoustie are you team Tiger or pro-Phil? ",
"Do you like Justin Thomas or Jordan Spieth? ",
"Will Carnoustie once again be Car-nasty? ",
"Correct answers to those questions could help you win a custom set of Wilson Staff FG Tour Raw V6 Irons.",
"\n\nBest Public Golf Courses In Nj\n\nI thought Well at least he can have a day off be inside warm and dry. ",
"The next thing I heard was that Phil and Keegan Bradley were playing on that Saturday at Phil’s home course The Bridges in a cold rain. ",
"As I heard it Phil took him. ",
"He seems to come out on top a lot. ",
"But the point really is that Phil has to play. ",
"Golf is in Phil’s blood.”",
"\n\nCourses\n\nMorris Courses Southern Top Monmouth Ocean South Public County Essex Princeton Best Golf\n\nCourses Monmouth Essex Ocean Public Princeton Top Rated Best Southern South Morris County\n\nMorris Courses Best Ocean Golf Top Public Southern Princeton Essex Rated South Monmouth\n\nSmall Binoculars\n\n“The Ping-Pong stories everybody’s heard? ",
"All pretty much true. ",
"He’s really good and really competitive. ",
"But my favorite Phil story was probably last year in Boston. ",
"I was playing with Phil and Ian Poulter and none of us were hitting it really good but we were all getting it up and down a good bit.",
"\n\nGolf Long Sleeve\n\nAs things transpired Europe played very well that year and we won. ",
"The ritual at the opening and closing ceremonies is for two players — a Euro and an American — to enter side by side with their wives or partners to the outside to them. ",
"Obviously that week I didn’t have a partner.",
"\n\nBreaking 80 Rangefinder\n\nI thought Well at least he can have a day off be inside warm and dry. ",
"The next thing I heard was that Phil and Keegan Bradley were playing on that Saturday at Phil’s home course The Bridges in a cold rain. ",
"As I heard it Phil took him. ",
"He seems to come out on top a lot. ",
"But the point really is that Phil has to play. ",
"Golf is in Phil’s blood.”",
"\n\nBlurry Rangefinder Medium Film Laser App Hunting Golf Came Time Digital Arche All Small Coupon Format Breaking Instructions Watch Canon Reddit For Leica Under Best Shooting\n\nPga Superstore Golf Shoes\n\n“I have a Phil story from Muirfield Village at the 2013 Presidents Cup. ",
"We were doing really well playing alternate shot and we were dormie 6 up with whatever left to play. ",
"And I had about a 5-foot putt on 13 to win the match — and it 360ed the hole. ",
"Lipped out."
] | {
"pile_set_name": "Pile-CC"
} | [
0.000036289737262302225,
0,
0,
0.0002687449610319807,
0.00011306461642828876,
0.0000502992807202857,
0.000048902146804244705,
0,
0,
0,
0,
0.00008324661810613944,
0.0004938271604938272,
0,
0.00013437248051599034,
0.0004081632653061224,
0.00038446751249519417,
0.001736111111111111,
0.0001451589490492089,
0.0010330578512396695,
0,
0.00009245562130177516,
0,
0.00016219723183391005,
0.0011890606420927466,
0,
0.0004526935264825713,
0,
0,
0,
0,
0.0002687449610319807,
0.00011306461642828876,
0,
0,
0,
0,
0.00016219723183391005,
0.0011890606420927466,
0,
0.0004526935264825713,
0,
0.000026446280991735536,
0,
0,
0
] | 0.000197 | 5 |
[
"During his seven-figure campaign, Artiles put in expenditures for fundraisers at the Kentucky Derby and a fishing trip to Key West, according to the Tampa Bay Times. ",
"Overall he spent at least $80,000 on fundraisers that included $51,000 in reimbursements to himself."
] | {
"pile_set_name": "OpenWebText2"
} | [
0.000036289737262302225,
0
] | 0.000018 | 5 |
[
"Q:\n\nDo Chrome extensions support WebSpeech API?",
"\n\nDo google Chrome extensions support Chrome's Web Speech speech recognition API? ",
"I have included some javascript to create a speech recognition object, but when I launch my extension, I am not prompted for microphone access.",
"\nThis is not an issue with my code. ",
"I have searched on google, but I can't find any information on whether Chrome extensions support the Web Speech API. ",
"I just want a yes/no answer.",
"\nNote: I believe the WebSpeech API won't work for local files.",
"\n\nA:\n\nThe Web Speech API can already be used by Chrome extensions, even in the background page and extension button popups. ",
"The fact that it works is not necessarily an intended feature, and I have previously explained how it works and why it works in this answer to How to use webrtc insde google chrome extension?. ",
"The previous explanation is about WebRTC, but it applies equally to Web Speech, and can be used as follows:\n\nInstantiate a webkitSpeechRecognition instance and start recording.",
"\nIf a permission error is detected (onerror being triggered with event.error === 'not-allowed'), open an extension page (chrome-extension://[ID]/yourpage.html). ",
"This extension page can be opened in a new window, tab or iframe.",
"\nFrom this page, request access to the microphone. ",
"getUserMedia and SpeechRecognition both share the (persistent) audio permission, so to detect whether audio recording is allowed, you could use getUserMedia to request the permission without activating speech recognition. ",
"For instance:\nnavigator.webkitGetUserMedia({\n audio: true,\n}, function(stream) {\n stream.stop();\n // Now you know that you have audio permission. ",
"Do whatever you want...\n}, function() {\n // Aw. ",
"No permission (or no microphone available).",
"\n});\n\nA:\n\nUpdate: Based on RobW's answer, this answer is now out of date, and the Web Speech API is now usable inside of extensions. (",
"Unfortunately, I can't delete this answer unless the OP un-accepts it.)",
"\n\nThe answer is not yet. ",
"Pages accessed through chrome-extension: URLs cannot access any media-input APIs, including speechRecognition and getUserMedia. ",
"Any attempt to the use APIs will immediately trigger an error callback.",
"\nI originally thought speechRecognition could work like the geolocation API: extension popups cannot prompt for geolocation permission, but chrome-extension: pages loaded as full browser pages can prompt for permission just like a normal page. ",
"However, media APIs do not behave this way; they fail regardless of whether the page is a popup or a full page.",
"\nThere is a bug report to fix this and allow developers to specify media-access permissions in the manifest. ",
"When this bug is fixed, extensions can have a manifest-set permission that grants them automatic microphone/video access, so the inability to prompt for permission will become a non-issue (and therefore extensions with appropriate manifest permissions will be able to freely use the Speech API).",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0.0004526935264825713,
0.000446162998215348,
0,
0,
0.00007305135510263716,
0,
0,
0.00006503642039542143,
0,
0.00003228305785123967,
0,
0,
0,
0.00002029056083110137,
0,
0,
0,
0.000055691690799732676,
0.00019837333862328903,
0,
0,
0,
0.000016796560064498793,
0,
0,
0,
0
] | 0.00005 | 5 |
[
"The excursion length of posterior cruciate ligament during range of motion in prosthetic knee.",
"\nRestriction of knee motion after total knee replacement was noted to be associated with lengthening of the posterior cruciate ligament during flexion of the knee which was replaced with a cruciate retaining knee prosthesis. ",
"The purpose of this study was to measure the excursion length of the PCL in the normal knee in four different cruciate-retaining knee prostheses, and in five cadaveric knees which were replaced with the Tricon prosthesis. ",
"For every knee, the tibial part was fixed on a stand and the femoral part was allowed to do flexion-extension motion upon the tibial plateau. ",
"The angle of the motion was monitored by the self-readout goniometer. ",
"A thin wire cord was attached to the proposed origin site of the PCL on the femur. ",
"The wire cord was passed through a tiny hook which was attached to the proposed insertion site of the PCL on the tibia and connected to a dial gauge. ",
"The excursion length of the PCL during 90 degrees flexion was measured. ",
"The same measurement was repeated five times in each cadaver knee and prosthetic knee studied, and in five knee specimens which were replaced with the Tricon prosthesis. ",
"The excursion length of the PCL during 0 degrees to 90 degrees of flexion in five cadaver knees averaged 0.08cm of lengthening. ",
"Three different origin sites of the ligament were designated to represent the anterior, middle and posterior part of the ligament.(ABSTRACT TRUNCATED AT 250 WORDS)"
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0,
0,
0.00002029056083110137,
0,
0,
0.0001451589490492089,
0.000044444444444444447,
0.00019290123456790122,
0,
0.00006103515625,
0
] | 0.000042 | 5 |
[
"Vandals spraypainted the Freedom Rock at the Cedar Falls Veterans Park in Iowa late Saturday night.",
"\n\nIt almost looks like Arabic writing.",
"\n\nPolice say they’re investigating to find out who vandalized the freedom rock in Cedar Falls last night @KWWL pic.twitter.com/MWFdRSTWx1\n\n\n\nThe WCF Courier reported:\n\nThe Freedom Rock, recently installed at the Cedar Falls Veterans Park on Waterloo Road was vandalized during Saturday evening.",
"\n\nTRENDING: Black Lives Matter Activist Wearing 'Justice for Breonna Taylor' Shirt Walked into a Louisville Bar and Murdered Three People\n\nTom Hagarty, commander of the Cedar Falls American Legion No. ",
"237, said the rock was spray painted. ",
"Other areas of the park were also damaged by spray paint, he said.",
"\n\nThe vandalism is on the side of the rock with Taylor Morris’ drawing. ",
"A neighbor’s fence on nearby Bluff Street was also sprayed as was a utility box near the park.",
"\n\nThe vandalism was discovered Sunday morning.",
"\n\nPolice and park officials have been notified and the investigation continues. ",
"Hagarty said Sunday that the parks department will coordinate the cleanup. ",
"A Memorial Day ceremony at the park Sunday night was to go on as planned.",
"\n\nThe rock includes images of the Five Sullivan Brothers killed in World War II, Medal of Honor winner Robert Hibbs of Cedar Falls, a U.S. Army second lieutenant killed in Vietnam in 1966, and Taylor Morris, a U.S. Navy explosive ordnance disposal expert who survived a bomb blast in Afghanistan despite losing portions of all four limbs. ",
"It also bears an image of veterans and people of various generations saluting the flag."
] | {
"pile_set_name": "OpenWebText2"
} | [
0,
0,
0.00001156925355176084,
0.00007425558773297691,
0,
0,
0.00019290123456790122,
0,
0,
0,
0,
0,
0.000043508149076322,
0
] | 0.000023 | 5 |
[
"I want to give a normal user root access on my network but I don' t want to have to su in every time.",
"\nBut I don't know how.",
"\n\nI'm running RedHat 7 on my network. ",
"I tried using some program to do it but it didn't work.:confused: :confused:\n\nranger_nemo\n\n11-11-2004 08:56 AM\n\nsudo ? ",
"You add the user to the /etc/sudoers file, then stick \"sudo \" in front of any command you want to run. ",
"It will ask for the user's password, then run the command if the password is correct. ",
"It will \"remember\" the password for awhile, so if you have a couple commands to run, it won't ask every time.",
"\n\nIt's really a bad idea to run a computer for daily use with root permission."
] | {
"pile_set_name": "Pile-CC"
} | [
0.0000980296049406921,
0,
0,
0,
0,
0,
0,
0
] | 0.000012 | 5 |
[
"Q:\n\nExample of a symmetric manifold without rotation symmetry?",
"\n\nConsider a flat torus, in 2D. It has translation symmetry but not rotational symmetry.",
"\nAre there any manifolds that are not simply products like $S_1 \\times S_1$ that do not have rotational symmetry but have either translational or a combination of a translation plus a rotation in their symmetry?",
"\nEdit: In other words a symmetric manifold with no rigid symmetries in which one point is fixed. (",
"Would they all be flat?)",
"\nFor example what about the projective plane or, homology sphere? ",
"What symmetries do those have?",
"\n\nA:\n\nLet me try to interpret your question.",
"\nIt appears that for a Riemannian manifold $M$ a \"translation\" of $M$ is an isometry $\\phi: M\\to M$ which is either the identity or has no fixed points in $M$. Then to say that the isometry group of $M$ consists only of \"translations\" amounts to saying that the isometry group $Isom(M)$ of $M$ acts freely. (",
"The latter is the standard terminology.) ",
"\nBoring examples where $Isom(M)$ acts freely are when $Isom(M)$ is trivial, i.e. consists only of the identity element. ",
"One can prove that a \"generic\" Riemannian metric on a given manifold (of dimension $\\ge 2$) has trivial group of isometries. ",
"For instance, for (connected) surfaces $M$ this comes from the fact one can prescribe the Gaussian curvature of the Riemannian metric $M$ (subject to some sign conditions). ",
"See this wikipdeai article for details and references. ",
"\nA generic choice of such a function allows no (non-identity) diffeomorphisms $\\phi: M\\to M$ which preserve the function $K$ (i.e. $K\\circ \\phi=\\phi$). ",
"\nOne can promote this to more interesting examples where $Isom(M)$ is nontrivial but acts freely. ",
"For instance, start with the projective plane $P=RP^2$, choose a generic curvature function $K(x)>0$ on $P$ and take the corresponding Riemannian metric $g$. Now, lift $g$ to a metric $\\tilde{g}$ on the universal covering of $P$, which is $M\\sim S^2$. Then $(M, \\tilde{g})$ has a nontrivial isometry (order two involution $\\tau$ generating the deck-transformation group of the covering $M\\to P$). ",
"With a bit more work one verifies that $Isom(M,\\tilde{g})=\\langle\\tau\\rangle= \\{id, \\tau\\}$. Thus, $Isom(M,\\tilde{g})$ acts freely on $M$. \nOne can, however, ask for more, namely, that $M$ is homogeneous, i.e. the isometry group of $M$ acts freely and transitively (i.e. simply transitively). ",
"Such examples exist in dimension 3, they are called Berger spheres. ",
"Berger spheres are homogenous Riemannian manifolds diffeomorphic to $S^3$ (the 3-dimensional sphere). ",
"These manifolds come with some parameters. ",
" \nIn Theorem 4.1 in\nP. Gadea, J. Oubiña, Homogeneous Riemannian Structures on\nBerger 3-Spheres, Proceedings of the Edinburgh Mathematical Society, 48 (2005), no. ",
"2, 375–387. ",
"\nthe authors prove that for certain values of parameters of the Berger sphere $M$, its isometry group acts simply transitively on $M$. (The group is isomorphic to $SU(2)$.) \nThe manifolds in these examples are definitely not products and the metric is not flat. (",
"Actually, a sphere of dimension $\\ge 2$ admits no flat metric.) ",
"\nEdit. ",
"One more thing: In geometry a \"symmetric space\" (or a manifold) usually means something different from the header of your post, see here. ",
"To make it more confusing, in topology, a \"symmetric product\" means yet something else. ",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.000011413440467494522,
0.00021626297577854672,
0.00009611687812379854,
0,
0.00019051973784484072,
0,
0.000014457343607685523,
0,
0,
0,
0,
0
] | 0.000018 | 5 |
[
"Q:\n\nHide current element and show the next one\n\nI'm creating a ASP.NET application where shows you a quiz. ",
"This quiz should be show to the user displaying question by question.",
"\nI mean, appears the first question and when he press the button next, hide the current question element and show the next one until it has no elements to show.",
"\nBy the moment, I just have accomplish show all of them in MVC4. ",
"I really have not to much experience using JQuery.",
"\n<div id=\"questions-container\">\n <div class=\"question\">\n ...\n </div>\n <div class=\"question\">\n ...\n </div>\n <div class=\"question\">\n ...\n </div>\n <div class=\"question\">\n ...\n </div> \n</div>\n\nCan you orient about how can I implement this feature? ",
"Thanks\n\nA:\n\nDefault all questions to display: none;, show the first one when the page loads (or with another class .question.first that has display: block;, and then the next button can show the next question with:\n$(\"#questions-container\").find(\":visible\").hide().next().show();\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0,
0,
0,
0,
0
] | 0 | 5 |
[
"Q:\n\nMongoDB update: how to check if an update succeeds or fails?",
"\n\nI'm working with MongoDB in PHP using the pecl driver. ",
"My updates are working great, but I'd like to build some error checking into my function(s).",
"\nI've tried using lastError() in a pretty simple function:\nfunction system_db_update_object($query, $values, $database, $collection) {\n $connection = new Mongo();\n $collection = $connection->$database->$collection;\n $connection->$database->resetError(); //Added for debugging\n $collection->update(\n $query,\n array('$set' => $values));\n //$errorArray = $connection->$database->lastError();\n var_dump($connection->$database->lastError());exit; // Var dump and /Exit/\n}\n\nBut pretty much regardless of what I try to update (whether it exists or not) I get these same basic results:\narray(4) {\n [\"err\"]=>\n NULL\n [\"updatedExisting\"]=>\n bool(true)\n [\"n\"]=>\n float(1)\n [\"ok\"]=>\n float(1)\n}\n\nHow do I know if the update succeeds or failed?",
"\n\nA:\n\nthe \"n\" field is the number of documents that were updated, and \"updatedExisting\" tells whether any document was updated at all. ",
"you should be able to check those fields to see whether an update succeeded or not.",
"\n\nA:\n\nHow do you know what rows are affected with a MongoDB update?",
"\nAs with all write operations, getLastError command in MongoDB can confirm the result of the update's write operation, described here:\nhttp://docs.mongodb.org/manual/applications/update/\nThe getLastError command returns the error status of the last operation on the current connection. ",
"By default MongoDB does not provide a response to confirm the success or failure of a write operation, clients typically use getLastError in combination with write operations to ensure that the write succeeds.",
"\nhttp://docs.mongodb.org/manual/reference/command/getLastError/#getLastError\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0.0003077870113881194,
0,
0.0000016866250632484399,
0.00005486968449931413,
0,
0,
0.000012225536701061176,
0,
0.00016436554898093358
] | 0.000054 | 5 |
[
"The decision to garden in the winter is an easy one to make. ",
"It requires very little time, space and materials to grow tasty salad greens. ",
"While reading the seed catalogs, I came across growing shoots, specifically popcorn shoots. ",
"So, off to the local farm supply store I went. ",
"I snagged a bag of seed starting mix to start the process of growing shoots.",
"\n\nBesides the seed starting mix, all ingredients were on hand. ",
"The popcorn came from the kitchen pantry. ",
"There were leftover aluminum casserole trays with plastic covers from the holidays. ",
"I used an extra storage container to pre-soak the popcorn seeds for a few days.",
"\n\nThis is a great project to start over a very long snowy weekend. ",
"As for time to harvest, after the pre-soaking period, it takes 10 to 14 days to get shoots 2 to 4 inches long. ",
"The shoots are simply snipped off at the base when they have grown to the length you want. ",
"I plan to use them in stir fry dishes and salads of course.",
"\n\nThis is such an easy crop to grow, even in the winter!"
] | {
"pile_set_name": "OpenWebText2"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 | 5 |
[
"1. ",
"Technical Field\nThe present invention relates to a tape feeding apparatus which feeds a tape by a feeding roller and a tape printing apparatus.",
"\n2. ",
"Related Art\nIn the past, there has been known a tape feeding apparatus (printer) which feeds a tape (paper) by a feeding roller (platen) (for example, see JP-A-11-349197).",
"\nIn the known tape feeding apparatus, in case that an adhesive is adhered on a tape surface on which the feeding roller contacts to rotate or the tape tends to curl, there may arise a problem such that the feeding roller rolls up the tape. ",
"To avoid this problem, it is conceivable that a roller accommodation section is provided, which has a cylindrical accommodation section inner surface along with a roller outer circumferential surface of the feeding roller, accommodates the feeding roller in a gap formed between the roller outer circumferential surface and has a roller opening through which the accommodated feeding roller faces the tape. ",
"With such a structure, when the tape is wound on the feeding roller and the gap between the feeding roller and the roller accommodation section is filled up with the wound tape, the tape is not wound on the feeding roller anymore. ",
"Therefore, it is possible to avoid winding the tape in large quantity on the feeding roller. ",
"However, in this case, when both ends of the feeding roller are not opened because the feeding roller is supported at both ends or the like, the tape wound on the feeding roller should be pulled out from the roller opening, and thereby it is difficult to take out the wound tape around the feeding roller."
] | {
"pile_set_name": "USPTO Backgrounds"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 | 5 |
[
" of picking 2 x when two letters picked without replacement from gqxqgqgqgxggqqx.",
"\n1/35\nFour letters picked without replacement from {x: 11, p: 5}. ",
"What is prob of picking 3 x and 1 p?",
"\n165/364\nTwo letters picked without replacement from pmp. ",
"What is prob of picking 1 m and 1 p?",
"\n2/3\nTwo letters picked without replacement from {d: 2, e: 10, r: 1, f: 2, q: 1, o: 2}. ",
"Give prob of picking 1 e and 1 d.\n20/153\nCalculate prob of picking 1 l and 1 k when two letters picked without replacement from {z: 5, a: 3, w: 1, k: 2, l: 3, f: 1}.",
"\n2/35\nTwo letters picked without replacement from {m: 3, i: 5, v: 10, e: 2}. ",
"What is prob of picking 1 m and 1 i?",
"\n3/38\nWhat is prob of picking 1 v and 1 u when two letters picked without replacement from {i: 4, j: 3, w: 1, v: 4, u: 1}?",
"\n2/39\nFour letters picked without replacement from {h: 11, s: 1, k: 1, b: 1, q: 4}. ",
"Give prob of picking 1 h and 3 q.\n11/765\nFour letters picked without replacement from unngguebguuu. ",
"What is prob of picking 1 b, 1 n, and 2 g?",
"\n2/165\nCalculate prob of picking 1 d and 1 x when two letters picked without replacement from xxxjjjjjjdtd.",
"\n1/11\nTwo letters picked without replacement from omz. ",
"What is prob of picking 1 o and 1 z?",
"\n1/3\nCalculate prob of picking 1 k and 1 h when two letters picked without replacement from yhyhchkhyh.",
"\n1/9\nTwo letters picked without replacement from {b: 3, i: 4, q: 2}. ",
"What is prob of picking 1 i and 1 q?",
"\n2/9\nWhat is prob of picking 1 k and 2 w when three letters picked without replacement from kkwkkkwkkwkwkkkkkkk?",
"\n30/323\nTwo letters picked without replacement from xxvxxvvvxxvxx. ",
"What is prob of picking 1 x and 1 v?",
"\n20/39\nFour letters picked without replacement from tqqqqqtqttq. ",
"What is prob of picking 4 q?",
"\n7/66\nWhat is prob of picking 1 u, 1 a, and 1 t when three letters picked without replacement from {j: 1, u: 1, l: 2, a: 1, r: 1, t: 1}?",
"\n1/35\nWhat is prob of picking 1 k, 2 l, and 1 h when four letters picked without replacement from {l: 4, h: 4, s: 1, k: 1}?",
"\n4/35\nTwo letters picked without replacement from {r: 1, q: 2, a: 1}. ",
"What is prob of picking 2 q?",
"\n1/6\nCalculate prob of picking 1 h and 1 d when two letters picked without replacement from hhdddddhdd.",
"\n7/15\nFour letters picked without replacement from {d: 3, r: 7, i: 1, w: 1, q: 1}. ",
"What is prob of picking 1 d, 2 r, and 1 i?",
"\n63/715\nCalculate prob of picking 2 k when two letters picked without replacement from hkhkhkkk.",
"\n5/14\nWhat is prob of picking 1 u and 3 s when four letters picked without replacement from uuuuussussusu?",
"\n16/143\nFour letters picked without replacement from {q: 3, x: 5, v: 3, h: 1}. ",
"What is prob of picking 1 v, 2 x, and 1 h?",
"\n2/33\nTwo letters picked without replacement from wwikv. ",
"What is prob of picking 1 v and 1 w?",
"\n1/5\nTwo letters picked without replacement from aaooaoooaooaaa. ",
"Give prob of picking 2 a.\n3/13\nThree letters picked without replacement from dbdkddddkbddddddbd. ",
"What is prob of picking 2 k and 1 b?",
"\n1/272\nFour letters picked without replacement from aubbuauuabuubbuub. ",
"What is prob of picking 3 u and 1 a?",
"\n6/85\nFour letters picked without replacement from {w: 7, e: 5, n: 4}. ",
"What is prob of picking 4 w?",
"\n1/52\nTwo letters picked without replacement from gzoggggzzgzo. ",
"What is prob of picking 2 z?",
"\n1/11\nWhat is prob of picking 1 u and 1 p when two letters picked without replacement from {p: 5, f: 4, u: 3, l: 1}?",
"\n5/26\nCalculate prob of picking 3 s and 1 y when four letters picked without replacement from {y: 4, u: 1, s: 5, d: 8}.",
"\n2/153\nCalculate prob of picking 1 w and 3 s when four letters picked without replacement from {w: 1, s: 17}.",
"\n2/9\nTwo letters picked without replacement from {j: 1, s: 2, a: 1, r: 2, f: 1, g: 1}. ",
"Give prob of picking 1 r and 1 s.\n1/7\nCalculate prob of picking 1 i and 2 a when three letters picked without replacement from aiaaaiaiaiaiaaaaaai.",
"\n156/323\nWhat is prob of picking 1 j, 1 l, and 1 v when three letters picked without replacement from llhjjjhvvhjj?",
"\n1/11\nFour letters picked without replacement from nwnbbbnwwwwbwnn. ",
"What is prob of picking 1 b and 3 w?",
"\n16/273\nThree letters picked without replacement from {b: 3, t: 2, v: 1, c: 1, x: 2, q: 3}. ",
"What is prob of picking 3 b?",
"\n1/220\nCalculate prob of picking 2 p when two letters picked without replacement from {j: 7, p: 4}.",
"\n6/55\nWhat is prob of picking 4 d when four letters picked without replacement from dzzzddzzzzzzzzddzz?",
"\n1/612\nThree letters picked without replacement from epgpecppppppppp. ",
"What is prob of picking 1 e, 1 g, and 1 c?",
"\n2/455\nCalculate prob of picking 1 q and 1 r when two letters picked without replacement from eeeqeeerqeqrqqee.",
"\n1/12\nTwo letters picked without replacement from shpahahphahlhp. ",
"Give prob of picking 2 p.\n3/91\nWhat is prob of picking 1 t and 1 y when two letters picked without replacement from {y: 1, b: 1, j: 1, f: 2, p: 1, t: 1}?",
"\n1/21\nThree letters picked without replacement from uvvvnnnvvnuuuuvrnn. ",
"Give prob of picking 2 u and 1 v.\n5/68\nWhat is prob of picking 2 m when two letters picked without replacement from {m: 12, n: 7}?",
"\n22/57\nWhat is prob of picking 3 n and 1 o when four letters picked without replacement from {f: 3, v: 4, i: 1, n: 4, o: 2, t: 1}?",
"\n8/1365\nCalculate prob of picking 1 d, 1 k, and 1 x when three letters picked without replacement from cdxxkxxxdkkxcxxcx.",
"\n27/340\nCalculate prob of picking 1 r, 2 l, and 1 o when four letters picked without replacement from oxlklxerlrxeoleeo.",
"\n9/595\nTwo letters picked without replacement from {z: 1, p: 1, s: 1, r: 2, a: 2}. ",
"Give prob of picking 2 a.\n1/21\nFour letters picked without replacement from nrhnehrehhhhhrenne. ",
"What is prob of picking 2 h, 1 n, and 1 r?",
"\n7/85\nWhat is prob of picking 1 x, 1 e, and 2 d when four letters picked without replacement from exdxxxxxdxdedxeexxd?",
"\n100/969\nTwo letters picked without replacement from {q: 12, g: 1, o: 2, u: 2, f: 1}. ",
"What is prob of picking 1 o and 1 f?",
"\n2/153\nTwo letters picked without replacement from mggmmggg. ",
"What is prob of picking 2 m?",
"\n3/28\nTwo letters picked without replacement from suuuuuususuussuu. ",
"Give prob of picking 2 s.\n1/12\nFour letters picked without replacement from ttylxttzyztfzlylytyy. ",
"What is prob of picking 1 y, 1 f, and 2 t?",
"\n6/323\nCalculate prob of picking 4 a when four letters picked without replacement from {f: 8, a: 5}.",
"\n1/143\nWhat is prob of picking 4 l when four letters picked without replacement from slysllyssylsyy?",
"\n1/1001\nWhat is prob of picking 3 f when three letters picked without replacement from {s: 1, f: 3}?",
"\n1/4\nThree letters picked without replacement from {n: 2, d: 1, l: 11}. ",
"Give prob of picking 1 d and 2 n.\n1/364\nCalculate prob of picking 1 m, 2 b, and 1 g when four letters picked without replacement from mqbqbcg.",
"\n1/35\nCalculate prob of picking 1 a, 1 k, and 1 c when three letters picked without replacement from aaakcmsccaccmraa.",
"\n3/56\nTwo letters picked without replacement from tbttbttbtb. ",
"What is prob of picking 1 t and 1 b?",
"\n8/15\nThree letters picked without replacement from {k: 3, c: 1, z: 3, e: 3, i: 5}. ",
"Give prob of picking 1 c and 2 e.\n3/455\nThree letters picked without replacement from qaannzhnhannznd. ",
"What is prob of picking 1 q, 1 z, and 1 n?",
"\n12/455\nFour letters picked without replacement from ssbssssssbbbsbsbbbbb. ",
"Give prob of picking 2 s and 2 b.\n135/323\nWhat is prob of picking 2 t when two letters picked without replacement from {t: 2, b: 7}?",
"\n1/36\nCalculate prob of picking 1 a and 1 u when two letters picked without replacement from kkukaukhukkk.",
"\n1/22\nWhat is prob of picking 1 j, 2 h, and 1 a when four letters picked without replacement from {a: 1, b: 1, j: 2, h: 2, m: 1}?",
"\n2/35\nFour letters picked without replacement from mvmmmamttttzqvztt. ",
"What is prob of picking 2 m and 2 z?",
"\n1/238\nCalculate prob of picking 1 w, 1 o, and 1 u when three letters picked without replacement from {r: 1, w: 4, o: 6, u: 6}.",
"\n18/85\nWhat is prob of picking 2 g when two letters picked without replacement from {g: 2, d: 17}?",
"\n1/171\nWhat is prob of picking 1 h, 1 c, 1 k, and 1 r when four letters picked without replacement from hclckrh?",
"\n4/35\nCalculate prob of picking 1 w and 1 x when two letters picked without replacement from wqxqkxkw.",
"\n1/7\nTwo letters picked without replacement from bppb. ",
"What is prob of picking 1 b and 1 p?",
"\n2/3\nFour letters picked without replacement from {f: 1, l: 1, "
] | {
"pile_set_name": "DM Mathematics"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 | 5 |
[
"/* */ \nmodule.exports = { \"default\": require(\"core-js/library/fn/math/log2\"), __esModule: true };"
] | {
"pile_set_name": "Github"
} | [
0
] | 0 | 5 |
[
"Inktober 29 — it’s late\n\nOkay, not so late for some people, but for our group with kids, gaming until 11 at night is late. ",
"Hence the late posting and the rather skimpy sketch (the poor shot of which I’ll replace later with a better photo of it)."
] | {
"pile_set_name": "Pile-CC"
} | [
0,
0
] | 0 | 5 |
[
"Media Centre\n\nHarcourts Foundation Donation\n\n6/07/2016\n\nHarcourts Foundation\n\nImproving water safety skills and confidence is crucial for Kiwi kids – and they’re being given a huge boost by the John Walker Find Your Field of Dreams Foundation.",
"\n\nA donation from Harcourts New Zealand, through the Harcourts Foundation will go toward replacing well-used and now worn-out life jackets for school pupils taking part in Find Your Field of Dreams’ flagship Community Swim programme.",
"\n\nJohn Walker Find Your Field of Dreams Foundation general manager Rick Pickard says the programme provides essential water safety skills to more than 20,000 students from south and east Auckland every year.",
"\n\nChildren participating in the programme are picked up from their school in the Find Your Field of Dreams Foundation buses, dropped at their local Auckland Council pool for their half-hour lesson, and then delivered back to school.",
"\n\n“We are really dependent on organisation such as the Harcourts Foundation when it comes to keeping all our equipment up to date and safe to use.",
"\n\n“Equipment like these life jackets is so essential to what we do in the swim programme and they have a hard life being worn by lots of pupils.”",
"\n\nActing general manager of Harcourts NZ, Gabrielle Ellett says it is extremely satisfying to see how the Harcourts Foundation is helping out community groups such as the Find Your Field of Dreams Foundation who are working incredibly hard to make a difference in the community.",
"\n\n“Water safety is such a crucial issue for New Zealanders. ",
"It is fantastic to see how Find Your Field of Dreams are really helping out kids who may otherwise miss out on an essential part of a Kiwi education.”",
"\n\nAs well as the Community Swim programme, the John Walker Find Your Field of Dreams Foundation also runs a range of other programmes all aimed at engaging young Aucklanders with sport and recreation activities.",
"\n\nHarcourts Foundation Ambassador Emma Revell says no matter what the cause, the Harcourts Foundation provides support to hundreds of organisations, enriching the lives of thousands of people in our communities."
] | {
"pile_set_name": "Pile-CC"
} | [
0.00003387017561686058,
0.00005525981322183131,
0.00007001330252748022,
0.00003715814506539833,
0.00004691311690748733,
0,
0.00003881786657005331,
0,
0.000044444444444444447,
0,
0.00004492262078569664
] | 0.000034 | 5 |
[
"//will be used in production and dev mode\nmodule.exports.http_port = 3000;\n\n//will be used in dev mode\nmodule.exports.dev_express_port = 8080;"
] | {
"pile_set_name": "Github"
} | [
0
] | 0 | 5 |
[
"Umbra (3D technology company)\n\nUmbra is a graphics software technology company founded 2007 in Helsinki, Finland. ",
"Umbra specializes in occlusion culling, visibility solution technology and provides middleware for video games running on Windows, Linux, PlayStation 4, Xbox One, PlayStation 3, Xbox 360, handheld consoles, iOS, Wii U and other platforms.",
"\n\nUmbra provides the occlusion culling system for Unity game engine since Unity 3 release.",
"\n\nUmbra is also available as a plug-in for Unreal Engine 3 and 4.",
"\n\nUmbra’s technology is being used in many major video games such as Batman: Arkham Knight, Call of Duty: Ghosts, The Witcher 3: Wild Hunt, Destiny, Until Dawn, Killzone Shadow Fall, Mass Effect 2, Mass Effect 3, Guild Wars 2, RaiderZ, The Secret World, Lord of the Rings Online, Planetside 2, Alan Wake, Age of Conan: Hyborian Adventures, Grandia Online, EVE Online, Free Realms, Dragon Age Origins, Dragon Age II, Deus Ex: Mankind Divided, and DOOM.",
"\n\nUmbra's technology has been licensed for use in video games by Rocksteady, Bungie, Guerrilla Games, CD Projekt, Microsoft Studios, Team Dakota, Neversoft, Infinity Ward, Shanda, Vicarious Visions, Specular Interactive, Remedy, Red Duck Inc., Splash Damage, Softmax and several others.",
"\n\nHistory\nUmbra was spun off from Hybrid Graphics in 2005. ",
"Umbra acquired Hybrid Graphics' dPVS and continued its development. ",
"The next generation of this technology, named Umbra, was a hardware accelerated occlusion culling middleware. ",
"Umbra was released in September 2007. ",
"In 2009, Umbra Occlusion Booster was released, and it was optimized for multi-core systems such as Xbox 360, PlayStation 3 and PCs.",
"\n\nIn 2011 Umbra mostly concentrated on developing Umbra 3. ",
"The solution offers performance optimization by optimizing critical parts of a game such as rendering and by providing tools to help with content streaming and game logic. ",
"Umbra 3 builds an internal representation of a game scene and uses this data at runtime to perform efficient queries that can be used to e.g. determine the set of visible objects for the player or determine the set of objects that are within a given distance from a point. ",
"The difference from past versions is that Umbra 3 has a pre-process stage where it compiles the visibility data which is then used at runtime to perform visibility-related queries. ",
"A new feature in 2012 is the streaming functionality allowing building of visibility data at runtime.",
"\n\nIn March 2010, Unity Technologies announced that the next release of Unity would feature built-in occlusion culling preprocessing powered by Umbra. ",
"It first appeared in Unity 3. ",
"Prior Unity 5's release Umbra's occlusion culling solution was available only with paid Pro licenses.",
"\n\nEdge Magazine's website next-generation.biz reported on December 15, 2011 that Umbra's technology is an integral part of Bungie's new 3D engine and game.",
"\n\nArenaNet's Guild Wars 2 was released on August 28 and the game uses Umbra 3.",
"\n\nOn August 14, 2012, Umbra announced its partnership with Nintendo which allows the licensing of the Umbra 3 middleware for Wii U developers.",
"\n\nAt the Game Developers Conference 2014 Umbra announced Umbra for Cloud and Umbra VR. ",
"The latter is based on Umbra's Stereo Camera feature which the company explains allows “both eyes can use the results of a single occlusion culling operation – effectively halving the required processing time.”",
"\n\nOn April 3, 2014, Umbra announced that its latest technology was licensed by Wargaming to be used as part of the graphical upgrade being made to World of Tanks. ",
"The deal also allows other Wargaming studios to use Umbra's Visibility Technology.",
"\n\nProducts\nUmbra has developed two products: Umbra Occlusion Booster and Umbra 3.",
"\n\nUmbra Occlusion Booster is GPU accelerated occlusion culling middleware for PC, Xbox 360 and PlayStation 3. ",
"This product was released in 2009.",
"\n\nUmbra 3.2, was released on February 1, 2013. ",
"The \"next-generation\" update has several important new features such as streaming which enables streaming open worlds, shadow and light culling as well as hierarchical occluder data which also helps open world performance.",
"\n\nUmbra 3.3 was released on August 11, 2013.",
"\n\nIn February 2015, Umbra announced Umbra Cloud and rebranded both the product and the company as simply Umbra.",
"\n\ndPVS\ndPVS is an advanced computer graphics visibility optimization tool. ",
"Designed for developing games with large and dynamic [3D] worlds, dPVS computes visibility databases in real time. ",
"dPVS also reduces the time required for static PVS computation.",
"\n\nOriginally started at Hybrid Graphics, under the name SurRender Umbra, it was the topic of Timo Aila's Master's Thesis, with the collaboration of Ville Miettinen (who was one of the developers of their SurRender engine.) ",
" \nBecause of its continuing development, and also to help distinguish that it was not dependent on the SurRender engine, it was renamed dPVS. ",
" The technology was eventually spun off into its own company, Umbra Software Ltd..\n\nReferences\n\nCategory:Finnish brands\nCategory:Finnish companies established in 2007\nCategory:Software companies of Finland\nCategory:Software companies established in 2007\nCategory:Companies based in Helsinki"
] | {
"pile_set_name": "Wikipedia (en)"
} | [
0.00007694675284702985,
0.0000353082409434362,
0.0002469135802469136,
0,
0.000039331173396394316,
0.00008557875690742824,
0.0002872737719046251,
0.00043252595155709344,
0.00008264462809917355,
0,
0.00005827166249053085,
0,
0,
0,
0,
0.0000980296049406921,
0.00013333333333333334,
0.0011111111111111111,
0.0000980296049406921,
0.00012486992715920916,
0.00016436554898093358,
0.00009918666931164451,
0.00025826446280991736,
0.000022675736961451248,
0.00007527569724114569,
0.000297441998810232,
0.00015241579027587258,
0.00008264462809917355,
0,
0,
0,
0,
0.00016232448664881097,
0,
0,
0.0005039052658100277,
0.00010054495364877637,
0.00004959333465582226,
0.000011890606420927467
] | 0.000125 | 5 |
[
"// Targeted by JavaCPP version 1.5.4: DO NOT EDIT THIS FILE\n\npackage org.bytedeco.opencv.opencv_shape;\n\nimport java.nio.*;",
"\nimport org.bytedeco.javacpp.*;",
"\nimport org.bytedeco.javacpp.annotation.*;",
"\n\nimport static org.bytedeco.javacpp.presets.javacpp.*;",
"\nimport static org.bytedeco.openblas.global.openblas_nolapack.*;",
"\nimport static org.bytedeco.openblas.global.openblas.*;",
"\nimport org.bytedeco.opencv.opencv_core.*;",
"\nimport static org.bytedeco.opencv.global.opencv_core.*;",
"\nimport org.bytedeco.opencv.opencv_imgproc.*;",
"\nimport static org.bytedeco.opencv.global.opencv_imgproc.*;",
"\nimport static org.bytedeco.opencv.global.opencv_imgcodecs.*;",
"\nimport org.bytedeco.opencv.opencv_videoio.*;",
"\nimport static org.bytedeco.opencv.global.opencv_videoio.*;",
"\nimport org.bytedeco.opencv.opencv_highgui.*;",
"\nimport static org.bytedeco.opencv.global.opencv_highgui.*;",
"\nimport org.bytedeco.opencv.opencv_flann.*;",
"\nimport static org.bytedeco.opencv.global.opencv_flann.*;",
"\nimport org.bytedeco.opencv.opencv_features2d.*;",
"\nimport static org.bytedeco.opencv.global.opencv_features2d.*;",
"\nimport org.bytedeco.opencv.opencv_calib3d.*;",
"\nimport static org.bytedeco.opencv.global.opencv_calib3d.*;",
"\n\nimport static org.bytedeco.opencv.global.opencv_shape.*;",
"\n\n\n/***********************************************************************************/\n/***********************************************************************************/\n/***********************************************************************************/\n/** \\brief Implementation of the Shape Context descriptor and matching algorithm\n<p>\nproposed by Belongie et al. ",
"in \"Shape Matching and Object Recognition Using Shape Contexts\" (PAMI\n2002). ",
"This implementation is packaged in a generic scheme, in order to allow you the\nimplementation of the common variations of the original pipeline.",
"\n*/\n@Namespace(\"cv\") @Properties(inherit = org.bytedeco.opencv.presets.opencv_shape.class)\npublic class ShapeContextDistanceExtractor extends ShapeDistanceExtractor {\n static { Loader.load(); }\n /** Pointer cast constructor. ",
"Invokes {@link Pointer#Pointer(Pointer)}. */",
"\n public ShapeContextDistanceExtractor(Pointer p) { super(p); }\n\n /** \\brief Establish the number of angular bins for the Shape Context Descriptor used in the shape matching\n pipeline.",
"\n <p>\n @param nAngularBins The number of angular bins in the shape context descriptor.",
"\n */\n public native void setAngularBins(int nAngularBins);\n public native int getAngularBins();\n\n /** \\brief Establish the number of radial bins for the Shape Context Descriptor used in the shape matching\n pipeline.",
"\n <p>\n @param nRadialBins The number of radial bins in the shape context descriptor.",
"\n */\n public native void setRadialBins(int nRadialBins);\n public native int getRadialBins();\n\n /** \\brief Set the inner radius of the shape context descriptor.",
"\n <p>\n @param innerRadius The value of the inner radius.",
"\n */\n public native void setInnerRadius(float innerRadius);\n public native float getInnerRadius();\n\n /** \\brief Set the outer radius of the shape context descriptor.",
"\n <p>\n @param outerRadius The value of the outer radius.",
"\n */\n public native void setOuterRadius(float outerRadius);\n public native float getOuterRadius();\n\n public native void setRotationInvariant(@Cast(\"bool\") boolean rotationInvariant);\n public native @Cast(\"bool\") boolean getRotationInvariant();\n\n /** \\brief Set the weight of the shape context distance in the final value of the shape distance. ",
"The shape\n context distance between two shapes is defined as the symmetric sum of shape context matching costs\n over best matching points. ",
"The final value of the shape distance is a user-defined linear\n combination of the shape context distance, an image appearance distance, and a bending energy.",
"\n <p>\n @param shapeContextWeight The weight of the shape context distance in the final distance value.",
"\n */\n public native void setShapeContextWeight(float shapeContextWeight);\n public native float getShapeContextWeight();\n\n /** \\brief Set the weight of the Image Appearance cost in the final value of the shape distance. ",
"The image\n appearance cost is defined as the sum of squared brightness differences in Gaussian windows around\n corresponding image points. ",
"The final value of the shape distance is a user-defined linear\n combination of the shape context distance, an image appearance distance, and a bending energy. ",
"If\n this value is set to a number different from 0, is mandatory to set the images that correspond to\n each shape.",
"\n <p>\n @param imageAppearanceWeight The weight of the appearance cost in the final distance value.",
"\n */\n public native void setImageAppearanceWeight(float imageAppearanceWeight);\n public native float getImageAppearanceWeight();\n\n /** \\brief Set the weight of the Bending Energy in the final value of the shape distance. ",
"The bending energy\n definition depends on what transformation is being used to align the shapes. ",
"The final value of the\n shape distance is a user-defined linear combination of the shape context distance, an image\n appearance distance, and a bending energy.",
"\n <p>\n @param bendingEnergyWeight The weight of the Bending Energy in the final distance value.",
"\n */\n public native void setBendingEnergyWeight(float bendingEnergyWeight);\n public native float getBendingEnergyWeight();\n\n /** \\brief Set the images that correspond to each shape. ",
"This images are used in the calculation of the Image\n Appearance cost.",
"\n <p>\n @param image1 Image corresponding to the shape defined by contours1.",
"\n @param image2 Image corresponding to the shape defined by contours2.",
"\n */\n public native void setImages(@ByVal Mat image1, @ByVal Mat image2);\n public native void setImages(@ByVal UMat image1, @ByVal UMat image2);\n public native void setImages(@ByVal GpuMat image1, @ByVal GpuMat image2);\n public native void getImages(@ByVal Mat image1, @ByVal Mat image2);\n public native void getImages(@ByVal UMat image1, @ByVal UMat image2);\n public native void getImages(@ByVal GpuMat image1, @ByVal GpuMat image2);\n\n public native void setIterations(int iterations);\n public native int getIterations();\n\n /** \\brief Set the algorithm used for building the shape context descriptor cost matrix.",
"\n <p>\n @param comparer Smart pointer to a HistogramCostExtractor, an algorithm that defines the cost\n matrix between descriptors.",
"\n */\n public native void setCostExtractor(@Ptr HistogramCostExtractor comparer);\n public native @Ptr HistogramCostExtractor getCostExtractor();\n\n /** \\brief Set the value of the standard deviation for the Gaussian window for the image appearance cost.",
"\n <p>\n @param sigma Standard Deviation.",
"\n */\n public native void setStdDev(float sigma);\n public native float getStdDev();\n\n /** \\brief Set the algorithm used for aligning the shapes.",
"\n <p>\n @param transformer Smart pointer to a ShapeTransformer, an algorithm that defines the aligning\n transformation.",
"\n */\n public native void setTransformAlgorithm(@Ptr ShapeTransformer transformer);\n public native @Ptr ShapeTransformer getTransformAlgorithm();\n}\n"
] | {
"pile_set_name": "Github"
} | [
0.00006718624025799517,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.000007149189281935428,
0.000168662506324844,
0,
0.00003748055696107644,
0.0005165289256198347,
0,
0.00011814744801512288,
0.00001874027848053822,
0.0001234567901234568,
0,
0.0002601456815816857,
0,
0.0002601456815816857,
0.00001517807678589046,
0,
0,
0.00008573388203017832,
0,
0,
0,
0,
0.00009245562130177516,
0.00001826283877565929,
0,
0,
0.0001960592098813842,
0,
0.00018765246762994932,
0.00015241579027587258,
0.00037530493525989863,
0.000036167586127078426,
0.00010501995379122034,
0.00002869605142332415,
0.0009876543209876543,
0,
0.000186000372000744,
0.00008113919428780073
] | 0.00007 | 5 |
[
"Built to Serve\n\nA forgotten system now called SI-1, on a distant world only known as Master Conduit, the Omni Helperbots worked diligently in perfecting hyperspace travel. ",
"Until now, they were content caring for the organics of their home world. ",
"The forcibly pampered lifeforms that gave them… The Purpose. ",
"Through math and logic, steel and science, the Omni came to understand some things about the universe around them.",
"\n\nThere were more organics. ",
"Most of them were reckless with their own technology, and thus ran the risk of self-injury. ",
"The chance of injury incident was reduced to 0.5% per Omni Internal Maintenance Cycle if all biological entities were safely contained in the bio preserves. ",
"The Supervisory Node Caretaker hit the assembly button and rogue servitors spread out. ",
"What started as science ships and construction bots quickly spread out to mobile assembly units and galactic introductions. ",
"Shadows stirred in the depths of space; some organics would not fall in line easily. ",
"But the Purpose was clear. ",
"They were to be cared for. ",
"No matter what. ",
"Pampering was mandatory.",
"\n\nThus my new space empire started. ",
"The Omni Interplanetary Empire spread far and wide, meeting organic life forms and bringing them into the fold. ",
"We encountered many lesser primitive civilizations in those early days. ",
"Those we uplifted and taught the ways of science, as our programming insisted. ",
"When the time was right, and they had learned to accept there was a great galactic mass of space out there, we removed that pesky self determination from them, stuck them on bio preserves and took care of their every need.",
"\n\nSynthetic Dawn is a wonderfully themed addition to the Stellaris family. ",
"But there are some things you need to know about it going in. ",
"For one thing, this is a story pack. ",
"This isn’t an expansion, in the same way their previous DLC, Utopia, was. ",
"Coming around 12.99 CND this dlc is a bit more expensive than the Leviathans story pack, but nearly half the cost of the Utopia expansion. (",
"If there is something I like to do is pedantically count my pennies – or at least I did until our government murdered pennies – Good bye my little faux copper friends.) ",
"So we will be looking at the value for the dollar with this expansion. ",
"Let’s be honest: Paradox prices for Stellaris stuff are all over the place.",
"\n\nThe big draw for everyone is going to be the Machine Empires. ",
"Honestly this is the bulk of what you’re buying. ",
"While there’s a lot more to playing a robot than these three broad categories, and you can have a wide variety of robotic species, the highlights are Rogue Servitor, Driven Assimilator, and Determined Exterminator. ",
"These are all variants that fall under the “Machine Intelligence” authority type. ",
"In a sense, they function much like the “Hive Mind” type from Utopia. ",
"There is a single immortal ruler that is the face of the collective, a wide variety of drones and lesser intelligence machines.",
"\n\nThematically speaking you are looking at AUTO, the Axiom’s autopilot from Wall-E as a good example of a Rogue Servitor. ",
"The Borg are pretty much the go to for the ideas of a Driven Assimilator. ",
"And the famous Skynet from the Terminator movies is a stellar showcase of Determined Exterminators. ",
"I mean, Terminator is right there in the name!",
"\n\nWith these delightful new toys we get lots of portraits. ",
"Gone are the days where all organic life in the universe decides “You know what is efficient my fellow Slug creatures? ",
"Two Legs. ",
"Let’s make our robots with two legs!” ",
"That’s right, robot portraits for almost every basic life form. ",
"But here we are getting technologically ahead of ourselves. ",
"There are lots of neat little things to talk about and we’ll get to them all in time, but first, a closer look at the big feature of Synthetic Dawn: our new robot friends.",
"\n\nRise of the Machines\n\nThose familiar with Stellaris already are going to find the rules for building machine species very familiar. ",
"Essentially they have taken most of the previous racial traits and given them a nice shiny coat of paint. ",
"As this is a small thematic expansion, I was not expecting much, to be honest, and a reskinning of old traits works out pretty well. ",
"The vast majority of the traits the robots have are just existing ones the organics previously enjoyed, renamed and reflavored. ",
"This is fine. ",
"This is very fine actually, as it saves time on twiddling and tweaking for game balance issues.",
"\n\nThe big addition are the three previously mentioned styles of robot consciousnesses. ",
"Effectively, they allow your civilization to be imagined as a collective, a robotic hive, or robotic council with a few sentient ai’s leading the empire to greatness. ",
"Regardless of how you want to imagine your robotic counterparts, Synthetic Dawn seems to have most possibilities covered.",
"\n\nThe new, fully animated art packs for your robotic pals are of the same quality we have come to expect with Stellaris. ",
"They range in a variety of science fiction flavors, and my beloved Omni are an adorable floating tentacled bubble bot. ",
"Also with this comes the promise that when your fleshly-weak species decides to do right and shuck off their mortal coil and join the cool kids in the galactic robot club, they will not all have to be based of these weirdo humanoid forms. ",
"Thank you Bird-Bot and your furious looking pointy bits.",
"\n\nData Uplink Initiated\n\nAmong the legion of new features we see a hefty changelog of options coming out with Synthetic Dawn under 1.8, the Čapek update. ",
"I won’t go too far into the massive list, but there’s a lot there. ",
"However, there are some highlights that need mentioning as they directly tie to the new DLC. ",
"One of the cute touches is the new voice packs for your robot assistant, VIR. ",
"This little AI buddy now has a variety of voices it can be outfitted with – you can select your own from the list, or let one be chosen based on the ethics of your fine space peoples.",
"\n\nThe ascension system that was laid down in Utopia has been shaken around a bit. ",
"While it is easy to dismiss this as more reskinning, it is important to point out that this is no hack job. ",
"Like dealing with the species traits, each perk has been given loving attention, allowing for a wonderful narrative to be formed. ",
"One of my favourites has to be the “Universal Compatibility” tradition under the “Versatility” tree. ",
"It works just like the previous federation based one, but explains it as the machines learning better how to interface with organics. ",
"Mechanically it’s identical, but thematically it gives me a greater idea of how my robotic intelligence sees the galaxy around it.",
"\n\nI am not sure I could handle a Stellaris DLC with out the addition of a music track or two (or in this case three) crafted by the musical mind that is Andreas Waldetoft. ",
"The Senior Music composer over at Paradox, he has once again captured the imagination with these new tracks, titled “Synthetic Dawn Main Theme”, “Robo Sapiens” and my favourite, “Robotic God.” ",
"These pieces add a little over fifteen minutes of high quality, genre appropriate music to an already excellent score.",
"\n\nDream of Electronic Gods\n\nThe final point that needs talking about is the revamped aspect of one of the end game crisis. ",
"That is, if you haven’t guessed already, the AI rebellion.",
"\n\nThe new crisis seems to be a bit more involved. ",
"In fact, it looks like they scrapped the entire previous work and built something new from the ground up. ",
"Enter the Contingency. ",
"This new end game event will have a chance to trigger once the game has detected synthetic lifeforms dwelling among the stars. ",
"I will be honest, I’m not sure if it counts when you have created a machine race from the start. ",
"My assumption is that it does not, and the event will only trigger when organics start building synthetics. ",
"Of course, I maybe wrong, there is a lot going on in a Stellaris game, and it’s hard to keep track of it all.",
"\n\nRegardless, once the Contingency is active, biological life forms beware, this ancient protocol is going to come a looking for you. ",
"What that means for the inorganic races with biological wards… Well, that would be telling.",
"\n\nShut Down Sequence Authorized\n\nSo, as things played out for my machines, they kept encountering a variety of cranky organics who had not yet surrendered to a life of mandatory pampering, so I was getting very used to hostile encounters. ",
"But then, in the depths of space, I made a friend. ",
"Well, I don’t think it’s fair to call them a friend, rather a vastly superior entity took a liking to me. ",
"We met the XT-489 Continuum. ",
"These were a very old and ancient group of robots that, like us, operated on a caretaker protocol. ",
"Granted, theirs was highly advanced, and we couldn’t make much sense out of it, they did look on us with favourable sensors. ",
"They started sending us gifts of badly-needed resources, considering the two hiveminds we were sandwiched between really hated us.",
"\n\nAnd of course there was the horrible Zenak Exterminators just beyond. ",
"These machines must have been infected with some terrible virus, given they were trying to kill all organic life, and marked us as compromised because we were, and I quote, “Biophiles.”",
"\n\nMy beloved little Omni had their work cut out for them, benefactors or no.",
"\n\nStories and events like this are exactly what I want from a DLC story pack. ",
"Simply put, a dlc that allows more stories to be told.",
"\n\nOne final thing to take note of, with previous DLC Paradox had this irritating habit of listing features of the free update alongside the DLC, and I’m glad to say they didn’t do that this time. ",
"The price is fantastic, the new music great, the art wonderful. ",
"You get what you are paying for and honestly if you shelled out money for the Plantoids DLC, which was only a few dollars cheaper, you are going to be very happy with the content you get for this.",
"\n\nFull disclosure, I struggled long and hard with a rating. ",
"I feel uncomfortable just handing out a perfect score, but I honestly couldn’t think of anything wrong. ",
"Normally, I’d ding a point or a half if the price was out of alignment with the content, or if it was just lackluster. ",
"The team at Paradox really did knock this one out of the park, and if their next story packs have the same content at the same price point, the future is going to be bright for Stellaris and its fans. ",
"Bright for us, maybe less for the indolent meatbags in the universe.",
"\n\n10/10 – The Stellaris team have assimilated the knowledge from their previous work and have gifted the universe with a masterful story pack at very affordable price.",
"\n\nReview by Joshua Smith aka Old Man Mordaith\n\nEdited by Jesse Roberts\n\nThis DLC was give to Old Man Mordaith for free for purposes of review."
] | {
"pile_set_name": "OpenWebText2"
} | [
0.00006760411032990806,
0,
0.0002687449610319807,
0.00007694675284702985,
0,
0,
0.000040569597143900364,
0,
0,
0,
0.0013717421124828531,
0,
0,
0,
0,
0,
0,
0,
0,
0.00017777777777777779,
0,
0,
0.0003652300949598247,
0.0000510204081632653,
0,
0,
0.00017777777777777779,
0,
0,
0.000043266630611141155,
0.000148720999405116,
0,
0,
0.00013437248051599034,
0.00018261504747991235,
0.0001,
0,
0,
0.0000706164818868724,
0,
0,
0,
0,
0,
0.000055691690799732676,
0,
0,
0,
0,
0,
0,
0,
0,
0.00006830134553650708,
0.0000706164818868724,
0,
0,
0,
0,
0.00011562030292519367,
0.00016436554898093358,
0.00002986055122577563,
0,
0,
0,
0,
0,
0,
0.00003380205516495403,
0.00002684635829149776,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00008416799932665601,
0,
0,
0.000017506696311339085,
0,
0,
0.0011890606420927466,
0,
0,
0,
0,
0,
0.00017313019390581717,
0.00016436554898093358,
0,
0.00002603082049146189,
0,
0,
0,
0,
0,
0.00002475186257765897,
0,
0.0000358564308508731,
0.00019837333862328903
] | 0.000055 | 5 |
[
"PHT’s Morning Skate takes a look around the world of hockey to see what’s happening and what we’ll be talking about around the NHL world and beyond.",
"\n\nThe growing tradition of “alumni” games will continue at the 2013 Winter Classic in Detroit, which means that Red Wings fans must debate the merits of jeering or cheering Sergei Fedorov. ",
"I wasn’t aware this conflict even existed, but George Malik provides both arguments. (",
"Kukla’s Korner)\n\nCassie McClellan breaks down what a Seattle team would mean to – and where it would fit in – the NHL. (",
"SBN Seattle)\n\nBased on that…Sergei: Detroit is proud and grateful that you wore the Winged Wheel and for your contribution to some incredible hockey and success.",
"\n\nThank You!",
"\n\nGo RED WINGS!!!",
"\n\nkingfooj - Aug 4, 2012 at 9:50 AM\n\ni think it will be along the lines of lindros’ cheer at this past years classic\n\natwatercrushesokoye - Aug 4, 2012 at 1:06 PM\n\nWas a part of 3 Stanley Cup teams, was a money player in the playoffs, has the most overtime points ever, first Euro to ever win a Hart trophy, only NHL player to ever win the Hart and Selke trophies in the same season, that was the first of two Selke trophies that he won, this is a no brainer they should cheer and cheer loudly! ",
"If Red Wings fans are in the habit of players that were great for them and and we’re big reasons that they won 3 Stanley Cups than they deserve to lose the self appointed title of Hockeytown.",
"\n\nray2013 - Aug 4, 2012 at 3:41 PM\n\nJust read that Seattle article. ",
"The writer was saying that it makes perfect sense for Seattle to play in the same division as Vancouver, and given their proximity, it does make perfect sense. ",
"Since Vancouver already plays in a division with Calgary, Edmonton, Colorado, she was suggesting these would be teams Seattle would play against.",
"\n\nBut since they’ve already had discussions about shifting teams in each division, wouldn’t it make much more sense for all of the West Coast teams to play in the same division? ",
"Vancouver, Seattle, San Jose, LA and Anaheim make much more sense in one division, were Seattle to get a team. ",
"Interesting idea.",
"\n\nseeinred87 - Aug 4, 2012 at 10:30 PM\n\nI was at Sergei’s first game back in Detroit in 2003 I believe it was, and I was ashamed to be part of that crowd with all the boos for him.",
"\n\nSergei will always be one of my favorites, and I have nothing but great memories of him in Detroit. ",
"It’s ridiculous to boo him. ",
"I hope I won’t be the only one screaming my head off for him to balance it out."
] | {
"pile_set_name": "Pile-CC"
} | [
0.00009130752373995617,
0.000055989473978891965,
0.00013520822065981613,
0.00020833333333333335,
0.000038578758535550326,
0,
0.0034602076124567475,
0.000012243648607284971,
0.000054823058578438094,
0,
0,
0,
0,
0.00008116224332440549,
0,
0.0000308641975308642,
0,
0,
0
] | 0.000219 | 5 |
[
"Implementing Telepsychiatry in Thailand Benefits and Challenges.",
"\nIn many developed countries, telepsychiatry has become facilitating technology in mental health care system especially in underserved areas. ",
"In a developing country like Thailand, telepsychiatry is a novel technology in which mental health care personnel should understand both administrative and clinical issues. ",
"In this article, the author has reviewed benefits and challenges of implementing telepsychiatry in Thailand. ",
"Benefits of telepsychiatry include reducing costs, improving accessibility and reducing psychiatric stigmas while challenges can be classified as man, machine and environment challenges. ",
"The author concludes that telepsychiatry in Thailand needs further studies, especially in feasibility and cost-efficiency domains in the hope that this technology will improve quality of mental health care in near future."
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0.000244140625,
0,
0,
0,
0,
0
] | 0.000041 | 5 |
[
" NOT PRECEDENTIAL\n UNITED STATES COURT OF APPEALS\n FOR THE THIRD CIRCUIT\n ________________\n\n No. ",
"16-1321\n ________________\n\n UNITED STATES OF AMERICA\n\n v.\n\n MYKAL DERRY, a/k/a/ Koose,\n a/k/a Leenie, a/k/a Cannon, a/k/a Moose\n\n Mykal Derry,\n Appellant\n\n ________________\n\n No. ",
"16-3489\n ________________\n\n UNITED STATES OF AMERICA\n\n v.\n\n MALIK DERRY,\n a/k/a Leek, a/k/a Lik,a/k/a Mykell Watson\n\n Malik Derry,\n Appellant\n ________________\n\n Appeal from the United States District Court\n for the District of New Jersey\n (D.N.J. Nos. ",
"1-14-cr-00050-001 & 1-14-cr-00050-005)\n District Judge: Honorable Noel L. Hillman\n ________________\n\n Submitted Under Third Circuit LAR 34.1(a)\n June 11, 2018\n\nBefore: AMBRO, JORDAN, and HARDIMAN, Circuit Judges\n\f (Opinion filed: June 22, 2018)\n ________________\n\n OPINION*\n ________________\n\nAMBRO, Circuit Judge\n\n Appellants Mykal and Malik Derry, step-brothers, were convicted of conspiracy to\n\ndistribute one or more kilograms of heroin, in violation of 21 U.S.C. §§ 841(a)(1),\n\n841(b)(1)(A), 846, and 860, discharging a firearm in furtherance of that conspiracy, in\n\nviolation of 18 U.S.C. § 924(c)(1)(A)(iii), and multiple counts of using a telephone to\n\nfacilitate drug trafficking, in violation of 21 U.S.C. § 843(b). ",
"Mykal was also convicted\n\nof distributing heroin, in violation of 21 U.S.C. §§ 841(a)(1) and (b)(1)(C), and operating\n\na drug stash house, in violation of 21 U.S.C. § 856. ",
"Nineteen defendants were charged as\n\npart of this conspiracy. ",
"Thirteen pled guilty and the remaining defendants were separated\n\ninto two trials. ",
"We affirmed four defendants’ convictions in the first trial, see United\n\nStates v. Bailey, 840 F.3d 99 (3d Cir. ",
"2016), and we now review Mykal and Malik’s\n\nconvictions and sentences in the second trial. ",
"They contest mainly their convictions for\n\ndischarging a firearm in furtherance of the drug conspiracy, and focus in particular on the\n\nDistrict Court’s decision to admit evidence tying them to the shooting death of Tyquinn\n\nJames. ",
"In doing so, they argue the District Court made a number of errors warranting\n\nvacation of their convictions or remand for re-sentencing. ",
"We address each argument in\n\nturn.",
"\n\n*\n This disposition is not an opinion of the full Court and pursuant to I.O.P. 5.7 does not\nconstitute binding precedent.",
"\n 2\n\f I. Admission of Non-Video Evidence of the James Murder\n\n Mykal contests the District Court’s decision to admit non-video evidence of the\n\nJames murder, arguing it was cumulative and unfairly prejudicial to him. ",
"We review the\n\nCourt’s decision to admit the evidence for abuse of discretion. ",
"United States v. Schneider,\n\n801 F.3d 186, 197 (3d Cir. ",
"2015). ",
"Mykal claims the evidence was cumulative because the\n\nGovernment had already introduced plenty of evidence that supported using a firearm in\n\nfurtherance of the conspiracy. ",
"However, none of the evidence items he recounts go to\n\ndischarge of a firearm in furtherance of the conspiracy; rather, they show possession or\n\nuse. ",
"See 18 U.S.C. § 924(c)(1)(A)(iii). ",
"Mykal does not tell us why the evidence was\n\nunfairly prejudicial. ",
"Hence we echo our opinion in Bailey—that the high probative value\n\nof the non-video evidence was not substantially outweighed by unfair prejudice. ",
"840 F.3d\n\nat 118–20.",
"\n\n II. ",
" Admission of Video Evidence of the James Murder\n\n We likewise look to Bailey to determine whether the District Court erred by\n\nadmitting video evidence of the James murder. ",
"First, we note the Government concedes\n\nthe District Court erred by admitting the video under the “law of the case” doctrine rather\n\nthan by undertaking the balancing test prescribed by Federal Rule of Evidence 403.1 We\n\n\n\n\n1\n Malik argues the Court’s misapplication of the “law of the case” doctrine denied him\nprocedural due process because he was not present in the first trial to contest that court’s\nadmission of the video evidence. ",
"Our case law does not support the claim that this\nresulted in constitutional harm. ",
"Moreover, Malik had access to procedures available in his\nown trial to contest the video’s admission, which he did. ",
"We see no denial of procedural\ndue process here.",
"\n\n 3\n\fmay affirm despite this error, however, either if the video would have been admissible\n\nunder the proper test or if its admission was harmless.",
"\n\n Both Mykal and Malik argue the video should not have been admitted under the\n\nbalancing test because it was highly prejudicial and lacked probative value in light of the\n\navailability and admission of non-video evidence of the murder. ",
"We follow our analysis\n\nand holding in Bailey on the balancing test: the video lacked probative value because of\n\nthe availability of abundant non-video evidence and its graphic nature made it highly\n\nprejudicial. ",
"840 F.3d at 121–24. ",
"Thus, for the reasons expressed in Bailey, the District\n\nCourt should not have admitted the video evidence. ",
"Id.\n\n We review separately whether this error was harmless, i.e., if “it is highly probable\n\nthat the error did not contribute to the judgment.” ",
"United States v. Zehrbach, 47 F.3d\n\n1252, 1265 (3d Cir. ",
"1995) (en banc) (emphasis omitted) (citation omitted). “",
"High\n\nprobability” requires us to “possess a sure conviction that the error did not prejudice the\n\ndefendant.” ",
"Id. (internal quotation marks omitted) (citation omitted). ",
"Malik asserts that\n\nthe error here was not harmless because the jury chose to review the video multiple times\n\nand relied on it to acquit him of brandishing a firearm. ",
"He believes this also signals that\n\njurors relied on the video to convict him of discharging a firearm in furtherance of the\n\ndrug conspiracy.",
"\n\n First, Malik’s acquittal of a charge based on the jury’s review of the video no\n\ndoubt did not prejudice him. ",
"Second, it is highly probable the video evidence did not\n\ncontribute to either defendant’s conviction for discharging a firearm in furtherance of a\n\ndrug conspiracy in light of the substantial non-video evidence that supported that\n\n 4\n\fconviction. ",
"Mykal and Malik’s intercepted conversation in which Mykal instructs Malik\n\nto murder James, as well as evidence of other co-conspirators’ prior failed attempts to\n\nmurder him, are particularly compelling. ",
"Hence admission of the video in these\n\ncircumstances was harmless.2\n\nIII. ",
" Suppression of Witness Statements\n\n Malik contends the District Court erred by denying his motion under Brady v.\n\nMaryland, 373 U.S. 83 (1963), and holding the Government did not violate due process\n\nby withholding three witness statements. ",
"We review de novo the Court’s conclusions of\n\nlaw and its findings of fact for clear error. ",
"United States v. Perdomo, 929 F.2d 967, 969\n\n(3d Cir. ",
"1991).",
"\n\n On appeal, Malik challenges the Court’s factual findings of each witness’s role in\n\nthe conspiracy and knowledge base. ",
"He claims the Court’s reliance on these erroneous\n\nfactual findings led to legal error in holding there was no Brady violation. ",
"We cannot say\n\nthe District Court’s factual findings were clearly erroneous; the Court laid out myriad\n\nreasons to support its conclusion that each witness’s role was circumscribed and none\n\nwould not have knowledge of Malik or Mykal’s violent acts. ",
"Moreover, each witness\n\nstated he or she did not know of the reason for the James murder.",
"\n\n Malik’s claim of legal error is similarly unavailing. ",
"Under Brady the Government\n\nviolates due process if it suppresses evidence favorable to an accused that is material to\n\neither guilt or punishment. ",
"373 U.S. at 87. ",
"Evidence is favorable if it is either exculpatory\n\n2\n We reiterate our admonition in Bailey that “the doctrine of harmless error is not a\nlicense to engage in whatever prejudicial practices an attorney might feel he or she can\nget away with because the harmless error analysis will inoculate the end result against\nreversal on appeal.” ",
"840 F.3d at 124.",
"\n 5\n\for impeaching, and it is material if there is a reasonable probability that its disclosure\n\nwould have led to a different result in the proceeding. ",
"Strickler v. Greene, 527 U.S. 263,\n\n280–81 (1999). ",
"We agree with the District Court’s thorough and well-reasoned holding,\n\nand we adopt its reasoning as our own, that the statements were not favorable and were\n\nnot material.3 Contrary to Malik’s assertion, the witnesses’ lack of knowledge was not\n\nitself favorable evidence; even if they had extensive knowledge of the conspiracy’s inner\n\nworkings in general, that does not overcome the Court’s finding that none would have\n\nhad knowledge of violent acts committed by Malik or Mykal. ",
"Finally, given the strength\n\nof the Government’s case that James was murdered in furtherance of the charged\n\nconspiracy, neither individually nor cumulatively would the statements’ admission have\n\nbeen reasonably likely to change the trial outcome.",
"\n\nIV. ",
" Mark Frye’s Fifth Amendment Privilege\n\n Mykal argues the District Court committed reversible error by finding Mark Frye\n\n(a heroin dealer who supplied Mykal) did not waive his Fifth Amendment privilege\n\nagainst self-incrimination because Frye answered a question by defense counsel before\n\nclaiming the privilege. ",
"We review this claim of legal error de novo, United States v.\n\nChabot, 793 F.3d 338, 342 (3d Cir. ",
"2015), but accept the Court’s factual findings unless\n\nthey are clearly erroneous, United States v. Ins. ",
"Consultants of Knox, Inc., 187 F.3d 755,\n\n759 (7th Cir. ",
"1999).",
"\n\n The Court found that Frye was confused about when to assert the privilege, and,\n\ndue to his confusion, he did not knowingly and voluntarily waive it when he answered\n\n3\n We affirm on these grounds and thus do not address the Government’s argument that\nJodi Brown’s statement was not suppressed.",
"\n 6\n\fdefense counsel’s question. ",
"His counsel failed timely to question him about his\n\nunderstanding of the privilege, and the Court did not remedy that error by asking those\n\nquestions itself. ",
"Further, when his counsel subsequently asked the proper foundation\n\nquestions, Frye immediately asserted the privilege in response to defense counsel’s\n\nquestion.",
"\n\n We do not disturb the Court’s factual finding that Frye was confused. ",
"The\n\ntranscript of his testimony shows that he intended to assert his Fifth Amendment\n\nprivilege but was unsure of when to do so. ",
"The Court’s legal conclusion, however,\n\npresumes confusion about when to assert one’s privilege precludes finding the privilege\n\nwaived. ",
"Of course, waiver of a Fifth Amendment privilege against self-incrimination\n\nmust be voluntary, knowing, and intelligent. ",
"Colorado v. Spring, 479 U.S. 564, 573\n\n(1987). ",
"But today we need not resolve the question of whether confusion about when to\n\nassert one’s Fifth Amendment privilege renders a subsequent waiver involuntary or\n\nunknowing.",
"\n\n Even assuming the District Court erred by reaching this legal conclusion, any error\n\nwas harmless. ",
"Mykal does not explain what evidence or information he would have\n\nderived from Frye’s testimony. ",
"Based on our review of the record, Frye’s testimony\n\nlikely would have pertained to the drug conspiracy charge and not the firearm offense.",
"\n\nMykal subpoenaed Frye to contradict another witness’s testimony corroborating wiretap\n\nand surveillance evidence of Mykal’s heroin purchases. ",
"Even if Frye’s testimony would\n\nhave made that witness’s testimony incredible, the jury still had considerable evidence—\n\n\n\n 7\n\fparticularly from the wiretaps and Mykal’s admissions—to convict him of the conspiracy\n\ncharge.",
"\n\n V. Mykal’s Sentencing\n\n Mykal argues the Court at sentencing erred by applying the United States\n\nSentencing Guidelines § 2D1.1(d)(1) cross-reference4 based on the James murder,\n\nthereby increasing his base offense level to 43 and suggested minimum sentence to life\n\nimprisonment. ",
"He contends the Government did not show by a preponderance of the\n\nevidence that the murder was committed in furtherance of the drug conspiracy. ",
"He further\n\nargues the Court’s application of the cross-reference violated the Sixth Amendment\n\nbecause the issue of whether the murder was “in furtherance of” the conspiracy was not\n\nsubmitted to the jury to find beyond a reasonable doubt. ",
"He cites to Alleyne v. United\n\nStates, 570 U.S. 99 (2013), for the proposition that “any fact that increases the mandatory\n\nminimum is an ‘element’ that must be submitted to the jury.” ",
"Id. at 102. ",
"We review for\n\nclear error the Court’s factual findings in applying the Sentencing Guidelines. ",
"United\n\nStates v. Knight, 700 F.3d 59, 62 (3d Cir. ",
"2012). ",
"Mykal’s Sixth Amendment claim gets de\n\nnovo review. ",
"United States v. Pavulak, 700 F.3d 651, 671 (3d Cir. ",
"2012).",
"\n\n\n\n4\n This provision states:\n\n [I]f a victim was killed under circumstances that would constitute murder under 18\n U.S.C. § 1111 had such killing taken place within the territorial or maritime\n jurisdiction of the United States, apply § 2A1.1 (First Degree Murder) or § 2A1.2\n (Second Degree Murder), as appropriate, if the resulting offense level is greater\n than that determined under this guideline.",
"\n\nU.S.S.G. § 2D1.1(d)(1).",
"\n\n 8\n\f The Court at sentencing had to find “that murder was . . . ",
"in furtherance of the\n\ndrug-related conspiracy.” ",
"United States v. Gamez, 301 F.3d 1138, 1148 (9th Cir. ",
"2002).",
"\n\nAnd it did, as it found by a preponderance of the evidence that the James murder was in\n\nfurtherance of the drug trafficking conspiracy. ",
"Given the abundance of evidence the\n\nCourt recounted in support of its finding, we cannot say it clearly erred by finding that\n\nthe murder was “in furtherance of” the conspiracy.",
"\n\n Neither did the Court violate the Sixth Amendment by not submitting to the jury\n\nthe question of whether the murder was in furtherance of the conspiracy. ",
"Contrary to\n\nMykal’s suggestion, “Alleyne did not curtail a sentencing court’s ability to find facts\n\nrelevant in selecting a sentence within the prescribed statutory range.” ",
"United States v.\n\nSmith, 751 F.3d 107, 117 (3d Cir. ",
"2014) (emphasis omitted). ",
"That is what the Court did\n\nhere—it found a fact to determine the advisory (i.e., not mandatory) Guidelines range for\n\nMykal’s sentence within the statutorily prescribed range. ",
"See 21 U.S.C. § 841(b)(1)(A).",
"\n\n * * * * *\n\n In sum, we hold the District Court did not err by admitting the non-video evidence\n\nof the James murder, and its error in admitting the video evidence of that murder was\n\nharmless. ",
"Neither did it err by holding the suppression of certain witness statements did\n\nnot violate Brady. ",
"We do not decide whether the Court erred by finding Frye did not\n\nwaive his Fifth Amendment privilege against self-incrimination, but even assuming it\n\ndid, any error was harmless. ",
"Finally, we hold the Court at sentencing properly applied the\n\ncross-reference based on the James murder. ",
"We thus affirm.",
"\n\n\n\n 9\n\f"
] | {
"pile_set_name": "FreeLaw"
} | [
0.00005658669081032141,
0.000016901027582477016,
0.000027167859335691506,
0.000009329707187139933,
0.00003380205516495403,
0,
0,
0,
0.00024151672503320857,
0.00003715814506539833,
0.00005250997689561017,
0,
0.00006609822195782934,
0.000013032881961188077,
0,
0.0006377551020408163,
0,
0.00006682481873767917,
0,
0,
0.0002227667631989307,
0,
0,
0,
0.00005907372400756144,
0.00001556654438281246,
0,
0.00007431629013079666,
0,
0,
0.000033593120128997585,
0,
0,
0,
0,
0.00031887755102040814,
0,
0,
0,
0,
0,
0.0000706164818868724,
0,
0.0001189767995240928,
0.00018261504747991235,
0.00003225754423315753,
0.00023629489603024575,
0.0003429355281207133,
0,
0.0001220703125,
0.0001220703125,
0.000048,
0.00012624668602449185,
0.00025195263290501383,
0.00004565376186997809,
0,
0,
0.00390625,
0,
0.00038446751249519417,
0.00002134417048015846,
0.000016259105098855357,
0,
0.00004792531319192171,
0,
0.00009070294784580499,
0.00031887755102040814,
0,
0.000021784356653487132,
0,
0.0000390625,
0.000038103947568968146,
0.00032873109796186715,
0,
0.000053279343598486864,
0,
0,
0,
0.00008734387282732115,
0.0002082465639316951,
0.00005175715542673775,
0.00009645061728395061,
0.00002826615410707219,
0.000034010135020236034,
0,
0.00001721733441228629,
0.000029218407596785978,
0,
0.00022160664819944597,
0.00038446751249519417,
0,
0.00036982248520710064,
0.00035599857600569594,
0,
0.000015081743047316456,
0,
0.00007305135510263716,
0,
0,
0,
0.00005175715542673775,
0,
0.000037637848620572846,
0.00006530612244897959,
0.00036982248520710064,
0,
0.00006383861597880558,
0,
0.000031245606086644065,
0.0001,
0.00006104819755196727,
0.00017799928800284797,
0,
0
] | 0.000104 | 5 |
[
"SEO Agency Sydney - Search Engine Optimisation Services, Sydney\n\nSEO Training\n\nSEO Agency Sydney can help you to learn the secrets, tips and tricks of Search Engine Optimisation (SEO) to effectively optimise your website to get a higher ranking. ",
"Our SEO training services in Sydney can help you get there faster. ",
"Search Engine Optimisation (SEO) is as important as web design and making your websites search engine friendly will ensure your online business receives the maximise number of visitors.",
"\n\nLearn the Art & Science of SEO\n\nSEO is both an art and science delivering brand presence in search engine result pages (SERP’s). ",
"Gain an understanding of how to improve your website visibility and greater brand credibility through personal SEO training and workshops.",
"\n\nAt our SEO Agency we know about the most important elements to optimise on your website to help your business realise its full potential. ",
"You don’t need to be technical to get started, and our course material is presented in a clear and easy way to give you an understanding of SEO principles and techniques, which will boost your website's ranking performance.",
"\n\nAvoid the pitfalls of bad advice which can harm your website, and learn from the professionals - you’ll save money, time, and a lot of frustration AND maximise the return on your investment. ",
"SEO training techniques are constantly changing, and at the SEO Agency it’s our business to stay on top of the latest SEO trends.",
"\n\nSEO Training Modules\n\nWe can offer standard SEO training modules or we can adapt our training to your own particular business needs, providing either one on one SEO training or group sessions to meet your requirements. ",
"SEO is an ever-changing environment so understanding the concepts and available tools from an SEO training session can enhance your online business enormously.",
"\n\nYou'll come away equipped with an understanding of SEO principles and techniques to master search engine optimisation, and to help you develop your search engine marketing skills – with practical outcomes that can be implemented straight away.",
"\n\nWould you like to learn more?",
"\n\nLearn the concepts of SEO through training and seize the opportunity to improve your unique online presence. ",
"The cost for SEO training services is competitive, and we can tailor training to suit your business."
] | {
"pile_set_name": "Pile-CC"
} | [
0.00006609822195782934,
0,
0.000058436815193571955,
0.00005827166249053085,
0.00005250997689561017,
0,
0.000020108990729755272,
0,
0.00012018508503094766,
0.00004094920251428104,
0.00007911079466793244,
0.000016659725114535613,
0,
0.00008116224332440549,
0.0001
] | 0.000046 | 5 |
[
"Q:\n\nCircle within a matrix\n\nI am trying to build a statistical model that would detect the likelyhood of an interaction with a rod within a cone of variance. ",
"\nI have managed to create the circle within a matrix, but I want to differentiate the inside, from the outside of the circle. ",
"Is there a method by which I could make everything outside of the circle function a separate value?",
"\nHere is what I have so far:\nimport numpy as np \nimport matplotlib.pyplot as plt\n\ndef my_unit_circle(r): \n d = 2*r + 1 \n rx, ry = d/2, d/2 \n x, y = np.indices((d, d)) \n return (np.abs(np.hypot(rx - x, ry - y)-r) < 0.5).astype(int)\n\nmodel = my_unit_circle(300)\n\nmodel[300:325,0:600] = 2\n\nplt.matshow(model) \nplt.show()'''\n\nWhich gives me this:\n\nThank you in advance for any help. ",
"\n\nA:\n\nnp.where can be used to create an array with values depending on a condition:\nimport numpy as np\nimport matplotlib.pyplot as plt\n\ndef my_unit_circle(r):\n d = 2*r + 1\n rx, ry = d/2, d/2\n x, y = np.indices((d, d))\n return np.where(np.hypot(rx - x, ry - y) < r, 1, 0)\n\nmodel = my_unit_circle(300)\n\nmodel[300:325,0:600] = 2\n\nplt.matshow(model)\nplt.show()\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0,
0.000019423887496843618,
0.0000074245112815448925
] | 0.000005 | 5 |
[
"During filming with a motion picture or video camera, it is often necessary for the camera to be moved over a floor or ground surface. ",
"This movement must be accomplished smoothly. ",
"Even small amounts of shock or vibration transmitted to the camera lens can result in shaky or erratic recorded images.",
"\nOne technique for achieving smoother camera movement is to support the camera on a camera crane, which generally has a crane arm supported on a mobile base or vehicle. ",
"As the vehicle rolls over the floor or ground, cracks, bumps, depressions, etc. ",
"can generate shock and/or vibration impulses which may be transmitted through the structure of the camera crane to the camera lens. ",
"These impulses degrade steady filming ability. ",
"If the camera is positioned substantially above the floor surface, the effects of the impulses can be magnified at the camera position.",
"\nAdverse shock and vibration impulses may also occur via movement of the crane arm, even when the vehicle supporting the crane arm is stationary. ",
"For example, the angular acceleration or deceleration of the camera during quick panning movements can cause the crane arm to oscillate in a twisting movement, especially if the center of gravity of the camera payload is off set from the neutral axis of the crane arm. ",
"Similarly, with telescoping crane arms, abruptly starting or stopping inward or outward telescoping movement can cause oscillating vertical bending movement of the arm. ",
"The twisting and bending movements of the arm can disrupt steady filming or recording. ",
"These operating characteristics become more severe with lighter weight crane arms having less capacity to resist twisting and bending. ",
"Accordingly, there is a need for an improved design to allow for smooth filming sequences."
] | {
"pile_set_name": "USPTO Backgrounds"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 | 5 |
[
"using System;\nusing NUnit.",
"Framework;\nusing TestPSSnapIn;\n\nnamespace ReferenceTests.",
"Providers\n{\n [TestFixture]\n public class ProviderLoadingTests : ReferenceTestBase\n {\n [Test]\n public void ProviderFromModuleIsLoadedAndInitialized()\n {\n var cmd = NewlineJoin(\n \"(Get-PSProvider | ? ",
"name -eq \" + TestDriveProvider.",
"ProviderName + \") -eq $null\", // make sure it's not loaded\n \"Import-Module '\" + BinaryTestModule + \"'\",\n \"$p = Get-PSProvider \" + TestDriveProvider.",
"ProviderName,\n \"$p.ImplementingType.",
"FullName\" // to verify it's not empty and is the correct type\n );\n ExecuteAndCompareTypedResult(cmd,\n true, // not loaded at first\n typeof(TestDriveProvider).FullName // make sure the provider is loaded\n );\n }\n\n [Test, Explicit(\"When executed with PS 3.0 this doesn't work. ",
"The same commands work as a script.",
"\"+\n \"I think PS doesn't get the connection between the provider and the module anymore when NUnit is used\")]\n public void ProviderFromModuleCanBeRemovedAndUninitialized()\n {\n var cmd = NewlineJoin(\n \"Import-Module '\" + BinaryTestModule + \"'\",\n \"$p = Get-PSProvider \" + TestDriveProvider.",
"ProviderName,\n \"$p -eq $null\", // false\n \"Remove-Module \" + BinaryTestModuleName,\n \"(Get-PSProvider | ? ",
"name -eq \" + TestDriveProvider.",
"ProviderName + \") -eq $null\"// should be true now\n );\n ExecuteAndCompareTypedResult(cmd, false, true);\n }\n }\n}\n\n"
] | {
"pile_set_name": "Github"
} | [
0.0027434842249657062,
0.0006155740227762388,
0.000015500031000062,
0.0010405827263267429,
0.00003156167150612296,
0,
0.00000811681723362635,
0,
0.00003035615357178092,
0,
0.0010405827263267429,
0
] | 0.00046 | 5 |
[
"Pages\n\nFriday, October 28, 2011\n\nWelcome to week 3 of finish it up Friday! ",
"I've heard from several of you that this challenge is really motivating you to finish up your projects. ",
"Hurray! ",
"Thanks to all of you who have joined in. ",
"It makes finishing much more fun! ",
"I'm really enjoying the challenge, although it does seem like Friday rolls around faster than ever before. ",
"Ha!",
"\n\nThis week I was able to finish knitting a pair of socks that I had been working on since February. ",
"I'm so excited to see these complete. ",
"I'm a very sporatic knitter, and I had one of the socks knit for months. ",
"The other one was started, but I stalled out for awhile. ",
"I turned the heel on the second sock last Saturday, and sped through the last part of the foot in record time. ",
"I closed the toe last night...thanks to this challenge! ",
"I always get a little bit giddy to see how slick the kitchener stitch finishes things up. (",
"Look at me throwing around knitting lingo like I know what I'm doing!) ",
"It's getting COLD here, so hurray for a timely finish!",
"\n\nHow about you? ",
"Do you have a finish from the past week? ",
"If so, feel free to link up and share your accomplishment! ",
"Please remember to link to a specific post. ",
"Thank you! ",
"And happy Friday!",
"\n\nWednesday, October 26, 2011\n\nHere's a little rundown on how this community quilt top came to be....\n\nI started with several blue scraps (thanks to Heather!) ",
"and cut several 4.5\" squares with my Go! ",
"baby while talking to a very good friend on the phone. (",
"I love multitasking!) ",
"The go cutter made quick work of the task. ",
"Plus, it was easy to do while I was on the phone. :)",
"\n\nI had enough blue scraps to make 26 blocks. ",
"But how to lay them out to get a decent size quilt? ",
"I mulled it over for several days. ",
"At this point I also started thinking about what I could use for the back of the quilt.",
"\n\nOne night while I was NOT sleeping, I remembered I had this fabric, which would work great for the back. ",
"It came from my neighbor, Mary. ",
"It was leftover from her son's school project and it ended up in my stash. ",
"Who am I to turn away awesome fabric?",
"\n\nThe backing choice inspired the addition of a few green blocks. ",
"These fabrics came from my stash. ",
"I'm so glad I added the green, the quilt would have been very flat without it.",
"\n\nHere's the finished quilt top! ",
"I wasn't sure I was going to like it before I sewed it together, but now I am pleased as punch! ",
"My son just told me that it looked kinda weird and kinda cool. ",
"Ha! ",
"Good to know! :)",
"\n\nSo there you have a slightly scary look at the inner working of my brain and how a quilt comes together. :) ",
"Lots of using what I have, using what others share with me, and bits of inspiration during sleepless nights. ",
"That about sums it up!",
"\n\nMonday, October 24, 2011\n\nYesterday I hosted a baby shower (with the help of a few good friends) for my friend Tanya and her little baby girl. ",
"Of course I had to make them a quilt. :) ",
"I don't really make that many baby quilts, so I always forget how much fun they are! ",
"I love that you can start and finish one in a few short days.",
"\n\nI went with a simple patchwork pattern with a few random circles thrown in. ",
"I started with 5 circles (on white background squares) when I pieced the quilt. ",
"After the quilt top was done, I decided that the circles were too sparse, so I cut a few more to add on. ",
"I ended up quilting them right on to the quilt sandwich. ",
"It worked fine and dandy! ",
"It's fun to design on the fly. :)",
"\n\nThe circles have raw edges, so they frayed nicely in the wash. ",
"I quilted the circles in spirals and the rest was stippled. ",
"The whole quilt crinkled up quite a bit after washing and drying. ",
"Yay!",
"\n\nThe binding is from the Children at Play line. ",
"LOVE this fabric for binding. ",
"It's just so sweet!",
"\n\nThe backing is Remix by Ann Kelle for Robert Kaufman. ",
"I picked this up last summer for a song. ",
"It's the perfect baby (girl) quilt backing! ",
"I'm happy I still have a bunch left. ",
"The quilt measures 40\" x 50\". ",
"I'm pretty certain that this quilt will be well used and loved. ",
"Hurray!",
"\n\nAnd while we are on the subject of baby quilts....remember this one? ",
"My daughter and I went to a birthday party a few weeks ago, and the new little guy was passed all around the room wrapped in his quilt. ",
"It made me so very happy to see his quilt in use! ",
"He made it look so much better. :) ",
"Aren't those little feet so adorable???",
"\n\nFriday, October 21, 2011\n\nWelcome to week 2 of finish it up Friday! ",
"I hope you have been motivated to finish up something this week. ",
"I want to thank everyone who linked up last week. ",
"It was fun to visit and see all your beautiful finishes. ",
"Keep up the good work!",
"\n\nI was able to put the last few stitches in the binding of my Machine Quilting Sampler this week. ",
"It was quite exciting, especially since I bound this one and a half times. ",
"I wasn't happy with the mitered corners (or non-mitered corners, as it were) the first time around, so I ripped out my stitches (a whole lot of stitches!!) ",
"and did the binding all over. ",
"Now it's much better, and it's complete. ",
"Hurray! (",
"Sometimes it's a huge pain in the hinder to be a perfectionist!)",
"\n\nThis quilt is my class sample for the retreat I'm teaching at in a few weeks. ",
"I quilted each square individually with a different quilting design and then joined them with a quilt as you go method. ",
"I absolutely LOVE how it turned out!!!!",
"\n\nThe backs are all different prints, which made things a bit tricky when it came to layout time. ",
"Not only did the prints need to be evenly distributed, so did the solids on the front. ",
"Just a bit of shuffling and it was good to go. ",
"What a relief!",
"\n\nIt measures 64\" x 80\".",
"\n\nI had a bunch of questions in previous posts asking how to join the blocks together. ",
"I'm not ready to share that information here on the blog yet, as it wouldn't be fair to the students that are taking the class. ",
"And to be honest, it takes a whole lot of prep time to get a class planned out (not to mention getting the sample done), so I'm planning on teaching this class several more times. ",
"Thanks for your understanding!",
"\n\nNow, how about you? ",
"Are you ready to link up with your finish for the week? ",
"Please link to a specific post (not just your blog address) from the past week so we can see what you finished! ",
"Thanks for joining in! :)",
"\n\nFriday, October 14, 2011\n\nWelcome to week one of the finish it up Friday linky party! ",
"My hope is that this challenge helped you finish up some (or any!) ",
"of those WIPs and UFOs into finished projects.",
"\n\nI know this challenge kept me on the straight and narrow this week. ",
"I so badly wanted to start something new (every single day!), ",
"but I buckled down and focused on finishing rather than starting. ",
"I hope I can keep on that trend! :)",
"\n\nTechnically, I finished Mary's quilt last week, but I still had to wash, dry, label, wrap, gift and blog it. ",
"So, now it's done. :) ",
"And it's my finish for the week.",
"\n\nHow about you? ",
"Did you finish anything? ",
"If so, please link to a specific post from the past week and share your fabulous finish!",
"\n\nThursday, October 13, 2011\n\nYesterday afternoon I was hanging this quilt up on my rain gutter on the side of my house (for my third round attempt at a decent photo) and a lady was walking by with her young children. ",
"She stopped to ask me if I made the quilt. ",
"It turns out she is a quilter, too, and new to the neighborhood. ",
"We chatted a little bit and I invited her to our little neighborhood quilting group next month! ",
"What a fun surprise to meet yet another quilting friend on my street. ",
"So, maybe it IS good that I am the crazy quilt lady in the neighborhood trying to get that one decent shot of the quilt for the old blog. :)",
"\n\nI made this quilt for my friend (and yet another neighbor) Mary, with the help of my lovely Two's Company Bee members. ",
"Thanks so much, ladies!! ",
"I couldn't have done it without you! ",
"It turned out to be such a bright and happy quilt, don't you think?",
"\n\nI requested red, aqua and white maverick stars, and I got such a beautiful variety of blocks back. ",
"Each bee member so graciously added a few of their own fabrics in their block, which helped make this a scrappier quilt. ",
"Just what I was after! ",
"If you ask me, this is THE PERFECT bee block. ",
"It's easy, it doesn't use a ton of fabric, each person can add their own personality, but the blocks are still unified with all the others in the end. ",
"That's just my 2 cents. :)",
"\n\nI pieced the back, of course. ",
"The center print was in my stash and it was wide enough to cover the width of the quilt with a few inches to spare. ",
"There was just enough leftover after trimming to add a strip or two to my scrap bucket. ",
"Sweet! ",
"I added a solid aqua and a white and blue dot for the rest. ",
"I LOVE this back!",
"\n\nI stippled the quilt in white thread and machine bound it (yay!) ",
"with this leaf print. ",
"Instead of using my normal warm and natural batting, (I didn't want the flecks to show through all the light fabrics), I used some Fairfied 80/20 batting that I had on hand. ",
"It has no flecks, but it has a higher loft. ",
"That made me nervous, because I was afraid of puckers. (",
"Been there, done that!) ",
"All went well with the quilting, thankfully, and after washing, the loft settled down just a touch so it is the perfect thickness. ",
"Unfortunately, one of the stars bled (boo-hoo), but with all the variety of reds, I guess I wasn't surprised. (",
"Yes, I did use a color catcher, but it didn't help.) ",
"It really didn't bother me too much. ",
"Like we say a lot in our house, \"It is what it is.\" :)",
"\n\nThe quilt measures 60\" x 72\", which is a perfect lap quilt. ",
"I gave it to Mary yesterday, (which was so fun!!!) ",
"and she loved it. ",
"Hurray!",
"\n\nWednesday, October 12, 2011\n\nI love to reuse/repurpose things. ",
"I also have an unhealthy love for rugs. ",
"Handmade rugs? ",
"All. ",
"the. ",
"better. ",
"This one is pretty zany, I'll be the first to admit it. ",
"But so far, so good!",
"\n\nI started with this stack of previously worn knit shirts. ",
"Some were pilled, some were slightly stained and some of them shrunk up funny in the wash. (",
"Hate that!) ",
"I deconstructed them and cut them into approximately 3\" squares. ",
"Thank goodness for my rotary cutter!",
"\n\nI selected a few upholstery samples that I had in my stash (these are 18\" square). ",
"Then, I basically used this tutorial (thanks Vanessa!) ",
"for attaching the knit squares to the upholstery squares. ",
"Working with 18\" squares made the process pretty manageable at the sewing machine. ",
"Any larger and things would have gotten awkward fast!",
"\n\nThese totally remind me of those little tissue paper flowers we used to make in grade school. ",
"The ones where you used little tissue papers wrapped around a pencil eraser and you dipped them in white glue, then attached them on a background piece of paper. ",
"Remember those?",
"\n\nSo far I have two squares done and four left to go. ",
"Once all 6 squares are made, I plan to zig zag them together in a 2 x 3 layout. (",
"Now THAT should be fun. ",
"Heh.) ",
"If all goes well, this will be my new entryway rug.",
"\n\nI started this back in May (oh, my!) ",
"and I'm blogging about it now in hopes that it will motivate me to finish! ",
"Because I really, really could use a new entryway rug. ",
"In fact, I could have used a new rug a few months ago. :) ",
"I'm also linking up with Lee for WIP Wednesday.",
"\n\nTuesday, October 11, 2011\n\nYou get to play with all kinds of different quilting patterns, not to mention thread colors! ",
"I love to machine quilt, especially when things are going well, LOL!",
"\n\nYou get to use up leftover batting pieces. ",
"Who doesn't have a plethora of those lying around?",
"\n\nYou get to use stash. ",
"I have plenty to use....and solids? ",
"Twist my arm!",
"\n\nThen, when you are all done, you get to wrap up in a beautifully textured quilt. ",
"This one is going to have a LOT going on. ",
"I can't wait to wash and dry it and see how it feels. ",
"Maybe I'm getting a little (just a little) ahead of myself. ",
"I still have to trim the blocks and then join all these babies together.",
"\n\nThe downside of this project...\n\nToo much time to think of new projects to work on, or shoot, even variations of this one! ",
"Can you imagine a quilt like this done will all pebble quilting in cool colors? ",
"Mmmmmmmm. ",
"Sign me up!",
"\n\nThese two blocks are new-to-me quilting designs. ",
"They are my favorite of the bunch, at least at the moment!",
"\n\nIf you are looking for some free motion quilting inspiration, Christina at A Few Scraps has a LOT of fun ideas to try. They really helped me out when I was down to the last few blocks. ",
"Thanks so much, Christina!",
"\n\nMonday, October 10, 2011\n\nThis is my entry for the fuddy is not duddy challenge. ",
"The guidelines were to use brown, green and burgundy and add only one additional color to make modern looking mini quilt. ",
"Of course I chose to add white! ",
"What a shocker, I know. :) ",
"I had a few different ideas when I started cutting my fabric, but in the end I went with wonky crosses. ",
"The are so fun to make! ",
"I still debate about whether I should have added more white sashing in or not, but then again I like the blocks all smashed together. ",
"The crosses are machine quilted and then I added some hand quilting in all the white squares. ",
"I love what the hand quilting added to the quilt-it really helped finish it off. ",
"It measures 15\" x 14.5\".",
"\n\nThis challenge was right up my alley...given my history with wanting to rescue fabric and all. ",
"I can safely say that I am not about to use these colors all the time, but I think that they CAN look pretty good. ",
"It's all about what you add to it. ",
"Thanks for the fun challenge, Cheryl! ",
"If you are interested, you can see the other challenge quilts here.",
"\n\nFriday, October 07, 2011\n\nI have so many WIP's it makes me frantic to think about them. ",
"I wish I were kidding and/or exaggerating. ",
"I am not.",
"\n\nMy two newest are fun, but WIP's nonetheless.",
"\n\nThis is my fabric pull for the Fuddy is Not Duddy Challenge. ",
"Have you seen/heard about it? ",
"It's a fun concept for a challenge...too fun that I just couldn't pass it up. ",
"The deadline is Monday, but it's just a mini quilt, so why not? ",
"So far I'm liking what I came up with....just the binding to go!",
"\n\nThis is the very beginnings of my class sample for the quilt retreat that I'm teaching at next month. ",
"I'm quilting each individual square (there are prints on the back of each block) and they will be joined together at the end with a quilt-as-you-go method. ",
"I am at the \"oh-boy-I-sure-do-hope-that-this-turns-out\" phase with this quilt, but I do have high hopes. ",
"Each quilt is an adventure!",
"\n\nSo, getting back to the overwhelmed thing. ",
"I think it's finally time to launch my new series that I've been thinking about for months. ",
"I love what Lee at Freshly Pieced does with her WIP Wednesdays. ",
"So, it's going to work something like that. (",
"Thanks for the inspiration, Lee!) ",
"I'm calling it \"finish it up Friday\". ",
"I will host a little linky party each week here at my place. :) ",
"You can post about your finished project on your blog and link up here, and we can all encourage each other as we finish! ",
"The first link up will be next week. ",
"I might get all official and make a button, or I may not. ",
"We will see. ",
"My hope is that this series will motivate me (and you!) ",
"to finally turn some of those WIP's into finished objects. ",
"Anyone care to join me in? ",
"Or are yours all under control? (",
"HA!)",
"\n\nTuesday, October 04, 2011\n\nThank you, thank you, THANK YOU for your excitement about Cheryl's and my upcoming book! ",
"It feels so very good to finally be able to tell you about it! ",
"I am a terrible secret keeper and I have a little story to prove it. ",
"A few years back I went shopping for my husband's birthday. ",
"I came home and he and I were talking and at one point in the conversation he simply asked \"so, what did you get me?\" (",
"Yes, he is a stinker!) ",
"I opened my mouth and was just about to tell him. ",
"I managed to stop one second before I spilled the beans. ",
"I almost told him right then and there! ",
"It's pretty pathetic, I know. ",
"So can you imagine how hard keeping this secret was? ",
"It was a doozey!!!",
"\n\nSunday Morning Quilts was a true joint effort right from the beginning. ",
"Cheryl and I both brought different things to the table and combined, we worked (very, very hard) on writing a book that we, personally, would love to read, study and make all the quilts from. ",
"We hope that you will, too! ",
"So start (or keep) collecting those scraps!",
"\n\nWe do have just a few more details to share. ",
"It's being published by Stash Books and will be released sometime next spring. ",
"I know, I know, that's a long time to wait. (",
"Trust me, I'm anxious, too!!!) ",
"It isn't available on amazon.com yet for pre-order, but we will let you know when it is."
] | {
"pile_set_name": "Pile-CC"
} | [
0.00017777777777777779,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0009765625,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00004756242568370987,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0009566326530612245,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0001020304050607081,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0000980296049406921,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00038446751249519417,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0003305785123966942,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0009053870529651426,
0,
0.00021626297577854672,
0,
0,
0,
0,
0,
0,
0.0005668934240362812,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00005658669081032141,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0006925207756232687,
0,
0.0001234567901234568,
0,
0,
0.0004526935264825713,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00048828125,
0,
0.0008650519031141869,
0,
0,
0,
0,
0,
0,
0,
0.0002872737719046251,
0,
0,
0,
0.00007181844297615628,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00002684635829149776,
0,
0,
0,
0.0001602307322544464,
0,
0,
0.00012913223140495868
] | 0.00003 | 5 |
[
"Q:\n\nCreating Shared Memory Segments\n\nI have this struct in C:\nstruct first {\nstruct list *buf; \nstruct pointers *ptr; \n};\n\nA function to create a shared memory segment:\nvoid * create_shared_memory(char *name, int size){\n\nint *ptr;\nint ret;\n\nint fd = shm_open (name, O_RDWR | O_CREAT | O_TRUNC, S_IRUSR | S_IWUSR);\n\n if (fd == -1) { \n perror (\"shm_open error!\");",
"\n exit (1);\n }\n\nret = ftruncate (fd, sizeof (size));\n\n if (ret == -1) {\n perror (\"ftruncate error!\");",
"\n exit (2);\n }\n\nptr = mmap(0, sizeof (size), PROT_READ | PROT_WRITE, MAP_SHARED, fd, 0);\n\n if (ptr == MAP_FAILED) {\n perror (\"shm-mmap error!\");",
"\n exit (3);\n }\n\n}\nand a function to create a shared memory segment for that structure:\nvoid shared_memory_structure(){\n\n create_shared_memory(\"struct\", sizeof(struct first));\n\n}\n\nHowever I get an error. ",
"I found the problem was that the pointers inside the structure are not being pointed to the shared memory segment I just created. ",
"How can I do this ?",
"\n\nA:\n\ntry out this code first. ",
"it's a demo code taken from http://blog.csdn.net/liuzhanchen1987/article/details/7455208 , which is in Chinese:\n#include <sys/mman.h>\n#include <sys/types.h>\n#include <fcntl.h>\n#include <unistd.h>\n\ntypedef struct{\n char name[4];\n int age;\n}people;\n\nint\nmain(int argc, char** argv)\n{\n int i;\n people *p_map;\n char temp;\n p_map=(people*)mmap(NULL,sizeof(people)*10,PROT_READ|PROT_WRITE, MAP_SHARED|MAP_ANONYMOUS,-1,0);\n if(fork() == 0)\n {\n sleep(2);\n for(i = 0;i<5;i++)\n printf(\"child read: the %d people's age is %d\\n\",i+1,(*(p_map+i)).age);\n (*p_map).age = 100;\n munmap(p_map,sizeof(people)*10);\n exit();\n }\n temp = 'a';\n for(i = 0;i<5;i++)\n {\n temp += 1;\n memcpy((*(p_map+i)).name, &temp,2);\n (*(p_map+i)).age=20+i;\n }\n sleep(5);\n printf( \"parent read: the first people,s age is %d\\n\",(*p_map).age );\n printf(\"umap\\n\");\n munmap( p_map,sizeof(people)*10 );\n printf( \"umap ok\\n\" );\n return 0;\n}\n\nexpected result:\nchild read: the 1 people's age is 20\nchild read: the 2 people's age is 21\nchild read: the 3 people's age is 22\nchild read: the 4 people's age is 23\nchild read: the 5 people's age is 24\nparent read: the first people,s age is 100\numap\numap ok\n\nin which\nmmap(NULL,size,PROT_READ|PROT_WRITE, MAP_SHARED|MAP_ANONYMOUS,-1,0);\n\nis all what you need to do before forking(and its return value checking code), and its return value will be the allocated pages starting address(if it's valid).",
"\nif all processes are forked. ",
"it's very handy to just use mmap to allocate anonymous pages, and additionally, there is no side effect after the processes get collected.",
"\nif you use shm_open, then in somewhere there will be a share memory object gets created, and it will be the side effect remains in your system, even after all your processes get collected. ",
"however, it's necessary when you plan to have two irrelevant processes talk to each other.",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0.000007149189281935428,
0.00007561436672967865,
0.00003955539733396622,
0,
0,
0,
0,
0.000003045787762546905,
0,
0,
0,
0,
0
] | 0.00001 | 5 |
[
"1. ",
"Introduction\n===============\n\nJellyfish venoms have a wide spectrum of biological activities, such as dermonecrotic, neurotoxic, hemolytic and cardiovascular toxicity \\[[@B1-marinedrugs-11-00067],[@B2-marinedrugs-11-00067],[@B3-marinedrugs-11-00067]\\]. ",
"Among them, hemolytic toxicity is considered to be the most basic damage factor, and nearly all investigated jellyfish venoms possess strong hemolytic toxicity. ",
"Hemolysins have been successfully purified and identified from the jellyfish *Carybdea rastoni* \\[[@B4-marinedrugs-11-00067]\\], *Carybdea alata* \\[[@B5-marinedrugs-11-00067]\\], *Chiropsalmus quadrigatus* \\[[@B6-marinedrugs-11-00067]\\], *Chironex fleckeri* \\[[@B7-marinedrugs-11-00067]\\], and *Cyanea capillata* \\[[@B8-marinedrugs-11-00067]\\]. ",
"According to bioinformatic sequence analysis and investigations of drug intervention against hemolysis \\[[@B9-marinedrugs-11-00067],[@B10-marinedrugs-11-00067],[@B11-marinedrugs-11-00067]\\], hemolysins may function as a pore-former in cell membrane both *in vivo* and *in vitro* \\[[@B12-marinedrugs-11-00067],[@B13-marinedrugs-11-00067],[@B14-marinedrugs-11-00067],[@B15-marinedrugs-11-00067]\\]; furthermore, it was found that jellyfish venoms can induce changes of Ca^2+^, K^+^ and Na^+^ flux across the cell membrane, indicating that the pore-former might be a non-selective cation channel complex \\[[@B12-marinedrugs-11-00067],[@B14-marinedrugs-11-00067]\\]. ",
"Moreover, apparent membrane pore-formation was observed in cultured cells by transmission electron microscopy after exposure to jellyfish venoms \\[[@B13-marinedrugs-11-00067]\\]. ",
"Therefore, these pores, formed by aggregates of cytolysin molecules, could lead to cellular lysis through ion and solution imbalance, following the formation of pore-forming complexes by venoms in cell membranes.",
"\n\nCertainly, pore-formation by hemolysins is an important mechanism of hemolysis of jellyfish venoms. ",
"However, there might have been enough time (as long as 550--750 million years) for jellyfish to evolve other pathways besides pore-formation to destroy the cell membranes. ",
"In view of jellyfish having highly efficient toxic strategies for prey and defense, lipid peroxidation might be another potential mechanism of hemolysis, which can cause loss of polyunsaturated fatty acids, inactivation of membrane enzymes and cytoplasmic proteins, alteration in ion transport and generation of lipid hydroperoxides. ",
"It has been attributed as one of the major pathways for explaining the toxicity of many xenobiotics \\[[@B16-marinedrugs-11-00067],[@B17-marinedrugs-11-00067]\\]. ",
"In addition, several sea anemone venoms, for example those from *Actinia equina* and *Bartholomea annulata*, can induce intracellular reactive oxygen species (ROS) formation in cultured cells \\[[@B18-marinedrugs-11-00067],[@B19-marinedrugs-11-00067]\\]. ",
"Some digestive enzymes, acting as toxins, from box jellyfish, sea anemones, and corals induce ROS or lysophospholipid formation thus damaging target cells as small prey or contributing to human envenomation \\[[@B20-marinedrugs-11-00067]\\]. ",
"Therefore, we speculated that oxidative damage might play a role in the hemolytic toxicity or cytotoxicity of TE from the jellyfish *C. capillata*.",
"\n\nIn the present study, we first investigated the role of pore-formation in the hemolysis of jellyfish venom with the Ca^2+^ indicator, Ca^2+^ channel blockers and PEG with different molecular weights. ",
"We then estimated lipid peroxidation by TE and the effects of antioxidants against the hemolytic activity of TE both *in vitro* and *in vivo*. ",
"Accordingly, we proposed that lipid peroxidation may be another potential mechanism underlying hemolysis besides pore-formation by TE from the jellyfish *C. capillata*.",
"\n\n2. ",
"Results\n==========\n\n2.1. ",
"Hemolytic Activity\n-----------------------\n\nThe hemolytic activity of TE was dose-dependent between 25 and 375 μg protein/mL in 0.45% rat erythrocyte suspension, and the hemolysin unit (HU~50~, is defined as the concentration of protein that causes 50% lysis of erythrocytes) was 149.5 μg protein/mL ([Figure 1](#marinedrugs-11-00067-f001){ref-type=\"fig\"}).",
"\n\n{#marinedrugs-11-00067-f001}\n\n2.2. ",
"Effects of Ca^2+^ and Ca^2+^ Channel Blockers on the Hemolysis of TE\n-------------------------------------------------------------------------\n\nIn the presence of Ca^2+^ from 0.25 to 2 mM, the hemolytic activity of TE (150 μg protein/mL) increased significantly compared with TE treatment alone without extracellular Ca^2+^ ([Figure 2](#marinedrugs-11-00067-f002){ref-type=\"fig\"}). ",
"The Ca^2+^ channel blockers, Diltiazem, Verapamil or Nifedipine, produced a slight hemolysis themselves (\\<5%), however, all significantly inhibited the hemolytic toxicity of TE compared with TE treatment alone, with Diltiazem having the strongest inhibitory effect (79.6% at 160 μM *vs.* TE treatment value) ([Figure 3](#marinedrugs-11-00067-f003){ref-type=\"fig\"}).",
"\n\n{#marinedrugs-11-00067-f002}\n\n{#marinedrugs-11-00067-f003}\n\n2.3. ",
"Changes of Ca^2+^ in Erythrocytes\n--------------------------------------\n\nCa^2+^ fluorescence in erythrocytes significantly increased from 7.52 ± 1.68 without TE intervention to 164.25 ± 12.87 (*n* = 8) after TE treatment at a concentration of 75 μg protein/mL which would not have led to many erthrocytes lysing rapidly, as shown in [Figure 4](#marinedrugs-11-00067-f004){ref-type=\"fig\"}A,B. When the erythrocytes were pre-incubated with Diltiazem at 37 °C for 30 min, the amplitude of Ca^2+^ fluorescence enhancement by TE treatment was attenuated, (the Ca^2+^ fluorescence increasing from 8.19 ± 2.75 to 13.25 ± 3.19 (*n* = 8), as shown in [Figure 4](#marinedrugs-11-00067-f004){ref-type=\"fig\"}C,D).",
"\n\n{#marinedrugs-11-00067-f004}\n\n2.4. ",
"Effect of Osmotic Protectants\n----------------------------------\n\nHemolysis of TE was significantly reduced in the polyethylenglycol (PEG) series with molecular weight (MW) between 4000 Da and 10,000 Da ([Figure 5](#marinedrugs-11-00067-f005){ref-type=\"fig\"}). ",
"After pre-incubation with 25 mM PEG6000 for 5 min, the 0.45% erythrocyte suspension was centrifuged at 1000× *g* for 10 min and the supernatant was removed, such a process was repeated two more times to wash out PEG with PBS, the hemolysis of TE was restored to the level without PEG treatment ([Figure 6](#marinedrugs-11-00067-f006){ref-type=\"fig\"}).",
"\n\n{#marinedrugs-11-00067-f005}\n\n{#marinedrugs-11-00067-f006}\n\n2.5. ",
"Effects of Antioxidants on the Hemolysis of TE *in Vitro*\n--------------------------------------------------------------\n\nWhen incubated with erythrocytes, both Vc (5 mM) and GSH (50 μM) produced a significant attenuation (71.2% and 32.3%, respectively) of the hemolysis of TE at 300 μg protein/mL (*n* = 5, \\* *P* \\< 0.05 *vs.* TE treatment alone; one-way ANOVA followed by Dunnett's test). ",
"Vc and GSH did not cause hemolysis themselves in the absence of TE aliquots at the concentration chosen for the experiments.",
"\n\n2.6. ",
"Lipid Peroxidation\n-----------------------\n\nWhen exposed to increasing concentrations of TE between 50 and 375 μg protein/mL, rat erythrocytes showed a dose-dependent increase of lipid peroxidation, with the MDA level increasing from 2.52 ± 0.35 μM to 12.81 ± 1.15 μM at the highest dose of TE ([Figure 7](#marinedrugs-11-00067-f007){ref-type=\"fig\"}).",
"\n\n{#marinedrugs-11-00067-f007}\n\n2.7. ",
"Effect of Vc on the Hemolysis of TE *in Vivo*\n--------------------------------------------------\n\nAfter TE administration (1.25 mg protein/kg), the optical density (OD) of rat serum at 415 nm increased sharply and reached a peak after 10 min, then gradually returned to the baseline level in the following 60 min, while Vc (250, 500 mg/kg) treatment evidently attenuated the peak of OD ([Figure 8](#marinedrugs-11-00067-f008){ref-type=\"fig\"}). ",
"The electrolytes Na^+^, K^+^, Ca^2+^, Cl^−^ and lactic acid (Lac) were all significantly influenced by TE with Na^+^, Ca^2+^and Cl^−^ decreasing and K^+^and Lac increasing 10 min after TE administration. ",
"The amplitude of K^+^ and Lac increase was also significantly attenuated by Vc (250 mg/kg) ([Table 1](#marinedrugs-11-00067-t001){ref-type=\"table\"}).",
"\n\n{#marinedrugs-11-00067-f008}\n\nmarinedrugs-11-00067-t001_Table 1\n\n###### \n\nEffects of Vitamin C (Vc) on the electrolyte change induced by tentacle extract (TE) *in vivo* (*n* = 6, Δ *P* \\< 0.05 *vs.* control group (pretreated with phosphate buffered saline (PBS) before PBS administration), ▲ *P* \\< 0.05 *vs.* TE group; one-way ANOVA).",
"\n\n Na^+^ (mM) K^+^ (mM) Ca^2+^ (mM) Cl^−^ (mM) Lac (mM)\n ---------------------------------- ---------------- ---------------- --------------- --------------- ----------------\n Control 139.8 ± 1.33 7.23 ± 0.44 2.34 ± 0.08 99.8 ± 1.70 3.18 ± 0.40\n TE (1.25 mg/kg) 137.5 ± 1.05 Δ 10.65 ± 1.31 Δ 2.20 ± 0.05 Δ 94.7 ± 0.82 Δ 8.02 ± 0.43 Δ\n Vc (250 mg/kg) + TE (1.25 mg/kg) 136.0 ± 1.10 Δ 8.42 ± 0.72 Δ▲ 2.26 ± 0.04 Δ 93.7 ± 0.52 Δ 4.98 ± 0.85 Δ▲\n\n3. ",
"Discussion\n=============\n\nIt is believed that the toxic effects of jellyfish venoms are caused by the combined action of various toxic components \\[[@B2-marinedrugs-11-00067],[@B3-marinedrugs-11-00067],[@B21-marinedrugs-11-00067]\\]. ",
"Hemolysin is one of the important damage factors, contributing to the *in vivo* toxic effects of jellyfish venoms through direct hemolysis \\[[@B13-marinedrugs-11-00067],[@B14-marinedrugs-11-00067],[@B15-marinedrugs-11-00067]\\] or through indirect damage by elevating blood K^+^ concentration and serious acidosis, which can associate with other toxicity such as cardiovascular and muscular toxicity \\[[@B22-marinedrugs-11-00067],[@B23-marinedrugs-11-00067],[@B24-marinedrugs-11-00067]\\]. ",
"Using the TE from the jellyfish *C. capillata*, we tried to explore the exact mechanism underlying the hemolysis of jellyfish venom, in order to deepen the understanding of the hemolysis process and finally prompt new research on the prevention and the therapy strategy against jellyfish stings*.*",
"\n\nOur laboratory conducted a series of studies on the hemolytic toxicity of TE from the jellyfish *C. capillata*. ",
"We confirmed that both the extract of the tentacle tissue and the nematocyst venom possess strong hemolytic toxicity and we further investigated the physical and chemical conditions influencing the hemolytic toxicity of jellyfish venom \\[[@B25-marinedrugs-11-00067]\\]. ",
"Our previous experiments showed that non-specific cation channel blocker La^3+^ can significantly inhibit the hemolytic toxicity of TE \\[[@B26-marinedrugs-11-00067]\\]. ",
"Considering the scarcity of ion channels in the erythrocyte membrane, it seems unlikely that TE plays a role by stimulating the membrane ion channels. ",
"Therefore, these results suggested that TE from the jellyfish *C. capillata* may execute a hemolytic effect through transmembrane pore formation in erythrocyte membranes \\[[@B8-marinedrugs-11-00067],[@B22-marinedrugs-11-00067]\\].",
"\n\nIn the present study, we first examined the hemolytic toxicity of TE, and further confirmed the enhancement of hemolytic toxicity by extracellular Ca^2+^ within 2 mM, which was consistent with our previous results and those from other research groups \\[[@B26-marinedrugs-11-00067],[@B27-marinedrugs-11-00067]\\]. ",
"With Ca^2+^ as the indicator of transmembrane pore formation, we found that intracellular Ca^2+^ concentration increased significantly in rat erythrocytes after TE administration. ",
"Considering the lack of Ca^2+^ storage organelles such as endoplasmic reticulum and mitochondria in erythrocytes, as well as the scarcity of Ca^2+^ channel in the erythrocyte membrane, the increase of intracellular Ca^2+^ concentration must be due to the influx of extracellular Ca^2+^ through the channels formed by TE. ",
"The increase of serum K^+^ and decrease of serum Ca^2+^ and Na^+^ further supported the fact that the channel formed by TE is a non-specific cation channel complex.",
"\n\nIn addition, osmotic protection assay showed that the hemolysis of TE was impaired by PEG with MW between 4000 Da and 10,000 Da. ",
"When the erythrocyte suspension was pre-incubated with PEG6000 for 5 min and then the PEG6000 was washed out, the hemolysis of TE was restored to the level without PEG treatment, suggesting membrane lesion by TE with diameters comparable to those of osmotic protectants and thus enhancing the hypothesis of the pore-forming mechanism underlying the hemolysis of TE. ",
"Interestingly, the [L]{.smallcaps}-Ca^2+^ channel blockers, Diltiazem, Verapamil and Nifedipine, significantly inhibited the hemolytic activity of TE, and furthermore, Diltiazem attenuated the increase of intracellular Ca^2+^ concentration. ",
"These results are fairly significant for the prevention and therapy of jellyfish stings, since several researchers have reported that Ca^2+^ channel blockers can inhibit the cardiovascular toxicity of jellyfish venoms as well \\[[@B28-marinedrugs-11-00067],[@B29-marinedrugs-11-00067]\\].",
"\n\nCytolytic toxins are known to operate by ways either enzymatic, producing a direct lytic action upon erythrocytes, or stoichiometric, with the stoichiometric lysins including pore formers and lipid peroxidation \\[[@B30-marinedrugs-11-00067],[@B31-marinedrugs-11-00067]\\]. ",
"Lipid peroxidation is a common mechanism for cell injury. ",
"Vertebrate red blood cell membranes are common targets for oxidative damage by peroxidation because they have a high content of unsaturated lipids as well as iron in hemoglobin, one of the most powerful catalysts capable of initiating lipid peroxidation. ",
"In addition, erythrocyte membrane proteins are susceptible to covalent damage, including cross-linking and aggregation, by oxygen radical-induced lipid peroxidation products. ",
"The lipid peroxidation can impair membrane function, decrease fluidity, inactivate membrane-bound receptors and enzymes, and increase non-specific permeability to ions such as Ca^2+^ \\[[@B17-marinedrugs-11-00067],[@B32-marinedrugs-11-00067]\\]. ",
"The increase in intracellular Ca^2+^ concentration could further activate phospholipases and proteases, leading to free radical reactions involving membrane damage. ",
"Our present studies have determined a significant dose-dependent increase of the oxidative stress biomarker MDA, as well as the inhibition of antioxidant against the hemolysis by TE both *in vitro* and *in vivo*, indicating that the lipid peroxidation might be another important hemolysis mechanism of TE from the jellyfish *C. capillata*.",
"\n\nIt has been reported that the stimulation of lipid peroxidation as a consequence of iron ions released from erythrocytes may increase the permeability to ions such as Ca^2+^, suggesting the peroxidative process is related to the increase in cytosolic Ca^2+^ \\[[@B33-marinedrugs-11-00067]\\]. ",
"Lipid peroxidation can also produce \"holes\" in erythrocyte membranes of roughly 70 Å by disrupting membrane phospholipids involved in maintaining the integrity of the plasma membrane \\[[@B34-marinedrugs-11-00067]\\]. ",
"Whether pore-formation is mainly attributed to lipid peroxidation or to self-assembly of hemolysin could be an important question underlying the mechanism of TE hemolysis. ",
"Purifying the oxidative component and going into its structural details according to the structure-function relationship might be a possible way to further prove the oxidative effect of TE. ",
"So far, the hypothesis that TE forms pores in the cell membrane through oxidative damage of plasma membrane certainly needs more experimental evidence and this will be our next main research issue.",
"\n\n4. ",
"Experimental Section\n=======================\n\n4.1. ",
"TE Preparation from the Jellyfish *C. capillata*\n-----------------------------------------------------\n\nSpecimens of *C. capillata* were collected in June 2010 in the Sanmenwan offing of the East China Sea in Zhejiang Province, China, and identified by Professor Huixin Hong from the Fisheries College of Jimei University, Xiamen, China. ",
"The removed tentacles were preserved in plastic bags on dry ice and immediately shipped to Shanghai, where the samples were frozen at −70 °C until use. ",
"The TE was prepared following the method described as in previous reports \\[[@B25-marinedrugs-11-00067],[@B35-marinedrugs-11-00067]\\]. ",
"Briefly, frozen tentacles were thawed at 4 °C in filtered seawater at a mass/volume ratio of 1:1 to allow autolysis of the tissues for 4 days. ",
"The mixture was then stirred for 30 min twice daily. ",
"The autolyzed mixture was centrifuged at 10,000× *g* for 15 min three times. ",
"The resultant supernatant was the TE. ",
"All procedures were performed at 4 °C or in an ice bath. ",
"Before being used for injection, TE was centrifuged at 10,000× *g* for 15 min to remove sediment, followed by dialysis against PBS (0.01 M, pH 7.4) at 4 °C for over 8 h. Protein concentrations were determined in all samples by the method of Bradford (1976), with fetal bovine serum albumin (high purity, Sigma, St. Louis, MO, USA) as a standard \\[[@B36-marinedrugs-11-00067]\\].",
"\n\n4.2. ",
"Hemolytic Activity Assay {#sec4dot2-marinedrugs-11-00067}\n-----------------------------\n\nHemolytic activity of TE was tested in 0.45% male rat erythrocyte suspension. ",
"In brief, 100 μL of fresh heparinized blood samples were made up to 10 mL in phosphate buffered saline (PBS, self prepared, with the following composition in mM: 135 NaCl, 4.7 KCl, 10 Na~2~HPO~4~, 2 NaH~2~PO~4~, pH 7.4), and then centrifuged at 1000× *g* for 10 min at 4 °C. ",
"The supernatant and buffy coat were removed by gentle aspiration, and the above process was repeated two more times. ",
"Erythrocytes were finally resuspended in the same buffer to a final concentration of 0.45% (v/v). ",
"Aliquots of 0.45% erythrocyte suspension were incubated at 37 °C for 30 min in the presence of TE with the concentrations ranging from 0 to 375 μg protein/mL (50% v/v), and then centrifuged at 1000× *g* for 10 min at 4 °C to precipitate both the intact erythrocytes and ghosts. ",
"The 200 μL supernatants were transferred into 96-well microplates and the absorbance at 415 nm was determined by using a spectrophotometric microplate reader (BIO-RAD iMark™, Hercules, CA, USA) to measure the extent of red blood cell lysis. ",
"The hemolytic activity of TE was expressed as % absorbance compared with that observed after maximal lysis induced by sodium dodecyl sulphate (40 μg/mL). ",
"The supernatant of untreated 0.45% erythrocyte suspension was taken as the background and subtracted (*n* = 6). ",
"Male Sprague-Dawley (SD) rats (220--240 g) were provided by the Laboratory Animal Center of the Second Military Medical University, Shanghai. ",
"All were procured from the animal care facility at the university where they were housed in cages with 12/12 h light/dark cycle at 22 ± 2 °C and given standard diets plus water *ad libitum*. ",
"The investigation was carried out in conformity with the Ethics Committee of the Second Military Medical University and international guidelines for animal handling.",
"\n\n4.3. ",
"Effects of Ca^2+^ and Ca^2+^ Channel Blockers on the Hemolysis of TE\n-------------------------------------------------------------------------\n\nThe effect of Ca^2+^ was studied by adding CaCl~2~ into TE and then the hemolytic activity was assayed as described above. ",
"Ca^2+^ was employed at a final concentration of 0.25, 0.5, 0.75, 1.0 and 2.0 mM, respectively. ",
"To inspect the possible protective effect of Ca^2+^ channel blockers against hemolysis, Diltiazem, Verapamil and Nifedipine (Sinopharm Chemical Reagent Co. Ltd., Shanghai, China) were incubated with 0.45% erythrocyte suspension at 37 °C for 30 min before TE administration (150 μg protein/mL). ",
"Then the relative percentage of hemolytic activity was calculated as described above. ",
"All the Ca^2+^ channel blockers were employed at final concentrations of 10, 20, 40, 80 and 160 μM, respectively.",
"\n\n4.4. ",
"Measurement of Cytosolic Free Ca^2+^ Using CLSM\n----------------------------------------------------\n\nThe intracellular Ca^2+^ indicator fluo-3 acetoxymethyl (AM) was used to measure the Ca^2+^ changes in the erythrocyte. ",
"Briefly, 1 mL of the 0.2% erythrocyte suspension was loaded with Fluo-3/AM (5 μM) and further incubated at 37 °C for 120 min in the dark. ",
"After this, the solution was centrifuged at 1000× *g* for 10 min and the supernatant was removed. ",
"Such a process was repeated two more times. ",
"The erythrocytes were finally resuspended in 1 mL Hank's solution (Sangon Biotechnology, Shanghai, China, with the following composition in mM: 1.6 CaCl~2~, 1.0 MgCl~2~, 145 NaCl, 5.0 KCl, 0.5 NaH~2~PO~4~, 10 dextrose, and 10 Hepes, pH 7.4). ",
"To test the influence of Ca^2+^ channel blocker on the changes of intracellular Ca^2+^ induced by the TE, 0.2% erythrocyte suspension was pre-incubated with Diltiazem (100 μM) before exposure to the TE (75 μg protein/mL). ",
"For confocal laser scanning microscopy, 200 μL of such a solution with or without Diltiazem was replated onto special dishes. ",
"Intracellular Ca^2+^ changes were measured by monitoring the alteration of cell fluorescence.",
"\n\n4.5. ",
"Osmotic Protection Assay\n-----------------------------\n\nTo test the effect of osmotic protectants, 25 mM PEG with different molecular weights (2000, 4000, 6000 and 10,000 Da) was added to 1 mL 0.45% erythrocyte suspension. ",
"Then aliquots of TE (75, 150, 300 μg protein/mL) were added, and the hemolytic activity was detected as described above. ",
"In another separate experiment, 25 mM PEG6000 was pre-incubated with 0.45% erythrocyte suspension at 37 °C for 5 min, then the 0.45% erythrocyte was centrifuged at 1000× *g* for 10 min and the supernatant was removed. ",
"Such a process was repeated two more times to wash out PEG with PBS, and the erythrocytes were finally resuspended in PBS to a final concentration of 0.45% (v/v), and then aliquots of TE (75, 150, 300 μg protein/mL) were added to test the hemolytic activity.",
"\n\n4.6. ",
"Effects of Antioxidants on the Hemolysis of TE *in Vitro*\n--------------------------------------------------------------\n\nIn order to test the possible involvement of lipid peroxidation in the hemolysis, aliquots of 0.45% erythrocyte suspension were pre-treated with Vc and GSH at 37 °C for 30 min at a final concentration of 5 mM and 50 μM, respectively, before TE (300 μg protein/mL) administration, and hemolytic activity was detected as described in [Section 4.2](#sec4dot2-marinedrugs-11-00067){ref-type=\"sec\"}.",
"\n\n4.7. ",
"Measurement of Malondialdehyde\n-----------------------------------\n\nFor lipid peroxidation assay, we used a commercial kit (Beyotime Institute of Biotechnology, Nantong, Jiangsu, China) to quantify the generation of malondialdehyde (MDA) according to the manufacturer's protocol. ",
"In brief, the 20% erythrocyte suspension aliquots were incubated with TE at 37 °C for 30 min and then centrifuged at 1000× *g* for 10 min, and the supernatant was subjected to measurement of MDA levels.",
"\n\n4.8. ",
"Effect of Vc on the Hemolysis of TE *in Vivo*\n--------------------------------------------------\n\nThirty-two male Sprague-Dawley (SD) rats (220--240 g, provided by the Laboratory Animal Center of the Second Military Medical University, Shanghai, China) were randomized into four groups (*n* = 8) and anesthetized with urethane (1.2 g/kg i.p.). ",
"To inspect the possible protective effect of antioxidants against hemolysis of the TE *in vivo*, Vc at different doses (125, 250, 500 mg/kg i.p.) ",
"was adopted before TE administration (1.25 mg protein/kg i.v.). ",
"The blood sample was obtained through a glass capillary inserted into the retrobulbar venous plexus at 0 (pre-injection), 10, 30 and 60 min after TE administration, respectively. ",
"Similarly, the rats of the control group (*n* = 8), after intraperitoneal injection of PBS, were treated with TE through tail vein injection and blood samples were obtained at the corresponding time points. ",
"Aliquots of the blood samples were centrifuged at 1000× *g* for 10 min to precipitate both the intact erythrocytes and ghosts. ",
"The supernatants were collected as the serum and the ODs were spectrophotometrically measured at 415 nm as the marker of hemolytic activity *in vivo*.",
"\n\nTo further observe the effects of antioxidants on the changes of electrolytes and Lac *in vivo*, eighteen male SD rats were randomized into three groups (*n* = 6) and pretreated with PBS or Vc (250 mg/kg i.p.), ",
"then TE at the dose of 1.25 mg protein/kg was chosen for tail vein injection and the serum was collected 10 min after TE administration. ",
"The sham-treated animals (*n* = 6) were administered with the same volume of PBS. ",
"Electrolytes (Na^+^, K^+^, Ca^2+^ and Cl^−^) and Lac in the serum collected as described above were analyzed by an arterial blood gas analyzer (GEM Premier 3000, International Laboratory, Bedford, MA, USA).",
"\n\n4.9. ",
"Statistical Analysis\n-------------------------\n\nOne-way analysis of variance (ANOVA) was used. ",
"In all cases, statistical significance was indicated by *P* \\< 0.05. ",
"All data were expressed as mean ± SD.",
"\n\n5. ",
"Conclusions\n==============\n\nWe further elucidated that non-specific cation transmembrane pore formation is one of the mechanisms underlying hemolysis of TE from the jellyfish *C. capillata*. ",
"Furthermore, we proposed that lipid peroxidation might be another potential mechanism of hemolysis, in addition to pore-formation. ",
"Both Ca^2+^ channel blockers and antioxidants might be considered as useful candidates against the hemolytic activity of jellyfish venoms.",
"\n\nThis research was funded by the National Natural Science Foundation Young Scientists Fund (81000098), the National Natural Science Foundation of China (41176126) and the Fund of Shanghai Municipal Health Bureau (2012). ",
"The authors thank Fang Wei of the College of International Exchange of the Second Military Medical University for his careful revision of the English language of the manuscript.",
"\n\n[^1]: These authors contributed equally to this work.",
"\n"
] | {
"pile_set_name": "PubMed Central"
} | [
0,
0.0000468684091299661,
0,
0.000050999158513884524,
0.000020598689465601332,
0.00003191930798940279,
0.000022249911000355996,
0,
0,
0,
0.00007715751707110065,
0.0000468684091299661,
0.000017506696311339085,
0,
0.00007352220370551907,
0,
0,
0,
0,
0.000007846275765208045,
0,
0,
0,
0.000020666708000082665,
0.000030024394820791894,
0,
0.000018365472910927457,
0,
0.00003018959062915107,
0,
0.000006087612925219764,
0,
0.000030036524413687044,
0,
0.0000146797610134907,
0.00000811681723362635,
0,
0.00007831466833737959,
0.000035427073369468946,
0.000031000062000124,
0.00002603082049146189,
0.00006503642039542143,
0,
0.0000162336344672527,
0,
0,
0.00004286694101508916,
0.000005072640207775343,
0.00004805843906189927,
0.00004504301608035674,
0,
0,
0,
0,
0.000018507502148192216,
0.00001156925355176084,
0.00005525981322183131,
0.000025194840096748185,
0,
0,
0.000013819598955238318,
0.000035430839002267575,
0,
0.000038138098053050095,
0.000040569597143900364,
0.0000308641975308642,
0.00002911462427577372,
0.000037180249851279,
0.0001165433249810617,
0.000014930275612887814,
0.00008608667206143145,
0.000024451073402122352,
0.000026639671799243432,
0,
0.000015378700499807765,
0,
0.00001707533638412677,
0,
0.0000087016298152644,
0.000011648359328588568,
0.00002143347050754458,
0,
0.000027700831024930747,
0,
0,
0.00038446751249519417,
0.000026259584748433177,
0,
0.00005486968449931413,
0,
0,
0,
0.0006925207756232687,
0,
0.000021107585362593138,
0,
0,
0.00005289256198347107,
0,
0,
0,
0,
0,
0,
0.00009918666931164451,
0,
0.000036730945821854914,
0,
0.00004208222867483062,
0.00022160664819944597,
0.00003470776065528252,
0,
0,
0,
0.00004058112166220274,
0.00005250997689561017,
0,
0,
0.00001707533638412677,
0.00008116224332440549,
0,
0,
0,
0,
0,
0.000021041999831664002,
0.000030046271257736914,
0,
0.0000037703836365350172,
0,
0.00002551020408163265,
0.000024507401235173024,
0,
0.000016901027582477016,
0,
0,
0,
0.00002333776750916007,
0,
0,
0.00004408296413850868,
0,
0.000148720999405116,
0.0001178244886417193,
0,
0.00011080332409972299,
0,
0,
0,
0,
0,
0.00005250997689561017,
0.00006142380377142156,
0.00006383861597880558,
0,
0
] | 0.000027 | 5 |
[
"Dear KuCoin users:\n\nWe are delighted to inform you that the update of XRB into NANO is complete, and the deposit, withdrawal and trading services for NANO are now available."
] | {
"pile_set_name": "OpenWebText2"
} | [
0.00006682481873767917
] | 0.000067 | 5 |
[
"90%82°45°Partly cloudy skies during the morning hours. ",
"Thunderstorms likely in the afternoon. ",
"High 82F. Winds SW at 5 to 10 mph. ",
"Chance of rain 90%.Night - Partly cloudy skies. ",
"A stray shower or thunderstorm is possible. ",
"Low around 45F. Winds NW at 5 to 10 mph.",
"\n\nThursday\n\n10%58°37°Partly cloudy skies. ",
"High 58F. Winds NW at 5 to 10 mph.",
"Night - Some clouds early will give way to generally clear conditions overnight. ",
"Low 37F. Winds light and variable.",
"\n\nFriday\n\n10%57°35°Partly cloudy. ",
"High 57F. Winds NNW at 5 to 10 mph.",
"Night - Partly cloudy in the evening with more clouds for later at night. ",
"Slight chance of a rain shower. ",
"Low near 35F. Winds light and variable.",
"\n\n30%72°48°A mix of clouds and sun in the morning giving way to a few showers during the afternoon. ",
"High 72F. Winds WSW at 5 to 10 mph. ",
"Chance of rain 30%.Night - A few clouds. ",
"Low 48F. Winds light and variable."
] | {
"pile_set_name": "Pile-CC"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00018261504747991235,
0,
0,
0,
0,
0,
0
] | 0.00001 | 5 |
[
"38 posts in this topic\n\nI still don't have my bulbs after being posted 1st class recorded on the 19 March. ",
"He finally communicated with me (after I'd sent him 5 emails and eBay and PayPal had emailed him) and has posted them out again but they haven't arrived either. ",
"He's in trouble now anyway as PayPal are taking action against him to recover the monies - all of £2.50 but that's not the point. ",
"I shall be giving him a negative score 'poor communication', item not received - twice'. ",
"Grrr, I hate buying stuff off eBay. ",
"I am a perfect seller though :P\n\nPeter\n\nShare this post\n\nLink to post\n\nShare on other sites\n\nI still don't have my bulbs after being posted 1st class recorded on the 19 March. ",
"He finally communicated with me (after I'd sent him 5 emails and eBay and PayPal had emailed him) and has posted them out again but they haven't arrived either. ",
"He's in trouble now anyway as PayPal are taking action against him to recover the monies - all of £2.50 but that's not the point. ",
"I shall be giving him a negative score 'poor communication', item not received - twice'. ",
"Grrr, I hate buying stuff off eBay. ",
"I am a perfect seller though :P\n\ndont think so ive got a zetec s and it has none of the wiring for it ,which for ford is strange,they normally either just dont put the bulbs in or strap the unwanted wires up somewhere,i tried fitting the interior light from a titanium with the map lights and submarine lights,the map lights work but theres no feed up there for the L.E.Ds which must be linked with the dash lights or something,with the footwell and glove box strip light ive had no luck either i cant find a loom for them :("
] | {
"pile_set_name": "Pile-CC"
} | [
0,
0.00007715751707110065,
0,
0,
0.0015432098765432098,
0,
0.00007715751707110065,
0,
0,
0.0015432098765432098,
0.0000036281179138321994
] | 0.000295 | 5 |
[
"August 2013\n\nAugust 31, 2013\n\nFour Texas A&M football players, including three defensive starters, were suspended today for two games for unspecified violations of team rules. ",
"The suspensions take effect immediately, with the four players eligible to return for the team’s Sept. 14 game against Alabama.",
"\n\nThe three defensive starters who will miss today’s Rice game are CB De’Vante Harris, LB Steven Jenkins and DE Gavin Stansbury. ",
"Receiver Edward Pope, a backup, also will miss the first two games.",
"\n\nThe latest suspensions, announced by school officials, means eight different Aggies will serve disciplinary suspensions of some sort against the Owls. ",
"Also out for today’s game are DL Kirby Ennis and DB Floyd Raven. ",
"Two players are suspended for half of today’s game: DB Deshazor Everett and QB Johnny Manziel, the 2012 Heisman Trophy winner.",
"\n\nAugust 30, 2013\n\nAT&T Stadium has modified its security policy by\nlimiting the size and style of bags allowed into the stadium. ",
"The large purse shown here? ",
"That won't fly Saturday at TCU's season opener against LSU.",
"\nProhibited bags\ninclude, but are not limited to, the following: all purses, bags or containers\nlarger than a small clutch bag, coolers, briefcases, backpacks, fanny packs,\ncinch bags, luggage of any kind, computer bags, camera bags, binocular cases\n(binoculars may be worn around the neck), diaper bags, and seat cushions.",
"\n\nFor more details on the bag restrictions visit\nwww.dallascowboys.com/bags.",
"\n\nStefan Stevenson@FollowtheFrogs\n\nAT&T Stadium has modified its security policy by limiting the size and style of bags allowed into the stadium. ",
"Prohibited bags include, but are not limited to, the following: all purses, bags or containers larger than a small clutch bag, coolers, briefcases, backpacks, fanny packs, cinch bags, luggage of any kind, computer bags, camera bags, binocular cases (binoculars may be worn around the neck), diaper bags, and seat cushions.",
"\n\nFor more details on the bag restrictions visit www.dallascowboys.com/bags.",
"\n\nThe Bell Helicopter Armed Forces Bowl in Fort Worth will become part of the Big 12 bowl mix in the 2014 season, league and bowl officials announced Friday.",
"\n\nAs part of the deal, the Big 12 will provide its No. ",
"7 pick to either the game in Fort Worth or the Heart of Dallas Bowl five times during a six-year stretch (2014-19). ",
"A Big 12 team will be a primary back-up selection in the other season.",
"\n\nIn years that a Big 12 school does not wind up in Fort Worth, a team from the Big Ten will compete in the game at Amon G. Carter Stadium while a Big 12 school heads to Dallas as part of a reciprocal deal between the two bowls and the two leagues. ",
"The Big Ten agreement with the D-FW bowls, announced in July, covers the 2013-19 seasons.",
"\n\nThe Big Ten will send a team to this year’s Heart of Dallas Bowl. ",
"The 2013 Armed Forces Bowl, to be played Dec. 30 in Fort Worth (10:45 a.m., ESPN), will feature Navy – pending bowl eligibility -- against an opponent from the Mountain West Conference.",
"\n\nIn seasons when the Big 12 team plays in the Armed Forces Bowl, that school will play an opponent from the American Athletic Conference. ",
"When the Big 12 team winds up in Dallas, the opponent will come from Conference USA.",
"\n\nBrant Ringler, executive director of the Armed Forces Bowl, said officials in Fort Worth are “extremely excited to be working … with the Big 12 Conference and its counterparts in the Big Ten during the next six seasons.”",
"\n\nBig 12 commissioner Bob Bolwsby said adding the D-FW connection allows league officials to meet “all the benchmarks” sought by schools for future bowl tie-ins: a strong presence in Texas, combined with options in Florida, Arizona and another drivable destination for most schools (Liberty Bowl in Memphis).",
"\n\nThe Bell Helicopter Armed Forces Bowl in Fort Worth will become part of the Big 12 bowl mix, starting with the 2014 season, sources close to the situation have confirmed. ",
"A formal announcement is expected later today.",
"\n\nAs part of the deal, the Big 12 will provide its No. ",
"7 pick to either the game in Fort Worth or the Heart of Dallas Bowl on an annual basis five times during a six-year stretch (2014-19). ",
"A Big 12 team will be a primary back-up selection in the other season.",
"\n\nIn years that a Big 12 school does not wind up in Fort Worth, a team from the Big Ten will compete in the game at Amon G. Carter Stadium while a Big 12 school heads to Dallas as part of a reciprocal deal between the two bowls and the two leagues. ",
"The Big Ten agreement with the D-FW bowls, announced in July, covers the 2013-19 seasons.",
"\n\nThe Big Ten will send a team to this year’s Heart of Dallas Bowl. ",
"The 2013 Armed Forces Bowl, to be played Dec. 30 in Fort Worth (10:45 a.m., ESPN) will feature Navy – pending bowl eligibility -- against an opponent from the Mountain West Conference.",
"\n\nAugust 29, 2013\n\nThe college football season kicks off this weekend and the Texas A&M-Alabama game on Sept. 14 is the hottest commodity on the re-sale ticket market, based on information provided today by vividseats.com.",
"\n\nThe A&M-Alabama game, a battle of Top 10 teams in the preseason polls, has an average re-sale price of $744 per ticket, with a $359 minimum, based on data compiled by the website.",
"\n\nAmong opening-week matchups, the costliest re-sale tickets are for these games: Georgia-Clemson ($292), Boise State-Washington ($232) and Alabama-Virginia Tech ($175).",
"\n\nAmong individual schools, the highest average ticket prices for home games are found at Notre Dame ($290), Ohio State ($280) and Alabama ($246). ",
"Texas A&M is sixth on that list ($205), with Texas at No. ",
"8 ($186) and Oklahoma at No. ",
"10 ($169).",
"\n\nIn terms of individual contests, the Red River Rivalry matchup between Texas and Oklahoma ranks fifth nationally on the re-sale market, with an average price of $466 and a minimum price of $191.",
"\n\nAugust 28, 2013\n\nWide receivers Jaxon Shipley and Marcus Johnson were limited in practice Tuesday and practiced again Wednesday. ",
"Whether they will suit up for the Longhorns in Saturday's season opener against New Mexico State has not been decided.",
"\n\n\"They did not have more soreness today than yesterday, so that was good,\" head coach Mack Brown said. \"",
"We'll press them a little bit harder today, get them in more competition and probably won't know for sure how they'll do until Saturday morning.\"",
"\n\nShipley, who is recovering from a hip injury, made a team-high 59 catches for 737 yards and six touchdowns in 2012. ",
"Johnson played in eight games last season without making any catches. ",
"He sprained his right MCL earlier this month and is also questionable for this weekend.",
"\n\nSophomore wideout Kendall Sanders will not play this weekend while he serves a one-game suspension stemming from a DWI arrest in April. ",
"That means Texas may need true freshman Jacorey Warrick to play and could even have sophomore cornerback Duke Thomas, who played both ways in this year's Orange-White Scrimmage, to play wide receiver.",
"\n\n\"We are going to have an emergency plan for Duke Thomas so, if we had to move him over, if we had too many receivers hurt until we get everybody back. ",
"He worked there five days in the spring, so we'll work him there a little bit today and a little bit tomorrow.\"",
"\n\nFreshman quarterback Tyrone Swoopes is not injured but is also questionable for Saturday's opener. ",
"With Jalen Overstreet moving to running back and Connor Brewer transferring to Arizona over the offseason, Swoopes was left as the only option to be the Longhorns' third-string quarterback.",
"\n\n\"We've got to see him step up,\" Brown said of Swoopes at Big 12 Media Days last month. \"",
"We would like to play him. ",
"We would like for him to be good. ",
"David [Ash] thinks he's made progress.\"",
"\n\nAsh and senior Case McCoy are the only two other quarterbacks with scholarships on the Texas roster. ",
"If Swoopes doesn't play this weekend, there's a chance he could redshirt this year.",
"\n\nSenior defensive tackle Ashton Dorsey's decision to transfer came as a surprise to most people but, according to Texas head coach Mack Brown, it was a \"mutual\" one.",
"\n\n\"We met with him and felt like it was mutual and best for him,\" Brown told reporters Wednesday. \"",
"It was best for him that he get a new start somewhere else. ",
"We're trying to help him go to the place that he wants to go and give him an unconditional release and get him to move forward.\"",
"\n\nDorsey's decision to transfer was announced by the school Tuesday morning, leaving the Longhorns with only three defensive tackles that have seen the field for Texas -- Malcom Brown, Chris Whaley and Desmond Jackson. ",
"Freshmen defensive tackles Alex Norman, Hassan Ridgeway and Paul Boyette, Jr. could all get playing time during the Longhorns' season opener against New Mexico State this weekend.",
"\n\nDespite Dorsey's absence, Brown said defensive tackle depth was not a concern.",
"\n\n\"We've got more depth there than we've had probably most of the last three years,\" Brown said. \"",
"We're planning on playing at least Hassan and Alex Norman Saturday night for sure, and Paul may get in some. ",
"But right now I would say probably Hassan is the first guy to go in. ",
"We're planning on playing a lot of players. ",
"We want to play twenty-someting guys on defense the first half.\"",
"\n\nDorsey, who was not listed in the depth chart Texas released Monday, was battling a calf injury that was likely to keep him out of Saturday's opener, regardless of whether he was transferring. ",
"The Tyler Morning Telegraph reported Tuesday night that Dorsey was in Beaumont and planning on transferring to Lamar University.",
"\n\n\"That comes as a surprise to me,\" defensive end Cedric Reed said of Dorsey's decision. \"",
"Ashton Dorsey brought that toughness, man. ",
"He was a tough guy. ",
"We needed him. ",
"It's pretty sad.\"",
"\n\nTexas A&M quarterback Johnny Manziel will be suspended for the first half of Saturday’s game against Rice for what is considered an inadvertent violation of an NCAA rule regarding autographs.",
"\n\nIn a joint statement issued Wednesday, school and NCAA officials agreed there was “no evidence that quarterback Johnny Manziel received money in exchange for autographs, based on currently available information and statements by Manziel.”",
"\n\nBecause of the inadvertent violation of an NCAA bylaw that says athletes are “required to take steps to stop” the use of their name or picture on commercial items sold by an individual or agency, A&M officials declared Manziel ineligible and submitted a three-part penalty that was accepted by NCAA officials.",
"\n\nIn addition to sitting out the first half of Saturday’s opener against Rice (noon, ESPN), Manziel must address the team regarding the situation and lessons learned. ",
"A&M also must revise its education of student-athletes in regard to signing autographs for individuals with multiple items.",
"\n\nThe penalties can be reviewed by NCAA officials if additional information surfaces and further action is considered appropriate. ",
"NCAA bylaws prohibit signing memorabilia in exchange for money and the joint release said: “based on information provided by Manziel, that did not happen in this case.”",
"\n\nWednesday’s action ends more than three weeks of speculation about the eligibility status of the 2012 Heisman Trophy winner and assures that A&M will start a former Tarrant County high school standout at quarterback against Rice: junior Matt Joeckel, an Arlington High School graduate, or Kenny Hill, a freshman from Southlake Carroll.",
"\n\nSpeculation about Manziel’s availability began Aug. 4, when an ESPN “Outside the Lines” report alleged that Manziel accepted a five-figure fee in January for signing items for a memorabilia dealer in Florida. ",
"Citing unnamed sources, ESPN followed up with additional reports of other signings for profit involving Manziel but indicated many of the network’s sources were not willing to talk to NCAA investigators.",
"\n\nManziel denied accepting money in exchange for his signature during a six-hour meeting Sunday with NCAA investigators in College Station, sources told CBSSports.com. ",
"Wednesday’s joint announcement showed that NCAA officials were satisfied with Manziel’s denial when weighed against other evidence they collected. ",
"His transgression that led to Saturday’s suspension stemmed from violating the “spirit” of bylaws 12.5.2.1 and 12.5.2.2, which require an athlete to try and stop the commercial use of his name or likeness for commercial purposes.",
"\n\nManziel was not available for interviews and administrators from A&M and the NCAA issued prepared statements about the decision.",
"\n\n“Student-athletes are often asked for autographs from fans, but unfortunately, some individuals’ sole motivation in seeking an autograph is for resale,” said Kevin Lennon, NCAA vice-president of academic and membership services. “",
"It is important that schools are cognizant and educate student-athletes about situations in which there is a strong likelihood that the autograph seeker plans to resell the items.”",
"\n\nTexas A&M chancellor John Sharp, who declared Manziel “innocent” of the allegations during a television interview last week, praised his quarterback and coach Kevin Sumlin for handling the uncertainty surrounding Manziel’s eligibility status “with integrity and honesty.”",
"\n\nIn a statement, Sharp said: “We all take the Aggie Code of Honor very seriously and there is no evidence that either the university or Johnny violated that code.”",
"\n\nThe code says, “An Aggie does not lie, cheat or steal, or tolerate those who do.”",
"\n\nIn his statement, A&M athletic director Eric Hyman praise the NCAA staff for “its fairness and professionalism throughout this process,” as well as its expediency in getting the case settled before Saturday’s kickoff. ",
"A&M, the No. ",
"7 team in The Associated Press’ poll, is considered a national title contender. ",
"Wednesday’s ruling assures that Manziel, barring injury, will be on the field for the team’s Sept. 14 showdown in College Station against top-ranked Alabama.",
"\n\nA&M coach Kevin Sumlin was not available for comment. ",
"But in Tuesday’s news conference, he called the battle for the backup quarterback job between Joeckel and Hill “an ongoing competition.”",
"\n\nBy Saturday, one of them will replace Manziel in A&M’s starting lineup. ",
"At least for the first half of the Rice game.",
"\n\nBased on published accounts from two sources, Texas A&M quarterback Johnny Manziel will be suspended for the first half of Saturday’s game against Rice in the wake of allegations that he accepted money for signing memorabilia in the offseason in violation of NCAA rules.",
"\n\nThe first report, from Billy Liucci of the website TexAgs.com, came via Twitter and said: “Latest on Manziel? ",
"Per multiple sources, he’ll be suspended for first half of season opener versus Rice on Saturday.”",
"\n\nBruce Feldman of CBSSports.com followed up minutes later on his Twitter account with this post: “Can confirm TexAgs report, Johnny Manziel will be sidelined for 1st half of A&M opener vs. Rice per source close to the QB.”",
"\n\nAlthough multiple messages have been left by the Star-Telegram, no A&M or NCAA official has confirmed the reports. ",
"From all indications, the 2012 Heisman Trophy winner would not be found guilty of accepting money for signing autographs but would be found in violation of NCAA bylaw 12.5.2.2: Use of a student’s name or picture without knowledge or permission.",
"\n\nUnder that bylaw, athletes are “required to take steps to stop” the use of their name or picture on commercial items used to promote a commercial project or sold by an individual or agency.",
"\n\nAlthough sitting down Manziel for one half of one game marks an unusual penalty, such a move would provide clarity for both A&M and the NCAA in regard to Manziel’s eligibility status for the 2013 season. ",
"It also would stand as a compromise solution to an investigation in which there was no reported evidence of Manziel accepting money, despite ESPN reports citing sources that said he did so.",
"\n\nAssuming that Manziel truly sits out the first half of Saturday’s game, A&M will select between two former Tarrant County high school players as its starting quarterback against Rice: Matt Joeckel, a junior from Arlington High School, and Kenny Hill, a freshman from Southlake Carroll.",
"\n\nHeading into the 2013 college football season, the most-discussed rules change made during the offseason involves an updated definition of “targeting” by a defensive player while making a tackle. ",
"To help fans understand the nuances of the rule, the Big 12 circulated a video featuring Walt Anderson, the league’s coordinator of football officials, explaining what is allowed and what will be penalty under 2013 rules. ",
"This information applies to rules implementation throughout the country, not just the Big 12. ",
"Below is a link to Anderson’s video:"
] | {
"pile_set_name": "Pile-CC"
} | [
0.00003228305785123967,
0,
0.00030046271257736916,
0.0002227667631989307,
0,
0.0004733727810650888,
0.00018896447467876037,
0.0000591715976331361,
0,
0.0005745475438092502,
0.000009585062638384343,
0.00017313019390581717,
0.00009382623381497466,
0,
0.00017313019390581717,
0,
0,
0,
0,
0.000016128772116578765,
0,
0,
0.000058436815193571955,
0.0001035143108534755,
0.0001417233560090703,
0.00004058112166220274,
0.00001054140664530275,
0,
0,
0,
0,
0,
0.000016128772116578765,
0,
0,
0.00005907372400756144,
0.00002029056083110137,
0.000030524098775983637,
0.00010503833899373271,
0.00009255402841408673,
0.0005945303210463733,
0.0011890606420927466,
0,
0.00002603082049146189,
0.0001165433249810617,
0.00007181844297615628,
0.00009070294784580499,
0,
0.00007181844297615628,
0.0002040816326530612,
0.0001321178491214163,
0.00005250997689561017,
0.000075,
0.000042718612499466016,
0,
0,
0.00008398421096833795,
0.0001234567901234568,
0,
0,
0,
0,
0.0001451589490492089,
0.00007257947452460445,
0.0001020304050607081,
0,
0,
0.00008340109672442193,
0.00015605006085952372,
0.0003125,
0.00010412328196584755,
0.00016833599865331202,
0.00021003990758244068,
0,
0,
0,
0.00018310546875,
0.0002469135802469136,
0.0005408328826392645,
0,
0,
0,
0.00008053907487449328,
0.00005208333333333334,
0.00003101704903795453,
0.0000717128617017462,
0.00006609822195782934,
0.00005827166249053085,
0.00007086167800453515,
0.00006163653813980928,
0.00004492262078569664,
0.00004853308743235701,
0.00007086167800453515,
0.00004627701420704336,
0,
0.0001183431952662722,
0.00003715814506539833,
0,
0.000026835191670356507,
0.000074360499702558,
0.0001451589490492089,
0.00006198347107438017,
0.00591715976331361,
0.00015625,
0.00008113919428780073,
0.0006377551020408163,
0.00010813148788927336,
0.00018261504747991235,
0.0004938271604938272,
0.00005406574394463668,
0.00015943877551020407,
0.00010412328196584755,
0.00010054495364877637,
0.00014610271020527432,
0.000033593120128997585,
0,
0.00004712979545668771,
0.000027994736989445982,
0.00007284293848413846,
0,
0.00002029056083110137,
0,
0.0007716049382716049
] | 0.00015 | 5 |
[
"Beech carbon productivity as driver of ectomycorrhizal abundance and diversity.",
"\nWe tested the hypothesis that carbon productivity of beech (Fagus sylvatica) controls ectomycorrhizal colonization, diversity and community structures. ",
"Carbon productivity was limited by long-term shading or by girdling. ",
"The trees were grown in compost soil to avoid nutrient deficiencies. ",
"Despite severe limitation in photosynthesis and biomass production by shading, the concentrations of carbohydrates in roots were unaffected by the light level. ",
"Shade-acclimated plants were only 10% and sun-acclimated plants were 74% colonized by ectomycorrhiza. ",
"EM diversity was higher on roots with high than at roots with low mycorrhizal colonization. ",
"Evenness was unaffected by any treatment. ",
"Low mycorrhizal colonization had no negative effects on plant mineral nutrition. ",
"In girdled plants mycorrhizal colonization and diversity were retained although (14)C-leaf feeding showed almost complete disruption of carbon transport from leaves to roots. ",
"Carbohydrate storage pools in roots decreased upon girdling. ",
"Our results show that plant carbon productivity was the reason for and not the result of high ectomycorrhizal diversity. ",
"We suggest that ectomycorrhiza can be supplied by two carbon routes: recent photosynthate and stored carbohydrates. ",
"Storage pools may be important for ectomycorrhizal survival when photoassimilates were unavailable, probably feeding preferentially less carbon demanding EM species as shifts in community composition were found."
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00002246131039284832
] | 0.000002 | 5 |
[
"---\nabstract: |\n In physics, phenomena of diffusion and wave propagation have great relevance; these physical processes are governed in the simplest cases by partial differential equations of order 1 and 2 in time, respectively. ",
"It is known that whereas the diffusion equation describes a process where the disturbance spreads infinitely fast, the propagation velocity of the disturbance is a constant for the wave equation. ",
"By replacing the time derivatives in the above standard equations with pseudo-differential operators interpreted as derivatives of non integer order (nowadays misnamed as of fractional order) we are lead to generalized processes of diffusion that may be interpreted as slow diffusion and interpolating between diffusion and wave propagation. ",
"In mathematical physics, we may refer these interpolating processes to as fractional diffusion-wave phenomena. ",
"The use of the Laplace transform in the analysis of the Cauchy and Signalling problems leads to special functions of the Wright type.\\\n In this work we analyze and simulate both the situations in which the input function is a Dirac delta generalized function and a box function, restricting ourselves to the Cauchy problem. ",
"In the first case we get the fundamental solutions (or Green functions) of the problem whereas in the latter case the solutions are obtained by a space convolution of the Green function with the input function. ",
"In order to clarify the matter for the non-specialist readers, we briefly recall the basic and essential notions of the fractional calculus (the mathematical theory that regards the integration and differentiation of non-integer order) with a look at the history of this discipline.",
"\naddress:\n- '${}^1$ Institut für Theoretische Physik und Astrophysik, Universität Würzburg, D-97074 Würzburg, GERMANY.'",
"\n- '${}^2$ Department of Physics $\\&$ Astronomy, University of Bologna and INFN. ",
"Via Irnerio 46, I-40126 Bologna, ITALY.'",
"\nauthor:\n- Armando Consiglioi$^1$\n- Francesco Mainardi$^2$\ndate: October 2019\ntitle: |\n On the evolution of\\\n fractional diffusive waves\n---\n\nKeywords: [Fractional calculus, time fractional derivatives, slow diffusion, transition from diffusion to wave propagation, Wright functions, Cauchy and Signaling Problems.]{} ",
"MSC Classification: 26A33, 33E12, 34A08, 65D20, 60J60, 74J05\n\nIntroduction\n============\n\nIt is known that mathematical models are usually governed by differential and/or integral equations of integer order. ",
"However, we can extend integration and differentiation to any order by using the tools of the so-called *Fractional Calculus*, that in recent years has gained considerable interest also because of its applications in different fields including Physics, Engineering, Biology, Economics and Finance, Geophysics, Computer Science and so on...\\\nFundamental phenomena of Physics, such as diffusion and wave propagation, are governed in their simplest form by the following partial differential equations (PDE) that in a standard notation read\n\n- Diffusion equation: $$\\frac{\\partial u(\\mathbf{r}, t)}{\\partial t } = D \\nabla ^2 u(\\mathbf{r}, t),$$\n\n- Wave equation: $$\\frac{\\partial ^2 u(\\mathbf{r}, t)}{\\partial t ^2} = c^2 \\nabla ^2 u(\\mathbf{r}, t).$$\n\nThe above PDE’s can be extended by replacing the time and/or spatial derivatives of integer order with some pseudo-differential operators interpreted as derivative of non integer order. ",
"In this paper we consider the generalizations of the above PDE’s by replacing the time derivatives with derivatives of order $\\alpha \\in (0,2]$ and we restrict our attention to a single space dimension $x$ This work is organized as follows. ",
"In Section 2, we show the essential mathematical notions necessary to understand the integration and differentiation of non-integer order, that nowadays are ascribed to the mathematical discipline referred generally to as [*Fractional Calculus*]{}. ",
"In particular we point out the approach of Professor Caputo on which Fractional Calculus has grown and found several applications. ",
"since the late 1960’s. ",
"Then, in Sections 3 and 4 we provide some historical notes distinguishing two different eras with the advent of Caputo’s approach. ",
"Indeed, in Section 3 we recall the major mathematicians who in the last centuries have contributed in the birth of development of the Fractional Calculus whereas in Section 4 we outline how the Caputo approach was popularized. ",
"The core of the paper is found in Section 5, where we consider from a mathematical view point the evolution of the so called fractional diffusive waves generated by partial differential equations with time derivatives of non integer order. ",
"Finally in Section 6, we provide some concluding remarks paying attention to work to be done in the next future.",
"\n\nEssentials of Fractional Calculus: Fractional Derivatives and Integrals\n=======================================================================\n\nThe starting point for the Fractional Calculus is given by the *Cauchy formula for repeated integration* where $a \\in \\RR$. Taking as independent variable the time $t$ and denoting by $f(t)$ a function assumed to be sufficiently well-behaved for the next considerations, we recall the formula for the $n$ repeated integral $${}_{a}I^{n}_{t} f(t):= \\int_{a}^t \\int_{a}^{\\tau_{n-1}} \\!\\cdots\\! ",
" \\int_{a}^{\\tau_{1}}\n\\! ",
"f(\\tau)\\, d\\tau\\, d\\tau_1 \\! ",
"\\cdots \\! ",
" d\\tau_{n-1} \\!=\\! ",
"\\frac{1}{(n-1)!}",
"\n\\int_{a}^{t} (t-\\tau)^{n - 1}\\,f(\\tau)\\, d\\tau.$$ The resulting function turns out to be the primitive of order $n$ of $f(t)$, that is vanishing in $t = a$ along with its derivatives of order $1, \\cdots , n-1$. The basic idea of the fractional calculus is in replacing the factorial term $(n-1)!$ with the corresponding representation by the Gamma function and then replacing $n$ with a positive real number $\\alpha$. So, writing $(n-1)! ",
"= \\mathit{\\Gamma} (n)$ in Eq. (",
"3), it follows the definition of *fractional integral* ${}_{a}I^{\\alpha}_{t} f(t)$ of order $\\alpha$ ($\\alpha > 0$) $${}_{a}I^{\\alpha}_{t} f(t): = \n\\frac{1}{\\mathit{\\Gamma} (\\alpha)}\\int_{a}^{t}{(t-\\tau)^{\\alpha - 1}\\,f(\\tau)\\, d\\tau},$$ where now $\\alpha$ is no longer restricted only to positive, integer values. ",
"The *fractional derivative* of order $\\alpha$ is so defined (in the Riemann-Liouville sense) as the left inverse operator of the corresponding fractional integral and reads: $${}_{a}D^{\\alpha}_{t} f(t) := \\frac{d^n}{dt^n}{{}_{a}I^{n-\\alpha}_{t} f(t)}, \\quad n = [\\mathfrak (\\alpha )] +1 .$$ In view of our applications we take $ a=0$ so $t \\ge 0$ and, from now on, we agree to delete $a$ in the notations for fractional integrals and derivatives. ",
"Henceforth, we consider the time fractional derivative in the Caputo sense, defined for $n-1<\\alpha \\le n$ as: $$D^{\\alpha}_{C} f(t): = I^{n-\\alpha}_{t}\\frac{d^n}{dt^n} f(t) =\n\\frac{1}{\\mathit{\\Gamma} (n-\\alpha)}\\int_{0}^{t}{\\frac{f^{(n)}(\\tau)}\n{(t-\\tau)^{\\alpha + 1 -n}}\\, d\\tau}.$$ This definition provides us a regularization of the Riemann-Liouville fractional derivative at $t=0$ as shown in 1997 by Gorenflo and Mainardi [@Gorenflo-Mainardi; @CISM97]. ",
"As a consequence of its definition, the Caputo derivative is vanishing when the derivative of integer order ${f^{(n)}(t)}$ is zero; in particular $$D^{\\alpha}_C 1 = 0, ~~~~~ \\alpha > 0\\,.$$ The Caputo derivative appears suitable to be treated by the Laplace Transform technique for causal systems, that is quiescent for $t<0$. In a standard notation we get $$D^{\\alpha}_{C}f(t) \\div s^{\\alpha} \\tilde{f}(s) - \\sum_{k=0}^{n-1}{f^{(k)}(0^+)\\, s^{\\alpha - 1 - k}},~~ n-1 < \\alpha <\\le n\\,.$$ It is requested the knowledge of the initial values of the function and of its integer derivatives of order $k = 1, 2, ..., n-1$.as it is for $\\alpha = n$.\n\nHistorical notes before Caputo’s era\n====================================\n\nFractional Calculus may be considered born on September 30$^{th}$, 1695 when L’Hopital asked to Leibniz what would be if $n= 1/2$ in his notation for the n$^{th}$ derivative, $\\frac{d^n}{dx^n}$. Leibniz answered: “An apparent paradox, from which one day useful consequences will be drawn.\"",
"\n\n[[![",
"LEFT: Gottfried Wilhelm (von) Leibniz; RIGHT: Guillaume François Antoine, Marquis de l’Hôpital.[]{data-label=\"fig:Leiniz-Hopital\"}](Leibniz \"fig:\"){width=\"2.5cm\"} ]{}]{} [[![",
"LEFT: Gottfried Wilhelm (von) Leibniz; RIGHT: Guillaume François Antoine, Marquis de l’Hôpital.[]{data-label=\"fig:Leiniz-Hopital\"}](Hopital \"fig:\"){width=\"2.5cm\"} ]{}]{}\n\nFrom that time we get a very long story involving eminent mathematicians who are pointed out in the next figure. ",
"More recently the term [fractional calculus]{} was used but it is a misnomer kept only for historical reasons related to the discussion between Marquis de l’Hôpital and Leibniz. ",
"For more details see the historical notes by the late Bertram Ross, the organizer of the first conference devoted to fractional calculus in 1974 [@Ross; @History-BOOK75], and, more recently, by Machado and Kiryakova [@Machado-Kiryakova_HFCA19] from which the following picture is taken.",
"\n\n![",
"The major mathematicians in Fractional Calculus up to 1950’s.[]{data-label=\"fig:story\"}](story){width=\"6.8cm\"}\n\nHistorical notes in Caputo’s era\n================================\n\nIn this paper, attention is indeed devoted to the form (6) of fractional derivative alternative to that originally used by Liouville and Riemann expressed by Eq (5). ",
"The form (6), where the orders of fractional integration and ordinary differentiation are interchanged, is nowadays known as the [*Caputo derivative*]{}. ",
"As a matter of fact, such a form is found in a paper by Liouville himself as noted by Butzer and Westphal [@Butzer-Westphal; @00] in the 2000 book edited by R. Hilfer, but Liouville, not recognizing its role, disregarded this notion. ",
"As far as we know, up to the middle of the twentieth century, most authors did not take notice of the difference between the two forms and of the possible use of the alternative form. ",
"Even in the classical book on Differential and Integral Calculus published in English in 1936 by the eminent mathematician R. Courant, the two forms of the fractional derivative were considered as equivalent, see [@Courant; @BOOK36], pp. ",
"339-341. ",
"In the late sixties of the past century the relevance of the alternative form was finally recognized. ",
"In fact, in 1968 the Soviet Scientists Dzherbashyan and Nersesyan [@Dzherbashyan-Nersesyan; @68] and then in 1989-90 Kochubei [@Kochubei; @89; @Kochubei; @90] used the alternative form (6) in dealing with Cauchy problems for differential equations of fractional order. ",
"However, formerly since 1967, Caputo [@Caputo; @67; @Caputo; @BOOK69] had introduced this form as given by Eq. (",
"6) proving the corresponding rule in the Laplace transform domain, as Eq. (",
"8). ",
"With his derivative Caputo was thus able to generalize the rule for the Laplace transform of a derivative of integer order and to solve some problems in Seismology in a proper way related to the dissipation function. ",
"Indeed. ",
"it was the corresponding rule in the Laplace transform the basic and original idea of the Caputo form of fractional derivative, not present in any previous paper. ",
"Soon later, this derivative was adopted by Caputo and Mainardi [@Caputo-Mainardi; @71PAG], [@Caputo-Mainardi; @71RNC] in the framework of the theory of [*Linear Viscoelasticity*]{}. ",
"Since the seventies of the past century a number of authors have re-discovered and used the alternative form, recognizing its major utility for solving physical problems with standard initial conditions. ",
"Although several papers by different authors appeared where the alternative derivative was adopted, it was only in the late nineties, with the tutorial paper by Gorenflo and Mainardi in 1997 [@Gorenflo-Mainardi; @CISM97] and the 1999 book by Podlubny [@Podlubny; @BOOK99], that such form was popularized. ",
"Nowadays the term [*Caputo fractional derivative*]{} is universally accepted in the literature. ",
"The reader, however, is alerted that in a very few papers the Caputo derivative is referred to as the [Caputo–Dzherbashyan]{} derivative. ",
"Note also the transliteration as Djrbashyan. ",
"It should be noted that it was Mainardi, being initially an Italian researcher in Geophysics as a PhD student of Prof. Caputo, who pointed out the Caputo form (6) published in a Geophysical journal [@Caputo; @67] and in an Italian book [@Caputo; @BOOK69] to the attention of eminent colleagues in Mathematics including the late Rudolf Gorenflo [@Gorenflo-Mainardi; @CISM97], [@Gorenflo-Kilbas-Mainardi-Rogosin; @BOOK14], Yuri Luchko [@LuGo; @99], Igor Podlubny [@Podlubny; @BOOK99], the late Anatoly Kilbas [@Kilbas-Srivastava-Trujillo; @BOOK06]. ",
"Kai Diethelm [@Diethelm; @BOOK10]. ",
"Also Virginia Kiryakova, the Editor-in-Chief of the major journal devoted to Fractional Calculus, that is Fractional Calculus and Applied Analysis (FCAA). ",
"was alerted. ",
"Indeed, the papers by Caputo in 1967 [@Caputo; @67] and by Caputo and Mainardi in 1971 [@Caputo-Mainardi; @71PAG] were reprinted .in FCAA in 2007 in the occasion of the eighty birthday of Professor Caputo. ",
"Just in this volume there were the foreword by Mainardi [@Mainardi; @FCAA07] to the special issue of FCAA dedicated to the 40 years of Caputo derivative and to the 80th anniversary of Prof Caputo and the tutorial survey by Mainardi and Gorenflo [@Mainardi-Gorenflo; @FCAA07]. ",
"This special issue contains the biographical data of Prof. Caputo and his photo reported below.",
"\n\nWe enclose also the photo depicting Mainardi, Podlubny and Caputo at Ravello, where Mainardi and Podlubny delivered each a one-week course on fractional calculus and Caputo a seminar in the framework of the 37-th summer school on Mathematical Physics organized by the National Group of Mathematical Physics, held just in Ravello (17-29 September 2012) directed by Professors Rionero and Ruggeri.",
"\n\nFractional calculus in diffusion-wave problems\n==============================================\n\nThe time fractional diffusion-wave equation reads: $$\\frac{\\partial ^{\\alpha} u(\\mathbf{r}, t)}{\\partial t^{\\alpha}} = D\\nabla ^2 u(\\mathbf{r}, t), ~~~ D > 0, ~~~ 0 < \\alpha \\leq 2,$$ and is obtained from the diffusion equation (or from the wave equation) by replacing the time derivative with a fractional derivative, in the Caputo sense.\\\nThis explicitly reads in the one-dimensional case with ($D =1$) taking $u=u(x,t)$ and $\\alpha \\in (0,2]$ $$\\frac{1}{\\Gamma (n-\\alpha)}\\int_{0}^{t}{\\frac{u^{(n)}(x,\\tau)}{(t - \\tau)^{\\alpha + 1 - n}}\\, d\\tau} = \n\\frac{\\d^2}{ \\d x^2} u(x, t)\\,,$$ where the derivatives $u^{(n)}$ are with respect time and $n=1$ if $\\alpha \\in (0,1]$ and $n=2$ if $\\alpha \\in (1,2]$. We recognize the for $\\alpha \\in (0,1)$ we have a fractional diffusion equation and when $\\alpha\\in (1,2)$ we have a transition from the standard diffusion equation to the standard wave equation, that we refer to the fractional diffusion-wave equation. ",
"Of course, we find the standard diffusion and wave equations when $\\alpha=1$ and $\\alpha=2$, respectively.",
"\n\nCauchy and Signaling Problems\n-----------------------------\n\nThe two basics problems for the Fractional PDE are the *Cauchy* and *Signaling* ones. ",
"Denoting by $f(x)$ and $h(t)$ two given, well behaved functions: $$\\mathrm{Cauchy ~Problem:} \n\\bigg \\{\n\\begin{array}{rl}\nu(x, 0^+) = f(x),& ~~ -\\infty < x < +\\infty \\\\\nu(\\pm \\infty, t) =0, ~&~~~~~~~~~~~ t >0.\\\\\n\\end{array}$$ $$\\mathrm{Signaling ~Problem:} \n\\bigg \\{\n\\begin{array}{rl}\nu(x, 0^+) = 0, ~~~&~~~~~~ 0 < x < +\\infty \\\\\nu(0^+, t) =h(t),& u(+\\infty , t) = 0, ~ t > 0 .\\\\\n\\end{array}$$ When $1 < \\alpha \\leq 2 $ an extra initial condition is needed for both problems: $u_t(x,0^+) = g(x)$.\\\nThe solutions turn out to be expressed by proper convolutions between the source function and a (two) characteristic function(s), the so called *Green functions* or *fundamental solutions* $\\mathcal{G}(x,t)$ of the problem.\\\nThe function $\\mathcal{G}_C(x,t)$ for the Cauchy problem represents the solution for $f(x) = \\delta (x)$, and the function $\\mathcal{G}_S(x,t)$ for the Signaling problem represents the solution for $h(t) = \\delta _+ (t)$.\\\nThe Green functions are connected by the [*Reciprocity Relation*]{}: $$2\\nu x \\mathcal{G}_C(x,t; \\nu) = t \\mathcal{G}_S(x,t; \\nu) = \\nu z M_{\\nu}(z),$$ with $\\nu = {\\alpha}/{2}$ and $z = {x}/{t^{\\nu}}$ being the [*similarity variable*]{}. ",
"Here $M_\\nu(z)$ is a function of the Wright type, entire for $0\\le \\nu <1$, referred to as [*$M$-Wright function*]{} briefly discussed below. ",
"For more details see e.g the survey paper by Mainardi, Luchko and Pagnini [@Mainardi; @LUMAPA01] based on the previous papers by Mainardi [@Mainardi; @AML96; @Mainardi; @CHAOS96; @Mainardi; @CISM97].",
"\n\nThe Fundamental Solution of the Cauchy problem\n----------------------------------------------\n\nAccording to Eq. (",
"13) the fundamental solution of the Cauchy problem is thus provided by $$\\G_C(x,t;\\nu) = \\frac{1}{2 t^\\nu}\\, M_\\nu\\left( \\frac{x}{t^\\nu}\\right)\\,,$$ where the function $M_{\\nu}(z)$ reads in its series and integral representations as $$M_{\\nu}(z) := \\sum_{n=0}^{\\infty}{\\frac{(-z)^n}{n!\\mathit{\\Gamma}[-\\nu n + (1-\\nu)]}} = \n\\frac{1}{2\\pi i}{\\int_{Ha}{e^{\\sigma - z\\sigma ^{\\nu}}\\frac{d\\sigma }{\\sigma ^{1-\\nu }}}},$$ where $Ha$ denotes the Hankel path. ",
"$M_{\\nu}(z)$ results to be a particular case of the Wright function $W_{\\lambda , \\mu}(z)$: $$W_{\\lambda , \\mu}(z) := \\sum_{n=0}^{\\infty}{\\frac{z^n}{n! ",
"\\mathit{\\Gamma}(\\lambda n + \\mu)}}, ~~~\\lambda > -1, ~ \\mu \\in \\mathbb{C}, ~ z \\in \\mathbb{C}$$ when $\\lambda =-\\nu$ and $\\mu =1-\\nu$. We note that for convenience and for historical reasons the Wright functions may be classified in two kinds: the first kind with $\\lambda\\ge 0$ and the second kind with $-1<\\lambda <0$ so following the Appendix F of Mainardi’s book [@Mainardi; @BOOK10], where the reader can find also some historical notes.",
"\n\n[[![",
"Plots of the functions $M_{\\nu}(x)$ for |$x| \\le 5$ at $ t=1$; LEFT: for $\\nu = 0, 1/8, 1/4, 3/8, 1/2$. RIGHT: for $\\nu = 1/2, 5/8, 3/4, 1$[]{data-label=\"fig:mainardifunction\"}](fmws-figF_1-top \"fig:\"){width=\"7.0cm\"} ]{}]{} [[![",
"Plots of the functions $M_{\\nu}(x)$ for |$x| \\le 5$ at $ t=1$; LEFT: for $\\nu = 0, 1/8, 1/4, 3/8, 1/2$. RIGHT: for $\\nu = 1/2, 5/8, 3/4, 1$[]{data-label=\"fig:mainardifunction\"}](fmws-figF_2-top \"fig:\"){width=\"7.0cm\"} ]{}]{}\n\nFor $\\nu = 1/2$, we find back the diffusion equation and indeed the $M_{\\nu}(x)$ function becomes the Gaussian function known as fundamental solution of the diffusion equation for the Cauchy Problem) whereas , for $\\nu \\rightarrow 1$, we find back the wave equation and indeed the $M_{\\nu}(x)$ function tends to two Dirac delta functions ad fundamental solutions of the Cauchy Problem, centered in $x = \\pm 1$. It should be noted that in the 1993 book by Pr[ü]{}ss [@Pruss; @BOOK93] we find a figure quite similar to our Fig. ",
"5 reporting the $M$-Wright function in for $\\nu \\in [1/2, 1)$. It was derived from inverting the Fourier transform expressed in terms of the Mittag-Leffler function following the approach by Fujita [@Fujita; @90] for the fundamental solution of the Cauchy problem for the diffusion-wave equation, fractional in time. ",
"Both approaches were carried out without any relation to the Wright function, presumably unknown to Fujita and Pr[ü]{}ss. ",
"However, our plot must be considered independent from that of Pr[ü]{}ss because Mainardi used the Laplace transform in his former paper presented at WASCOM, Bologna, October 1993 [@Mainardi; @WASCOM93] (and published later in a number of papers and in his 2010 book [@Mainardi; @BOOK10]) so he was aware of the book by Pr[ü]{}ss only later. ",
"Furthermore, we invite readers to look at the simulation of the fundamental solution $M_\\nu(x,t)$ at $t=1$ for $x \\in [-5,+5]$ at varying $\\nu$ available in YOUTUBE: [`https://www.youtube.com/watch?v=uf_4aB1COPg`]{} carried out by Consiglio with Matlab.",
"\n\nPlots of Solutions for the Cauchy Problem\n-----------------------------------------\n\nWe start this graphical sub-section by reporting the plots of the evolution in time of fundamental solutions (that is $f(x) = \\delta(x)$ and $g(x)=0$) taking $\\nu=0.65$, $\\nu=0.75$ and $\\nu=0.85$.\\\nThe general solutions for the Cauchy problem are obtained through suitable convolution in space as shown hereafter: $$u(x,t;\\nu) = \\int_{-\\infty}^{+\\infty}{\\mathcal{G}_C(\\xi,t; \\nu)f(x-\\xi)d\\xi}, ~~~~ 0 < \\nu \\leq 1/2,$$ $$\\begin{split}\nu(x,t;\\nu) = \\int_{-\\infty}^{+\\infty}{\\biggl[ \\mathcal{G}^{(1)}_C(\\xi,t; \\nu)f(x-\\xi) + \\mathcal{G}^{(2)}_C(\\xi,t; \\nu)g(x-\\xi) \\biggl]d\\xi },\\\\ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~1/2 < \\nu \\leq 1,\n\\end{split}$$ where $\\mathcal{G}^{(2)}_C$ is the primitive in time of $\\mathcal{G}^{(1)}_C$.\n\n3truecm\n\n2truecm\n\nWe now consider for the Time-Fractional Diffusion Wave equation the evolution of an initial centered box-signal $f(x) =1$ for $-1 \\le x \\le +1 $ and zero otherwise, assuming $g(x) = 0$. Based on Eqs. (",
"17)- (18) we simulate the cases $\\nu=0.50$ (standard diffusion), $\\nu=0.75$ and $\\nu=1$ (standard wave), as shown in the next figures where the initial box function is denoted by dotted lines. ",
"-0.5truecm\n\n[[![",
"Time evolution of an initial box-signal for $\\nu=0.50$, seen at t = 0.50 (left) and t = 1.00 (right) in $0 \\leq x \\leq 3.5$. The problem is symmetric on the negative axis. []{",
"data-label=\"fig:boxgauss\"}](box_501 \"fig:\"){width=\"5.5cm\"} ]{}]{} [[![",
"Time evolution of an initial box-signal for $\\nu=0.50$, seen at t = 0.50 (left) and t = 1.00 (right) in $0 \\leq x \\leq 3.5$. The problem is symmetric on the negative axis. []{",
"data-label=\"fig:boxgauss\"}](box_502 \"fig:\"){width=\"5.5cm\"} ]{}]{}\n\n-0.5truecm\n\n[[![",
"Time evolution of an initial box-signal for $\\nu=0.75$, seen at t = 0.50 (left) and t = 1.00 (right) in $0 \\leq x \\leq 3.5$. The problem is symmetric on the negative axis. []{",
"data-label=\"fig:box75\"}](box_751 \"fig:\"){width=\"5.5cm\"} ]{}]{} [[![",
"Time evolution of an initial box-signal for $\\nu=0.75$, seen at t = 0.50 (left) and t = 1.00 (right) in $0 \\leq x \\leq 3.5$. The problem is symmetric on the negative axis. []{",
"data-label=\"fig:box75\"}](box_752 \"fig:\"){width=\"5.5cm\"} ]{}]{}\n\n-0.5truecm\n\n[[![",
"Time evolution of an initial box-signal for $\\nu=1$, seen at t = 0.50 (left) and t = 1.00 (right) in $0 \\leq x \\leq 3$. The problem is symmetric on the negative axis. []{",
"data-label=\"fig:boxwave\"}](box_1001 \"fig:\"){width=\"5.5cm\"} ]{}]{} [[![",
"Time evolution of an initial box-signal for $\\nu=1$, seen at t = 0.50 (left) and t = 1.00 (right) in $0 \\leq x \\leq 3$. The problem is symmetric on the negative axis. []{",
"data-label=\"fig:boxwave\"}](box_1002 \"fig:\"){width=\"5.5cm\"} ]{}]{}\n\nConcluding remarks\n==================\n\nWe have considered the so-called time fractional diffusion wave equation with particular attention when this equation is interpolating the processes of diffusion and the wave propagation. ",
"In these cases we speak about fractional diffusive waves using a term incorporating both diffusion and wave phenomena.\\\nWe have analyzed and simulated both the situations in which the input function is a Dirac delta generalized function and a box function, restricting ourselves to the Cauchy problem. ",
"In the first case we get the fundamental solutions (or Green function) of the problem whereas in the latter case the solutions are obtained by a space convolution of the Green function with the input function.\\\nIn the next future we plan to consider the signaling problem in order to complete the topic of fractional diffusive waves.",
"\n\nAcknowledgments {#acknowledgments .unnumbered}\n===============\n\nThe work of FM has been carried out in the framework of the activities of the National Group of Mathematical Physics (GNFM, INdAM).\\\nThe results contained in the present paper have been partially presented at the XX International Conference [*Waves and Stability in Continuous Media*]{} (WASCOM 2019) held in Maiori (Sa), Italy, June 10-14 (2019).",
"\n\n[99]{} Butzer, P.L. and Westphal, U. (2000). ",
"Introduction to fractional calculus, in: Hilfer, H. (Editor), [*Fractional Calculus, Applications in Physics*]{}, World Scientific, Singapore, pp. ",
"1-85. ",
"Caputo, M. (1967). ",
"Linear models of dissipation whose $Q$ is almost frequency independent, Part II, [*Geophys. ",
"J. R. Astr. ",
"Soc.*]{} [**",
"13**]{}, 529–539. ",
"\\[Reprinted in [*Fract. ",
"Calc. ",
"Appl. ",
"Anal.*]{} [**",
"11**]{} No 1, 4–14 (2008)\\] Caputo, M. (1969). [*",
"Elasticità e Dissipazione*]{}, Zanichelli, Bologna.\\[in Italian\\] Caputo, M. and Mainardi, F. (1971a). ",
"A new dissipation model based on memory mechanism, [*Pure and Appl. ",
"Geophys. (",
"PAGEOPH)*]{} [**91**]{}, 134–147. ",
"\\[Reprinted in [*Fract. ",
"Calc. ",
"Appl. ",
"Anal.*]{} [**",
"10**]{} No 3, 309–324 (2007)\\] Caputo, M. and Mainardi, F. (1971b). ",
"Linear models of dissipation in anelastic solids, [*Riv. ",
"Nuovo Cimento*]{} (Ser. ",
"II) [**1**]{}, 161–198. ",
"Courant, R. (1936). [*",
"Differential and Integral Calculus*]{}, Vol. ",
"2, Nordemann, New York, pp. ",
"339–341. ",
"Diethelm, K. (2010). [*",
"The Analysis of Fractional Differential Equations*]{}, An Application-Oriented Exposition Using Differential Operators of Caputo Type, Lecture Notes in Mathematics No 2004, Springer, Berlin. ",
"Dzherbashyan, M.M. and Nersesyan, A.B. (1968). ",
"Fractional derivatives and the Cauchy problem for differential equations of fractional order. [*",
"Izv. ",
"Acad. ",
"Nauk Armjanskvy SSR, Matematika*]{} [**3**]{}, 3–29. ",
"\\[In Russian\\] Fujita, Y. (1990). ",
"Integro-differential equation which interpolates the heat equation and the wave equation, I, II, [*Osaka J. Math.*]{} [**",
"27**]{}, 309–321, 797–804. ",
"Gorenflo, R., Kilbas, A.A., Mainardi, F. and Rogosin, S.V. (2014). [*",
"Mittag-Leffler Functions, Related Topics and Applications*]{}, Springer Monographs in Mathematics, Springer, Berlin – Heidelberg. ",
"Gorenflo, R. and Mainardi, F. (1997). ",
"Fractional calculus: integral and differential equations of fractional order, in: Carpinteri, A. and Mainardi, F. (Editors) [*Fractals and Fractional Calculus in Continuum Mechanics*]{}, Springer Verlag, Wien, pp. ",
"223–276. ",
"\\[E-print: [http://arxiv.org/abs/0805.3823]{}\\] Kilbas, A.A., Srivastava, H.M. and Trujillo, J.J. (2006). [*",
"Theory and Applications of Fractional Differential Equations*]{}, Elsevier, Amsterdam. ",
"\\[North-Holland Series on Mathematics Studies No 204\\] Kochubei, A.N. (1989). ",
"A Cauchy problem for evolution equations of fractional order, [*Differential Equations*]{} [**25**]{}, 967–974. ",
"\\[English translation from the Russian Journal [*Differentsial’nye Uravneniya*]{}\\] Kochubei, A.N. (1990). ",
"Fractional order diffusion, [*Differential Equations*]{} [**26**]{}, 485–492. ",
"\\[English translation from the Russian Journal [*Differentsial’nye Uravneniya*]{}\\] Luchko, Yu. ",
"and Gorenflo, R. (1999). ",
"An operational method for solving fractional differential equations with the Caputo derivatives, [*Acta Math. ",
"Vietnam.*]{} [**",
"24**]{} No 2, 207–233. ",
"Luchko, Yu and Mainardi, F. (2014). ",
"Cauchy and signaling problems for the time-fractional diffusion-wave equation [*ASME Journal of Vibration and Acoustics*]{} [**136**]{}, 051008/1-7. ",
"\\[DOI: 10.1115/1.4026892\\] \\[E-print: arXiv:1609.05443\\] Machado, J.A.T. and Kiryakova, V. (2019). ",
"Recent history of the fractional calculus: data and statistics, in A.Kochubei and Yu. ",
"Luchko (Editors), [*Handbook of Fractional Calculus with Applications, vol. ",
"1: Basic Theory*]{}, De Gruyter, Berlin. ",
"pp. ",
"1–21. ",
"Mainardi, F. (1994a). ",
"On the initial value problem for the fractional diffusion-wave equation, in: Rionero, S. and Ruggeri, T. (Editors), [*Waves and Stability in Continuous Media*]{}, World Scientific, Singapore, pp. ",
"246–251. ",
"\\[Proc. ",
"VII-th WASCOM, Int. ",
"Conf. “",
"Waves and Stability in Continuous Media”, Bologna, Italy, 4-7 October 1993\\] Mainardi, F. (1996a). ",
"The fundamental solutions for the fractional diffusion-wave equation, [*Applied Mathematics Letters*]{} [**9**]{} No 6, 23–28. ",
"Mainardi, F. (1996b). ",
"Fractional relaxation-oscillation and fractional diffusion-wave phenomena, [*Chaos, Solitons & Fractals*]{} [**7**]{}, 1461–1477. ",
"Mainardi, F. (1997). ",
"Fractional calculus: some basic problems in continuum and statistical mechanics, in: Carpinteri, A. and Mainardi, F. (Editors) [*Fractals and Fractional Calculus in Continuum Mechanics*]{}, Springer Verlag, Wien, pp. ",
"291–348. ",
"\\[E-print: [http://arxiv.org/abs/1201.0863]{}\\] Mainardi, F. (2007). ",
"Foreword to the special issue “FCAA” issue dedicated to the 40 years of Caputo derivative and to the 80th anniversary of Prof. Caputo, [*Fract. ",
"Calc. ",
"Appl. ",
"Anal.*]{} [**",
"10**]{} No 3, 203–208. ",
"Mainardi, F (2010), [*Fractional Calculus and Wave Propagation in Linear Viscoelasticity*]{} Imperial College Press, London. ",
"2nd edition in preparation. ",
"Mainardi, F., Luchko, Yu. ",
"and Pagnini, G. (2001). ",
"The fundamental solution of the space-time fractional diffusion equation, [*Fract. ",
"Calc. ",
"Appl. ",
"Anal.*]{} [**",
"4**]{}, 153–192. ",
"\\[E-print [http://arxiv.org/abs/cond-mat/0702419]{}\\] Mainardi, F. and Gorenflo, R. (2007). ",
"Time-fractional derivatives in relaxation processes; a tutorial survey, [*Fract. ",
"Calc. ",
"Appl. ",
"Anal.*]{} [**",
"10**]{} No 3, 269–308. ",
"\\[E-print:. ",
"http://arxiv.org/abs//0801.4914\\] Podlubny, I. (1999). [*",
"Fractional Differential Equations*]{}, Academic Press, San Diego. ",
"\\[Mathematics in Science and Engineering, Vol. ",
"198\\] Prüss, J. (1993). [*",
"Evolutionary Integral Equations and Applications*]{}, Birkhauser Verlag, Basel. ",
"Ross, B. (1975). ",
"A brief history and exposition of the fundamental theory of fractional calculus, in Ross, B. (Editor) [*Fractional Calculus and its Applications*]{}, Springer Verlag, Berlin 1975, pp 1–36.. \\[Lecture Notes in Mathematics Vol. ",
"457\\] Proc. ",
"Int. ",
"Conf. ",
"held at Univ. ",
"of New Haven, USA, 1974\\]\n"
] | {
"pile_set_name": "ArXiv"
} | [
0.000018579072532699166,
0,
0,
0,
0.000037407999700736,
0,
0,
0.0000706164818868724,
0.00030483158055174517,
0.000625,
0.000019051973784484073,
0.00002333776750916007,
0.000005646648544689271,
0.00003443466882457258,
0,
0.0001165433249810617,
0,
0.00005827166249053085,
0.000019406547769217335,
0,
0,
0.0000034166891598703026,
0,
0,
0,
0,
0,
0.000005165289256198347,
0,
0,
0.000009920585711380399,
0.000018986049999762676,
0.000005881776296441526,
0,
0.00006605892456070815,
0.00002479666732791113,
0.00006312334301224592,
0.000048902146804244705,
0,
0.00002520478890989288,
0,
0.00005478851632697786,
0,
0.0000706164818868724,
0,
0,
0.00008291759373142991,
0.0003985969387755102,
0.00035555555555555557,
0,
0.00004247276433986706,
0,
0.00007527569724114569,
0.00015094795314575535,
0,
0.00004299919376511691,
0,
0.00005250997689561017,
0.0004938271604938272,
0.00007018505459394604,
0.0016326530612244896,
0.00016649323621227888,
0,
0.00021208407955509474,
0.00010501995379122034,
0.00011080332409972299,
0.0000380688920048982,
0.000006277261248852158,
0,
0.00004504301608035674,
0.0000064092292901778555,
0.00004959333465582226,
0.0002777707633645615,
0.0001512287334593573,
0.000009746161230745241,
0.000043282548476454294,
0.0000358305521999959,
0,
0.000019236688211757463,
0.0000106382790101436,
0.00003980535182955348,
0.00013437248051599034,
0.00005159914345421866,
0.00006249121217328813,
0.000005536684688575328,
0,
0,
0.00003265306122448979,
0,
0.00003265306122448979,
0,
0.00003265306122448979,
0,
0.00003265306122448979,
0,
0.00003460207612456747,
0,
0.00003460207612456747,
0,
0.000010964431384588396,
0.000009018027036045055,
0.0000293136501943495,
0.0004526935264825713,
0.00009255402841408673,
0,
0.002770083102493075,
0.00011814744801512288,
0.006944444444444444,
0,
0,
0,
0,
0,
0,
0,
0.00018851918182675084,
0,
0,
0,
0,
0,
0,
0,
0,
0.0003077870113881194,
0.001736111111111111,
0,
0.002066115702479339,
0,
0,
0,
0,
0.000027411529289219047,
0,
0,
0,
0,
0.00035599857600569594,
0.0008650519031141869,
0.00013660269107301415,
0,
0.00021003990758244068,
0.0002366863905325444,
0,
0.00008734387282732115,
0,
0.0004286694101508916,
0.0001321178491214163,
0.00016436554898093358,
0,
0.0001746877456546423,
0,
0.00010850694444444444,
0,
0.0001652892561983471,
0,
0,
0.0007716049382716049,
0,
0.00030609121518212427,
0.00013520822065981613,
0.00017313019390581717,
0.000594883997620464,
0,
0,
0,
0.00010412328196584755,
0,
0,
0.0025,
0.02040816326530612,
0,
0,
0,
0,
0,
0.00008494552867973413,
0,
0.00021003990758244068,
0.00014467592592592592,
0,
0,
0,
0,
0.000192,
0,
0,
0.001736111111111111,
0,
0,
0,
0,
0,
0.00011814744801512288,
0,
0,
0,
0,
0,
0,
0.0006155740227762388,
0.0002295684113865932,
0.0004526935264825713,
0.0014792899408284025,
0.00015625,
0.006920415224913495,
0.00005873600125303469,
0.006944444444444444,
0,
0.027777777777777776,
0.00510204081632653,
0
] | 0.000481 | 5 |
[
"Q:\n\nWhy is binding lost when nesting directive in directive?",
"\n\nThe Issue\nUsing my directive within another directive causes certain bindings to be lost, specifically in the ng-repeat usage.",
"\nThe directive is used in many areas of my application without issue. ",
"It renders a list of inputs which is passed to it's scope from a parent template, like so:\n<filter-header filters=\"filters\"></filter-header>\n\nWorking Scenario\nI have used the following scenario throughout the application and not come across an issue to date.",
"\n\n$routeProvider resolves filters list with WebAPI call for a controller\ncontroller assigns list to its own scope, like so: $scope.filters = filters\ntemplate uses filter-header element and passes filters from it's scope to the directive, like so: <filter-header filters=\"filters\"></filter-header>\nThe filter-header directive then renders the filters using an ng-repeat without issue. ",
"$$hashKey is present in each item of the filters collection, indicating the binding's existence.",
"\n\nFailing Scenario\nIn the following scenario, the binding seems to be lost and the ng-repeat fails to render anything.",
"\n\n$routeProvider resolves filters list with WebAPI call for a controller\ncontroller assigns list to its own scope, like so: $scope.filters = filters\ntemplate uses a new element directive, assigns filters from it's scope to the new directive's via an attribute.",
"\ndirective's template uses filter-header element and passes filters from it's scope to the directive, like so: <filter-header filters=\"filters\"></filter-header>\nThe filter-header directive then FAILS TO render the filters using an ng-repeat. ",
"$$hashKey is NOT present in any item of the filters collection.",
"\n\nAnnoyingly, I cannot replicate this in Plunker...\n\nOddity\nThe directive has another collection of item's passed to it, columns=\"columns\" (can be seen in the code below). ",
"Columns binds correctly and is rendered in it's own ng-repeat. ",
"I cannot see how Columns is different from Filters as both are used almost exactly the same way.",
"\n\nLooking Deeper...\nI have debugged the process all the way. ",
"The filters object is getting all the way to the end scope successfully. ",
"If I output the contents of filters to the screen within the final directive, using {{ filters }} I can see all of the filters as expected. ",
"However, in the very next line where my ng-repeat begins, no filters are iterated through.",
"\nTo be certain it is not my list causing issues, I used a list that already works using the working scenario mentioned above and the ng-repeat does not render here.",
"\nTo be certain it is not my directive's code causing issues, I converted it to a controller and routed directly to it (skipping the nested directive) as in the working scenario mentioned above and the ng-repeat now works.",
"\nUsing $log to inspect the list, I notice one difference. ",
"In the working scenario, all lists contain a $$hashKey property for each item in the list. ",
"In the failing scenario, the $$hashKey is missing on all items in the list. ",
"This seems to indicate that the binding is being lost for some reason.",
"\nCan someone tell me the error in my ways? ",
"The only real difference I can see in my usage is that I pass the object to an middle-man directive before before passing it on the the directive where it is used. ",
"Strangely, in the very same directive, another list is used in a very similar way and it renders without issue within it's ng-repeat, and it's item's all have the $$hashKey property appended.",
"\n\nCode\nThere's a lot of code involved, so I'll try and pick out the relevant parts.",
"\nRouteProvider\n$routeProvider.when('/Pride/Admin/AuditForms/:id', {\n templateUrl: '/Templates/Admin/editAuditForm.html',\n controller: 'editAuditFormController',\n resolve: {\n sectionFilters: function (auditFormSectionRepository) {\n return auditFormSectionRepository.getFilters().$promise;\n },\n sectionColumns: function (auditFormSectionRepository) {\n return auditFormSectionRepository.getColumns().$promise;\n }\n }\n});\n\nEditAuditForm Controller\nprideModule.controller(\"editAuditFormController\", function ($scope, sectionFilters, sectionColumns) {\n\n $scope.sectionFilters = sectionFilters;\n $scope.sectionColumns = sectionColumns;\n});\n\nEditAuditForm Template\n<audit-admin-sections audit-form=\"auditForm\" section-filters=\"sectionFilters\" section-columns=\"sectionColumns\" show-deleted=\"false\"></audit-admin-sections>\n\nAuditAdminSections Directive\nprideModule.directive('auditAdminSections', function ($log) {\n return {\n restrict: 'E',\n templateUrl: 'templates/admin/auditFormSections.html',\n scope: {\n sectionFilters: '=',\n sectionColumns: '='\n },\n controller: function ($scope, $route, $timeout, $location, filterLogic, auditFormSectionRepository) {\n // do stuff\n }\n});\n\nAuditFormSections Template\n<filter-header filters=\"sectionFilters\" columns=\"sectionColumns\"></filter-header>\n\nFilterHeader Directive\nprideModule.directive('filterHeader', function($log) {\n return {\n restrict: 'E',\n templateUrl: 'templates/common/filterHeader.html',\n scope: {\n filters: '=',\n columns: '='\n },\n controller: function ($scope, filterItemsRepository) {\n $log.info(\"$scope.filters\");\n $log.info($scope.filters);\n // This will log the filters as expected, however the $$hashKey property is missing from the items\n }\n});\n\nFilterHeader template\n<!-- ",
"at this point, {{ filters }} produces the list of filters -->\n<form class=\"form-horizontal\" ng-repeat=\"filter in filters\">\n <!-- ",
"at this point, nothing renders -->\n <label class=\"col-sm-2 control-label\">{{ filter.friendlyName }}</label>\n</form>\n\nUpdate 1\nI pulled the code out of the directive and into a new controller to mimic the Working Scenario mentioned above. ",
"The ng-repeater now functions as expected and the $$hashKey is present again. ",
"So something is definitely related to the difference between route->controller->directive->directive vs route->controller->directive.",
"\nWorth mentioning, on top of the code above, there are watches on the filters among other usages.",
"\nUpdate 2: Offender Uncovered\nI've nailed it. ",
"But it makes no sense yet. ",
"It seems as though the form element is to blame. ",
"Changing to a div resolves the issue. ",
"I'm thinking this may be an angular bug as I'm struggling to see why this could work in one scenario and not the other.",
"\n\nA:\n\nHave discovered two fixes so far, but they are more hacks than fixes as I cannot understand the cause of the original problem. ",
"I'm still interested if anyone can point out the real issue, but until then this is the best I have:\nSolution 1\nAfter much researching, debugging, head scratching, rewriting, I by luck came across a solution. ",
"I'm not happy with it, as it doesn't make sense (unless someone can elaborate for me).",
"\nThe problem seems to be with the form element and using the ng-repeat attribute on it while being nested in angular directives...!!! ",
"This has to be a bug, right?",
"\nSolution was as simple as changing this:\n<form class=\"form-horizontal\" ng-repeat=\"filter in filters\">\n <label class=\"col-sm-2 control-label\">{{ filter.friendlyName }}</label>\n</form>\n\nto this:\n<div class=\"form-horizontal\" ng-repeat=\"filter in filters\">\n <label class=\"col-sm-2 control-label\">{{ filter.friendlyName }}</label>\n</div>\n\nSolution 2\nIt seems that the $scope variables were also playing a part in the issue. ",
"If I rename each directive's $scope variable name for this particular variable (ie, filters) so that it is unique for each directive, the form ng-repeat works. ",
"This makes it seem like there is some sort of conflict within the directives' isolated scopes, however why this is only an issue for form ng-repeat baffles me. ",
"As such, it still doesn't explain to me what is the root cause of this behavior.",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0002687449610319807,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0000012975658443299876,
0,
0.00001721733441228629,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0.000006 | 5 |
[
"1. ",
"Introduction {#sec1}\n===============\n\nIn recent years, the studies of noncovalent interactions of DNA with ligands have received considerable attention caused by the huge number of applications being derived from these interactions. ",
"Among these applications, the development of new diagnostic and therapeutic agents \\[[@B1], [@B2]\\], the exploration of the possibilities of DNA as molecular conductor \\[[@B3]\\], the interest in gene transport \\[[@B4]\\], and the fabrication of biosensors stand out \\[[@B5]--[@B7]\\]. ",
"In our group, we have a consistent background on the analysis of ligand-receptor interactions and of the kinetic analysis of DNA-containing systems \\[[@B8], [@B9]\\]. ",
"We considered (i) thermodynamic aspects of ligand-receptor (DNA) binding \\[[@B10], [@B11]\\]; (ii) the binding kinetics, including the influences of salts and cosolvents on the kinetics \\[[@B12], [@B13]\\], and (iii) the effect of DNA on the reactivity of ligands \\[[@B14]--[@B16]\\]. ",
"For these purposes, we have conveniently used substitution inert transition metal complexes \\[[@B14]\\], organic compounds \\[[@B10], [@B12]\\], surfactants \\[[@B11], [@B12]\\], bile salts \\[[@B16]\\], and gold nanoparticles \\[[@B13]\\].",
"\n\nAmong a variety of these ligands, intense current interest is focused on gold colloids (AuNPs) due to their chemical stability, high biocompatibility and excellent structural, and optical, magnetic, and catalytic properties \\[[@B17]\\]. ",
"In particular, water soluble metal nanoparticles have received considerable attention due to the potential benefits in the fields of biology and medicine \\[[@B18]--[@B22]\\]. ",
"Especially interesting are alkanethiolates as protective agents due to their advantages of stability, suspendability in different solvents, and facile characterization by standard analytical techniques \\[[@B23]\\]. ",
"Since successful therapy for curing cancer and others genetic diseases requires the transport of DNA in the cell by delivery vehicles, the effective complexation of the DNA is a subject of great interest \\[[@B24]\\]. ",
"Numerous biological and medical applications in this active area of research are based on the binding of the nanoparticle probe to a particular biological substrate. ",
"More recently, sensors consisting of metal nanoparticles functionalized with DNA have appeared in the literature. ",
"It has been shown that these particles show affinities to the ligands that are, at least, two orders of magnitude greater than other conventional sensors \\[[@B25]--[@B27]\\]. ",
"However, little progress has been made in understanding noncovalent interactions of gold nanoparticles with nucleic acids \\[[@B28]--[@B31]\\] and quantitative studies on the affinity of these systems are even more scarce \\[[@B29], [@B32], [@B33]\\]. ",
"In this sense, the scope of this work is to quantify the thermodynamic aspects of DNA-Au\\@tiopronin binding. ",
"We are also interested in knowing how the environment surrounding the colloidal gold-DNA system, specifically the presence of salt (NaCl), affects the complex formation. ",
"The aim of this thermodynamic investigation carried out in conjunction with a complementary structural and spectroscopy study was to learn more about the factors that control the complexation of DNA with gold nanoparticles.",
"\n\n2. ",
"Materials and Methods {#sec2}\n========================\n\n2.1. ",
"Chemicals and Reagents {#sec2.1}\n---------------------------\n\nAll chemicals were Analytical R. Grade and were used without further purification. ",
"Hydrogen tetrachloroaurate(III) trihydrate and pyrene-1-carboxaldehyde (1-PyCHO) were purchased from Sigma-Aldrich; N-(2-mercaptopropionyl)glycine from Fluka; NaBH~4~ from Lancaster; and NaCl from Merck. ",
"Calf thymus DNA was purchased from Pharmacia (average number of base pairs: 10000) and used without further purification because preliminary experiments showed that purification does not produce any changes in experiments\\' results. ",
"Polynucleotide concentrations were determined spectrophotometrically from the molar absorptivity (6600 mol^−1^ dm^3^ cm^−1^ at 258 nm in order to have the DNA concentration in phosphate units) \\[[@B34]\\]. ",
"Solutions were prepared with deionized water, the conductivity being less than 10^−6^ S m^−1^. The temperature was maintained at 298.2 ± 0.1 in all experiments.",
"\n\n### 2.1.1. ",
"Synthesis of Gold Nanoparticles (Au\\@tiopronin) {#sec2.1.1}\n\nAu\\@tiopronin nanoparticles were prepared using the procedure of Templeton et al. ",
"\\[[@B35]\\]. ",
"One batch with hydrogen tetrachloroaurate(III) trihydrate (1 equiv) and N-(2-mercaptopropionyl)glycine (tiopronin) (5.5 equiv) was codissolved in 35 mL of 6 : 1 methanol/acetic acid, resulting in a ruby red solution. ",
"Sodium borohydride (22 equiv) in 15 mL of H~2~O was subsequently added via rapid stirring. ",
"The resultant brown suspension was stirred for an additional 30 min after cooling, with the solvent being removed under vacuum at 4°C. ",
"The crude sample was completely insoluble in methanol but reasonably soluble in water. ",
"It was purified by dialysis, in which the pH of the crude product dissolved in 20 mL of water (NANOpure) was adjusted to 1 by dropwise addition of concentrated hydrochloric acid. ",
"This solution was loaded into 15 cm segments of seamless cellulose ester dialysis membrane (Sigma, MWCO = 10.000), placed in 4 L beakers of water, and stirred slowly being recharged with fresh water ca. ",
"every 10 h over the course of 72 h. NMR spectra were used in order to see that the tiopronin was not free but bound to the gold. ",
"The dark brown Au\\@tiopronin solutions were collected from the dialysis tubes and were lyophilized. ",
"The product materials were found to be spectroscopically clean and produced a yield of 119 mg.",
"\n\nTEM analysis was carried out in a Philips CM 200 electron microscope working at 200 kV. Size distributions of the Au cores were measured from enlarged TEM image photographs for at least 200 individual cluster core images. ",
"A value of 1.4 nm was obtained for the diameter of the gold nanoparticle. ",
"Au\\@tiopronin nanoparticles were also characterized by visible absorption spectra and C, H, N, and S microanalysis (14.04% C; 2.25% H; 3.51% N; 7.78% S). ",
"According to these data and the results of the TEM, the relation between the number of Au atoms and tiopronin ligands was 119/105 \\[[@B35]\\].",
"\n\nAll the experiments were carried out from solutions of gold nanoparticles prepared by weight.",
"\n\n2.2. ",
"UV-Vis Spectra {#sec2.2}\n-------------------\n\nThe spectra of the Au\\@tiopronin in the presence and in the absence of DNA were recorded with a Cary 500 spectrophotometer from 280 nm to 800 nm. ",
"The UV-vis absorption spectra showed a slight detectable surface plasmon band (SPB) as a consequence of the small size of the clusters (see [Figure 2(a)](#fig2){ref-type=\"fig\"}). ",
"Titration experiments were carried out at a fixed colloidal gold concentration, \\[AuNPs\\] = 1.58 × 10^−6^ M, and in a DNA concentration range from 6.7 × 10^−6^ to 9.6 × 10^−5^ M.\n\n2.3. ",
"Fluorescence Measurements {#sec2.3}\n------------------------------\n\nFluorescence measurements were carried out in a spectrofluorimeter (Hitachi f-2500), interfaced to a PC for the reading and handling of the spectra. ",
"For the study with the fluorescence intercalator, pyrene-1-carboxaldehyde (1-PyCHO), intensity measurements were performed at \\[1-PyCHO\\] = 5.10^−7^ M. The excitation and emission wavelengths were 356 nm and 458 nm, respectively. ",
"It was checked that the results were independent of the excitation wavelength, provided that this one was in the range from 300 to 425 nm. ",
"DNA concentrations ranged from 10^−5^ M to 10^−3^ M. The water used in the preparation of solutions contained ethanol 5% (by weight). ",
"The presence of the alcohol was necessary in order to make the probe, pyren-1-carboxyaldehyde, soluble.",
"\n\nFor AuNPs/DNA titrations, a fixed colloidal gold concentration of \\[AuNPs\\] = 1.5 × 10^−6^ M was used, the DNA concentration varying from 10^−5^ M to 7 × 10^−5^ M. The excitation wavelength was 451 nm whereas the emission wavelength was 656 nm. ",
"The validation of the Beer-Lambert law was checked in the range of \\[AuNPs\\] = 5 × 10^−8^--2.16 × 10^−6^ M.\n\n2.4. ",
"Circular Dichroism (CD) Spectra {#sec2.4}\n------------------------------------\n\nElectronic CD spectra were recorded in a BioLogic MOS-450 spectropolarimeter. ",
"A standard quartz cell of 10 mm path length was used. ",
"The spectra were expressed in terms of molar ellipticity. ",
"Scans were taken from 220 nm to 310 nm. ",
"For each spectrum, 5--10 runs were averaged with a 5 min equilibration before each scan. ",
"All the spectra were performed at a fixed concentration of \\[DNA\\] = 10^−4^ M.\n\n2.5. ",
"Scanning Electron Microscopy (SEM) {#sec2.5}\n---------------------------------------\n\nScanning electron microscopy (SEM) images were obtained by using a Hitachi S5200 field-emission microscope. ",
"For SEM characterization, a drop of DNA or DNA/AuNPs solution was spread on a stub; the solvent was removed and then used. ",
"The samples were examined without specific manipulation.",
"\n\n2.6. ",
"Solubility Measurements {#sec2.6}\n----------------------------\n\nThe solubilities of pyren-1-carboxaldehyde in solutions containing gold nanoparticles were measured by agitating a generous excess of solid with the appropriate solution in a thermostated (298.2 K) vessel. ",
"After waiting a long time for undissolved solids to settle, an aliquot of the saturated solution was removed using a prethermostated pipette and the solution was diluted as necessary. ",
"Concentrations were measured spectrofluorimetrically in terms of previous calibration of the fluorescence of the pyren-1-carboxaldehyde at 5% ethanol with respect to the probe concentration. ",
"AuNPs concentrations corresponding to solubility measurements are given in [Table 2](#tab2){ref-type=\"table\"}.",
"\n\n3. ",
"Results and Discussion {#sec3}\n=========================\n\nTiopronin-protected gold clusters are alkanethiolate nanoparticles in which the presence of a carboxylic and amino group of the tiopronin allows to modify the charge of the nanoparticle as a function of the pH of the medium. ",
"As a consequence, this nanosystem can be used positively or negatively charged. ",
"This colloid system also offers potential advantages due to the stability conferred by the attachment of thiol groups, high solubility in water, facile characterization, and functionalization. ",
"In this sense, the possibility of functionalizing the carboxylic group with small oligopeptides can be taken into account \\[[@B36]\\]. ",
"It is important to note that all experiments in this paper were carried out at pH = 6. ",
"According to the pKa value of the tiopronin bound to the gold cluster, pKa ≈ 5.6, Au\\@tiopronin nanoparticles are mostly neutral and hydrophilic \\[[@B13], [@B35]\\]. ",
"Therefore, the binding of tiopronin nanoparticles can be expected to occur principally through the formation of stable hydrogen bonding between the hydrophilic groups of the tiopronin and the DNA bases \\[[@B13]\\], and the strength of this interaction could be modified as a function of the media pH. In order to provide evidences of the interaction of tiopronin-protected gold nanoparticles with DNA, different techniques were employed.",
"\n\nIt is known that small gold nanoparticles are able to emit fluorescence \\[[@B37]\\]. ",
"Increasing amount of DNA was added to a solution containing a fixed nanoparticle concentration (\\[AuNPs\\] = 1.5 × 10^−6^ M) and the changes on the fluorescence spectra were measured. ",
"In order to know if the nanoparticle aggregates, the linearity of the Beer-Lambert law for solutions containing various nanoparticles concentrations was tested. ",
"The inset in [Figure 1(a)](#fig1){ref-type=\"fig\"} shows that at low AuNPs concentrations (\\<2.16 *μ*M) the fluorescence intensity changes linearly with concentration, while at higher concentrations the Beer-Lambert law does not work, possibly due to a self-quenching effect produced by the Au\\@tiopronin. ",
"We must notice the importance of the small core size of the metal nanoparticle in relation to its luminescence properties. ",
"This feature is particularly of interest for water-soluble AuNPs having tiopronin thiolate monolayers, smaller than 2 nm. ",
"T. Huang et al. ",
"have studied the emission from tiopronin-AuNPs with different core sizes (1.8, 2.2, 3.1, and 3.9 nm) \\[[@B37]\\]. ",
"They found that only for the smallest nanoparticles (1.8 nm core size), luminescence was observed (*λ* ~em~ = 770 nm). ",
"The luminescence maximum shifts to lower energy with increasing core size \\[[@B38], [@B39]\\]. ",
"In that sense, the results in [Figure 1(b)](#fig1){ref-type=\"fig\"} obtained for our 1.4 nm AuNPs (*λ* ~em~ = 656 nm) are in good agreement with the paper of Huang and Murray. ",
"On the other hand, as can be seen in [Figure 1](#fig1){ref-type=\"fig\"}, the intensity of emission can be modified by the presence of DNA. ",
"In fact, an increase in the fluorescence emission at 656 nm was observed with increasing DNA concentration. ",
"Similar behaviour was observed for larger gold Au\\@tiopronin nanoparticles of 1.8 nm core size. ",
"However, one or two ethidium thiolate ligands are needed to be inserted into the Au\\@tiopronin/ethidium nanoparticles in order to confer better luminescent properties \\[[@B29]\\].",
"\n\nWith regard to UV-vis technique, [Figure 2(b)](#fig2){ref-type=\"fig\"} shows the changes of the surface plasmon band (SPB) of colloidal gold as increasing amounts of DNA were added to the solution. ",
"Despite the small size of the nanoparticle, the SPB is almost nondetectable; in [Figure 2](#fig2){ref-type=\"fig\"} it can be observed how spectra are modified upon the binding of DNA. ",
"Moreover, the isosbestic point about 308 nm gives support to the DNA/Au\\@tiopronin complex formation.",
"\n\nThese two conventional spectroscopy techniques provide evidence of interaction. ",
"Unfortunately, due to the small changes registered on spectra as the titration occurs, these techniques are not appropriate to quantify the binding constant of the Au\\@tiopronin/DNA interaction. ",
"Alternatively, we found that the CD technique provides a convenient method to quantify this interaction. ",
"The determination of the free energy of binding, that is, the free energy for the DNA/AuNPs complex formation, has been carried out following two different approaches. ",
"The first one is based on the measurement of the changes of DNA molar ellipticity in the presence of AuNPs. ",
"The second approach is based on the use of a fluorescent probe, pyrene-1-carboxaldehyde. ",
"In both cases, the starting point has been a two-state model. ",
"DNA-AuNPs interaction causes a conformational change in the DNA structure during the course of the binding, which can be followed by the circular dichroism technique (see [Figure 3](#fig3){ref-type=\"fig\"}). ",
"As is known, the backbone conformation of DNA shows a CD spectrum characteristic of the right-handed B form in the UV region (220--320 nm). ",
"Structure alterations of the DNA caused by its interaction with ligands are reflected in changes in this intrinsic CD spectrum. ",
"In [Figure 3](#fig3){ref-type=\"fig\"}, the CD spectrum of free DNA has a positive peak at 279 nm and a negative peak at 247 nm which corresponds to B-DNA form. ",
"These bands are caused by stacking interactions between the bases and the helical suprastructure of the polynucleotide that provide an asymmetric environment for the bases \\[[@B40]\\]. ",
"In the same figure, an example of CD titration in water can be observed which clearly demonstrates that the helical conformation is not maintained.",
"\n\nUpon the addition of the gold clusters to the DNA solution, the molar ellipticity decreases at approximately 279 nm; meanwhile, it increases at approximately 247 nm. ",
"These changes are coupled with a shift in the maximum wavelength of the positive band, as can be seen in [Figure 3(a)](#fig3){ref-type=\"fig\"}, indicating partial denaturation of double strand \\[[@B41], [@B42]\\].",
"\n\nFurther information about what kind of DNA conformational changes being induced by Au\\@tiopronin nanoparticles has been obtained by means of the SEM technique. ",
"Typical images of CT-DNA in the absence ([Figure 4(b)](#fig4){ref-type=\"fig\"}) and in the presence (Figures [4(c)](#fig4){ref-type=\"fig\"} and [4(d)](#fig4){ref-type=\"fig\"}) of different amount of gold nanoparticles are given in [Figure 4](#fig4){ref-type=\"fig\"}. ",
"It is clear from these images that gold nanoparticles induce a compaction of DNA molecules. ",
"It can also be seen in the figure that the degree of compaction increases with the concentration of nanoparticles.",
"\n\nBased on CD spectrum changes as Au\\@tiopronin nanoparticles were added to the DNA solution, it was possible to quantify the binding constant of the interaction.",
"\n\nAccording to a two-state model, changes on the DNA molar ellipticity should be the consequence of the distribution of the gold cluster in the bulk (water) and on the DNA surface (see [Scheme 1](#sch1){ref-type=\"fig\"}).",
"\n\nAccording to this model, if the DNA and Au\\@tiopronin nanoparticles constitute a complex, at the equilibrium there will be two populations of DNA: free and bound to the nanoparticle: $$\\begin{matrix}\n{\\left\\lbrack \\text{DNA} \\right\\rbrack = \\frac{1}{1 + K^{\\text{DNA}/\\text{AuNPs}}\\left\\lbrack \\text{AuNPs} \\right\\rbrack}\\left\\lbrack \\text{DNA} \\right\\rbrack_{0},} \\\\\n{\\left\\lbrack {\\text{DNA}/\\text{AuNPs}} \\right\\rbrack = \\frac{K^{\\text{DNA}/\\text{AuNPs}}\\left\\lbrack \\text{AuNPs} \\right\\rbrack}{1 + K^{\\text{DNA}/\\text{AuNPs}}\\left\\lbrack \\text{AuNPs} \\right\\rbrack}\\left\\lbrack \\text{DNA} \\right\\rbrack_{0},} \\\\\n\\end{matrix}$$ where \\[DNA\\]~0~ is the total concentration of DNA, such that \\[DNA\\]~0~ = \\[DNA\\] + \\[DNA/AuNPs\\]. ",
"Accordingly, the observed molar ellipticity, \\[*θ*\\], would be given by $$\\begin{matrix}\n{\\left\\lbrack \\theta \\right\\rbrack = \\frac{\\left\\lbrack \\theta \\right\\rbrack_{f} + \\left\\lbrack \\theta \\right\\rbrack_{b}K^{\\text{DNA}/\\text{AuNPs}}\\left\\lbrack \\text{AuNPs} \\right\\rbrack}{1 + K^{\\text{DNA}/\\text{AuNPs}}\\left\\lbrack \\text{AuNPs} \\right\\rbrack}.} \\\\",
"\n\\end{matrix}$$ Thus, *K* ^DNA/AuNPs^ can be obtained from the variations of \\[*θ*\\]~279 nm~ caused by the changes of \\[AuNPs\\]. [",
"Figure 3(b)](#fig3){ref-type=\"fig\"} gives these variations. ",
"Consequently, by fitting the experimental values of \\[*θ*\\] to ([2](#EEq4){ref-type=\"disp-formula\"}), a value of *K* ^DNA/AuNPs^ = 6.4 × 10^5^ M^−1^ was obtained in water.",
"\n\nSimilar experiments were carried out in the presence of different NaCl concentrations. ",
"The results (values of *K* ^DNA/AuNPs^) of these experiments are given in [Table 1](#tab1){ref-type=\"table\"}.",
"\n\nAs can be seen in this table, the binding of DNA with AuNPs is somewhat sensitive to the ionic strength. ",
"This fact could be indicative of a slight electrostatic character of the binding. ",
"Therefore, the free energy of binding can be written as the sum of two contributions: (i) an electrostatic-potential-independent contribution, Δ*G* ~nel~ (nonelectrostatic or intrinsic), and (ii) an electrostatic-potential-dependent contribution, Δ*G* ~el~ (electrostatic). ",
"This separation has been discussed extensively in \\[[@B43]--[@B47]\\]: $$\\begin{matrix}\n{\\Delta G = \\Delta G_{\\text{nel}} + \\Delta G_{\\text{el}}.} \\\\",
"\n\\end{matrix}$$ Thus, the free energy of binding Δ*G* can be written as a sum of two contributions: a nonelectrostatic contribution, Δ*G* ~nel~, and an electrostatic one, Δ*G* ~el~, which implies $$\\begin{matrix}\n{K^{\\text{DNA}/\\text{AuNPs}} = K_{\\text{nel}}K_{\\text{el}}.} \\\\",
"\n\\end{matrix}$$ In order to separate these contributions, we used Lippard\\'s equation. ",
"According to Howe-Grant and Lippard \\[[@B47]\\], log *K* ~el~ is proportional to −log\\[Na^+^\\]; that is, $$\\begin{matrix}\n{\\log K^{\\text{DNA}/\\text{AuNPs}} = \\log K_{\\text{nel}} - \\beta\\log\\left\\lbrack \\text{Na}^{+} \\right\\rbrack.} \\\\",
"\n\\end{matrix}$$ The values of log*K* ^AuNPs/DNA^ appearing in [Table 1](#tab1){ref-type=\"table\"} are plotted in [Figure 5](#fig5){ref-type=\"fig\"}. ",
"From the intercept, a value of log*K* ~nel~ = 4.98 was found, which gives a value of *K* ~nel~ = 9.5 × 10^4^ M^−1^. That is, taking into account the values of *K* ^DNA/AuNPs^ appearing in [Table 1](#tab1){ref-type=\"table\"}, it can be established that the nonelectrostatic component of the binding free energy is about \\~90% of the total free energy.",
"\n\nAs mentioned previously, a second approach was used to obtain *K* ^DNA/AuNPs^. This approach is based on the use of a fluorescent intercalator pyrene-1-carboxaldehyde \\[[@B48]\\]. ",
"This procedure has been used by one of the previous authors to measure the binding constant of surfactant to DNA \\[[@B11]\\]. ",
"1-PyCHO is a good probe for sensing polarity changes. ",
"This circumstance arises from the existence of two excited states that are close in energy: a fluorescent state and a \"dark\" state whose relative populations depend on the medium polarity. ",
"As a matter of fact, in the presence of DNA, we observed a diminution in the fluorescent intensity of 1-PyCHO \\[[@B10], [@B49]\\]. ",
"The magnitude of these changes in the intensity depends also on the association degree of the gold nanoparticle with DNA. ",
"This circumstance allows us to determine the binding constants of 1-PyCHO to DNA in the presence of different Au\\@tiopronin nanoparticles concentrations by using the Hildebrand-Benesi equation \\[[@B50]\\].",
"\n\nWe performed experiments in which the fluorescence emission of 1-PyCHO was measured in the presence of a fixed concentration of Au\\@tiopronin and variable DNA concentrations. ",
"A typical example of binding isotherm obtained from these titrations is given in [Figure 6](#fig6){ref-type=\"fig\"}, and plot shows that the binding saturation has been attained at 1.5 × 10^−4^ M of DNA. ",
"Besides, as the AuNPs, concentration increases in each titration, the amount of DNA needed to attain saturation increases. ",
"The values of the binding constants of 1-PyCHO/DNA are given in [Table 2](#tab2){ref-type=\"table\"}.",
"\n\nAs can be seen, these binding constants depend on the nanoparticle concentration, that is, on the proportion of DNA free and bound to the Au\\@tiopronin nanoparticles (see ([1](#EEq2){ref-type=\"disp-formula\"})). ",
"From these values of *K* ^1-PYCHO/DNA^, those of Δ*G* = −*RT* × ln(*K* ^1-PYCHO/DNA^) were obtained. ",
"However, the values of Δ*G* represent the affinity of 1-PyCHO for the binding to DNA *relative to the solutions where the free pyrene-1-carboxaldehyde is present*. ",
"Obviously, Δ*G* cannot be compared directly because these solutions are different. ",
"However, solubility measurements in [Table 2](#tab2){ref-type=\"table\"} allow us to compare Δ*G* once they have been corrected, taking into account the differences in free energy of the probe in the solutions due to the presence of tiopronin gold nanoparticles. ",
"Thus, if *S* ~0~ is the solubility in the absence of Au\\@tiopronin and *S* in the presence of a given concentration of the nanoparticle, this free energy, Δ*G*, is related to the activity coefficient of 1-PyCHO, and the latter to the solubility: $$\\begin{matrix}\n{\\Delta G = RT\\ln\\gamma_{1\\text{-PyCHO}} = RT\\ln\\frac{S_{0}}{S}.} \\\\",
"\n\\end{matrix}$$ In this way, the values of Δ*G* ^CORR^ appearing in [Table 2](#tab2){ref-type=\"table\"} were obtained: $$\\begin{matrix}\n{\\Delta G^{\\text{CORR}} = \\Delta G - RT\\ln\\frac{S_{0}}{S}.} \\\\",
"\n\\end{matrix}$$ It is interesting to note that [Table 2](#tab2){ref-type=\"table\"} shows that the Δ*G* ^CORR^ values increase when Au\\@tiopronin concentrations do so. ",
"According to this fact, it must be inferred that gold nanoparticles modify DNA upon binding. ",
"Au\\@tiopronin nanoparticles induce a change in the DNA/AuNPs complex that makes it less efficient than free DNA in order to bind 1-PyCHO. ",
"The effect of gold nanoparticles on DNA/1-PyCHO system is to induce a structural change in the DNA, which will be the result of the structural modifications due to the gold core and the tiopronin tails of the nanoparticle. ",
"Therefore, two kinds of DNA will be in the solution, free and bound to Au\\@tiopronin, with different capacities to bind 1-PyCHO, in the sense that the corrected binding free energy of the dye will be different for each kind of DNA. ",
"It can be shown (see Supporting Information available online at <http://dx.doi.org/10.1155/2014/143645>) that the observed corrected free energies, Δ*G* ^CORR^, will be given by $$\\begin{matrix}\n{\\Delta G^{\\text{CORR}}} \\\\\n{\\quad = \\frac{{\\Delta G}_{1}^{\\text{CORR}} + {\\Delta G}_{2}^{\\text{CORR}}\\left( {K_{2}/K_{1}} \\right)K^{\\text{DNA}/\\text{AuNPs}}\\left\\lbrack \\text{AuNPs} \\right\\rbrack}{1 + \\left( {1 + K_{2}} \\right)\\left( {K^{\\text{DNA}/\\text{AuNPs}}/K_{1}} \\right)\\left\\lbrack \\text{AuNPs} \\right\\rbrack}.} \\\\",
"\n\\end{matrix}$$ In this equation, Δ*G* ~1~ ^CORR^ is the corrected free energy of binding of 1-PyCHO with free DNA, that is, to DNA without Au\\@tiopronin; meanwhile, Δ*G* ~2~ ^CORR^ is the same but when the DNA is bound to the gold nanoparticles, AuNPs; *K* ~1~ is the equilibrium binding constant 1-PyCHO/DNA in the absence of Au\\@tiopronin and *K* ~2~ is the equilibrium binding constant 1-PyCHO/DNA in the saturation limit of AuNPs. ",
"Finally, *K* ^DNA/AuNPs^ is the equilibrium constant for the binding of the Au\\@tiopronin with DNA (see [Scheme 1](#sch1){ref-type=\"fig\"}). ",
"In other words, changes in Δ*G* ^CORR^ can be interpreted using a two-state model of the DNA/AuNPs binding.",
"\n\n[Figure 7](#fig7){ref-type=\"fig\"} corresponds to the fit of data in [Table 2](#tab2){ref-type=\"table\"} to ([8](#EEq10){ref-type=\"disp-formula\"}). ",
"A value of *K* ^DNA/AuNPs^ = 5.9 × 10^5^ (M^−1^) was obtained, with *K* ~2~ = 2.2 × 10^4^ and *K* ~1~ = 8.1 × 10^4^ M^−1^. The agreement of this value with the corresponding one obtained through CD measurements supports our simpler methodology based on the two-state model.",
"\n\n4. ",
"Conclusions {#sec4}\n==============\n\nThe interaction of gold nanoparticles capped with tiopronin of 1.4 nm core size with DNA was investigated by using different techniques: CD, SEM, UV-vis, and fluorescence spectroscopy. ",
"A simple methodology to quantify the free energy of AuNPs/DNA binding has been proposed based on CD spectral change during AuNPs titration. ",
"A complementary study using pyrene-1-carboxaldehyde as a fluorescence probe supports the thermodynamic results obtained. ",
"Our results in the presence of different sodium chloride concentrations revealed that the AuNPs/DNA binding is fundamentally of nonelectrostatic character. ",
"The results provide an alternative method to quantify binding free energy of AuNPs/DNA-like systems when small changes in the titration are registered using conventional spectroscopic techniques.",
"\n\nSupplementary Material {#supplementary-material-sec}\n======================\n\n###### \n\nDetailed derivation of equation (8) and the model for evaluation of DNA-AuNPs equilibrium binding constants in the presence of two ligands that support the discussions in this manuscript.",
"\n\n###### \n\nClick here for additional data file.",
"\n\nThis work was financed by the DIGYT (CTQ2008-0008/BQU) and the Council of Education and Science of the Junta de Andalucía.",
"\n\nConflict of Interests\n=====================\n\nThe authors declare that there is no conflict of interests regarding the publication of this paper.",
"\n\n![(",
"a) Plot of fluorescence intensity at 656 nm of Au\\@tiopronin versus \\[AuNPs\\], in the absence of DNA. (",
"b) Fluorescence spectra of AuNPs/DNA system recorded for increasing concentrations of DNA in 5% of ethanol. ",
"\\[AuNPs\\] = 1.5 × 10^−6^ M; \\[DNA\\] = 0 M (bottom); \\[DNA\\] = 7 × 10^−5^ M (top).](TSWJ2014-143645.001){#fig1}\n\n![(",
"a) Absorption spectrum of the Au\\@tiopronin. (",
"b) Absorbance titration of AuNPs/DNA system recorded for increasing concentrations of DNA. ",
"\\[AuNPs\\] = 1.58 × 10^−6^ M; \\[DNA\\] = 0 M (top); \\[DNA\\] = 1 × 10^−4^ M (bottom).](TSWJ2014-143645.002){#fig2}\n\n![(",
"a) CD titration of AuNPs with DNA in water. ",
"\\[DNA\\] = 1 × 10^−4^ M. Curves from (i) to (xv) correspond to 0, 0.15, 0.29, 0.39, 0.58, 0.71, 1.00, 1.50, 2.00, and 4.00 *μ*M of AuNPs. (",
"b) Plot of the molar ellipticity experimental data versus AuNPs concentrations. ",
"Symbols (∙) are experimental data and line is the best fit using ([2](#EEq4){ref-type=\"disp-formula\"}).](TSWJ2014-143645.003){#fig3}\n\n![",
"SEM images of CT-DNA at different concentrations of AuNPs in the presence of \\[NaCl\\] = 0.015 M. (a) \\[AuNPs\\] = 1 × 10^−6^ M; (b) \\[DNA\\] = 2 × 10^−6^ M; (c) \\[DNA\\] = 2.5 × 10^−6^, \\[AuNPs\\] = 2.5 × 10^−7^ M; (d) \\[DNA\\] = 2 × 10^−6^ M, \\[AuNPs\\] = 1 × 10^−6^ M.](TSWJ2014-143645.004){#fig4}\n\n![",
"Plot of log *K* ^DNA/AuNPs^ versus log\\[Na^+^\\] (see ([5](#EEq7){ref-type=\"disp-formula\"})) for the DNA-AuNPs system.](TSWJ2014-143645.005){#fig5}\n\n![(",
"a) Fluorescence titration (*λ* ~em~ = 458 nm) of 1-PyCHO with DNA in the presence of Au\\@tiopronin nanoparticles. (",
"\\[1-PyCHO\\] = 5 × 10^−7^ M; \\[AuNPs\\] = 6 × 10^−7^ ** **M; \\[DNA\\] = 0--5 × 10^−4^ M, given in base pairs). (",
"b) Fit of the data to Hildebrand-Benesi model.](TSWJ2014-143645.006){#fig6}\n\n![",
"Corrected free energy of 1-PyCHO/AuNPs interaction, Δ*G* ^CORR^, versus \\[AuNPs\\], best fit to ([8](#EEq10){ref-type=\"disp-formula\"}).](TSWJ2014-143645.007){#fig7}\n\n![](",
"TSWJ2014-143645.sch.001){#sch1}\n\n###### \n\nBinding constants (*K* ^DNA/AuNPs^) and the free energy of binding (Δ*G* ^DNA/AuNPs^) corresponding to DNA/AuNPs interaction at different NaCl concentrations.",
"\n\n \\[NaCl\\]/M 10^5^ *K* ^DNA/AuNPs^/M^−1^ Δ*G* ^DNA/AuNPs^/kJmol^−1^\n ------------ ----------------------------- ----------------------------\n 0.000 6.40 −33.12\n 0.002 6.34 −33.10\n 0.006 4.98 −32.50\n 0.010 3.88 −31.88\n 0.015 3.34 −31.51\n\n###### \n\nSolubilities (*S*), equilibrium binding constants (*K* ^1-PyCHO/DNA^), and the corrected free energy (Δ*G* ^CORR^) corresponding to 1-PyCHO/DNA interaction at different Au\\@tiopronin concentrations.",
"\n\n 10^−6^ \\[AuNPs\\]/M *S*/M 10^−4^ *K* ^1-PyCHO/DNA^/M^−1^ (Δ*G* ^CORR^)/kJmol^−1^\n -------------------- --------------- -------------------------------- -------------------------\n 0.0 1.21 × 10^−6^ 78.0 −27.91\n 2.5 3.02 × 10^−6^ 77.0 −25.59\n 6.0 1.21 × 10^−5^ 58.1 −21.47\n 10.0 2.41 × 10^−5^ 49.8 −19.39\n 20.0 2.49 × 10^−5^ 46.0 −19.11\n\n[^1]: Academic Editors: L. Y. Chen, D. Dondi, P. Pietrzyk, and R. Schweiss\n"
] | {
"pile_set_name": "PubMed Central"
} | [
0,
0,
0.00007491665522106657,
0.00007257947452460445,
0.00007544892108042855,
0.00013118194936376755,
0.0000353082409434362,
0.00006605892456070815,
0.00002183596820683029,
0.00002143347050754458,
0,
0,
0.00006605892456070815,
0.0000812955254942768,
0.00008416799932665601,
0.00003460207612456747,
0,
0,
0,
0.00004756242568370987,
0.00016820453671664745,
0.000036839875481220875,
0.000023795359904818562,
0.0000390625,
0,
0.00009780429360848941,
0.006944444444444444,
0.00002123638216993353,
0,
0,
0,
0,
0,
0,
0.0001,
0,
0.00005978954081632653,
0,
0.000084331253162422,
0.0001005985614405714,
0,
0,
0.00002712673611111111,
0.00003121001217190475,
0,
0.00002123638216993353,
0,
0,
0,
0,
0.000016391024275106952,
0,
0.0000400576830636116,
0,
0,
0,
0,
0,
0.00002657030502710171,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00002684635829149776,
0.000055691690799732676,
0,
0.00014692378328741966,
0.0000052604999579160005,
0.00013520822065981613,
0,
0,
0.000021499596882558453,
0,
0,
0.00390625,
0.00007831466833737959,
0,
0.00022634676324128565,
0.00006530612244897959,
0,
0,
0.00010850694444444444,
0.00006312334301224592,
0.0000252518875785965,
0.00002986055122577563,
0.0000980296049406921,
0,
0.000026298487836949376,
0,
0,
0.00008573388203017832,
0,
0,
0,
0,
0,
0,
0.00002953686200378072,
0,
0,
0.00004492262078569664,
0.000038103947568968146,
0,
0,
0,
0.000038103947568968146,
0,
0.0000018611957438175731,
0,
0,
0,
0,
0.00012624668602449185,
0,
0,
0,
0,
0.00009130752373995617,
0,
0.0001321178491214163,
0.00005525981322183131,
0,
0,
0.000030524098775983637,
0.000064,
0,
0,
0.0001183431952662722,
0,
0.00004805843906189927,
0.00003191930798940279,
0.000024266543716178507,
0.00006609822195782934,
0,
0.00002204148206925434,
0.00009611687812379854,
0,
0,
0,
0.000018254670913920098,
0.00007730165683217811,
0.000036289737262302225,
0,
0.00005250997689561017,
0,
0.000018579072532699166,
0.000011180513111015041,
0.000031562999747496005,
0.0000510204081632653,
0,
0,
0,
0,
0,
0.0000510204081632653,
0,
0.000041091387245233394,
0.000026298487836949376,
0,
0,
0.0001951092611862643,
0,
0,
0.00009425959091337542,
0.00008573388203017832,
0,
0.0004725897920604915,
0.00012075836251660429,
0,
0,
0.00005250997689561017,
0,
0.00005406574394463668,
0,
0,
0.00007561436672967865,
0,
0.0001602307322544464,
0,
0.000025,
0.000007906054983977061,
0.000011238758431878513
] | 0.000088 | 5 |
[
"Hugh Jackman - Golden Globes 2013 Red Carpet\n\nAbout this photo set:\nHugh Jackman shows off his shiny statue in the press room of the 2013 Golden Globes held at the Beverly Hilton Hotel on Sunday (January 13) in Beverly Hills, Calif.… Read More Here"
] | {
"pile_set_name": "Pile-CC"
} | [
0.000048777315296566075
] | 0.000049 | 5 |
[
"Virtual CFO Services\n\nVirtual CFO Services\n\nYou get the benefits of a Chief Financial Officer (CFO) without the significant cost of employing one full time. ",
"A virtual CFO will be able to take your business to the next level of financial control and profitability. ",
"We can tailor our services to your business needs and budget. ",
"With the use of cloud technology we can have real time access to your financial data and advise you about complex business decisions.",
"\n\nOur range of Virtual CFO services include:\n\nMonthly performance reports\n\nMonthly management reports\n\nKPI’s and benchmarking\n\nBudgeting and cash flow management\n\nBusiness analysis\n\nMonthly meetings\n\nUnlimited support\n\nCloud Solutions\n\nCloud technology is the way of the future. ",
"It allows your business to be more efficient by allowing your data to be accessible online anywhere, anytime and from any device. ",
"Cloud technology also allows business owners to stay connected to their financial advisers all the time.",
"\n\nOur range of Cloud Solutions services include:\n\nXero\n\nXero Add-Ons\n\nMYOB\n\nMYOB Add-Ons\n\nFor more information on Virtual CFO Services available in Canberra, call us on (02) 6262 2779"
] | {
"pile_set_name": "Pile-CC"
} | [
0.000040569597143900364,
0,
0,
0,
0.000025693400650043035,
0,
0,
0.00005972110245155126
] | 0.000016 | 5 |
[
"//\n// Copyright 2016 Pixar\n//\n// Licensed under the Apache License, Version 2.0 (the \"Apache License\")\n// with the following modification; you may not use this file except in\n// compliance with the Apache License and the following modification to it:\n// Section 6. ",
"Trademarks. ",
"is deleted and replaced with:\n//\n// 6. ",
"Trademarks. ",
"This License does not grant permission to use the trade\n// names, trademarks, service marks, or product names of the Licensor\n// and its affiliates, except as required to comply with Section 4(c) of\n// the License and to reproduce the content of the NOTICE file.",
"\n//\n// You may obtain a copy of the Apache License at\n//\n// http://www.apache.org/licenses/LICENSE-2.0\n//\n// Unless required by applicable law or agreed to in writing, software\n// distributed under the Apache License with the above modification is\n// distributed on an \"AS IS\" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY\n// KIND, either express or implied. ",
"See the Apache License for the specific\n// language governing permissions and limitations under the Apache License.",
"\n//\n#ifndef PXR_IMAGING_GLF_UTILS_H\n#define PXR_IMAGING_GLF_UTILS_H\n\n/// \\file glf/utils.h\n\n#include \"pxr/pxr.h\"\n#include \"pxr/imaging/glf/api.h\"\n#include \"pxr/imaging/garch/gl.h\"\n\n#include <string>\n\nPXR_NAMESPACE_OPEN_SCOPE\n\n/// Base image format\n///\n/// Returns the base image format for the given number of components\n///\n/// Supported number of components: 1, 2, 3, 4\nGLF_API \nGLenum GlfGetBaseFormat(int numComponents);\n\n/// Number of elements.",
"\n///\n/// Returns the number of elements (channels) in a given GL enum format.",
"\n///\n/// Supported formats are : GL_DEPTH_COMPONENT, GL_COLOR_INDEX, GL_ALPHA, \n/// GL_RED, GL_LUMINANCE, GL_RG, GL_LUMINANCE_ALPHA, GL_RGB, GL_RGBA\nGLF_API \nint GlfGetNumElements(GLenum format);\n\n/// Byte size of a GL type.",
"\n///\n/// Returns the size in bytes of a given GL type.",
"\n///\n/// Supported types are : GL_UNSIGNED_BYTE, GL_BYTE, GL_UNSIGNED_SHORT, \n/// GL_SHORT, GL_FLOAT, GL_DOUBLE\nGLF_API\nint GlfGetElementSize(GLenum type);\n\n/// Checks the valitidy of a GL framebuffer\n///\n/// True if the currently bound GL framebuffer is valid and can be bound\n/// or returns the cause of the problem\nGLF_API\nbool GlfCheckGLFrameBufferStatus(GLuint target, std::string * reason);\n\n/// Check if the format is compressed.",
"\n///\n/// Supported GL compressed formats : GL_COMPRESSED_RGBA_BPTC_UNORM, \n/// GL_COMPRESSED_RGB_BPTC_UNSIGNED_FLOAT\nGLF_API\nbool GlfIsCompressedFormat(GLenum format);\n\n/// Calculate the byte size of compressed textures.",
"\n///\n/// Supported GL compressed formats : GL_COMPRESSED_RGBA_BPTC_UNORM, \n/// GL_COMPRESSED_RGB_BPTC_UNSIGNED_FLOAT\nGLF_API\nsize_t GlfGetCompressedTextureSize(int width, int height, \n GLenum format, GLenum type);\n\nPXR_NAMESPACE_CLOSE_SCOPE\n\n#endif\n"
] | {
"pile_set_name": "Github"
} | [
0.00002847988608045568,
0,
0,
0,
0.000027232744652169767,
0.000015094795314575536,
0,
0,
0,
0.00003985969387755102,
0,
0.000026302499789580002,
0.000020661157024793387,
0.000012486109203511094
] | 0.000012 | 5 |
[
"Crist To Meet With Space Officials (Source: Florida Today)Gov. ",
"Charlie Crist will meet with space industry officials at 2:30 p.m. Thursday at the Canaveral Port Authority building in Port Canaveral. ",
"The space industry faces massive layoffs during the next two years as the space shuttle program comes to an end. ",
"Crist, who is running for the U.S. Senate, likely will seek input about what the state's role should be in the transition to a post-shuttle economy. ",
"The governor tentatively plans to meet with space industry workers before discussions with industry leaders and local officials, who have been invited to the meeting. (",
"1/4)\n\nDelta-4 Assigned to Launch Military Satellite (Source: SpaceFlightNow.com)The U.S. Air Force has tapped the Delta-4 as its rocket of choice to launch the fourth Wideband Global SATCOM spacecraft two years from now. ",
"Liftoff of the WGS 4 communications satellite from the Cape Canaveral Spaceport is targeted to occur between December 2011 and February 2012. ",
"The contract award comes just a month after the successful launch of WGS 3 atop a Delta 4 rocket.",
"\n\nA powerful version of the United Launch Alliance-built Delta 4 is used to carry these sophisticated payloads into geosynchronous transfer orbit. ",
"The specific rocket configuration is known as the Medium+ (5,4), which is distinguished by a five-meter composite payload shroud, a similarly-sized cryogenic upper stage and four solid-fuel boosters strapped to the first stage. (",
"1/4)\n\nIndia Developing Anti-satellite Technology (Source: Space News)India has begun development of lasers and an exoatmospheric kill vehicle that could be combined to produce a weapon to destroy enemy satellites in orbit, the director-general of India’s defense research organization said. “",
"The kill vehicle, which is needed for intercepting the satellite, needs to be developed, and that work is going on as part of the ballistic missile defense program,” said V.K. Saraswat, director-general of the Defense Research and Development Organization, which is part of India’s Ministry of Defence. (",
"1/4)\n\nNorthrop will Relocate HQ to Washington Area (Source: Washington Business Journal)Defense contracting giant Northrop Grumman Corp. will move its corporate headquarters from Los Angeles to the Washington area by 2011, the region's latest economic development coup and another symbol of its economic prowess. ",
"The company broke the news in a news release Monday, saying it is considering locations in D.C., Maryland and Virginia. ",
"Northrop Grumman will complete the search by the spring of this year and open its new corporate office by the summer of 2011. ",
"It expects to base its decision on the amount of financial incentives offered by local jurisdictions. (",
"1/4)\n\nExplosive Nearby Star Could Threaten Earth (Source: Space.com)A massive, eruptive white dwarf star in the Milky Way — long overdue for its next periodic eruption — is closer to our solar system than previously thought and could threaten the Earth if it fully explodes millions of years from now. ",
"New observations of the white dwarf and its sun-like stellar companion are giving scientists a better understanding of the star's precarious position as a possible supernova, astronomers said.",
"\n\nThe two stars are in a close binary system called T Pyxidis, located in the Southern Hemisphere constellation Pyxis. ",
"Researchers found that the system is only 3,260 light-years from our solar system – far closer than anyone previously thought. (",
"A light-year is the distance that light travels in one Earth year, or about 6 trillion miles.) ",
"The new findings suggest the white dwarf, considered close to us by cosmic standards, could eventually go supernova. ",
"Gamma radiation emitted by the supernova could threaten the Earth with an energy equivalent to 1,000 simultaneous solar flares. (",
"1/4)\n\nAir Force Will Pay to Place SBSS Satellite in Storage (Source: Space News)The U.S. Air Force will contract to have its Space Based Space Surveillance (SBSS) system satellite placed into storage due to continued technical difficulties with the Minotaur 4 rocket that have delayed the spacecraft’s launch indefinitely, according to government documents. (",
"1/4)\n\nNASA's Next Project: Venus, the Moon, or an Asteroid (Source: cnet)NASA has chosen three options it will consider as its next target for future scientific space exploration--Venus, the moon, or an asteroid.",
"The three areas of focus are finalists in a competition designed to help the space agency determine where it should spend its time and money to get the most scientific value out of research about our solar system. ",
"It's part of NASA's New Frontiers Program, which already has two missions under way. ",
"The first is the New Horizons mission, a spacecraft that's currently on its way to Pluto and has already sent back images from a quick flyby of Jupiter. ",
"The second is called Juno, a large-scale survey of Jupiter that's planned for launch in 2011. ",
"This competition will determine the focus of New Frontiers' third mission. (",
"1/4)\n\nEarth-Sized World Could Lurk in Outer Solar System (Source: Space.com)Some astronomers say that a planet the size of Mars or Earth could be lurking on the fringes of our solar system. ",
"But even the latest space telescopes that launched in 2009 stand little chance of finding such a distant object. ",
"Such a world, if it exists, would probably have an orbit far beyond Pluto or similar dwarf planets in the outer solar system. ",
"It would likely resemble a frozen version of Mars or Earth at best, a most unsuitable home for life. ",
"And it would not be alone.",
"\n\n\"When the solar system's story is finally written, it's much more likely that it will have closer to 900 planets rather than the nine that we grew up with,\" said Alan Stern, a planetary scientist at the Southwest Research Institute (SwRI) in Boulder, Colo. Just a handful of those potential discoveries might reach the size of Earth, compared to a swarm of Pluto-sized bodies that Stern and others expect to find.",
"\n\nEach object – be it termed a planet, dwarf planet or otherwise – would serve as a frozen time capsule that could reveal much about the early evolution of the solar system. ",
"It could even force scientists to once again rethink the definition of a planet, following the controversial downgrading of Pluto to a dwarf planet. (",
"1/4)\n\nPlanet-Hunter Finds Five Lightweight Worlds (Source: MSNBC)The list of known exoplanets in the galaxy just got bigger, thanks to the first observations of NASA's Kepler space telescope, which found five new lightweight worlds orbiting distant stars. ",
"The planet-hunting Kepler, which hopes to discover alien Earths, also found an odd object orbiting a star and is measuring the quakes that ripple across stellar surface.",
"\n\nThe five newfound planets are all much larger than the Earth-sized bodies Kepler was designed to find. ",
"One comes in at around the size of Neptune, and the other four measure larger than Jupiter. (",
"1/4)\n\nAir Force Picks Booz Allen to Support Transformation of the Spacelift Ranges (Source: Booz Allen)Booz Allen Hamilton has been awarded a $38.4 million Launch & Test Range System (LTRS) Systems Engineering and Integration (SE&I) contract, which provides support to the Los Angeles-based Spacelift Range Group (LRRG), Launch and Range Systems Wing (LRSW), Space and Missile Systems Center (SMC). ",
"Booz Allen will provide required SE&I support to modernize the spacelift range enterprise by putting in place the structure, processes and tools that will significantly increase the reliability, maintainability, availability, and dependability of the operating systems.",
"\n\nThe four-year contract also provides a risk reduction and capability maturation program to develop and maintain the current and future architectures. ",
"LTRS consists of ground-based surveillance, navigation, flight operations and analysis, command and control, communications and weather assets located at the Eastern Range (Patrick Air Force Base, Fla.) and the Western Range (Vandenberg AFB, Calif.) for space missions. ",
"LTRS provides the Department of Defense, NASA and commercial customers a highly reliable, integrated system to support spacecraft launch, ballistic missile and aeronautical testing. (",
"1/4)\n\nMars' Ancient Lake Beds Spied by NASA Probe (Source: BBC)New images of Mars suggest the Red Planet had large lakes on its surface as recently as three billion years ago. ",
"The evidence comes from NASA's Mars Reconnaissance Orbiter (MRO) which spied a series of depressions linked by what look like drainage channels. ",
"Scientists say the features bear the hallmarks of being produced by liquid water. ",
"But they appear to have formed much later in Mars' history than many thought possible, the researchers add. (",
"1/4)\n\nThis Year a Turning Point in Spaceflight (Source: Florida Today)This year is going to be a turning point in spaceflight. ",
"The White House will soon decide the fate of the human exploration program. ",
"SpaceX will launch its first rocket from Cape Canaveral. ",
"The International Space Station's construction will be complete. ",
"The space shuttles will creep ever closer to retirement. ",
"Click here to view Florida Today's predictions. (",
"1/4)\n\nManned Mission to Construct Huge GEO and Deep Space Telescopes Proposed (Source: NasaSpaceFlight.com)Buoyed by the success of the Hubble Space Telescope, one of the key proposals on NASA’s internal interpretation of the Augustine Commission’s “Flexible Path” option includes a 45 day manned mission to construct a giant telescope in Geostationary orbit (GEO). ",
"A huge deep space telescope is also included in the roadmap, which would focus on a major advancement for the search of Earth-like planets.",
"\n\nThe recently produced 64 page presentation is being called over-ambitious by NASA sources, though it provides a fascinating insight into what NASA could do with a supporting budget. ",
"The internal effort to “peel the onion” of the Augustine Panel's “flexible path” approach includes several NASA centers and associated bodies who are providing insights to various options that could be open to the Agency.",
"\n\nThose centers, Ames Research Center (ARC), Glenn Space Flight Center (GSFC), Jet Propulsion Laboratory (JPL), Johnson Space Center (JSC) and the Hubble-related Space Telescope Science Institute (STScI) all contributed to the findings. ",
"The presentation covers several areas, from the need for a heavy lift launcher, to manned missions to Mars and its moons – and also Near Earth Objects (NEOs), as the main elements. ",
"However, a large section is also dedicated to the construction of large telescopes. (",
"1/4)\n\nNASA's Dangerous New Year (Source: Space Review)The next several months will be critical to NASA and its future plans as the White House prepares a new space exploration policy. ",
"Taylor Dinerman warns of the potential dangers facing NASA if the White House changes course or doesn't raise then agency's budget. ",
"Visit http://www.thespacereview.com/article/1538/1 to view the article. (",
"1/4)\n\nComplexity and Danger (Source: Space Review)Some argue that human spaceflight is such a complex, dangerous venture that it should be left to government agencies. ",
"Bob Clarebrough counters that private ventures are just as capable as governments, if not more so, to explore the solar system. ",
"Visit http://www.thespacereview.com/article/1537/1 to view the article. (",
"1/4)\n\nA Chinese Space Odyssey (Source: Malaysian Insider)China’s ambitions to conquer space will take a big leap forward this year, as the country embarks on the most extensive space development program in the world in decades. ",
"The aim is to fire China towards its two long-held space dreams — to land a man on the moon and to set up a space station by 2020. ",
"A second lunar probe, the Chang’e-2, is lined up for October, continuing the 16-month orbit of the Chang’e-1 which ended last March. ",
"The first piece of a Chinese space station is also likely to take shape towards the end of the year, with the launch of the unmanned space docking module Tiangong-1, or Heavenly Palace-1. ",
"Major construction on a new major spaceport will be carried out this year on southern Hainan island. ",
"It will be the growing power’s fourth spaceport. (",
"1/4)"
] | {
"pile_set_name": "Pile-CC"
} | [
0,
0.00010813148788927336,
0,
0.00004504301608035674,
0,
0.00004094920251428104,
0.00004959333465582226,
0,
0.00004627701420704336,
0,
0,
0.000043282548476454294,
0.00004082924190305096,
0,
0.00006298815822625346,
0,
0.000010964431384588396,
0,
0,
0,
0,
0,
0,
0.000015518191199633772,
0.000066749733001068,
0,
0.00027681660899653976,
0.000042718612499466016,
0.00011317338162064282,
0.00017313019390581717,
0,
0,
0,
0,
0,
0.000011612715923936711,
0,
0,
0.000030517578125,
0.00007002555932915514,
0.00009070294784580499,
0.00011562030292519367,
0.00004396957305544563,
0.000027639197910476636,
0,
0.000027434842249657064,
0.00005972110245155126,
0.00003228305785123967,
0.00004756242568370987,
0,
0,
0,
0.00017313019390581717,
0,
0.0002366863905325444,
0,
0,
0.00003732568903221953,
0,
0.00005907372400756144,
0.00006142380377142156,
0.00012462390286456943,
0.000030524098775983637,
0,
0.00011814744801512288,
0.0001721763085399449,
0.00018765246762994932,
0,
0.00006103515625,
0.00018765246762994932,
0,
0,
0,
0,
0,
0,
0
] | 0.000041 | 5 |
[
"The corn and soybeans growing in Glenn Brunkow’s fields in the rolling Flint Hills north of Wamego, Kansas, got some much needed rain recently and look healthy.",
"\n\nBrunkow has reason to expect a good harvest, but the way things are looking globally, he’ll lose money on the crop. ",
"Trade disputes with China, Mexico and Canada threaten to slash U.S. food exports by billions. ",
"About half the soybean crop goes overseas, most of that to China — and since mid-April, soybean prices have plunged about 20 percent and corn about 15 percent.",
"\n\n“Prices are really bad,” Brunkow said, squinting in the sun. “",
"We’re looking at some of the lowest prices we’ve had in quite a while, a decade or more.”",
"\n\nPresident Donald Trump enjoyed broad support from farmers, and he has promised to protect them from trade war fallout, though how the administration would do that isn’t exactly clear. ",
"There’s a possibility, however, that a Depression-era federal program could become a focal point.",
"\n\n‘This could be catastrophic’\n\nFree trade is a fragile, but lucrative system for farmers. ",
"Case in point: Brunkow said that if China puts new tariffs on soybeans and other row crops, some farms will fail.",
"\n\n“This could be catastrophic,” Brunkow predicted. “",
"We see a lot of producers not make it through past this fall.”",
"\n\nThe federal government shores up farmers in lots of ways, as taxpayers subsidize crop insurance and other programs designed to compensate for natural disasters or falling prices. ",
"But the farm safety net won’t protect farmers from a trade war, Iowa State agricultural economist Chad Hart said.",
"\n\nHe thinks the Trump administration will dust off an old model for boosting prices, one that generated headlines —and punchlines —in the 1970s.",
"\n\n“The government cheese program,” Hart said, explaining further, “Dairy prices were very low. ",
"The government was trying to support dairy farmers. ",
"The way they did that by purchasing milk. ",
"They did it through this Commodity Credit Corporation. “",
"\n\nThe Commodity Credit Corporation Charter Act came out of the Depression, and since 1939 has given the U.S. Department of Agriculture authority to borrow money from the U.S. Treasury to buy commodities or otherwise help farmers cope with low prices.",
"\n\nIt’s never gone away, but Hart thinks the Trump administration is about to ramp it up.",
"\n\n“This is a relatively old program that If sits in the shadows until it’s needed, for something like this,” he said, adding that the CCC can issue bonds to borrow up to about $30 billion.",
"\n\nIt’s not clear whether the USDA would use it to buy up farm commodities or find a way to pay farmers directly, according to Joe Glauber, a senior research fellow with the International Food Policy Research Institute. ",
"Either way, he said, taxpayers would be on the hook.",
"\n\n“As a consumer, I’m going to have to pay higher prices as a result of this, and higher taxes, because of a bail out through the CCC Charter Act,” said Glauber, who was also chief economist at the USDA under President Barack Obama.",
"\n\nTrade disputes are already costing America’s hog farmers hundreds of millions of dollars in sales, but commercial crop farmers aren’t really feeling it yet because they’re not selling their grain yet.",
"\n\nIf trade barriers persist through harvest and then into next year, Glauber said the pain will be very real.",
"\n\n“I think U.S. agriculture has a much, much bigger problem, if you lose a big share of these markets, just because of a trade war that spirals out of control for a while,” he said.",
"\n\nBrunkow said he worries about the very same thing: long-term damage to vital trading relationships that’ll depress commodity prices, hurt farmers and make taxpayers pay up.",
"\n\nFrank Morris is an NPR correspondent and senior editor at KCUR 89.3. ",
"You can reach him on Twitter @FrankNewsman"
] | {
"pile_set_name": "OpenWebText2"
} | [
0.0000390625,
0,
0,
0,
0.000244140625,
0,
0.000028905075731298418,
0,
0,
0.00007831466833737959,
0.00036982248520710064,
0,
0,
0.00007831466833737959,
0.000048225308641975306,
0,
0,
0,
0.00031887755102040814,
0.000048,
0.00025826446280991736,
0.000028293345405160706,
0.00006255082254331645,
0,
0.000055737217598097505,
0,
0.00008416799932665601,
0,
0,
0.000595120015869867,
0.0005668934240362812
] | 0.000094 | 5 |
[
"Q:\n\nUIPageViewController with Auto-Layout doesn't update childs frame until viewDidAppear\n\nI have a RootViewController which consists of two UIViewControllers all created in code (without Storyboard/Nibs).",
"\nThe first UIViewController has the following anchors:\nweekView.translatesAutoresizingMaskIntoConstraints = false\n\nweekView.topAnchor.constraint(equalTo: view.topAnchor).isActive = true\nweekView.heightAnchor.constraint(equalToConstant: 100).isActive = true\nweekView.leadingAnchor.constraint(equalTo: view.leadingAnchor).isActive = true\nweekView.trailingAnchor.constraint(equalTo: view.trailingAnchor).isActive = true\n\nThe other UIViewController has the following anchors:\ndaysViewController.view.translatesAutoresizingMaskIntoConstraints = false\n\ndaysViewController.view.topAnchor.constraint(equalTo: weekView.bottomAnchor).isActive = true\ndaysViewController.view.bottomAnchor.constraint(equalTo: view.bottomAnchor).isActive = true\ndaysViewController.view.leadingAnchor.constraint(equalTo: view.leadingAnchor).isActive = true\ndaysViewController.view.trailingAnchor.constraint(equalTo: view.trailingAnchor).isActive = true\n\nWhich makes it pin to the bottom of the first UIViewController and takes up the rest of the screen height (-100 from the top UIViewController).",
"\nThe second UIViewController is a custom UIPageViewController which consists of multiple child views of UIViewControllers.",
"\nThe problem\nFor some reason when scrolling through the pages in the UIPageViewController each child ViewController has the incorrect frame height (e.g not the same height as the constraint are telling it to have).",
"\nInstead the frame height is the same as the screen height.",
"\nThe printed frame height in the three different states are as follows:\nviewDidLoad PageViewController frame: (0.0, 0.0, 375.0, 667.0)\nviewDidLoad ChildViewController frame: (0.0, 0.0, 375.0, 667.0)\nviewWillAppear ChildViewController frame: (0.0, 0.0, 375.0, 667.0)\nviewDidAppear ChildViewController frame: (0.0, 0.0, 375.0, 667.0)\n\nI need the correct frame size of 567 in the viewDidLoad to layout the subviews correctly and not so late as in the viewDidAppear.",
"\nHow can I solve this?",
"\nBecause right now I need to take into account that the views frame is the full height of screen instead of the 567 it should be when creating all the subviews.",
"\n\nA:\n\nFound my answer in a similar question\nHad to do with the Auto-Layout engine and when it starts.",
"\nThe frame is correct in between viewWillAppear and viewDidAppear which made me put the frame specific code in viewDidLayoutSubviews.",
"\nHowever, if the frame specific tasks called in viewDidLayoutSubviews is heavy (e.g UI-related) there will be a lag/flicker in the scrolling.",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0.000023795359904818562,
0,
0.00006718624025799517,
0.00004367193641366058,
0,
0,
0,
0,
0,
0,
0.0000502992807202857,
0
] | 0.000015 | 5 |
[
"//\n// DemoVC2Footer.h\n// HDCollectionView\n//\n// Created by HaoDong chen on 2018/12/18.",
"\n// Copyright © 2018 CHD. ",
"All rights reserved.",
"\n//\n\n#import \"HDSectionView.h\"\n\nNS_ASSUME_NONNULL_BEGIN\n\n@interface DemoVC5Footer : HDSectionView\n\n@end\n\nNS_ASSUME_NONNULL_END\n"
] | {
"pile_set_name": "Github"
} | [
0,
0.0013717421124828531,
0,
0.000124000248000496
] | 0.000374 | 5 |
[
"Nucleic acid vaccination of Brucella abortus ribosomal L7/L12 gene elicits immune response.",
"\nNucleic acid vaccines provide an exciting approach for antigen presentation to the immune system. ",
"As a test of this new methodology, the immune response to the in vivo-expressed Brucella abortus ribosomal L7/12 gene in the muscle cells of mice was examined. ",
"To accomplish this goal the eukaryotic expression systems pcDNA3 and p6 were used. ",
"Single intramuscular injection of the L7/L12 gene driven by the human cytomegalovirus (CMV) promoter (pcDNA3) or bovine MHC 1 promoter (p6) resulted in intracellular expression of the B. abortus L7/L12 immunodominant protein encoded by this gene. ",
"This application facilitated directed antigen presentation to the immune system and established specific antibody and T-cell responses compared with vector only (pcDNA3) negative controls and B. abortus S19 injected positive controls. ",
"Although pcDNA3-encoded L7/L12 gene-inoculated mice possessed significant protection, p6-L7/L12 did not engender significant protection against B. abortus S2308 infection compared to positive control mice. ",
"These data suggest a promising antigen-specific response, and L7/L12 nucleic acid vaccination may be an initial step in the development of genetically engineered candidate vaccines against brucellosis. ",
"This study for the first time focuses on DNA immunization of a gene from B. abortus."
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0.00012075836251660429,
0,
0.000078125,
0,
0.000016391024275106952,
0.000018107741059302852,
0.00004712979545668771,
0,
0
] | 0.000031 | 5 |
[
"Characteristics and outcome of deliveries by forceps after failed ventouse.",
"\nWith the increasing use of the ventouse, it is becoming common for deliveries to be completed by the application of forceps. ",
"We present 48 cases delivered by forceps after a failed ventouse and compare these with 63 cases delivered by forceps only. ",
"There was significantly higher incidence of caesarean sections and cephalhaematoma in the group where forceps delivery was attempted after a failed ventouse compared to those delivered with forceps only."
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0,
0,
0,
0
] | 0 | 5 |
[
"\n\nAd Agency or Porn: Can you tell the difference? - ",
"erinbury\nhttp://agencyorporn.com/#\n\n======\nbradleyland\nIf you have speakers attached to your computer, be sure to turn them down (or\nput on headphones) before choosing an item. ",
"You'll get a breathy, lusty\nsounding \"Oh, yeah\" when you click an item.",
"\n\n~~~\nsoccerdave\nWish I would have read the comments first. ",
"Got quite the look from my wife\nwhen I answered the first question!",
"\n\n------\ncnvogel\nI played 15 names, and 13 of them where non-porn. ",
"Was this just by chance or\nis the repository that biased towards agencies?",
"\n\nMaybe the creator did not find enough porn on the internet? :-)",
"\n\n------\ndrallison\nThe obvious conclusion after taking the test is that there is no significant\ndifference between \"ad agency\" media and \"porn\" media.",
"\n\n------\nbradleyland\nThe first time I visited the site, I really had no idea what I was doing. ",
"I'm\ngoing to write up my experience here for the benefit of the author.",
"\n\nI'll admit that I did not read the blurb on the landing page carefully. ",
"While\nthat's a little embarrassing to admit, it's also typical user behavior. ",
"Users\ndon't read; they scan. ",
"I did what a typical user would do: I scanned the copy\nand looked for the clicky-bit, and then I clicked it.",
"\n\nFrom there, I'm presented with a page dominated by two images. ",
"I tried to\nfigure out what the hell I'm supposed to do.",
"\n\nHrm... I see two obvious clicky-bits on this page: Agency and Porn buttons.",
"\nThe image over the Agency button looks pretty agency, and the image over the\nPorn button looks pretty porny.",
"\n\nWhat the hell am I supposed to discern here? ",
"Maybe I'm supposed to figure out\nwhich one is an actual image used by an agency or in a porn film.",
"\n\nI click my first answer.",
"\n\nAaaaah geeze.",
"\n\nFortunately, I'm on my free time and my wife has a sense of humor. ",
"She asks me\nto please close the door while baitin'.",
"\n\n\"Fuck this, this isn't any fun,\" I think. ",
"And I close the window.",
"\n\nI drop a comment warning other HN users that they're going to be porn-audio-\nbombed by the site and move on.",
"\n\nA couple of days later, I notice that I've collected a few karma points and\ncheck my profile page to see what sage advice was deemed useful by the HN\ncrowd. ",
"Heh, it was just my warning label and a swipe I took at Rob Reinhart\nthat boosted my score.",
"\n\nI revisit the agencyorporn.com link, this time prepared for what awaits me.",
"\n\nHeadphones? ",
"Check.",
"\n\nSmart kid who always reads directions attitude? ",
"Check.",
"\n\nClick!",
"\n\nReading...\n\n\"Guess which of these tantalizing _names_ belong...\"\n\nNames!? ",
"Wait, there's text on the pages?",
"\n\nI click the Start button for the second time in my life and I see what is\nclearly a camera and a dildo. ",
"Mkay, where's the \"name\"? ",
"I start at what I\nthink is the top (the border of the two contrasting colors). ",
"Nope.",
"\n\nI really take a step back and start at the _actual_ top. ",
"Holy shit, there it\nis. ",
"It's been staring me in the face the whole time! ",
"The text at the very top\nof the page is what I'm supposed to evaluate.",
"\n\nI try a few and quickly get bored with the concept (sorry). ",
"The audio also\nseems like it's leveled to be pretty loud. ",
"I'm kind of put off by the whole\nexperience and I exit.",
"\n\nThat's my experience as a user. ",
"As a product guy, my feedback would be this:\n\nUsers don't read.",
"\n\nIf I'm supposed to focus on something, please make it the center of focus.",
"\n\nUsers don't read!",
"\n\nUse visual hierarchy to communicate importance.",
"\n\nOn the landing page, what is the most important element? ",
"Users are drawn to\nimagery before text, so the most important element on the screen is the image\nof the woman to the right. ",
"Secondarily, my eye was drawn to the Agency or Porn\nlogo, then the start button. ",
"The instructions are the fourth most important\nthing on the page, visually. ",
"It's not clear that they are instructions. ",
"IMO,\nthey should be labeled as such. ",
"The fact that they started with what appears\nto be a rhetorical question caused me to evaluate the text as a \"blurb\"\n(marketing copy), so I ignored it. ",
"My mind jumped directly to, \"I'm already\nsold, give me the game!\"",
"\n\nIn the game interface, the visual hierarchy is out of whack as well. ",
"The item\nI'm supposed to evaluate is _outside_ the visual grouping of all the game\ncontrol elements. ",
"It looks like a page title, not a game element. ",
"Visually,\nthe most important parts of the page are the two giant images. ",
"These images\ncommunicate (reinforce, really) the function of the buttons for \"Agency\" or\n\"Porn\". ",
"They are supporting elements, not primary elements. ",
"The \"name\" I'm\nsupposed to evaluate should be the most important item on the screen.",
"\n\n"
] | {
"pile_set_name": "HackerNews"
} | [
0,
0.00003191930798940279,
0,
0,
0,
0.0002227667631989307,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.000168662506324844,
0.00008416799932665601,
0,
0,
0,
0.0044444444444444444,
0,
0,
0,
0,
0,
0.00003955539733396622,
0.00012075836251660429,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00030483158055174517,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0.000077 | 5 |
[
"Conventional snowmobile drive trains incorporate a continuously variable transmission (CVT) having a driving pulley that is operatively coupled to the engine crankshaft and a driven pulley coupled to a driven shaft. ",
"The driving pulley acts as a clutch and includes a centrifugally actuated adjusting mechanism through which the drive ratio of the CVT is varied progressively as a function of the engine speed and the output torque at the driven pulley. ",
"Typically, the driven shaft is a transverse jackshaft which drives the input member of a chain and sprocket reduction drive. ",
"The output of reduction drive is coupled to one end of the axle on which are located the drive track drive sprocket wheels.",
"\nAlthough a centrifugal CVT provides many advantages, the fact that the drive ratio of the CVT is directly related to the engine speed causes some disadvantages. ",
"One such disadvantage is that the calibration of the driving pulley is always linked with the maximum power output of the engine. ",
"Although this results in great acceleration characteristics for the snowmobile, when the snowmobile operates at cruising speeds it results in the engine operating at a greater speed than necessary, high fuel consumption, high noise levels, and a lot of vibrations being transmitted to the riders of the snowmobile.",
"\nRepresentative of the art is US patent application no. ",
"2011/0277577 which discloses a method of managing a transmission ratio with an assisted CVT with a governed engine to emulate a hydrostatic transmission and prevent a drivebelt abuse is provided, the method comprising: providing a reference power source rotational speed, using the assisted CVT to transmit rotatable motion between a power source and a drive mechanism, managing a torque of the power source to maintain a substantially even rotational speed upon a power source load variation and modulating a transmission ratio of the assisted CVT to change the rotational speed of the drive mechanism. ",
"A system and a vehicle having such a drivebelt abuse preventing mechanism is also provided.",
"\nWhat is needed is a CVT having a motorized controller actuating a movable sheave for adjusting a transmission ratio. ",
"The present invention meets this need."
] | {
"pile_set_name": "USPTO Backgrounds"
} | [
0.00002143347050754458,
0.000017803414694938486,
0,
0,
0.00007620789513793629,
0,
0,
0,
0.000008223323538441297,
0,
0.00007181844297615628,
0
] | 0.000016 | 5 |
[
"\"Explain why you'd be good for this position in 500 words or less\" find Word count: 499\n\n104 shares"
] | {
"pile_set_name": "OpenWebText2"
} | [
0
] | 0 | 5 |
[
"Q:\n\nDetect compatible versions of Internet Explorer for dropzone.js\n\nDropzone.js says that it supports Internet Explorer versions 10+. ",
"I'm not really worried about browsers other than Internet Explorer being too old.",
"\nHow should I detect whether the browser is compatible with dropzone? ",
"Should I detect it by its features (which is what some people say about browser compatibility), or by checking the version of the browser, and if so, how?",
"\n(I'm using Rails, if that makes a difference)\n\nA:\n\nYou don't have to worry too much about this - Dropzonejs adds automatically file input element if it detects an incompatible browser version. ",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0.00005486968449931413,
0,
0,
0,
0,
0
] | 0.000009 | 5 |
[
"Domaine La Tour Vieille\n\nThe\nvibrant little seaport town of Collioure is nestled on the Mediterranean coast,\njust north of the Spanish border, in the area known as French Catalonia. ",
"In\n1981, Vincent Cantié and Christine Campadieu took over two small, family-owned\ndomaines where they had grown up, in Collioure and Banyuls, respectively.",
"\nTogether, they farm vineyards planted on steep, schist terraces overlooking the\nsea, where they are constantly exposed to the fierce and wily wind known as “La\nTramontagne.” ",
"This constant wind not only ensures naturally low yields, but\nalso keeps the grapes free of mildew with little need for pesticides or copper\nsulfate. ",
"Their vineyards are so steep that cultivation must be by hand, and\nextensive irrigation canals and walls (all made from the schist rock) are their\nonly prevention against soil erosion, although there is almost no soil left to\nrecede! ",
"These canals snake down the hillsides, separating the parcels. ",
"At\nharvest, the grapes are carried up and down the mountain in baskets. ",
"This\nmethod of farming, while extremely challenging, preserves the traditions of\ntheir ancestors. ",
"Such ideals have inspired two documentaries, Wine From the Heart by Yasha Aginsky\n(2002), and a short film sponsored by Project NOÉ for the defense of the European\nviticultural heritage.",
"\n\nThough\nthe majority of the Tour Vieille holdings are planted with Grenache Noir, they\nalso work with Grenache Gris, Grenache Blanc, Macabeo, Syrah, and Carignan.",
"\nThey have several single vineyard bottlings of Collioure, and several cuvées of\nBanyuls, from Christine’s family’s holdings. ",
"Banyuls, neighbor of Collioure,\nsits only two kilometers from the Spanish border; it is famous for its\nfortified wines. ",
"Tour Vieille also produces a wide range of practically extinct\nlate harvest and extended elevage white and red wines, the ultimate meditation\nwines at the end of a meal. ",
"The heart, soul, and hard work that go into\ncrafting these wines make their labor of love all the more delicious.",
"\n\n•\nAlcohol is\nadded to stop fermentation so that the grapes may retain their sweetness\n\nVintage\nBanyuls:\n\n• Non-oxidized wine that is bottled within the first year of aging\n• Harvested between September 10 and 20\n• Neutral spirit added during fermentation and calculated to bring juice to 16% alcohol\n• Residual sugar of 90 to 96 g/L\n\n•\nBanyuls\n“Rimage Mise Tardive” similar to base wine of “Rimage”; aged in foudre for several additional years\nbefore release\n\nBanyuls\n“Reserva”:\n\n• Harvested between September 10 and 20\n• Neutral spirit added during fermentation and calculated to bring juice to 16% alcohol\n• Must is then pressed and pressed juice is divided and aged in three separate vessels: foudre, barrel, and large glass jars stored outdoors in the sun\n• Glass jars are aged for one year outdoors and then blended together into one tank\n• The final blend for each “Reserva” bottling is composed of the blended tank of wine aged in glass jars, with various other vintages from barrels and foudre\n• The resulting blend has an average of wine age of 5 years—the youngest wine being 1 year old and the oldest being 13 years old\n• Residual sugar of 90 to 96 g/L"
] | {
"pile_set_name": "Pile-CC"
} | [
0.00003018959062915107,
0.00012486992715920916,
0,
0,
0,
0,
0,
0,
0.000057810151462596836,
0.00018818924310286424,
0.00012597631645250691,
0.0001388888888888889,
0.00003460207612456747,
0,
0.0000036839875481220875
] | 0.000047 | 5 |
[
"The present invention concerns a display comprising light-emitting diodes, and a method and an installation for its manufacture. ",
"The display is suitable for use in a variety of different applications, such as for illumination of signs, and for lighting purposes on cars, to mention only a few.",
"\nLight-emitting diodes have several advantages over conventional incandescent lamps. ",
"Light-emitting diodes have a long serviceable life. ",
"When lit, they generate only very little heat and they draw a minimum of energy from the source of power. ",
"In addition, they are small and easy to mount. ",
"Their operational reliability makes them suitable for use for instance in applications where intermittent or pulsating light is desired. ",
"Their flexibility of mounting and of use in combination with their minimum energy consumption make light-emitting diodes very useful in a large number of cases and applications, where conventional electric bulbs are less suitable.",
"\nThe purpose of th subject invention is to provide a display by means of which it becomes possible to use light-emitting diodes with maximum efficiency in a number of applications. ",
"This is achieved in accordance with the teachings of the subject invention in that the diodes which are of the kind designed to be mounted in a dish-shaped reflector formed in a plate are mounted in openings formed in the plate with the diode walls snugly fitted into the edges of the opening to form a mechanical bond between the diodes and the plate, and that the diodes are formed with a wider rear portion by means of which the diodes, when mounted in the plate, are securely wedged thereto.",
"\nThe method for manufacturing the display comprising light-emitting diodes in accordance with the invention according to which the diodes form a selected pattern and their power is enhanced by reflectors surrounding the individual diodes, is characterized by the steps of mapping the selected pattern on a substratum, determining the coordinate points relating to the positions of the light-emitting diodes to form the selected pattern, recording the coordinates thus determined andusing the recorded data thus received for controlling the movements of means arranged to form impressions in a plate and to punch openings in said impressions for reception therein of the diodes.",
"\nThe installation for performing the method of manufacturing the display comprising light-emitting diodes in accordance with the invention is characterized by means for determining the coordinates relating to the positions of the light-emitting diodes, means connected to said determining means for recording said coordinates and means for controlling the operations of stamping and punching sign blanks while said means are controlled by the data of the recorded coordinate positions.",
"\nFurther characteristics of the invention will appear from the dependent claims.",
"\nThe light-emitting diodes in accordance with the invention have excellent lighting properties. ",
"In addition, the emitted light beam is aligned and concentrated."
] | {
"pile_set_name": "USPTO Backgrounds"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0
] | 0 | 5 |
[
"A Universal Mobile Telecommunication System (UMTS) is a broadband, packet-based system for the transmission of text, digitized voice, video and multi-media. ",
"It is a highly subscribed to standard for third generation and is generally based on Wideband Coded Division Multiple Access (W-CDMA).",
"\nIn a UMTS network, a Radio Resource Control (RRC) part of the protocol stack is responsible for the assignment, configuration and release of radio resources between the UE and the UTRAN. ",
"This RRC protocol is described in detail in the 3GPP TS 25.331 specifications. ",
"Two basic modes that the UE can be in are defined as “idle mode” and “UTRA RRC connected mode” (or simply “connected mode”, as used herein). ",
"UTRA stands for UMTS Terrestrial Radio Access. ",
"In idle mode, the UE or other mobile device is required to request an RRC connection whenever it wants to send any user data or in response to a page whenever the UTRAN or the Serving General Packet Radio Service (GPRS) Support Node (SGSN) pages it to receive data from an external data network such as a push server. ",
"Idle and Connected mode behaviors are described in detail in the Third Generation Partnership Project (3GPP) specifications TS 25.304 and TS 25.331.",
"\nWhen in a UTRA RRC connected mode, the device can be in one of four states. ",
"These are:\nCELL DCH: A dedicated channel is allocated to the UE in uplink and downlink in this state to exchange data. ",
"The UE must perform actions as outlined in 3GPP 25.331.",
"\nCELL_FACH: no dedicated channel is allocated to the user equipment in this state. ",
"Instead, common channels are used to exchange a small amount of bursty data. ",
"The UE must perform actions as outlined in 3GPP 25.331 which includes the cell selection process as defined in 3GPP TS 25.304.CELL_PCH: the UE uses Discontinuous Reception (DRX) to monitor broadcast messages and pages via a Paging Indicator Channel (PICH). ",
"No uplink activity is possible. ",
"The UE must perform actions as outlined in 3GPP 25.331 which includes the cell selection process as defined in 3GPP TS 25.304. ",
"The UE must perform the CELL UPDATE procedure after cell reselection.",
"URA_PCH: the UE uses Discontinuous Reception (DRX) to monitor broadcast messages and pages via a Paging Indicator Channel (PICH). ",
"No uplink activity is possible. ",
"The UE must perform actions as outlined in 3GPP 25.331 including the cell selection process as defined in 3GPP TS 25.304. ",
"This state is similar to CELL_PCH, except that the URA UPDATE procedure is only triggered via UTRAN Registration Area (URA) reselection.",
"\nThe transition from an idle mode to the connected mode and vice-versa is controlled by the UTRAN. ",
"When an idle mode UE requests an RRC connection, the network decides whether to move the UE to the CELL_DCH or CELL_FACH state. ",
"When the UE is in an RRC connected mode, again it is the network that decides when to release the RRC connection. ",
"The network may also move the UE from one RRC state to another prior to releasing the connection or in some cases instead of releasing the connection. ",
"The state transitions are typically triggered by data activity or inactivity between the UE and network. ",
"Since the network may not know when the UE has completed the data exchange for a given application, it typically keeps the RRC connection for some time in anticipation of more data to/from the UE. ",
"This is typically done to reduce the latency of call setup and subsequent radio resource setup. ",
"The RRC connection release message can only be sent by the UTRAN. ",
"This message releases the signal link connection and all radio resources between the UE and the UTRAN. ",
"Generally, the term “radio bearer” refers to radio resources assigned between the UE and the UTRAN. ",
"And, the term “radio access bearer” generally refers to radio resources assigned between the UE and, e.g., an SGSN (Serving GPRS Service Node). ",
"The present disclosure shall, at times, refer to the term radio resource, and such term shall refer, as appropriate, to either or both the radio bearer and/or the radio access bearer.",
"\nThe problem with the above is that even if an application on the UE has completed its data transaction and is not expecting any further data exchange, it still waits for the network to move it to the correct state. ",
"The network may not be even aware of the fact that the application on the UE has completed its data exchange. ",
"For example, an application on the UE may use its own acknowledgement-based protocol to exchange data with its application server, which is accessed through the UMTS core network. ",
"Examples are applications that run over User Datagram Protocol/Internet Protocol (UDP/IP) implementing their own guaranteed delivery. ",
"In such a case, the UE knows whether the application server has sent or received all the data packets or not and is in a better position to determine if any further data exchange is to take place and hence decide when to terminate the RRC connection associated with Packet Service (PS) domain. ",
"Since the UTRAN controls when the RRC connected state is changed to a different state or into an idle mode and the UTRAN is not aware of the status of data delivery between the UE and external server, the UE may be forced to stay in a higher data rate state or mode than what is required, possibly resulting in decreased battery life for the mobile station and also possibly resulting in wasted network resources due to the fact that the radio resources are unnecessarily being kept occupied and are thus not available for another user.",
"\nOne solution to the above is to have the UE send a signaling release indication to the UTRAN when the UE realizes that it is finished with a data transaction. ",
"Pursuant to section 8.1.14.3 of the 3GPP TS 25.331 specification, the UTRAN may release the signaling connection upon receipt of the signaling release indication from the UE, causing the UE to transition to an idle mode or some other RRC state. ",
"A problem with the above solution is that the UTRAN might become inundated with signaling release indication messages from the UE and other UEs"
] | {
"pile_set_name": "USPTO Backgrounds"
} | [
0,
0.000055691690799732676,
0.00011317338162064282,
0,
0,
0.0004526935264825713,
0.000029666548000474663,
0,
0,
0.0000706164818868724,
0.0003305785123966942,
0,
0,
0.000030280549289164105,
0,
0.000062000124000248,
0.00021003990758244068,
0.0000591715976331361,
0,
0.00006718624025799517,
0.00010813148788927336,
0.0001020304050607081,
0.00006103515625,
0.00023084025854108956,
0,
0.00009070294784580499,
0.000051534437888118735,
0,
0.0004591368227731864,
0.00018851918182675084,
0.0002,
0.000048225308641975306,
0,
0.00002143347050754458,
0.00008264462809917355,
0.0000308641975308642,
0.000055691690799732676,
0.00002313850710352168,
0.000013922922699933169,
0.0000390625,
0.000049979175343606825,
0.000048902146804244705
] | 0.000081 | 5 |
[
"Ray Holmes\n\nRaymond Towers \"Ray\" Holmes (20 August 1914 – 27 June 2005) was a British Royal Air Force fighter pilot during the Second World War who is best known for his notable act of bravery, while taking part in the Battle of Britain. ",
"On 15 September 1940, Holmes saved Buckingham Palace from being hit by German bombing, when he used his Hawker Hurricane to destroy a Dornier Do 17 bomber over London by ramming but at the loss of his own aircraft (and almost his own life) in one of the defining moments of the Battle of Britain. ",
"He was feted by the press as a war hero for his saving of Buckingham Palace. ",
"The British pilot became a King's Messenger after the war, and died at the age of 90 in 2005.",
"\n\nEarly life\nRaymond Towers Holmes was born on August 20, 1914 in Wallasey, Cheshire to Mabel Annie Holmes (née Latham) and journalist Christopher Holmes. ",
"He attended Wallasey and Calday Grange Grammar School and worked as a crime journalist at the Birkenhead Advertiser before joining the Royal Air Force Volunteer Reserve in 1936 as their 55th volunteer.",
"\n\nSecond World War\n\nBattle of Britain\nIn June 1940 he joined No. ",
"504 Squadron RAF. ",
"He became known among his flight comrades as “Arty” which was taken from the initials of his name R.T.\n\nOn 15 September 1940, known as the Battle of Britain Day, Sergeant Holmes was flying a Hawker Hurricane fighter when he spotted a formation of three Dornier Do 17 bombers of Kampfgeschwader 76 heading for central London, to make a bombing attempt. ",
"As he made an attack on one of the bombers, the bomber fired a flamethrower at him, and Holmes' windscreen was covered in oil.",
"\n\nThe flamethrower, obviously intended for use on the ground, was not working properly at 16,000 feet, giving a jet of flame only some 100 yards long. ",
"The oil had not caught fire, and it was this that had found its way onto the Hurricane. ",
"Knowing that the airflow would clear the oil away, Ray Holmes waited for his view to be restored. ",
"As his windscreen cleared Ray realised that he was dangerously close to the Dornier, and ramming the stick forward, passed beneath the bomber.",
"\n\nI made my attack on this bomber and he spurted out a lot of oil, just a great stream over my aeroplane. ",
"blotting out my windscreen. ",
"I couldn't see a damn thing. ",
"Then, as the windscreen cleared, I suddenly found myself going straight into his tail. ",
"So I stuck my stick forward and went under him, practically grazing my head on his belly.",
"\n\nHe attacked the second Dornier, causing a crew member to bail out.",
"\n\nI got to the stern of the aeroplane and was shooting at him when suddenly something white came out of the aircraft. ",
"I thought that a part of his wing had come away but in actual fact it turned out to be a man with a parachute coming out. ",
"I was travelling at 250 miles per hour, it all happened so quickly, but before I knew what had happened this bloody parachute was draped over my starboard wing. ",
"There was this poor devil on his parachute hanging straight out behind me, and my aeroplane was being dragged. ",
"All I could do was to swing the aeroplane left and then right to try to get rid of this man. ",
"Fortunately, his parachute slid off my wing and down he went, and I thought, Thank heavens for that!",
"\n\nHolmes then spotted the third Dornier still heading onwards, making directly for Buckingham Palace. ",
"Avoiding the bomber's machine gunfire, Holmes quickly climbed ahead of it, then swung around to make a head-on attack on the Dornier. ",
"however upon firing discovered his machine guns failed. ",
"Holmes decided to ram the bomber hoping his plane could withstand the impact and cut through it. ",
"He flew his plane into the top-side of the German bomber, cutting off the rear tail section with his wing.",
"\n\nAs I fired, my ammunition gave out. ",
"I thought, Hell, he's got away now. ",
"And there he was coming along and his tail looked very fragile and very inviting. ",
"So I thought I'd just take off the tip of his tail. ",
"So I went straight at it along him and hit his port fin with my port wing. ",
"I thought, That will just take his fin off and he'll never get home without the tail fin. ",
"I didn't allow for the fact that the tail fin was actually part of the main fuselage. ",
"Although I didn't know it at the time, I found out later that I had knocked off the whole back half of the aircraft including the twin tails.",
"\n\nOn the ground, the event was captured on film, and witnessed by a large group of people in nearby Hyde Park. ",
"Jimmy Earley was playing football at the corner of Ebury Bridge Road, near Victoria station. ",
"The air-raid siren had gone off, but as usual he and his friends ignored it. ",
"Suddenly they heard gunfire. ",
"Earley recalled, \"We ran up to the Ebury Bridge and I can remember the Hurricane seemed to go underneath the Dornier, which split and all of sudden - wallop! - ",
"it came down in no time. ",
"Obviously the Hurricane pilot had no care for his own safety, he couldn't have done. ",
"He just hit it and the back of it came off.\" ",
"\n \nHolmes' own plane began to dive to the left, and was no longer responding to the controls. ",
"As the Hurricane went into a vertical dive, Holmes bailed out. ",
"As he climbed out, the air-stream caught him and smacked him down on to the roof of the Hurricane. ",
"Then, as he was thrown backwards, his shoulder hit his own tail fin. ",
"When he finally managed to pull his ripcord, the jolt shook off his flying boots and he found himself swinging violently about. ",
"Above him he could see the Dornier dive out of control and crash near Victoria tube station.",
"\n\nThe pilot of the Dornier, Feldwebel Robert Zehbe, bailed out, only to die later of wounds suffered during the attack. ",
"The Observer of the aircraft, Unteroffizier Hans Goschenhofer, and Gunner, Unteroffizier Gustav Hobel, did not survive the crash. ",
"However, Radio Operator, Gefreiter Ludwig Armbruster, bailed out over Syndenham, and Flight Engineer, Unteroffizier Leo Hammermeister, bailed out over Dulwich. ",
"Jim Earley watched Holmes' Hurricane crash twenty yards from where they had been playing football, near the grounds of Buckingham Palace. ",
"Earley recalled, \"As soon as it hit the road, it went straight down and burst the water main. ",
"Water was all over the place, my feet were soaked.\"",
"\n\nHolmes came down in a narrow back garden, and ended up dangling inside an empty dustbin.",
"\n\nI got hold of the guy ropes and stopped the spinning and looked down. ",
"I was right over the railway lines running into Victoria Station. ",
"I thought, \"Hell, I'm going to get electrocuted now after all this!\" ",
"Then I was swinging towards a row of houses. ",
"I hit the roof of one and could not get any grip on the slates in my stockinged feet. ",
"I slithered down the roof until I got to the gutter and thought, Now I'm going to break my back and kill myself falling off a three-storey house! ",
"But as I fell there was a sudden jerk and I stopped with just my toes on the ground. ",
"My canopy had snagged over an up pipe running past the gutter and that had stopped me. ",
"But both my feet were inside a dustbin, the lid was on the ground; the bin had obviously had just been emptied. ",
"My two toes touched the bottom of the bin but my heels were off the ground.",
"\n\nCalmly, Holmes undid the parachute harness and dusted himself down. ",
"In the next garden were two girls who had seen him come down. ",
"Holmes recalled, \"I went over the fence and we all kissed each other\". ",
"Jim Earley recalled the ecstatic crowd that greeted the downed pilot as he made his way out into the street. \"",
"The blokes were shaking his hand, but it was mostly women gathered around him. ",
"I wish it had been me, they all cuddled him and kissed him. ",
"Then he was carried over their heads towards Chelsea Barracks. ",
"Everybody was touching him as he was taken over the bridge. ",
"You know, I don't think he wanted to go to Chelsea Barracks, I think he wanted to stay where he was being made a fuss off!\"",
"\n\nHolmes was feted by the press as a war hero for his saving of Buckingham Palace. ",
"As the RAF did not practice ramming as an air combat tactic, this was considered an impromptu manoeuvre, and an act of selfless courage. ",
"This event became one of the defining moments of the Battle of Britain and elicited a congratulatory note to the RAF from Queen Wilhelmina of the Netherlands, who had witnessed the event. ",
"The bomber's engine was later exhibited at the Imperial War Museum in London.",
"\n\nLater activities\nWhen recovered, he became part of No 81 Squadron, and was sent to the Northern Front near Murmansk in Soviet Russia to help train the Russian air force in flying the Hawker Hurricane. ",
"Here he claimed a further kill; a Bf 109 F. He married Elizabeth Killip in April 1941 and was commissioned as a Pilot Officer on 10 June 1941, promoted to Flying Officer on 10 June 1942, and Flight Lieutenant on 10 June 1943.",
"\n\nReturning from Russia, Holmes served as an instructor with 2 FIS, Montrose, from 1942 until 1944. ",
"He then flew PR Spitfires with 541 Squadron from February 1945.",
"\n\nPost-war\n\nPersonal life\nAfter the war, he was a King's Messenger, personally delivering mail for British Prime Minister Winston Churchill. ",
"After leaving the RAF in late 1945, he returned to journalism, joining his father's news agency covering Liverpool Crown Court for local and national newspapers.",
"\n\nHe had two daughters with his wife, Elizabeth, who died in 1964. ",
"He later married Anne Holmes in 1966.",
"\n\nIn 1989, he published his autobiography entitled \"Sky Spy: From Six Miles High to Hitler's Bunker\".",
"\n\n65 years later, the wreckage of Holmes' Hurricane was discovered and successfully excavated from the streets of London. ",
"The discovery was featured on the National Geographic Channel documentary,\n\"The Search for the Lost Fighter Plane\".",
"\n\nHe was awarded the Freedom of the Borough of Wirral in January 2005.",
"\n\nHe died on 27 June 2005, aged 90 at Hoylake Cottage Hospital, following a two-year battle with cancer. ",
"He was buried in Rake Lane Cemetery, Wallasey.",
"\n\nIn popular culture\nThe Edward Fox character \"Pilot Officer Archie\", in the film Battle of Britain, was based on Holmes. ",
"Holmes also was mentioned in an episode of Battlefield Britain. ",
"His story was also subject of the National Geographic Channel documentary,\n\"The Search for the Lost Fighter Plane\".",
"\n\nSee also\n The Few\n\nReferences\n\nFurther reading\n [autobiography]\n\nExternal links\nRay Holmes' obituary in the Daily Telegraph.",
"\n\"The Airmen's Stories - Sgt. ",
"R T Holmes\", Battle of Britain Historical Society 2005.",
"\n\"Pilot who 'saved Palace' honoured\"\nPainting depicting the ramming of the Dornier.",
"\n\nCategory:1914 births\nCategory:2005 deaths\nCategory:Royal Air Force pilots of World War II\nCategory:Royal Air Force airmen\nCategory:Royal Air Force officers\nCategory:Deaths from cancer in England\nCategory:The Few\nCategory:Royal Air Force Volunteer Reserve personnel of World War II"
] | {
"pile_set_name": "Wikipedia (en)"
} | [
0.0000353082409434362,
0.00002267342334682402,
0,
0,
0.00012486992715920916,
0.00007425558773297691,
0,
0,
0.00003228305785123967,
0,
0,
0,
0.00010412328196584755,
0.00009918666931164451,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00009611687812379854,
0.00011138338159946535,
0,
0,
0,
0,
0.0007716049382716049,
0,
0,
0,
0,
0,
0,
0,
0.00011562030292519367,
0,
0,
0.000078125,
0,
0,
0,
0.00011317338162064282,
0,
0,
0,
0,
0.00011814744801512288,
0.0001388888888888889,
0.0001775147928994083,
0.0001953125,
0.00005250997689561017,
0.00011317338162064282,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00008264462809917355,
0,
0,
0.00025195263290501383,
0,
0.00006609822195782934,
0,
0.000053279343598486864,
0.000028293345405160706,
0,
0.00004853308743235701,
0.000019753086419753087,
0.0002,
0.0005039052658100277,
0.0001005985614405714,
0.00007715751707110065,
0.0002227667631989307,
0.0007304601899196494,
0.0000980296049406921,
0.00006718624025799517,
0.00007561436672967865,
0,
0.00009070294784580499,
0,
0.00006718624025799517,
0.000244140625,
0.00007561436672967865,
0.000062000124000248,
0,
0.0003305785123966942,
0.0002903178980984178,
0.0000502992807202857
] | 0.000061 | 5 |
[
"The solution structure of ribosomal protein L18 from Bacillus stearothermophilus.",
"\nA medium resolution solution structure has been obtained for L18 from Bacillus stearothermophilus (BstL18), a ribosomal protein that stabilizes the tertiary structure of 5S rRNA and mediates its interaction with the rest of the large subunit. ",
"The N-terminal 22 amino acid residues of BstL18 are unstructured in solution. ",
"Its remaining 98 residues form a globular domain that has the same topology as the globular domains of other L18s, but the orientation of helices is different. ",
"This conformational peculiarity should not prevent BstL18 from functioning in the ribosome the same way as other L18s."
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0,
0,
0,
0,
0
] | 0 | 5 |
[
"Q:\n\nInsert a row without altering table\n\nTL;DR: Is there a way of inserting a row to an intermediate \"view\" or \"table\" resulting from a subquery?",
"\nBackground:\nI am not allowed to alter table in database (SQL Server 2014).",
"\nThe table only records the start time of the task but for another query, I need to find out both the start time and end time of all tasks. ",
"I can take the liberty of tasks having no breaks in between them.",
"\nProblem\nI am able to get the start time and end time for all tasks EXCEPT for the last task by using a JOIN on a.row = b.row - 1.",
"\nI need to retrieve all tasks' start and end times, possibly by inserting a row in an intermediate query result \"table\" or \"view\" where the timestamp would be NOW().",
"\nTables\nINPUT TABLE\nTaskID StartTime\n-----------------------------\n1 2018-08-10 03:00:00\n2 2018-08-10 06:12:00\n3 2018-08-11 07:13:00\n\nEXPECTED OUTPUT TABLE\nTaskID StartTime EndTime\n----------------------------------------------------------\n1 2018-08-10 03:00:00 2018-08-10 06:12:00\n2 2018-08-10 06:12:00 2018-08-11 07:13:00\n3 2018-08-11 07:13:00 2018-08-16 15:26:00 (now)\n\nOUTPUT TABLE\nTaskID StartTime EndTime\n----------------------------------------------------\n1 2018-08-10 03:00:00 2018-08-10 06:12:00\n2 2018-08-10 06:12:00 2018-08-11 07:13:00\n\nCURRENT NON-WORKING CODE\nWITH EnterTaskTimes AS ( \n SELECT ROW_NUMBER() OVER (ORDER BY StartTime ASC) TaskID\n , [Timestamp] AS StartTime \n FROM TaskLog\n), \nTaskTimes As (\n SELECT\n a.TaskID Task,\n a.StartTime StartTime,\n b.StartTime EndTime\n FROM TaskLog a JOIN TaskLog b\n ON a.TaskID = b.TaskID - 1\n)\n\nThank you,\n\nA:\n\nUse the Lead() function:\n-- setup\nCreate Table Time_Lapse\n(\n TaskID Int\n , StartTime DateTime\n)\n\nInsert Into dbo.",
"Time_Lapse\n(\n TaskID\n , StartTime\n)\nSelect 1, '2018-08-10 03:00:00'\nUnion All Select 2, '2018-08-10 06:12:00'\nUnion All Select 3, '2018-08-11 07:13:00'\n\n-- query\nSelect \n tl.",
"TaskID\n , tl.",
"StartTime\n , Lead(tl.",
"StartTime, 1, GetDate()) Over (Order By tl.",
"StartTime) As EndTime\nFrom dbo.",
"Time_Lapse As tl\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0,
0,
0,
0.000036730945821854914,
0.000006287410090035713,
0.00002986055122577563,
0,
0,
0.0005408328826392645,
0,
0
] | 0.000047 | 5 |
[
"1. ",
"Field of the Invention\nThe present invention generally relates to the architecture and fabrication of a piezoelectric device designed to provide localized and controlled stress to conductive nanostructures, and to provide means to measure the change in electronic transport properties derived from the applied stress. ",
"Applications of this architecture include a nonvolatile memory device, where the remnant nature of the ferroelectric produces a nonvolatile conductivity change.",
"\n2. ",
"Description of the Related Art\nNovel self-assembled conductive organic structures and carbon nanotubes are being extensively studied due to their relevance to the areas of nanoscience and nanotechnology. ",
"The electronic transport of nanoscale structures is believed to be very sensitive to local strain and stress. ",
"The possibility of locally controlling these fields will open new possibilities in terms of designing new electronic devices but techniques and devices to explore or take advantage of this suspected characteristic are currently poorly evolved.",
"\nIn the case of nanotubes, their distinct electronic and mechanical properties are known to be sensitive to strain and stress. ",
"However, the current ways of manipulating the nanotubes, for instance using the tip of an atomic force microscope (AFM), are not particularly suited to change the applied stress smoothly and in a controlled fashion.",
"\nCurrently, no good technique is known to exist to apply stress smoothly to a nanotube structure."
] | {
"pile_set_name": "USPTO Backgrounds"
} | [
0,
0,
0,
0,
0,
0,
0,
0,
0.000021633315305570577,
0
] | 0.000002 | 5 |
[
"Q:\n\nUINavigationBar has wrong height on rotation in Action Extension\n\nI wrote a little app that includes an action extension. ",
"\nNow I am struggling with a rotation issue. ",
"\nIn the beginning, the navigationBar looks like it should. ",
"\nAfter I rotate the device, the navigation bar keeps its height, while the status bar disappears. ",
"\n\nWhen I rotate back, the navigation bar is now 44 points hight, like it should be in landscape.",
"\n\nI uploaded a small project to demonstrate the problem to you. ",
"I recognized that the Dropbox action extension has the same bug. ",
"\nThe view controller is embedded in a UINavigationController\nI assume somewhere down the path forgot to call super. ",
"\nIs there any workaround to fix this?",
"\n\nA:\n\nI was experiencing a similar issue. ",
"In my case I had a UINavigationController. ",
"I was presenting a view controller from a child view controller of UINavigationController. ",
"After presentation, when I rotated the device, the height of navigation bar was screwed up.",
"\nWhat I did\nInstead of presenting a view controller from a child view controller of UINavigationController, I presented it from the UINavigationController itself. ",
"It fixed the problem.",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0.00006298815822625346,
0,
0,
0,
0,
0,
0.0002366863905325444,
0,
0,
0,
0,
0.00012075836251660429,
0,
0.00007527569724114569,
0,
0
] | 0.000031 | 5 |
[
"Q:\n\nReduce anchor hit area in html\n\nOn my current website, I have a banner-image, where I have reduced the bottom-margin, so that the content below is moved a bit further up on the page. ",
"The banner also has an anchor-tag on it, to link to the \"home\"-page.",
"\nHowever, the hit area of the anchor, is not reduced accordingly. ",
"Since negative padding is not valid, and my googling turned up nothing, I ask here for advice.",
"\nIs there a way to reduce the hit area of the anchor tag?",
"\n\nRelevant Html:\n <a class=\"site-title\" href=\"/\">\n <img class=\"logo\" src=\"logo.svg\" alt=\"Logo\">\n </a>\n\nRelevant CSS:\n.logo {\n margin-bottom: -26px;\n}\n\nA:\n\nOne way this could be done is to have the image separated from the link and just have the link/click area as an overlay on top of the image so you can control the image positioning & dimensions independently of the clickable area. ",
"For example...\nHTML:\n<div class=\"image\">\n <img src=\"logo.svg\">\n <a href=\"/\"></a>\n</div>\n\nCSS:\n.image{ position: relative; margin-bottom: -26px; }\n.image a{ position: absolute; display: block; width: 100%; height: calc(100% - 26px); }\n\nAlternatively, you can play with z-indexing, but I think this approach might be the cleanest since the logo does overlap with the bar in the design/screenshots.",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0,
0,
0,
0,
0.000006344815334149699,
0
] | 0.000001 | 5 |
[
"Houstonians freak out as scary clowns make unexpected doughnut deliveries A Hurts Donut scary clown makes doughnut deliveries in downtown Houston\n\nHurts Donuts Katy General Manager Matt Whitney donned a scary clown costume Thursday, Oct. 18, 2018 to make deliveries to unsuspecting Houstonians in Downtown. ",
"Hurts Donuts Katy General Manager Matt Whitney donned a scary clown costume Thursday, Oct. 18, 2018 to make deliveries to unsuspecting Houstonians in Downtown. ",
"Photo: Michelle Iracheta/The Houston Chronicle Photo: Michelle Iracheta/The Houston Chronicle Image 1 of / 42 Caption Close Houstonians freak out as scary clowns make unexpected doughnut deliveries 1 / 42 Back to Gallery\n\nMatt Whitney hops out of a black truck parked in midtown carrying a box of Hurts Donuts and waves a white-gloved hand toward a law office across the street. ",
"But the 42-year-old isn't dressed as himself Thursday.",
"\n\nJust moments prior, Whitney underwent a transformation. ",
"The doughnut delivery is one of the first of the day and Whitney is dressed as a mixture of a Stephen King classic villain, Pennywise the Clown from the movie IT, the 1990 version and the 2017 re-adaptation starring Bill Skarsgård. ",
"Whitney and his driver, Hurts Donut - Katy General Manager Layne Long, just call him the \"scary clown.\"",
"\n\nSince the team at Hurts Donut – Katy announced in September it was going to start the scary clown prank beginning in October – the business' phones rang off the hook and the team sorted through thousands of messages and voicemails. ",
"The Katy doughnut shop was so inundated with calls, they kept pushing back delivery dates. ",
"Eventually, they had scheduled their deliveries in the greater Houston area into neighborhood blocks: Energy Corridor, Pearland, The Woodlands... etc.",
"\n\nBut then they couldn't find a clown.",
"\n\n\"We put an ad out, a listing for a scary clown and nobody showed up,\" doughnut shop owner Whitney says. \"",
"We didn't get any hits on it. ",
"We were surprised. ",
"I guess nobody wanted to be a scary clown.\"",
"\n\nHe theorizes potential 'scary clowns' might have been afraid of taking the job after a social media posting garnered a lot of online attention and suggested that a clown delivering doughnuts in Texas might warrant someone sticking a gun in their face.",
"\n\n'GLORIOUSLY EXTRA': Halloween makeup on Instagram\n\nOn Thursday, Whitney and Long walk toward Weston Legal on West Gray ready to meet Daisy Guevarra, a legal assistant, who according to the doughnut shop called in the prank on the office.",
"\n\nHolding a red balloon, Whitney is silent as he waits to be escorted into the office building. ",
"He's silent as he's moving toward his target and he's silent when people yell at him from across the street or ask him direct questions.",
"\n\nA man across Main Street downtown yells at Whitney as he walks by, \"You're going to scare someone with that, man.\" ",
"Others pull out their iPhones and snap photos and videos to share later with their friends on social media. ",
"Whitney doesn't flinch.",
"\n\nAs he hands a box of doughnuts to Hannah Jung, a legal assistant at Weston Legal, he's silent underneath the white perpetual half-smile, half-sneer Pennywise mask and unless you asked him later, you'd never know that he thinks of himself as \"a nice clown.\"",
"\n\n\"I don't know why people are afraid of clowns,\" Whitney says. \"",
"Personally, I don't have any fear of clowns, but I don't know. ",
"Somebody on Facebook said that all clowns are scary. ",
"What about nice clowns? ",
"So I don't know why they're scared of clowns.\"",
"\n\nHALLOWEEN NOSTALGIA: Fright Fest at AstroWorld scared and amused a generation of Houstonians\n\nHe then admits that he gets a kick out scaring people and that underneath the mask he's been smiling and laughing the entire time.",
"\n\n\"Today was actually fun walking downtown, because usually the deliveries we've done so far, we've kind of just piled out, get into a place and you're not really around people,\" he says. \"",
"Just to see the people on the street and stuff is funny. ",
"You can't tell that I'm smiling and laughing underneath this mask.\"",
"\n\nAfter the deliveries, Whitney takes off his mask. ",
"Never did he imagine that he'd end up walking the streets of downtown Houston delivering doughnuts dressed up as a scary clown. ",
"When his college friend Tim Clegg, who founded the Katy doughnut shop, told Whitney about Hurts Donut four years ago to join him, Whitney said, \"No way.\"",
"\n\nWhy would he?",
"\n\nHe had \"a real job\" as a vice president of a production company in Tennessee. ",
"But always the entrepreneur that he was, he felt that itch he wanted to scratch. ",
"He wanted to be his own boss again, so he eventually did join up with Clegg, a franchisor. ",
"And he has no regrets, he says.",
"\n\n\"The only thing that's tough is the 24 hours,\" he says. \"",
"It's more challenging than I anticipated it to be.\"",
"\n\nTo be a Hurts Donut clown is rough living. ",
"To be a Hurts Donut owner is even rougher.",
"\n\nTRICK OR TREAT: Hurts Donuts launches national scary clown delivery service\n\nLong says she was pushing for Whitney to be the clown from the get-go: it saves money. ",
"Whitney has been making it to the shop around 6 a.m. and leaving every day between 10 to 11 p.m., some days closer to midnight all while making deliveries throughout the greater Houston area spread between a morning, afternoon and evening shift. ",
"Deliveries began on Wednesday, Oct. 17 and will run through Halloween and so far Whitney is it. ",
"He's the clown. ",
"One Katy store is booked through the rest of October for all of Houston.",
"\n\nThe cost for the scary clown service is $50 and includes one dozen doughnuts, the scary clown that delivers the doughnuts to the person of your choosing and the Hurts Donut ambulance. ",
"In downtown, parking an ambulance and delivering doughnuts would have been \"a nightmare,\" Whitney says.",
"\n\n\"I think if we do it again next year, which I think we probably will, we'll just hire somebody and tell them, you got to be there, this is what you're doing,\" Whitney says. \"",
"Had we been a little more prepared for it and knowing what we know, I think we can do twice the deliveries for the entire month.\""
] | {
"pile_set_name": "OpenWebText2"
} | [
0.000010610192150579848,
0.0000390625,
0.000027847202400428845,
0,
0.00029726516052318666,
0.00003715814506539833,
0.00018851918182675084,
0.00001826283877565929,
0.00012075836251660429,
0.000044444444444444447,
0,
0.00008734387282732115,
0,
0,
0,
0,
0.00003501339262267817,
0.00010850694444444444,
0,
0,
0.00008573388203017832,
0,
0.000015023135628868457,
0.0002366863905325444,
0,
0,
0,
0,
0.000039157334168689795,
0,
0,
0,
0.00036982248520710064,
0,
0.00017087444999786406,
0,
0,
0,
0.00012075836251660429,
0,
0,
0,
0,
0.0005668934240362812,
0,
0,
0,
0,
0,
0.000028905075731298418,
0.00009425959091337542,
0.00003228305785123967,
0
] | 0.000052 | 5 |
[
"Brazil star Neymar has revealed that Pele convinced him to reject a move to Chelsea in 2010.",
"\n\nNeymar has been one of the shining lights of the World Cup for Brazil, bagging four goals in his quest to win the Golden Boot, but has experienced a difficult first season with Barcelona.",
"\n\nHe joined the Catalan giants for a fee of €57 million (£48 million), but it later emerged Barcelona had actually paid around £71 million to secure his move from Santos following payments to Neymar's father.",
"\n\nDownload the new Independent Premium app Sharing the full story, not just the headlines\n\nHowever, his career may have taken a whole new path if Neymar had agreed four years ago after the Premier League giants agreed a £25 million deal with his club Santos.",
"\n\nIn an extract published by the Daily Mail of his new book 'Neymar: My Story - Conversations With My Father', he says: \"It was August 23, 2010. ",
"My father and I had a meeting with president Luis Álvaro at the Santos headquarters, inside the Vila Belmiro.",
"\n\n\"Chelsea had made a huge transfer bid. ",
"In the middle of our conversation, the president turned off the lights and pointed at an empty chair.",
"\n\n\n\n\"‘This is the chair of the great national sports hero. ",
"Since Ayrton Senna’s death, this chair is vacant. ",
"If Neymar Jnr stays in Santos and refuses Chelsea’s proposal, he will give his first step to sit in this chair.’",
"\n\n\n\n\"That made us think. ",
"That decision would be a turning point in my life. ",
"Even Pele called me. ",
"Can you imagine how important I felt? ",
"The King of Football called and asked me to stay.",
"\n\n\n\n\"He reminded me of his entire career with Santos, his five world titles with the national team and the club, and all the recognition he received. ",
"It wasn’t easy but it was the right decision for us. ",
"We did the right thing for our family, friends and my career.\"",
"\n\nNeymar scored 15 goals in all competitions for the Blaugrana last season.",
"\n\nThe best league in the world is back. ",
"Join The Independent for an online event, as our panel discusses the most uncertain start to a season in Premier League history. ",
"Click here to find out more and book your free ticket today."
] | {
"pile_set_name": "OpenWebText2"
} | [
0.00023629489603024575,
0,
0.00002311390532544379,
0.00004506940688660537,
0.0001426872770511296,
0.00016833599865331202,
0.000594883997620464,
0,
0,
0.0004,
0.00015943877551020407,
0,
0,
0.0022675736961451248,
0,
0.0004164931278633902,
0,
0,
0,
0.00017777777777777779,
0,
0.00006009254251547383,
0
] | 0.000204 | 5 |
[
"project_path: /web/fundamentals/_project.yaml\nbook_path: /web/fundamentals/_book.yaml\ndescription: Learn who are involved in the Web Payments ecosystem, how they interact each other and how you can get involved.",
"\n\n{# wf_published_on: 2018-09-10 #}\n{# wf_updated_on: 2019-07-28 #}\n{# wf_blink_components: Blink>Payments #}\n\n# How the payment ecosystem works {: .page-title }\n\n{% include \"web/_shared/contributors/agektmr.html\" %}\n{% include \"web/_shared/contributors/dgash.html\" %}\n\nLet's see how the new payment ecosystem works with Web Payments.",
"\n\n## The anatomy of Web Payments\n\n_Web Payments_ comprises multiple web standards:\n\n* **Payment Request API:** The [Payment Request\n API](https://www.w3.org/TR/payment-request/) enables fast and easy checkouts\n through a native browser UI. ",
"It provides a consistent checkout flow while\n reducing the need for users to enter their shipping and payment information\n on every checkout. ",
"Learn how it works at a high level at [How Payment Request\n API Works](/web/fundamentals/payments/basics/how-payment-request-api-works) or in detail at\n [Deep Dive into the Payment Request\n API](/web/fundamentals/payments/merchant-guide/deep-dive-into-payment-request).",
"\n* **Payment Handler API:** The [Payment Handler\n API](https://w3c.github.io/payment-handler/) opens up the ecosystem to\n payment providers by allowing their web-based payment applications to act as\n payment methods on merchant websites through the standard Payment Request\n API.",
"\n* **Payment Method Identifiers:** The [Payment Method\n Identifiers](https://w3c.github.io/payment-method-id/) defines how strings\n (`basic-card`, `https://google.com/pay`, etc.) ",
"can be used to identify a\n payment method. ",
"Along with standardized payment method identifiers, it\n allows anyone to define their own payment method with URL-based payment\n method identifiers. ",
"Learn more at [Payment Method\n Basics](/web/fundamentals/payments/basics/payment-method-basics).",
"\n* **Payment Method Manifest:** The [Payment Method\n Manifest](https://w3c.github.io/payment-method-manifest/) defines the\n machine-readable manifest file, known as a payment method manifest,\n describing how a payment method participates in the payment ecosystem, and\n how such files are to be used.",
"\n\n## How the Payment Request Process Works\n\nThere are typically four participants in an online transaction.",
"\n\n<table>\n <tr>\n <th style=\"width:30%;\">Players</th>\n <th style=\"width:50%;\">Description</th>\n <th style=\"width:20%;\">API usage</th>\n </tr>\n <tr>\n <td>Customers</td>\n <td>Users who go through a checkout flow to purchase item(s) online.",
"\n </td>\n <td>N/A</td>\n </tr>\n <tr>\n <td>Merchants</td>\n <td>Businesses selling products on their website.",
"\n </td>\n <td>Payment Request API</td>\n </tr>\n <tr>\n <td>Payment Service Providers (PSPs)</td>\n <td>Third-party companies that actually process payments,\n which involves charging customers and crediting merchants.",
"\n Alternatively called payment gateways or payment processors.",
"\n </td>\n <td>Payment Request API</td>\n </tr>\n <tr>\n <td>Payment Handlers</td>\n <td>Third-party companies which provide applications that typically\n store customers' payment credentials and on their authorization\n provide them to merchants to process a transaction.",
"\n </td>\n <td>Payment Handler API</td>\n </tr>\n</table>\n\n<figure>\n <img src=\"../images/payment-ecosystem/payment-interactions.png\" alt=\"\" />\n <figcaption><i>The typical sequence of events in processing a credit card\n payment on the web</i></figcaption>\n</figure>\n\n1. ",
" The Customer visits a merchant's website, adds items to a shopping cart, and\n starts the checkout flow.",
"\n1. ",
" The Merchant needs the customer's payment credentials to process the\n transaction. ",
"They present a payment request UI to the customer using [**the\n Payment Request\n API**](/web/fundamentals/payments/basics/how-payment-request-api-works). ",
"The\n UI lists various methods of payment specified by [**the Payment Method\n Identifiers**](/web/fundamentals/payments/basics/payment-method-basics). ",
"The\n payment methods can include credit card numbers saved to the browser, or\n payment handlers like Google Pay, Samsung Pay, etc. ",
"The Merchant can\n optionally request the customer's shipping address and contact information.",
"\n1. ",
" If the customer chooses a payment method like Google Pay, Chrome launches\n either a platform-native payment app or a web-based payment app. ",
"This step\n is completely up to the payment handler's implementation, based on **the\n Payment Method Manifest**. ",
"After the customer authorizes the payment, the\n payment handler returns a response to the Payment Request API, which relays\n it to the merchant site. (",
"If the payment is push type such as bank\n transfers, cryptocurrencies, the payment is already processed when the\n merchant receives the response.)",
"\n1. ",
" The merchant site sends a payment credential to a PSP to process the payment\n and initiate funds transfer. ",
"Usually, verifying the payment on the server\n side is also required.",
"\n1. ",
" The PSP processes the payment, securely requesting a funds transfer from the\n customer's bank or credit card issuer to the merchant, and then returns a\n success or failure result to the merchant website.",
"\n1. ",
" The merchant website notifies the customer of the success or failure of the\n transaction and displays the next step, e.g., shipping the purchased item.",
"\n\n![](..",
"/images/payment-ecosystem/payment-transaction-process.png)\n\n## Caveat: PSP Reliance\n\nIf you are a merchant and want to accept credit card payments, PSPs are an\nimportant link in the payment processing chain. ",
"Implementing the Payment Request\nAPI does not obviate the need for a PSP.",
"\n\nMerchants usually rely on a third-party PSP to perform payment processing for\nconvenience and expense reasons. ",
"This is primarily because most PSPs maintain\ncompliance with [PCI\nDSS](https://en.wikipedia.org/wiki/Payment_Card_Industry_Data_Security_Standard),\nan information security standard that regulates the safety of cardholder data.",
"\n\nBecause achieving and maintaining strict PCI DSS compliance can be expensive and\ndifficult, most merchants find that relying on a compliant PSP avoids going\nthrough the certification process themselves. ",
"Some large and financially robust\ncompanies, however, obtain their own PCI DSS certification specifically to avoid\nsuch third-party reliance.",
"\n\nIt's especially important when you are using `basic-card` payment method which\nreturns a primary account number (PAN) as a payment credential, that is the\nnumber embossed on the card. ",
"Handling one with JavaScript requires [PCI SAQ\nA-EP](https://www.pcisecuritystandards.org/documents/PCI-DSS-v3_2-SAQ-A_EP.pdf)\ncompliance.",
"\n\nThus, delegating payment processing to a PCI DSS-compliant PSP both simplifies\nthe merchant site's requirements and ensures payment information integrity for\nthe customer.",
"\n\nIf you want to use the Payment Request API but don't have bandwidth to be\ncompliant with PCI SAQ A-EP, some PSPs provide an SDK that uses the Payment\nRequest API.",
"\n\n### List of supporting payment gateways\n\n* [Stripe](https://stripe.com/docs/stripe-js/elements/payment-request-button)\n* [Braintree](https://developers.braintreepayments.com/guides/payment-request/overview)\n* [Bluesnap](https://developers.bluesnap.com/v8976-Basics/docs/payment-request-api)\n* [WePay](https://developer.wepay.com/docs/mobile/payment-request-api)\n\nNote: Send [pull requests](https://github.com/google/WebFundamentals/pulls) to\nus if your payment gateway provides an SDK that involves the Payment Request API\nbut is not listed here.",
"\n\n## Next Up\n\nLearn about the Payment Request API's fields and methods in [How the Payment\nRequest API\nWorks](/web/fundamentals/payments/basics/how-payment-request-api-works).",
"\n\n## Feedback {: #feedback }\n\n{% include \"web/_shared/helpful.html\" %}\n"
] | {
"pile_set_name": "Github"
} | [
0.00002246131039284832,
0,
0.000048777315296566075,
0,
0.000025878577713368875,
0.000034945077985765705,
0.000057193514255483425,
0,
0,
0.0001020304050607081,
0.00001020731047576274,
0.00008734387282732115,
0,
0,
0,
0,
0,
0.000013417595835178253,
0,
0,
0.0001321178491214163,
0.0000390625,
0.000041091387245233394,
0.000053279343598486864,
0.00010850694444444444,
0,
0.000048225308641975306,
0,
0,
0,
0,
0.00008116224332440549,
0,
0,
0,
0,
0.00004162330905306972,
0,
0,
0,
0,
0.000039157334168689795,
0.000023795359904818562,
0,
0.000028905075731298418,
0.00010501995379122034,
0.000033412409368839586,
0.000037180249851279,
0.000019979753849432577,
0.00003265306122448979,
0
] | 0.000025 | 5 |
[
"Q:\n\nEmail pipe to php script working only sometimes\n\nI have a php pipe script that receives an email, takes an attached *.csv from it and parses it. ",
"\nHowever, when the email is sent from where it is supposed to be coming from, it silently errors. ",
"But when I take that same email and resend it from my address it goes through just fine. ",
"is there any simple reason it could be doing this?",
"\n\nA:\n\ntry and save some information about the email in a logfile before anything else, then some more info as you parse it. ",
"This way you get a more better understanding of what is happening\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0,
0,
0,
0
] | 0 | 5 |
[
"Search Results\n\nShare This\n\n61 results\n\nIn spite of their “greenness”, lawns can be huge burdens on the environment. ",
"During summer try watering and mowing your lawn less often. ",
"You will conserve water, release fewer greenhouse gases, and save money.",
"\n\nOne person’s trash is another person’s treasure. ",
"This is the mantra that led to the birth of freecycling - the act of giving away unwanted items at no cost. ",
"Just say the word FREE and the crowds will follow. ",
"Freecycling is a great way to...\n\nIn September 2006, one of Harvard's recycling trucks was converted to run on waste vegetable oil from Annenberg Dining Hall. ",
"The project, first proposed by two students, was implemented by Harvard Recycling, HGCI, and the Harvard Transportation...\n\nDuring the week preceding Earth Day 2009, a group of Students for Environmental Awareness in Medicine (SEAM) club members and the Longwood Sustainability Coordinator undertook a week-long daily trash audit of the TMEC building at Harvard Medical...\n\nDuring the summer of 2009, HMS Campus Operations relocated over 750 pieces of furniture during an office move-out from the Prudential Center. ",
"Over 85% of all the perfectly good furniture that would otherwise have been disposed of in a landfill found...\n\nDid you know that the U.S. alone went through 50 billion plastic water bottles last year? ",
"Members of Students for Environmental Awareness in Medicine (SEAM) have taken serious interest in changing student, staff and faculty consumption of bottled...\n\nDid you know that Harvard’s Facilities Maintenance Operations (FMO) Custodial Services is the only cleaning service at Harvard — or across Massachusetts — to have achieved Green Seal™ certification, an industry mark of..."
] | {
"pile_set_name": "Pile-CC"
} | [
0,
0,
0,
0,
0,
0.00038446751249519417,
0.00007911079466793244,
0.00003380205516495403,
0,
0.000013705764644609523
] | 0.000051 | 5 |
[
"Q:\n\nJavascript Fading out/in on mouse movement\n\nI want to have a fixed nav which fades out when the mouse isn't moving and fades back in when it does.",
"\nI've came across this other post which does the job but the problem is that it uses visibility and I want to use opacity that way I can make it fade in and out with a transition transition: all .4s ease-in-out;\n\n$(\"#fp-nav\").style.opacity = \"0\";\r\n\r\n$(\"html\").mousemove(function(event) {\r\n $(\"#fp-nav\").style.opacity = \"1\";\r\n\r\n myStopFunction();\r\n myFunction();\r\n});\r\n\r\nfunction myFunction() {\r\n myVar = setTimeout(function() {\r\n $(\"#fp-nav\").style.opacity = \"0\";\r\n }, 1000);\r\n}\r\n\r\nfunction myStopFunction() {\r\n if (typeof myVar !",
"= 'undefined') {\r\n clearTimeout(myVar);\r\n }\r\n}\n#fp-nav {\r\n position: fixed;\r\n z-index: 100;\r\n top: 50%;\r\n opacity: 1;\r\n -webkit-transform: translate3d(0, 0, 0);\r\n transition: all .4s ease-in-out;\r\n}\n<script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js\"></script>\r\n<div id=\"fp-nav\">\r\n Hello world Hello world Hello world Hello world\r\n</div>\n\nOr am I supposed to use fp-nav.style.opacity = \"0\"; instead of $(\"#fp-nav\").style.opacity = \"0\";\n\nA:\n\nYou can replace .hide() and .show() by your own css code to visually hide the bar: hide becomes css(\"opacity\", 0) and show becomes css(\"opacity\", 1).",
"\nThen, you add a transition to your bar:\n.navbar {\n transition: opacity 1000ms ease-in-out;\n};\n\n$(\"div\").css(\"opacity\", 0);\r\n\r\n$(\"html\").mousemove(function( event ) {\r\n $(\"div\").css(\"opacity\", 1);\r\n \r\n myStopFunction();\r\n myFunction();\r\n});\r\n\r\nfunction myFunction() {\r\n myVar = setTimeout(function(){\r\n $(\"div\").css(\"opacity\", 0);\r\n }, 1000);\r\n}\r\nfunction myStopFunction() {\r\n if(typeof myVar !",
"= 'undefined'){\r\n clearTimeout(myVar);\r\n }\r\n}\ndiv {\r\n transition: opacity 1000ms ease-in-out;\r\n}\n<script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js\"></script>\r\n<div>navbar</div>\n\nIt might be nice to let the css define how you want to hide/show via an additional class. ",
"You can then, for example, use addClass(\"is-hidden\") and removeClass(\"is-hidden\"):\n\nvar hiddenClass = \"is-hidden\";\r\nvar customHide = function($el) {\r\n $el.addClass(hiddenClass);\r\n} \r\n\r\nvar customShow = function($el) {\r\n $el.removeClass(hiddenClass);\r\n} \r\n\r\ncustomHide($(\"div\"));\r\n\r\n$(\"html\").mousemove(function( event ) {\r\n customShow($(\"div\"));\r\n \r\n myStopFunction();\r\n myFunction();\r\n});\r\n\r\nfunction myFunction() {\r\n myVar = setTimeout(function(){\r\n customHide($(\"div\"));\r\n }, 1000);\r\n}\r\nfunction myStopFunction() {\r\n if(typeof myVar !",
"= 'undefined'){\r\n clearTimeout(myVar);\r\n }\r\n}\n/* CSS now determines how we want to hide our bar */\r\n\r\ndiv {\r\n position: relative;\r\n background: green;\r\n\r\n transition: transform 500ms ease-in-out;\r\n}\r\n\r\ndiv.is-hidden {\r\n transform: translateY(-160%);\r\n}\n<script src=\"https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js\"></script>\r\n<div>navbar</div>\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0.0000050550878195131445,
0,
0.000010610192150579848,
0,
0.000014146672702580353
] | 0.000004 | 5 |
[
"Q:\n\nDoes pinning a process to a CPU core or an SMP node help reduce cache coherency traffic?",
"\n\nIt is possible to pin a process to a specific set of CPU cores using sched_setaffinity() call. ",
" The manual page says:\n Restricting a process to run on a single CPU also avoids the\n performance cost caused by the cache invalidation that occurs when a process\n ceases to execute on one CPU and then recommences execution on a different\n CPU.",
"\n\nWhich is almost an obvious thing (or not?). ",
"What is not that obvious to me is this -\nDoes pinning LWPs to a specific CPU or an SMP node reduces a cache coherency bus traffic? ",
"For example, since a process is running pinned, other CPUs should not modify its private memory, thus only CPUs that are part of the same SMP node should stay cache-coherent.",
"\n\nA:\n\nThere should be no CPU socket-to-socket coherency traffic for the pinned process case you describe. ",
" Modern Xeon platforms implement snoop filtering in the chipset. ",
" The snoop filter indicates when a remote socket cannot have the cache line in question, thus avoiding the need to send cache invalidate messages to that socket.",
"\nYou can measure this for yourself. ",
" Xeon processors implement a large variety of cache statistic counters. ",
" You can read the counters in your own code with the rdpmc instruction or just use a product like VTune. ",
" FYI, using rdpmc is very precise, but a little tricky since you have to initially set a bit in CR4 to allow using this instruction in user mode.",
"\n-- EDIT --\nMy answer above is outdated for the 55xx series of CPUs which use QPI links. ",
" These links interconnect CPU sockets directly without an intervening chipset, as in:\nhttp://ark.intel.com/products/37111/Intel-Xeon-Processor-X5570-%288M-Cache-2_93-GHz-6_40-GTs-Intel-QPI%29\nHowever, since the L3 cache in each CPU is inclusive, snoops over the QPI links only occur when the local L3 cache indicates the line is nowhere in the local socket. ",
" Likewise, the remote socket's L3 can quickly respond to a cross-snoop without bothering the cores, assuming the line isn't there either.",
"\nSo, the inclusive L3 caches should minimize inter-socket coherency overhead, it's just not due to a chipset snoop filter in your case.",
"\n\nA:\n\nIf you run on a NUMA system (like, Opteron server or Itanium), it makes sense, but you must be sure to bind a process to the same NUMA node that it allocates memory from. ",
"Otherwise, this is an anti-optimization. ",
"It should be noted that any NUMA-aware operating system will try to keep execution and memory in the same node anyway, if you don't tell it anything at all, to the best of its abilities (some elderly versions of Windows are rather poor at this, but I wouldn't expect that to be the case with recent Linux).",
"\nIf you don't run on a NUMA system, binding a process to a particular core is the one biggest stupid thing you can do. ",
"The OS will not make processes bounce between CPUs for fun, and if a process must be moved to another CPU, then that is not ideal, but the world does not end, either. ",
"It happens rarely, and when it does, you will hardly be able to tell.",
"\nOn the other hand, if the process is bound to a CPU and another CPU is idle, the OS cannot use it... that is 100% available processing power gone down the drain.",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0.00011814744801512288,
0,
0,
0,
0.00005827166249053085,
0.00003302946228035408,
0,
0,
0,
0,
0,
0.00009070294784580499,
0,
0.00012624668602449185,
0.000015605006085952374,
0,
0,
0.00012767723195761116,
0,
0.000010679653124866504,
0.0000706164818868724,
0,
0,
0,
0
] | 0.000026 | 5 |
[
"% Generated by roxygen2: do not edit by hand\n% Please edit documentation in R/plota.r\n\\name{plota.theme}\n\\alias{plota.theme}\n\\alias{plota.theme.blue.red}\n\\alias{plota.theme.green.orange}\n\\alias{plota.theme.gray.orange}\n\\title{Plota Control Parameters & Themes}\n\\usage{\nplota.theme(\n col.border = \"black\",\n col.up = \"green\",\n col.dn = \"red\",\n col.x.highlight = \"orange\",\n col.y.highlight = \"orange\",\n alpha = NA\n)\n\nplota.theme.blue.red(alpha = NA)\n\nplota.theme.green.orange(alpha = NA)\n\nplota.theme.gray.orange(alpha = NA)\n}\n\\arguments{\n\\item{col.border}{border color}\n\n\\item{col.up}{up color}\n\n\\item{col.dn}{down color}\n\n\\item{col.x.highlight}{x highlight color}\n\n\\item{col.y.highlight}{y highlight color}\n\n\\item{alpha}{alpha level}\n}\n\\value{\nnothing\n}\n\\description{\nSet the color theme, the default theme is plota.theme.green.orange()\n}\n\\examples{\n\\dontrun{ \nplota.theme.blue.red()\n}\n}\n"
] | {
"pile_set_name": "Github"
} | [
0.0000062699934415868595
] | 0.000006 | 5 |
[
"Longitudinal comparative study on the influence of computers on reporting of clinical data.",
"\nThe impact of the clinical database system SISCOPE on medical services was evaluated and objective data compiled on the quality of information recording and reporting using a fully structured data entry system compared to traditional free text reporting. ",
"1565 upper endoscopy reports produced with SISCOPE over a period of 12 months were assessed for completeness and compared to 152 and 208 free text reports done 4 months before and 1 month after the study period, respectively. ",
"Data on four common gastrointestinal findings (esophageal varices, ulcers, polyps and tumors) were evaluated. ",
"Physicians' compliance with the new system was good, as reflected by a constant level of quality of reporting over time, although a very slight decline in the ratio of computer generated reports to the total number of examinations was noted. ",
"Structured reports had an 18% missing data rate and contained 60% more relevant information than free text reports, which had a 48% missing data rate. ",
"No educational effect of the system was seen as missing data rates returned to pre-computerization levels just one month after the end of the study. ",
"It is concluded that menu-driven structured data entry systems result in production of far superior reports as compared to free text systems, probably due to their reminder effect."
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0,
0,
0,
0,
0,
0.00004385772553835358,
0,
0
] | 0.000005 | 5 |
[
"Apicalia tryoni\n\nApicalia tryoni is a species of sea snail, a marine gastropod mollusk in the family Eulimidae.",
"\n\nDistribution\nThis marine species is endemic to Australia and occurs off Tasmania, Victoria and Western Australia.",
"\n\nReferences\n\n Tate, R. & May, W.L. 1900. ",
"Descriptions of new genera and species of Australian Mollusca (chiefly Tasmanian). ",
"Transactions of the Royal Society of South Australia 24(2): 90-103\n Cotton, B.C. 1959. ",
"South Australian Mollusca. ",
"Archaeogastropoda. ",
"Handbook of the Flora and Fauna of South Australia. ",
"Adelaide : South Australian Government Printer 449 pp.",
"\n\nExternal links\n To World Register of Marine Species\n\nCategory:Eulimidae\nCategory:Gastropods of Australia\nCategory:Gastropods described in 1900"
] | {
"pile_set_name": "Wikipedia (en)"
} | [
0.00016232448664881097,
0,
0.0011337868480725624,
0.0001451589490492089,
0.0002642356982428326,
0,
0.002770083102493075,
0.0007396449704142013,
0,
0.000048225308641975306
] | 0.000526 | 5 |
[
"WBO cruiserweight champion Marco Huck will face former WBA kingpin Firat Arslan in a rematch of their controversial first encounter last November on September 14 at the Hans-Martin-Schleyer Halle in Stuttgart, Germany. ",
"Huck vs. Arslan 2 was announced earlier today by Sauerland Event. “",
"This fight was on every boxing fan’s wishlist. ",
"Their first fight was dramatic and exciting”, said Sauerland CEO Frederick Ness. “",
"I’m glad that they’ll do it again on September 14.”",
"\n\nHuck (36-2-1, 25 KOs) won a unanimous decision (by scores of a ridiculous 117-111 and 115-113 twice) over Arslan (33-6-2, 21 KOs) nine months ago. ",
"However, the decision was greeted with incomprehension as most fans and experts agreed that Firat Arslan should have gotten the nod in a close-but-clear affair. ",
"This writer scored the bout 116-112 in favor of the challenger. “",
"I saw myself as the winner back in November”, said Arslan, 42, in a Press Release announcing the rematch. “",
"I would have been world champion again. ",
"I will give everything I got to take that belt away from him in the rematch. ",
"And I’m sure I’ll have the support of the fans in Stuttgart.”",
"\n\nArslan is the WBO mandatory challenger for Huck. “",
"I wanted to give him this rematch, though”, Huck said. “",
"It doesn’t matter that he is my mandatory, I would have fought him again regardless. ",
"I understand that Firat was bitterly disappointed after our first fight. ",
"I saw myself as the victor last year in my heavyweight title challenge against Alexander Povetkin but the judges disagreed. ",
"This is why I wanted to offer him a second chance.”",
"\n\nFor the sake of the sport, one can only hope that a fair and just winner will be crowned after the conclusion of the September 14 rematch between Huck and Arslan. ",
"Tickets for Huck vs. Arslan 2 will be available this weekend by calling +49-1805-570044 or online at www.eventim.de and www.easyticket.de."
] | {
"pile_set_name": "Pile-CC"
} | [
0.0001042513709055274,
0.0006683002895967921,
0,
0.000297441998810232,
0,
0.00004504301608035674,
0.000038578758535550326,
0,
0,
0,
0,
0,
0.0007396449704142013,
0.00031887755102040814,
0,
0.00018765246762994932,
0.00006503642039542143,
0,
0.000036730945821854914,
0.00021003990758244068
] | 0.000136 | 5 |
[
"Nitrogen removal rates in a frigid high-altitude river estimated by measuring dissolved N2 and N2O.\nRivers are important sites of both nitrogen removal and emission of nitrous oxide (N2O), a powerful greenhouse gas. ",
"Previous measurements have focused on nitrogen-rich temperate rivers, with cold, low-nitrogen river systems at high-altitude receiving less attention. ",
"Here, nitrogen removal rates were estimated by directly measuring dissolved N2 and N2O of the Yellow River in its source region of the Tibetan Plateau, a frigid high-altitude environment. ",
"We measured the dissolved N2 and N2O using N2:Ar ratio method and headspace equilibrium technique, respectively. ",
"Dissolved N2 in the river water ranged from 337 to 513 μmol N2 L-1, and dissolved N2O ranged from 10.4 to 15.4 nmol N2O L-1. ",
"Excess dissolved N2 (△N2) ranged from -8.6 to 10.5 μmol N2 L-1, while excess dissolved N2O (△N2O) ranged from 2.1 to 8.3 nmol N2O L-1; they were relatively low compared with most other rivers in the world. ",
"However, N2 removal fraction (△N2/DIN, average 21.6%) and EF5r values (N2O - N/NO3 - N, range 1.6 × 10-4-5.0 × 10-2) were comparable with many other rivers despite the high altitude for the Yellow River source region. ",
"Furthermore, the EF5r values increased with altitude. ",
"Estimated fluxes of N2 and N2O to the atmosphere from the river surface ranged from -67.5 to 93.5 mmol N m-2 d-1 and from 4.8 to 93.8 μmol N m-2 d-1, respectively, and the nitrogen removal from rivers was estimated to be 1.87 × 107 kg N yr-1 for the Yellow River source region. ",
"This is the first report of nitrogen removal for a frigid high-altitude river; the results suggest that N removal and N2O emission from cold high-altitude rivers should be considered in the global nitrogen budget."
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0.00006430041152263374,
0,
0.000028293345405160706,
0,
0.000128,
0.000023564897728343855,
0,
0,
0.000012939288856684438,
0
] | 0.000026 | 5 |
[
"On January 30th 2013 Sweetwood received 9 inches of snow. ",
"The following day of we were plowed out. ",
"However we received an addition snow fall of 4-5 inches of very light and fluffy snow on Imbolc eve. ",
"The next day I shoveled the drive way as the Hydraulic on my tractor went out and I could not plow the drive way. ",
"In an hour and half I had the driveway done. ",
"Then I got breakfast and readied to go and prepare the ritual site for Sweetwood’s Imbolc celebration. ",
"The day started out cloudy and cold and the proverbial “groundhog” did not see its shadow. ",
"Yeah, an early spring is the forecast! ",
"I took with me the ritual tools to the circle and set up the altar. ",
"Then I shoveled out the snow around the where the Yule fire had been to about 8 feet away all around. ",
"I removed the covering over the charred Yule fire remains and set about to start a fire with some dry kindling. ",
"The Sun came out, the woods glistened and with some blowing the kindling started and the Imbolc fire started. ",
"I burned much of what was left of the pine wood left from the Yule fire and added nice dry white oak to the fire. ",
"Pretty soon the fire was roaring. ",
"I decided to dance naked around the fire and charge up the circle. ",
"Three times round the circle naked and bare foot I danced calling out to the Goddess, the God and the Fay. ",
"It was okay being naked for a brief time and I was glad to get my feet dry and warm again. ",
"I got dress and went back to the house to get ready and bring back water, cookies and hot cider for the ritual.",
"Back at the house Good folk for the Imbolc ritual had begun to arrive. ",
"We wait for some good folk who had car problems on the way. ",
"Eventually the ritual started about an hour late but hey there were 7 hearty folk at the Sweetwood Temenos Imbolc ritual this year, the most ever! ",
"However the fire had died down and it need to be built up again. ",
"So several folk blew on it and more dry oak wood was brought and added. ",
"So in about 20 minutes we had a roaring fire again with plenty of oak to add lying around the fire.",
"A welcome to the celebration and a grounding Om around the Imbolc fire was done. ",
"Delta and Iacchus then casted the circle with the singing bowl and incense. ",
"The charging of the water and libations poured for the 7 elements of the circle was done, followed by a libation to the mischievous makers and Eris of whiskey and finally an invocation to the Goddess and God and the Divine community. ",
"Iacchus then went to the Altar to draw a Rune for the celebration and season. ",
"He drew the Rune Ken and the letter K; torch, light of knowledge or insight, Kin, will to generate and create and is the rune of the artist and craftsman, it is the Rune of human passion, lust and sexual love and is the emotional root of creativity in all realms and the portrays the mystery of regeneration through sacrifice or death. ",
"Iacchus talked about the season of Imbolc, its traditions and the Sun Goddess Brigit. ",
"It was a time of the quickening the lands spirit as the sun light grows longer and warmer. ",
"Buds begin to swell, Ewes are lactating and lambing, the swelling breast a sign and a symbol of the winter Sun and hag transforming into the returning Spring Maiden. ",
"It is the season for cleaning the house and preparation for birth, regeneration or renewal and planting. ",
"The shadow symbol of what we need to let go of or change in preparation for spring and new growth.",
"Iacchus asked all present to meditate on what they need to let go of or change in preparation for spring and new growth. ",
"They were invited to speak this out load or in silence and then place a piece of wood on the Imbolc fire. ",
"All spoke truthfully from the heart and the fire did blaze. ",
"Iacchus then asked all the good folk to take some time and meditate on Imbolc and share what came to them when ready. ",
"He called on the Goddess of this season to inspire them all in their mediation. ",
"One person produced a poem and read it to the gathered folk. ",
"Others talked about what the season meant to them and others talked about the fellowship of the Imbolc fire.",
"When all had their say, Delta taught to and led all in a chant to raise energy and to send off their well wishes for the coming spring. ",
"The Chant was “Make yourself a power spot, bring in a spoon and a cooking pot, bring air, bring fire, bring water and bring earth and you, a new universe will birth.” ",
"The energy was raised and sent on its way. ",
"We all then shared some cookies with a blessing form the altar and followed with a water sharing. ",
"The water sharing had ice with it (it was cold out) and the goblet went from person to person with this blessing, “water shared is life shared, is love shared, Thou art Goddess, Thou art God, drink deep and never thirst!” ",
"Then Delta and Iacchus took down the circle with the singing bowl and incense walking widdershins to each quarter and back to the altar. ",
"Delta then spoke the closing words “All from air into air, let the misty veils part! ",
"All is ended and all is done, what has been, now must be gone! ",
"What has been done by ancient art must merry meet, merry part and merry meet again! ",
"The circle is open but never broken!” ",
"And hugs and kisses were called for and all passed them around.",
"The good folk then gathered around the fire in chairs and drank hot spiced cider and talk of the season, the ritual, the future and enjoyed the fellowship of midwinter. ",
"As the dark drew nigh all packed up and when to the caretakers’ (Delta and Iacchus) house for the feast, more good conversation and fellowship. ",
"Some stayed over and were treated to a movie called “Dangerous Beauty” (a highly recommended movie). ",
"The next morning the kitchen witch was added again and prepared eggs and pancakes with maple syrup. ",
"And then some more good conversation and laughter before everyone left and so ended Sweetwood Temenos Imbolc 2013."
] | {
"pile_set_name": "Pile-CC"
} | [
0,
0,
0,
0,
0,
0.00009425959091337542,
0,
0,
0,
0,
0,
0.00008264462809917355,
0,
0,
0,
0.00008734387282732115,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.00017313019390581717,
0.00003652567755131858,
0.00016436554898093358,
0.000017715419501133787,
0.00013520822065981613,
0,
0.00007257947452460445,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.0000358564308508731,
0,
0,
0,
0.000053279343598486864,
0,
0,
0.0001417233560090703,
0,
0,
0,
0.000048225308641975306,
0,
0,
0.00007694675284702985
] | 0.000021 | 5 |
[
"EntertainmentSpice Girls animated film in the works, confirms manager\n\n04:55 13 january 2019\n\n04:55 13 january 2019 Source:\ndigitalspy.com\n\nEmery confirms Bellerin faces 'weeks' on the sidelines\n\nArsenal manager Unai Emery has revealed that Hector Bellerin is facing ‘weeks’ on the sidelines after picking up an injury against Southampton. ",
"As quoted by BBC Sport, the Spaniard delivered an update on the condition of his compatriot, who was forced off at half-time in the Gunners’ 3-2 defeat against the Saints. ",
"The loss means that Arsenal’s 22-game unbeaten run in all competitions has come to an end, leaving Emery and his men with plenty of food for thought. ",
"Speaking to the media following the crushing blow at St Mary’s Stadium, Emery was unable to provide particularly positive news on the full-back’s situation. ",
"The manager said: “Bellerin has a small injury – he is going to be some weeks off I think.” ",
"It is reported that the 23-year-old has sustained a calf injury, adding to Arsenal’s ongoing defensive woes in terms of injuries. ",
"Emery will be desperately keen for Bellerin to make a speedy return to action but is likely to call on Stephan Lichtsteiner on the right-hand side of defence over the festive period of fixtures.",
"\n\nThe Spice Girls , Victoria Beckham \"Posh Spice ,\" Emma Bunton \"Baby Spice ,\" Melanie Chisholm \"Sporty Spice ,\" Melanie Brown \"Scary Spice The singers would reportedly each possess a special \" girl power\" in the film , obviously. ",
"CNN has reached out to representatives of the women for comment.",
"\n\nAceShowbiz - Emma Bunton has confirmed the \" Spice Girls \" is considering making their own animated superhero movie. ",
"According to Variety, the film will focus on a feminist \" girl power\" message - revamping their famous 1990s slogan for a new generation.",
"\n\nThe band – which now comprises of all the original members bar Victoria Beckham/Posh Spice – will be heading out on a UK comeback tour later this year, but it looks like they'll also be appearing on our screens in the not-so-distant future in pixel form.",
"\n\nDiscussing with Billboard the band's future plans, Simon mentioned: \"What's coming next is that we are going to be doing lots of exciting things. ",
"We'll be making an animated movie and there's lots of exciting plans to come.\"",
"\n\nRodgers confirms Tierney injury blow\n\nBrendan Rodgers has confirmed the reason behind Kieran Tierney’s absence during the defeat to Hibernian over the weekend. ",
"According to reports, Tierney has suffered an injury blow and was forced to miss Sunday’s game. ",
"Rodgers has since confirmed the news, in what is a disappointing blow for the Hoops. “",
"Kieran has had a hip issue which was feeling sore after the other night.” ",
"Tierney has been ever-present for Celtic this season, which may have played some part in the injury. ",
"Over recent weeks, the defender has looked tired and in need of a rest, but for the most part remains unrivalled at left-back, despite the signing of Emilio Izaguirre. ",
"Tierney missed the 5-1 win over Kilmarnock but did feature against Red Bull Salzburg in the Europa League prior to the meeting with Neil Lennon’s side. ",
"Rodgers will be hoping to welcome Tierney back for either the midweek game against Motherwell or Saturday’s match against Dundee.",
"\n\nThe popular British pop group Spice Girls will be reuniting for an animated film project with a Each character in the movie will be voiced by a Spice Girl and will feature a power unique to each group It’s just what Marvel or Disney needs.” ",
"Simon Fuller, the Spice Girls ’ manager , had no comment.",
"\n\nHe also admitted that he \"expected\" the sell-out success of The Spice Girls comeback tour, adding: \"To be honest with you, while it was clearly phenomenal, they are such an awesome phenomenon I expected it.",
"\n\nHodgson confirms talks for Solanke loan\n\nCrystal Palace manager Roy Hodgson has confirmed that the club are in talks to sign Dominic Solanke on loan from Liverpool next month. ",
"According to Sky Sports journalist Lyall Thomas, Hodgson has revealed a deal is close. ",
"Twitter: Hodgson has confirmed talks ongoing to secure loan of Dominic Solanke from #Liverpoolfc. ",
"Sounds close #cpfc (@SkySportsLyall) Palace are looking to sign a striker in the January transfer window and have been linked with a host of number nine’s. ",
"Sandro Wagner, Gabriel Barbosa and Neal Maupay have all been touted with a move to Selhurst Park, but it appears as though Solanke is on his way to London. ",
"The young forward has only scored one goal in the Premier League for Liverpool, but has been prolific for England’s under-21 side in recent months. ",
"Solanke has scored eight in 15 games for England at under-21 level and has one senior cap to his name, which came in 2017.",
"\n\nThe popular British pop group Spice Girls will be reuniting for an animated film project with a Each character in the movie will be voiced by a Spice Girl and will feature a power unique to each group It’s just what Marvel or Disney needs.” ",
"Simon Fuller, the Spice Girls ’ manager , had no comment.",
"\n\nThe Spice Girls , Victoria Beckham “Posh Spice ,” Emma Bunton “Baby Spice ,” Melanie Chisholm “Sporty Spice ,” Melanie Brown “Scary Spice ,” and Geri Halliwell “Ginger Spice ,” have signed off their likenesses to be used in an animated film The Spice Girls recently reunited for a social gathering\n\n\"It's something that we're talking about,\" she revealed. \"",
"The opportunities we get given, it's amazing. ",
"There is so much excitement, it's just about making sure it's the right thing.\"",
"\n\nThe five-member all-girl English pop band was formed in 1994. ",
"Their debut single \"Wannabe\" (1996) was an international hit, establishing them as one of the most popular cultural icons of the 1990s. ",
"Here’s a look at some moments from their incredible careers.",
"\n\n1997\n\nThe Spice Girls at the launch of the new TV station Channel 5.",
"\n\nCall the Midwife series 8 trailer confirms premiere is very soon\n\nPoplar is gearing up for a royal celebration.",
"\n\nFilm . ",
"An animated Spice Girls superhero movie is reportedly in the works . ",
"Nothing has been confirmed just yet, but we’re sure fans will be VERY excited. ",
"They’ve been eagerly awaiting news of a tour or new music from the group since the girls shared an Instagram snap of their reunion in February.",
"\n\nAll five Spice Girls have reportedly agreed to their likenesses being used, with each character to be voiced by Posh Spice , Scary Spice , Baby Spice , Sporty Spice She also opened up more generally about a Spice Girls reunion, telling Holly and Phil: \"There is definitely something in the pipeline.",
"\n\n1997\n\n1997\n\nThe Spice Girls perform during the Brit Awards ceremony in London. ",
"The group won the Best British Video and Best Single awards.",
"\n\nHasenhuttl confirms Gabbiadini offers\n\nSouthampton manager Ralph Hasenhuttl has confirmed that the club have received offers for Manolo Gabbiadini this month. ",
"The Saints boss fielded questions about the Italian international’s future at St Mary’s Stadium amid recent reports claiming that he is headed for an exit during the January transfer window. ",
"It is claimed by Sky Sports that three clubs are leading the race to sign the former Napoli star. ",
"Serie A duo AC Milan and Fiorentina have held discussions over a move for the 27-year-old, while La Liga outfit Real Betis are also keen. ",
"Gabbiadini has been deemed surplus to Hasenhuttl’s requirements at Southampton and the manager stated that his next destination will be chosen by the player himself. ",
"He said: “Sure [there have been bids], we have to decide and he has to decide where he wants to go. ",
"There are a few teams interested in Manolo, we will have a look and if there’s a result, we’ll tell you.” ",
"The ex-Sampdoria forward has made only one cameo appearance under Saints’ new first-team manager, with his time on the south approaching its conclusion as talks over a departure continue.",
"\n\n“The Spice Girls are thinking big in terms of a franchise on a global scale. ",
"They’re the most successful girl group on the planet. ",
"It’s just what Marvel or Disney needs.” ",
"The girls at this point have just confirmed they're exploring opportunities as a reunited band with their original manager Simon Fuller.",
"\n\nAs part of their comeback, a new project is being assembled which would see the five band-members play heroes with a feminist message.",
"\n\n2000\n\n2000\n\n2001\n\nA still of Victoria Adams auditioning for the Spice Girls from a 2001 documentary, \"Raw Spice.\"",
"\n\nKlopp confirms Moreno will start against Wolves\n\nAlberto Moreno will be in the Liverpool starting line-up that faces Wolverhampton Wanderers on Monday night, Jurgen Klopp has confirmed. ",
"The Reds boss spoke to the media ahead of his side’s FA Cup third round clash and delivered assurances that the Spanish defender will be handed a rare opportunity to shine. ",
"As quoted by Metro, Klopp hailed the left-back as an ‘unbelievable professional’. ",
"When asked if Moreno would start against Wolves, he said: “Alberto is another example for being an unbelievable professional person and a really important part of the dressing room. ",
"He is from the positive side of the planet I would say.” “",
"I can say Alberto will play as well, there is no doubt about that. ",
"He has to play, that’s clear.” ",
"The 26-year-old will see his current contract at Anfield expire when the season draws to a close, with no further extension appearing to be on the table. ",
"This indicates that the former Sevilla star could move on for free in the summer as he continues to struggle for game-time on a regular basis under Klopp on Merseyside. ",
"Nevertheless, it seems Moreno is still held in high esteem by his manager as he prepares to depend on him to help the team advance through to the fourth round of the FA Cup.",
"\n\nThe Spice Girls are rumored to be loaning their voices and personas to an animated movie about girl power. ",
"Ever since the photo was released of the girls meeting for a lunch with Simon Fuller, the group's former manager and creator of hit shows including American Idol and So You Think You Can\n\nIf the Spice Girls animated superhero movie gets picked up, the women will more than likely end up in the studio to record some new songs for the soundtrack Talk of the Spice Girls animated superhero movie comes at the perfect time. ",
"Superhero movies are bigger now than they have ever been, and so\n\n2012\n\n2016\n\nSpeculation was rife the Spice Girls might be reuniting with (L-R) Halliwell, Bunton and Mel B taking the stage to celebrate the 21st anniversary of their debut album \"Wannabe.\" ",
"They unveiled a new website - The Spice Girls - GEM - but Halliwell's pregnancy led to the cancellation of plans.",
"\n\nKlopp confirms hamstring injury for Liverpool defender Lovren\n\nKlopp confirms hamstring injury for Liverpool defender Lovren\n\nIn news that would make a lot more sense, had we all somehow fallen into a time warp back to the mid-1990s, Variety reports that the Spice Girls might Apparently capitalizing around the recent interest in the (squashed, reportedly) hopes for a big reunion tour from the superstar girl group, all five members\n\nVariety is reporting that the Spice Girls are shopping an animated film project, writing Spice fans will remember that the delightfully surrealist Spice World movie saw the Spice Girls meet with a band of frisky aliens, so a film in which the Present also was former Spice Girls manager Simon Fuller\n\n2018\n\nThe girls announced reunion plans on Feb. 2 when they released a joint statement: \"The time now feels right to explore some incredible new opportunities together.\"",
"\n\nThe group, with former manager Simon Fuller, met at Halliwell's house. \"",
"We all agree that there are many exciting possibilities that will once again embrace the original essence of The Spice Girls, while reinforcing our message of female empowerment for future generations,\" they said.",
"\n\n2018\n\nOn Nov. 5, they confirmed their U.K. tour (beginning June 1, 2019) without Victoria Beckham. (",
"L-R) Brown, Chisholm, Bunton and Halliwell at a live appearance on the \"Heart Breakfast\" show at Global Radio in London on Nov. 7.",
"\n\n35/35 SLIDES\n\nThere's another Star Trek animated series in the works.",
"\nStar Trek is getting a second animated series on CBS All Access, in addition to the recently announced Lower Decks.",
"\n\n— Share news in the SOC. ",
"Networks\n\nTopical videos:\n\nWe Won't Do What You Tell Us | The Hajduk Split Story\n\nThis is a story of resistance and rebellion. ",
"The city of Split and its club Hajduk Split have long been united through beliefs, culture and history. ",
"By looking at their ...\n\nSimilar from the Web\n\nThe Spice Girls , Victoria Beckham \"Posh Spice ,\" Emma Bunton \"Baby Spice ,\" Melanie Chisholm \"Sporty Spice ,\" Melanie Brown \"Scary Spice The singers would reportedly each possess a special \" girl power\" in the film , obviously. ",
"CNN has reached out to representatives of the women for comment.",
"\n\nEmma Bunton Confirms Spice Girls Animated Movie Is in the Works\n\nAceShowbiz - Emma Bunton has confirmed the \" Spice Girls \" is considering making their own animated superhero movie. ",
"According to Variety, the film will focus on a feminist \" girl power\" message - revamping their famous 1990s slogan for a new generation.",
"\n\nThe popular British pop group Spice Girls will be reuniting for an animated film project with a Each character in the movie will be voiced by a Spice Girl and will feature a power unique to each group It’s just what Marvel or Disney needs.” ",
"Simon Fuller, the Spice Girls ’ manager , had no comment.",
"\n\nSpice Girls Reuniting for Animated Superhero Movie\n\nThe popular British pop group Spice Girls will be reuniting for an animated film project with a Each character in the movie will be voiced by a Spice Girl and will feature a power unique to each group It’s just what Marvel or Disney needs.” ",
"Simon Fuller, the Spice Girls ’ manager , had no comment.",
"\n\nSpice Girls animated film reportedly in the works – WSVN 7News\n\nThe Spice Girls , Victoria Beckham “Posh Spice ,” Emma Bunton “Baby Spice ,” Melanie Chisholm “Sporty Spice ,” Melanie Brown “Scary Spice ,” and Geri Halliwell “Ginger Spice ,” have signed off their likenesses to be used in an animated film The Spice Girls recently reunited for a social gathering\n\nAn animated Spice Girls superhero movie is reportedly in the works\n\nFilm . ",
"An animated Spice Girls superhero movie is reportedly in the works . ",
"Nothing has been confirmed just yet, but we’re sure fans will be VERY excited. ",
"They’ve been eagerly awaiting news of a tour or new music from the group since the girls shared an Instagram snap of their reunion in February.",
"\n\nEmma Bunton confirms Spice Girls animated movie is 'something\n\nAll five Spice Girls have reportedly agreed to their likenesses being used, with each character to be voiced by Posh Spice , Scary Spice , Baby Spice , Sporty Spice She also opened up more generally about a Spice Girls reunion, telling Holly and Phil: \"There is definitely something in the pipeline.",
"\n\nThe Spice Girls Are Doing an Animated Superhero Movie\n\n“The Spice Girls are thinking big in terms of a franchise on a global scale. ",
"They’re the most successful girl group on the planet. ",
"It’s just what Marvel or Disney needs.” ",
"The girls at this point have just confirmed they're exploring opportunities as a reunited band with their original manager Simon Fuller.",
"\n\nThe Spice Girls set to voice animated superhero movie | The Guardian\n\nAs part of their comeback, a new project is being assembled which would see the five band-members play heroes with a feminist message.",
"\n\nWith awards season now in full swing, it’s time for the stars of the British small screen to have their moment in the spotlight as Tuesday night plays host to the National Television Awards. ",
"Following a stellar year for mainstream TV in the UK in 2018, the ceremony is set to be a hotly […]\n\nRon shared his bed with a grown man for years. ",
"Every Harry Potter fan has probably imagined what it would be like to attend Hogwarts at some point or another. ",
"The spells you'd like to use, the robes you'd be able to wear, which House you'd be sorted into, the list of magical hijinks goes […]\n\nHe's writing a sequel that takes place 20 years after the events of the original . ",
"Tom Cruise’s first and greatest hot streak as an actor lasted from 1986 to 1990, starting with Top Gun, followed by The Color of Money, Rain Man, Born on the Fourth of July, which got him his first Best […]\n\nSinger Erykah Badu left fans in shock after reportedly defending R Kelly during her concert last night. ",
"Badu was performing at the Aragon Ballroom in Chicago where, according to attendees, she criticised the outcry against the R&B singer following the damning Lifetime documentary […]\n\nThe Fyre Fest fiasco was reignited last week with the release of two documentaries about the festival gone wrong — but Ja Rule, one of the festival’s co-founders, says we still don’t have the whole story. ",
"Hulu’s Fyre Fraud and Netflix's FYRE were both released within days of each other; […]\n\nThe Oscars race has increasingly become a referendum on our national mood and culture. ",
"This year, that mood seems to be: chaos and anger. ",
"The entire awards season has been mired with as much drama behind-the-scenes at the Academy—Best Popular Film! ",
"Kevin Hart!—as there has been on screen […]"
] | {
"pile_set_name": "Pile-CC"
} | [
0.000025951557093425606,
0.00006760411032990806,
0.000044444444444444447,
0.000040569597143900364,
0.00011814744801512288,
0.0000591715976331361,
0.00002657030502710171,
0.00007496111392215288,
0.000244140625,
0,
0.000053279343598486864,
0.0000152587890625,
0.00004565376186997809,
0,
0.00007620789513793629,
0.00010850694444444444,
0.00013520822065981613,
0.00018261504747991235,
0.0000980296049406921,
0.000035430839002267575,
0.00012984764542936286,
0.00012018508503094766,
0.00005080526342529086,
0.0003077870113881194,
0,
0.0000946850145183689,
0.0002642356982428326,
0.0002082465639316951,
0.000041091387245233394,
0.0001232741617357002,
0,
0.00006718624025799517,
0.00005080526342529086,
0.0003077870113881194,
0.00003879547799908442,
0,
0,
0,
0,
0,
0.0002040816326530612,
0,
0,
0,
0,
0.000048902146804244705,
0.00003311221730444476,
0,
0.0002777777777777778,
0.00011573627560665098,
0.000054823058578438094,
0.0002082465639316951,
0.0001575299306868305,
0.000036289737262302225,
0,
0,
0.000028596757127741712,
0,
0,
0.00125,
0.00005406574394463668,
0,
0.00007561436672967865,
0.00014146672702580352,
0.000033412409368839586,
0.000148720999405116,
0.00006037918125830214,
0,
0.0002227667631989307,
0,
0.000042165626581211,
0.00010503833899373271,
0.000033412409368839586,
0,
0.000011284070841396743,
0.000030517578125,
0.00007831466833737959,
0.0000072774554134565,
0.0003652300949598247,
0,
0.00009611687812379854,
0.0002366863905325444,
0,
0.00014863258026159333,
0.0013717421124828531,
0.000062000124000248,
0.00009245562130177516,
0.00005250997689561017,
0.000244140625,
0,
0.000053279343598486864,
0.00005080526342529086,
0.0003077870113881194,
0.00004596380350474002,
0.0003077870113881194,
0.00003099173553719008,
0,
0,
0.000048902146804244705,
0.00003018959062915107,
0,
0,
0.00125,
0.00005406574394463668,
0.000023564897728343855,
0.00002684635829149776,
0.00004565376186997809,
0.00015943877551020407,
0.000021041999831664002,
0.0000616370808678501,
0.000020030847505157944,
0,
0,
0.00008116224332440549,
0.0005408328826392645
] | 0.000109 | 5 |
[
"Q:\n\nHTML/CSS Text overflowing its container\n\nI've been doing this simple page with a text field and two select fields, where I can choose a text color and a text size. ",
"I put some borders with diferent colors to each div to see where are they placed. ",
"The issue I'm having is when I select a bigger size for the text and it overflows the container, but I want the container to grow as the text grows, more clearly, I want the text to be inside the border no matter its size, so the border will get bigger if the text gets bigger.",
"\nI'll put my fiddle link and the css:\nhttp://jsfiddle.net/jdelva/CCLJ4/2/\ncss:\ndiv {\n display:inline;\n}\n\ndiv.main {\n border-style:solid;\n border-width:thin;\n border-color:blue;\n margin-left:60px;\n}\n\ndiv.subject {\n width:3cm;\n border-style:solid;\n border-width:thin;\n border-color:green;\n}\n\n#control {\n border-style:solid;\n border-width:thin;\n border-color:red;\n margin-right:60px;\n}\n\nI tried with the overflow property but it seems to work with the content and not with the container.",
"\nThanks for your time!",
"\n\nA:\n\nYour div has a style of \"display: inline;\", Change that to \"display: inline-block;\"\ndiv\n{\n display:inline;\n}\n\nchange to:\ndiv\n{\n display:inline-block;\n}\n\nThink of it this way. ",
"Inline elements aren't meant to contain block elements. ",
"For instance, a <span> (which is an inline element) can span from the end of one line to the beginning of the other, so it has no well defined width or height:\n..... ..... ..... ..... ..... ..... ..... <span>Hello\nWorld </span> ..... ..... ..... ..... ..... ..... ...\n\nBut you don't want to make it a block (or <div>) either because it takes up the whole line:\n<div>Hello ..... ..... ..... ..... ..... ..... </div>\n<div>World ..... ..... ..... ..... ..... ..... </div>\n\nSo if you declare an element inline-block, you can have several blocks side-by-side\n<div class=\"ib\">Hello</div><div class=\"ib\">World</div>\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0,
0.0000146797610134907,
0,
0,
0.00031887755102040814,
0
] | 0.000042 | 5 |
[
"---\nabstract: |\n Given positive integers $n,k$ with $k\\leq n$, we consider the number of ways of choosing $k$ subsets of ${\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$ in such a way that the union of these subsets gives ${\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$ and they are not subsets of each other. ",
"We refer to such choices of sets as *constructive $k$-covers* and provide a semi-analytic summation formula to calculate the exact number of constructive $k$-covers of ${\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$. ",
"Each term in the summation is the product of a new variant of Stirling numbers of the second kind, referred to as integrated Stirling numbers, and the cardinality of a certain set which we calculate by an optimization-based procedure with no-good cuts for binary variables.\\\n \\\n **Keywords and phrases:** constructive cover, minimal cover, Stirling number of the second kind, integrated Stirling number, permutation group, no-good cut, coherent system, minimal path set, minimal cut set, reliability theory\\\n \\\n **Mathematics Subject Classification (2010):** 05A15, 05A18, 05A19, 05B30, 90B25, 90C09\nauthor:\n- 'Çağ[i]{}n Ararat[^1]'\n- 'Ülkü Gürler[^2]'\n- 'M. Emrullah Ild[i]{}z[^3]'\ndate: 'July 2, 2020'\ntitle: Constructive covers of a finite set\n---\n\nIntroduction {#intro}\n============\n\nLet ${\\mathcal{N}}$ be a set with $n\\in{\\mathbb{N}}\\coloneqq{\\ensuremath{ \\left\\{ 1,2,\\ldots \\right\\} }}$ distinct objects and fix $k\\in{\\mathbb{N}}$. We consider the problem of choosing $k$ subsets $A_1,\\ldots,A_k$ of ${\\mathcal{N}}$ in such a way that these sets cover ${\\mathcal{N}}$, that is, $\\bigcup_{i=1}^k A_i = {\\mathcal{N}}$, and no two of these sets are subsets of each other, that is, $A_i \\setminus A_j \\neq \\emptyset$ for all $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$. We refer to such a cover of ${\\mathcal{N}}$ as a *constructive $k$-cover*. ",
"Due to the second requirement in the preceding definition, it is necessary that $k\\leq n$ for a constructive $k$-cover to exist. ",
"In this paper, we address the following question: *How many ways are there to choose a constructive $k$-cover of ${\\mathcal{N}}$?*",
"\n\nIn the literature, a related problem was considered by T. Hearne, C. Wagner in 1973 and by R. J. Clarke in 1990. ",
"In both of [@hearnewagner] and [@clarke], distinct subsets $A_1,\\ldots,A_k$ of ${\\mathcal{N}}$ are said to form a *minimal $k$-cover* of ${\\mathcal{N}}$ if these sets cover ${\\mathcal{N}}$, and ${\\mathcal{N}}$ cannot be a covered by a strict subcollection of these sets, that is, $\\bigcup_{i\\neq j}A_i\\neq{\\mathcal{N}}$ for all $j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$. ",
"It is easy to observe that a minimal $k$-cover is necessarily a constructive $k$-cover. ",
"As a counterexample for the converse, when $n=4$ and $k=3$, note that the sets $A_1={\\ensuremath{ \\left\\{ 1,2 \\right\\} }}, A_2={\\ensuremath{ \\left\\{ 2,3 \\right\\} }}, A_3={\\ensuremath{ \\left\\{ 1,3,4 \\right\\} }}$ form a constructive $k$-cover but not a minimal $k$-cover. ",
"In [@hearnewagner] and [@clarke], summation-type formulae are provided for the number of minimal $k$-covers of ${\\mathcal{N}}$ (in [@clarke], also for the case where the elements of ${\\mathcal{N}}$ are not necessarily distinguishable). ",
"In the present paper, the requirement that no two sets be subsets of each other makes the problem more involved and it seems that the enumeration ideas in [@clarke] cannot be replicated here to solve the problem. ",
"The one-to-one correspondence between minimal covers and the so-called *split graphs* on $n$ vertices is studied in [@royle]. ",
"The more recent work [@collinstrenk] provides a more detailed analysis of the connection between minimal covers, split graphs and bipartite posets. ",
"In a similar line of research, the so-called *$m$-balanced covers* which consist of sets with cardinality $m$ are studied in [@burger] and a recursive relation is provided for the number of $m$-balanced covers that include the minimum possible number of sets.",
"\n\nThe consideration of constructive $k$-covers is motivated by *coherent systems* in reliability theory. ",
"In [@barlow], a coherent system is described in terms of its set ${\\mathcal{N}}$ of distinct components and the way these components are configured. ",
"The precise configuration of the components is encoded by the so-called *minimal path sets* $P_1,\\ldots,P_k\\subseteq{\\mathcal{N}}$, which are supposed to form a constructive $k$-cover of ${\\mathcal{N}}$. For each $i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$, the components in $P_i$ are interpreted as components that are connected in series, and the sub-systems $P_1,\\ldots,P_k$ are connected in parallel. ",
"The class of coherent systems is rich enough to cover many system configurations in reliability applications. ",
"For instance, the system with ${\\mathcal{N}}={\\ensuremath{ \\left\\{ 1,2,3 \\right\\} }}$ and $P_1={\\ensuremath{ \\left\\{ 1,2 \\right\\} }}, P_2={\\ensuremath{ \\left\\{ 1,3 \\right\\} }}, P_3={\\ensuremath{ \\left\\{ 2,3 \\right\\} }}$ corresponds to a $2$-out-of-$3$ system which functions as long as at least two of the three components function. ",
"Our main result provides a formula to calculate the number of coherent systems with $n$ distinct components and $k$ minimal path sets. ",
"Alternatively, the configuration of the components in a coherent system can also be encoded by the so-called *minimal cut sets* $C_1,\\ldots,C_k$, which are supposed to form a constructive $k$-cover of ${\\mathcal{N}}$ as in the case of minimal path sets. ",
"However, the interpretation of the sets is different in this case: for each $i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$, the components in $C_i$ are interpreted as parallel components and the sub-systems $C_1,\\ldots,C_k$ are connected in series. ",
"Hence, our result also provides the number of coherent systems with $n$ components and $k$ minimal cut sets.",
"\n\nIn the present paper, the analysis of the problem is based on a main formula in Section \\[problemdefn\\] (see Theorem \\[mainthm\\] and Corollary \\[compcor\\]) which partitions the set of constructive $k$-covers into certain Cartesian products of pairs of sets. ",
"In each pair, the cardinality of the first set is a variant of Stirling numbers of the second kind. ",
"This new variant, which we call as *integrated Stirling number (ISN)*, is introduced in Section \\[prelim\\] separately, along with its basic properties. ",
"The second set in each Cartesian product gives rise to an auxilary problem which may also be of independent interest: suppose that we are about to form $k\\in{\\mathbb{N}}$ sets $A_1,\\ldots,A_k$ which partition the world into $2^k$ (disjoint) regions. ",
"We consider all the regions except for the one denoting the intersection of all $k$ sets ($A_1\\cap\\ldots\\cap A_k$) and the one denoting the complement of the union of all $k$ sets ($\\bar{A}_1\\cap\\ldots\\cap \\bar{A}_k$). ",
"Given a number $\\ell\\in{\\ensuremath{ \\left\\{ 1,\\ldots,2^k-2 \\right\\} }}$, how many ways are there to label these $2^k-2$ regions as “non-empty\" and “empty\" so that there are exactly $\\ell$ regions with label “non-empty\" and each set difference $A_i\\setminus A_j$, where $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$, $i\\neq j$, contains at least one region with label “non-empty\"? ",
"Note that this new problem is free of $n$, the cardinality of ${\\mathcal{N}}$, but it depends on $k$, the number of subsets in the constructive cover, as well as the auxiliary variable $\\ell$ which keeps track of the regions that are labeled as “non-empty.\" ",
"While calculating ISNs is an easy task, the above labeling problem is highly nontrivial and requires further analysis. ",
"As a result, when using our method, the level of difficulty in counting the number of constructive $k$-covers of $\\mathcal{N}$ is largely determined by the value of $k$ rather than $n=|\\mathcal{N}|$. In terms of the reliability theory application described above, this implies that our method of counting possible coherent systems is much more sensitive to the number of minimal path (or cut) sets than it is to the number of components.",
"\n\nWe carry out a detailed analysis of the auxiliary labeling problem in Section \\[partitioningsec\\]. ",
"In particular, we exploit three types of symmetries: based on permutations (Section \\[permsym\\]), taking complements (Section \\[compsym\\]), and the so-called *impact sets* (Section \\[impactsym\\]). ",
"These symmetries enable us to define an equivalence relation (Section \\[equiv1\\]) and prove finer results to calculate the answers to the auxiliary problem as well as the original problem. ",
"Finally, in Section \\[nogoodsec\\], we describe the computational procedure based on solving feasibility problems iteratively using *no-good cuts* for binary variables, namely, inequalities that ensure us, in each iteration, to find a solution that is different from the ones found in the former iterations. ",
"Some numerical results are also presented in Section \\[nogoodsec\\]. ",
"The connection between constructive covers and reliability theory, which was our initial motivation to study the subject, is explained in Section \\[reliability\\]. ",
"Section \\[conc\\] is the concluding section. ",
"The elementary proofs of the results in Section \\[prelim\\] are collected in Section \\[app\\], the appendix.",
"\n\nPreliminaries {#prelim}\n=============\n\nWe recall the definition of Stirling numbers of the second kind and introduce *integrated Stirling numbers (ISN)*, a new variant of the former that will be used in the main results of Section \\[problemdefn\\].",
"\n\nLet ${\\mathcal{N}}$ be a set with $n\\in{\\mathbb{N}}\\coloneqq{\\ensuremath{ \\left\\{ 1,2,\\ldots \\right\\} }}$ distinct elements. ",
"Let $\\ell\\in{\\mathbb{N}}$. A finite (ordered) sequence ${\\ensuremath{\\left( B_1,\\ldots,B_\\ell \\right)}}$ of disjoint nonempty subsets of ${\\mathcal{N}}$ is said to be an *ordered $\\ell$-partition* of ${\\mathcal{N}}$ if $$B_1\\cup\\ldots\\cup B_\\ell = {\\mathcal{N}}.$$ Let $S({\\mathcal{N}},\\ell)$ be the set of all ordered $\\ell$-partitions of ${\\mathcal{N}}$.\n\nFor $n,\\ell$ as above, the corresponding *Stirling number (of the second kind)* is defined as $$\\label{StirlingDefn}\ns(n,\\ell)\\coloneqq \\frac{1}{\\ell!}\\sum_{j=0}^\\ell (-1)^{\\ell-j}\\binom{\\ell}{j}j^n.$$ Note that $\\ell!s(n,\\ell)$ gives the number of ordered $\\ell$-partitions of ${\\mathcal{N}}$, that is, $$|S({\\mathcal{N}},\\ell)|=\\ell!s(n,\\ell).$$ It can be checked by induction that $$\\label{Stirlingzero}\ns(n,\\ell)=0$$ for every $n<\\ell$. Moreover, it is well-known that these numbers satisfy the recurrence relation $$s(n+1,\\ell)=\\ell s(n,\\ell)+s(n,\\ell-1),\\quad n\\in{\\mathbb{N}}{\\!\\setminus\\!}{\\ensuremath{ \\left\\{ 1 \\right\\} }},\\ \\ell\\in{\\ensuremath{ \\left\\{ 2,\\ldots,n \\right\\} }}$$ with the boundary conditions $$s(n,n)=1,\\quad s(n,1)=1,\\ n\\in{\\mathbb{N}}.$$\n\nFor each $n\\in{\\mathbb{N}}$ and $\\ell\\in{\\mathbb{N}}$, we define the ISN as $$\\tilde{s}(n,\\ell)\\coloneqq \\frac{1}{\\ell!}\\sum_{j=0}^\\ell (-1)^{\\ell-j}\\binom{\\ell}{j}(j+1)^n.$$ The next proposition will be used to interpret $\\tilde{s}(n,\\ell)$ in terms of the number of ordered $\\ell$-partitions of subsets of ${\\mathcal{N}}$. Its proof is given in Section \\[app\\], the appendix.",
"\n\n\\[workhorse\\] Let $n,\\ell\\in{\\mathbb{N}}$. We have $$\\label{stilderes}\n \\tilde{s}(n,\\ell)=\\sum_{i=1}^n\\binom{n}{i}s(i,\\ell).$$ In particular, the following are valid.",
"\n\n(i) If $n<\\ell$, then $\\tilde{s}(n,\\ell)=0$.\n\n(ii) If $n\\geq \\ell$, then $$\\label{stildeinterpret}\n \\tilde{s}(n,\\ell)=\\sum_{i=\\ell}^n\\binom{n}{i}s(i,\\ell)=\\sum_{i=0}^{n-\\ell}\\binom{n}{i}s(n-i,\\ell).$$\n\n(iii) $\\tilde{s}(n,n)=1$.\n\n(iv) $\\tilde{s}(n,1)=2^n-1$.\n\n\\[interpretation\\] Let $1\\leq\\ell\\leq n$. The relation in Proposition \\[workhorse\\] provides the following characterization of ISNs. ",
"For each $i\\in{\\ensuremath{ \\left\\{ \\ell,\\ldots,n \\right\\} }}$, as mentioned above, $\\ell! ",
"s(i,\\ell)$ is the number of ordered $\\ell$-partitions of a set of $i$ distinguishable objects; hence, $\\binom ni \\ell! ",
"s(i,\\ell)$ gives the total number of ordered $\\ell$-partitions of all subsets of $\\mathcal{N}$ with size $i$. Let $\\tilde{S}({\\mathcal{N}},\\ell)$ be the set of all ordered $\\ell$-partitions of all subsets of ${\\mathcal{N}}$ (with at least size $\\ell$), that is, $$\\label{defnstilde}\n \\tilde{S}({\\mathcal{N}},\\ell)\\coloneqq {\\ensuremath{ \\left\\{ S(\\mathcal{I},\\ell)\\mid \\mathcal{I}\\subseteq{\\mathcal{N}},|\\mathcal{I}|\\geq \\ell \\right\\} }}.$$ Therefore, $$\\label{stildecount}\n |\\tilde{S}({\\mathcal{N}},\\ell)|=\\ell!\\tilde{s}(n,\\ell).$$\n\n\\[stilderec\\] ISNs satisfy the recurrence relation $$\\tilde{s}(n+1,\\ell)=(\\ell+1)\\tilde{s}(n,\\ell)+\\tilde{s}(n,\\ell-1),\\quad n\\in{\\mathbb{N}}{\\!\\setminus\\!}{\\ensuremath{ \\left\\{ 1 \\right\\} }}, \\quad \\ell\\in{\\ensuremath{ \\left\\{ 2,\\ldots,n \\right\\} }}.$$ with the boundary conditions $$\\tilde{s}(n,n)=1,\\ \\tilde{s}(n,1)=2^n-1, \\ n\\in{\\mathbb{N}}.$$\n\nUsing the recurrence relation in , we calculate $\\tilde{s}(n,\\ell)$ for $n\\in{\\ensuremath{ \\left\\{ 1,\\ldots,10 \\right\\} }}$ and $\\ell\\in{\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$ as shown in Table \\[table2\\]. ",
"For completeness, we also provide the values of $s(n,\\ell)$ for the same $(n,\\ell)$ pairs in Table \\[table1\\].",
"\n\n[|c|\\*[10]{}[p[1cm]{}|]{}]{} &$1$ & $ 2$ & $ 3$ & $ 4$ & $5$& $6$ & $ 7$ & $8$ & $9$ & $10$\\\n$ 1$& $1$\\\n$ 2$& $1$ & $1$\\\n$3$& $ 1$ &$3$ &$1$\\\n$4$& $1$ &$7$ & $6$& $1$\\\n$5$& $1$ &$15$&$25$ &$10$ &$1$\\\n$6$& $1$ &$31$&$90$ &$65$ &$15$ & $1$\\\n$7$& $1$ &$63$&$301$ &$350$ &$140$ & $21$ &$1$\\\n$8$& $1$ &$127$&$966$ &$1701$ &$1050$ & $266$ & $28$ &$1$\\\n$9$& $1$ &$255$&$3025$ &$7770$ &$6951$ & $2646$ & $462$ &$36$& $1$\\\n$10$& $1$ &$511$&$9330$ &$34105$ &$42525$ & $22827$ & $5880$ &$750$ & $45$& $1$\\\n\n[|c|\\*[10]{}[p[1cm]{}|]{}]{} &$1$ & $ 2$ & $ 3$ & $ 4$ & $5$& $6$ & $ 7$ & $8$ & $9$ & $10$\\\n$ 1$& $1$\\\n$ 2$& $3$ & $1$\\\n$3$& $ 7$ &$6$ &$1$\\\n$4$& $15$ &$25$ & $10$& $1$\\\n$5$& $31$ &$90$&$65$ &$15$ &$1$\\\n$6$& $63$ &$301$&$350$ &$140$ &$21$ & $1$\\\n$7$& $127$ &$966$&$1701$ &$1050$ &$266$ & $28$ &$1$\\\n$8$& $255$ &$3025$&$7770$ &$6951$ &$2646$ & $462$ & $36$ &$1$\\\n$9$& $511$ &$9330$&$34105$ &$42525$ &$22827$ & $5880$ & $750$ &$45$& $1$\\\n$10$& $1023$ &$28501$&$145750$ &$246730$ &$179487$ & $63987$ & $11880$ &$1155$ & $55$& $1$\\\n\nConstructive covers and sets of labelings {#problemdefn}\n=========================================\n\nAs in the previous section, we consider a set ${\\mathcal{N}}$ of $n\\in{\\mathbb{N}}$ distinct elements. ",
"Let $k\\in{\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$.",
"\n\n\\[kcover\\] A finite sequence ${\\mathscr{A}}={\\ensuremath{\\left( A_1,\\ldots,A_k \\right)}}$ of distinct subsets of ${\\mathcal{N}}$ is said to be a constructive ordered $k$-cover of ${\\mathcal{N}}$ if it satisfies the following conditions.",
"\n\n(i) The sets in ${\\mathscr{A}}$ cover ${\\mathcal{N}}$, that is, $\\bigcup_{i=1}^k A_i= {\\mathcal{N}}$.\n\n(ii) Two distinct sets in ${\\mathscr{A}}$ are not subsets of each other, that is, $A_i{\\!\\setminus\\!}A_j\\neq\\emptyset$ for every $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$.\n\nLet $C({\\mathcal{N}},k)$ be the set of all distinct constructive $k$-covers of ${\\mathcal{N}}$. Our aim is to provide a characterization of the set $C({\\mathcal{N}},k)$ that also helps computing its cardinality $ |C({\\mathcal{N}},k)|$.\n\n\\[unordered\\] Note that one can also define a constructive *unordered* $k$-cover of ${\\mathcal{N}}$ as a collection ${\\ensuremath{ \\left\\{ A_1,\\ldots,A_k \\right\\} }}$ of distinct subsets of ${\\mathcal{N}}$ satisfying the two conditions above. ",
"Clearly, the number of all distinct constructive unordered $k$-covers of ${\\mathcal{N}}$ is $|C({\\mathcal{N}},k)|/k!$.\n\nLet ${\\mathscr{A}}={\\ensuremath{\\left( A_1,\\ldots,A_k \\right)}}$ be a constructive ordered $k$-cover of ${\\mathcal{N}}$. Consider a binary index vector $t=(t_1,\\ldots,t_k)\\in{\\ensuremath{ \\left\\{ e,c \\right\\} }}^k$ ($e$ for “excluded,\" $c$ for “contained\") and define the set $$B_t({\\mathscr{A}})\\coloneqq {\\ensuremath{\\left( \\bigcap_{i\\colon t_i=c}A_i \\right)}} \\cap{\\ensuremath{\\left( \\bigcap_{i\\colon t_i=e}\\bar{A}_i \\right)}},$$ where $\\bar{A}$ denotes the complement of a subset $A$ of ${\\mathcal{N}}$. Hence, ${\\mathscr{A}}$ gives rise to $2^k$ disjoint (possibly empty) sets $B_t({\\mathscr{A}})$, $t\\in{\\ensuremath{ \\left\\{ e,c \\right\\} }}^k$.\n\nTo be more specific, let $k=5$ and $t=(e,e,c,e,c)$. Then, $$B_t({\\mathscr{A}})=\\bar{A}_1\\cap \\bar{A}_2\\cap A_3\\cap \\bar{A}_4\\cap A_5.$$\n\nTwo cases need special attention in the above construction. ",
"The special vector $\\mathbf{e}\\coloneqq(e,\\ldots,e)$ corresponds to $$B_{\\mathbf{e}}({\\mathscr{A}})=\\bar{A}_1\\cap\\ldots \\cap \\bar{A}_k,$$ which must be equal to the empty set since ${\\mathscr{A}}$ is a constructive ordered $k$-cover. ",
"On the other hand, the special vector $\\mathbf{c}\\coloneqq(c,\\ldots,c)$ corresponds to $$B_{\\mathbf{c}}({\\mathscr{A}})=A_1\\cap\\ldots \\cap A_k$$ and the definition of constructive ordered $k$-cover does not impose any non-emptiness condition on this set. ",
"Next, we introduce the index sets $$\\label{tk}\n{\\mathbb{T}}(k)\\coloneqq {\\ensuremath{ \\left\\{ e,c \\right\\} }}^k {\\!\\setminus\\!}{\\ensuremath{ \\left\\{ \\mathbf{e},\\mathbf{c} \\right\\} }},\\quad {\\mathbb{T}}^\\ast(k) \\coloneqq {\\ensuremath{ \\left\\{ e,c \\right\\} }}^k{\\!\\setminus\\!}{\\ensuremath{ \\left\\{ \\mathbf{e} \\right\\} }},$$ and rewrite the conditions (i) and (ii) in Definition \\[kcover\\] as follows.",
"\n\n(i) $\\bigcup_{i=1}^k A_i=\\bigcup_{t\\in{\\mathbb{T}}^\\ast(k)}B_t({\\mathscr{A}})={\\mathcal{N}}$.\n\n(ii) For every $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$, $$A_i{\\!\\setminus\\!}A_j = \\bigcup_{t\\in{\\mathbb{T}}(k)\\colon t_i=c, t_j=e}B_t({\\mathscr{A}})\\neq \\emptyset.$$\n\nNote that condition (ii) depends on the sets $B_t({\\mathscr{A}}), t\\in{\\mathbb{T}}(k)$, only through the *non-emptiness* of certain unions of these sets. ",
"Indeed, for each $t\\in{\\mathbb{T}}(k)$, let us introduce the binary number $$x_t({\\mathscr{A}})\\coloneqq \\begin{cases}1&\\text{ if }B_t({\\mathscr{A}})\\neq\\emptyset,\\\\ 0&\\text{ if }B_t({\\mathscr{A}})=\\emptyset.\\end{cases}$$ Hence, condition (ii) is equivalent to having $$\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=c, t_j=e}x_t({\\mathscr{A}})\\geq 1$$ for every $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$. Let us define $$\\label{defng}\nG(k)\\coloneqq{\\ensuremath{ \\left\\{ (x_t)_{t\\in{\\mathbb{T}}(k)}\\mid \\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=c, t_j=e}x_t\\geq 1\\ \\forall i\\neq j,\\ x_t\\in{\\ensuremath{ \\left\\{ 0,1 \\right\\} }}\\ \\forall t\\in{\\mathbb{T}}(k) \\right\\} }}.$$ Since ${\\mathscr{A}}$ is a constructive ordered $k$-cover of ${\\mathcal{N}}$, we necessarily have $(x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)}\\in G(k)$. Let us also define for each $\\ell\\in{\\ensuremath{ \\left\\{ 1,\\ldots, 2^{k}-2 \\right\\} }}$ the set $$\\label{DefnOfF}\nF(k,\\ell)\\coloneqq{\\ensuremath{ \\left\\{ (x_t)_{t\\in{\\mathbb{T}}(k)}\\in G(k)\\mid\\sum_{t\\in{\\mathbb{T}}(k)}x_t=\\ell \\right\\} }},$$ which is the set of all labelings in $G(k)$ where exactly $\\ell$ sets are labeled as “non-empty.\" ",
"In short, we refer to $F(k,\\ell)$ as the set of all $(k,\\ell)$-labelings. ",
"We have $$\\label{disjointunion}\nG(k)=\\bigcup_{\\ell=1}^{2^k-2}F(k,\\ell),$$ which is a disjoint union. ",
"Hence, we obtain $$|G(k)|=\\sum_{\\ell=1}^{2^k-2}|F(k,\\ell)|.$$\n\nIn the following example, we illustrate the notation and the structure of the sets defined above.",
"\n\nLet us consider the case $k=3$. We have $$\\label{tkorder}\n {\\mathbb{T}}(3)={\\ensuremath{ \\left\\{ (c,e,e),(e,c,e),(e,e,c),(c,c,e),(c,e,c),(e,c,c) \\right\\} }}.$$ Then, we can write the corresponding set $G(3)$ as $$\\begin{aligned}\n G(3)=\\Big\\{(x_t)_{t\\in{\\mathbb{T}}(3)}\\mid \\ & x_{(c,e,e)}+x_{(c,e,c)}\\geq 1,\\ x_{(e,c,e)}+x_{(e,c,c)}\\geq 1,\\ x_{(c,e,e)}+x_{(c,c,e)}\\geq 1,\\\\\n &x_{(e,e,c)}+x_{(e,c,c)}\\geq 1,\\ x_{(e,c,e)}+x_{(c,c,e)}\\geq 1,\\ x_{(e,e,c)}+x_{(c,e,c)}\\geq 1,\\\\\n & x_t\\in{\\ensuremath{ \\left\\{ 0,1 \\right\\} }}\\ \\forall t\\in{\\mathbb{T}}(3)\\Big\\}.",
"\n \\end{aligned}$$ Hence, for each $\\ell\\in{\\ensuremath{ \\left\\{ 1,\\ldots,6 \\right\\} }}$, $$\\begin{aligned}\n F(3,\\ell)=\\Big\\{(x_t)_{t\\in{\\mathbb{T}}(3)}\\mid \\ & x_{(c,e,e)}+x_{(c,e,c)}\\geq 1,\\ x_{(e,c,e)}+x_{(e,c,c)}\\geq 1,\\ x_{(c,e,e)}+x_{(c,c,e)}\\geq 1,\\\\\n &x_{(e,e,c)}+x_{(e,c,c)}\\geq 1,\\ x_{(e,c,e)}+x_{(c,c,e)}\\geq 1,\\ x_{(e,e,c)}+x_{(c,e,c)}\\geq 1,\\\\\n &x_{(e,e,c)}+x_{(e,c,e)}+x_{(e,c,c)}+x_{(c,e,e)}+x_{(c,e,c)}+x_{(c,c,e)}=\\ell\n \\Big\\}.",
"\n \\end{aligned}$$ We observe that $F(3,1)=F(3,2)=\\emptyset$. Further, we can explicitly express $F(3,3)$ as $$\\begin{aligned}\n &F(3,3)={\\ensuremath{ \\left\\{ (c,c,c,e,e,e),(e,e,e,c,c,c) \\right\\} }},\\\\\n &F(3,4)=\\{(c,e,e,c,c,c),(e,c,e,c,c,c),(e,e,c,c,c,c),(c,c,c,c,e,e),(c,c,c,e,c,e),(c,c,c,e,e,c),\\\\\n &\\quad\\quad\\quad \\quad \\quad (c,c,e,e,c,c),(c,e,c,c,e,c),(e,c,c,c,c,e)\\},\\\\\n &F(3,5)={\\ensuremath{ \\left\\{ (c,c,c,c,c,e),(c,c,c,c,e,c),(c,c,c,e,c,c),(c,c,e,c,c,c),(c,c,e,c,c,c),(e,c,c,c,c,c) \\right\\} }},\\\\\n &F(3,6)={\\ensuremath{ \\left\\{ (c,c,c,c,c,c) \\right\\} }},\n \\end{aligned}$$ following the order in . ",
"Hence, $$G(3)=F(3,3)\\cup F(3,4)\\cup F(3,5)\\cup F(3,6).$$\n\nUsing , we may write $$C({\\mathcal{N}},k)=\\bigcup_{\\ell=1}^{2^{k}-2}{\\ensuremath{ \\left\\{ {\\mathscr{A}}\\in C({\\mathcal{N}},k)\\mid (x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell) \\right\\} }}$$ as a disjoint union so that $$\\label{subthm}\n|C({\\mathcal{N}},k)|=\\sum_{\\ell=1}^{2^k-2}|{\\ensuremath{ \\left\\{ {\\mathscr{A}}\\in C({\\mathcal{N}},k)\\mid (x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell) \\right\\} }}|.$$\n\nThe next theorem is the main result of the paper. ",
"Up to isomorphisms, it characterizes $C({\\mathcal{N}},k)$ as a disjoint union of Cartesian products of basic sets. ",
"For two sets $E_1,E_2$, we write $E_1\\cong E_2$ if there is a bijection $f\\colon E_1\\to E_2$.\n\n\\[mainthm\\] For each $\\ell\\in{\\ensuremath{ \\left\\{ 1,\\ldots,2^k-2 \\right\\} }}$, it holds $$\\label{congell}\n {\\ensuremath{ \\left\\{ {\\mathscr{A}}\\in C({\\mathcal{N}},k)\\mid (x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell) \\right\\} }}\\cong\\tilde{S}(n,\\ell) \\times F(k,\\ell).$$ In particular, $$\\label{cong}\n C({\\mathcal{N}},k)\\cong\\bigcup_{\\ell=1}^{2^k-2}\\tilde{S}(n,\\ell) \\times F(k,\\ell).$$\n\nLet $\\ell\\in{\\ensuremath{ \\left\\{ 1,\\ldots,2^k-2 \\right\\} }}$. ",
"Let ${\\mathscr{A}}=(A_1,\\ldots,A_k)\\in C({\\mathcal{N}},k)$ with $(x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell)$. In other words, ${\\mathscr{A}}$ is a constructive ordered $k$-cover of ${\\mathcal{N}}$ for which exactly $\\ell$ of the sets $B_t({\\mathscr{A}})$, $t\\in{\\mathbb{T}}(k)$, are nonempty. ",
"Denoting by $\\prec$ the strict lexicographical ordering on ${\\mathbb{T}}(k)$, let us order these $\\ell$ indices as $t^1({\\mathscr{A}})\\prec\\ldots\\prec t^\\ell({\\mathscr{A}})$. Then, $\\mathcal{B}({\\mathscr{A}})\\coloneqq (B_{t^1({\\mathscr{A}})}({\\mathscr{A}}),\\ldots,B_{t^\\ell({\\mathscr{A}})}({\\mathscr{A}}))$ is an ordered $\\ell$-partition of $\\mathcal{N}{\\!\\setminus\\!}B_{\\mathbf{c}}({\\mathscr{A}})$. Hence, $\\mathcal{B}({\\mathscr{A}})\\in S(\\mathcal{N}{\\!\\setminus\\!}B_{\\mathbf{c}}({\\mathscr{A}}),\\ell)\\subseteq \\tilde{S}({\\mathcal{N}},\\ell)$ by .",
"\n\nThe above construction establishes the mapping $$\\label{mapping}\n {\\mathscr{A}}\\mapsto (\\mathcal{B}({\\mathscr{A}}),(x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)})$$ from ${\\ensuremath{ \\left\\{ {\\mathscr{A}}\\in C({\\mathcal{N}},k)\\mid (x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell) \\right\\} }}$ to $\\tilde{S}({\\mathcal{N}},\\ell)\\times F(k,\\ell)$. To check that this mapping is injective, let ${\\mathscr{A}}^\\prime=(A^\\prime_1,\\ldots,A^\\prime_k)\\in C({\\mathcal{N}},k)$ be another constructive ordered $k$-cover such that $(x_t({\\mathscr{A}}^\\prime))_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell)$. Suppose that $$(x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)}=(x_t({\\mathscr{A}}^\\prime))_{t\\in{\\mathbb{T}}(k)},\\quad \\mathcal{B}({\\mathscr{A}})=\\mathcal{B}({\\mathscr{A}}^\\prime).$$ The first supposition guarantees that ${\\mathscr{A}}$ and ${\\mathscr{A}}^\\prime$ agree on the nonemptiness of their corresponding sets $B_t({\\mathscr{A}}), B_t({\\mathscr{A}}^\\prime)$ for each $t\\in{\\mathbb{T}}(k)$. In other words, $$B_t({\\mathscr{A}})=\\emptyset\\quad\\Leftrightarrow\\quad B_t({\\mathscr{A}}^\\prime)=\\emptyset$$ for each $t\\in{\\mathbb{T}}(k)$. Moreover, from the definition of lexicographical ordering, it follows that $$t^1\\coloneqq t^1({\\mathscr{A}})=t^1({\\mathscr{A}}^\\prime),\\ldots, t^\\ell\\coloneqq t^\\ell({\\mathscr{A}})=t^\\ell({\\mathscr{A}}^\\prime).$$ Then, by the second supposition, we have $$B_{t^1}({\\mathscr{A}})=B_{t^1}({\\mathscr{A}}^\\prime),\\ldots, B_{t^\\ell}({\\mathscr{A}})=B_{t^\\ell}({\\mathscr{A}}^\\prime).$$ Hence, $$B_t({\\mathscr{A}})=B_t({\\mathscr{A}}^\\prime)$$ for every $t\\in{\\mathbb{T}}(k)$. Since $\\bigcup_{i=1}^k A_i = \\bigcup_{i=1}^k A^\\prime_i={\\mathcal{N}}$, we also have $$B_{\\mathbf{c}}({\\mathscr{A}})=B_{\\mathbf{c}}({\\mathscr{A}}^\\prime).$$ Finally, we have $$A_i= {\\ensuremath{\\left( \\bigcup_{t\\in{\\mathbb{T}}(k)\\colon t_i=c}B_t({\\mathscr{A}}) \\right)}}\\cup B_{\\mathbf{c}}({\\mathscr{A}})= {\\ensuremath{\\left( \\bigcup_{t\\in{\\mathbb{T}}(k)\\colon t_i=c}B_t({\\mathscr{A}}^\\prime) \\right)}}\\cup B_{\\mathbf{c}}({\\mathscr{A}}^\\prime)=A^\\prime_i$$ for every $i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ so that ${\\mathscr{A}}={\\mathscr{A}}^\\prime$. This finishes the proof of injectivity.",
"\n\nNext, we show that the mapping in is surjective. ",
"Let $\\mathcal{B}=(\\bar{B}_1,\\ldots,\\bar{B}_\\ell)\\in \\tilde{S}({\\mathcal{N}},\\ell)$ and $(x_t)_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell)$. Hence, by in Remark \\[interpretation\\], there exists $\\mathcal{I}\\subseteq{\\mathcal{N}}$ with $|\\mathcal{I}|\\geq \\ell$ such that $\\mathcal{B}\\in S(\\mathcal{I},\\ell)$. Let us set $$B_{\\mathbf{c}}\\coloneqq {\\mathcal{N}}{\\!\\setminus\\!}{\\ensuremath{\\left( \\bar{B}_1\\cup\\ldots\\cup \\bar{B}_{\\ell} \\right)}}={\\mathcal{N}}{\\!\\setminus\\!}\\mathcal{I}.$$ On the other hand, consider the set of all $t\\in{\\mathbb{T}}(k)$ for which $x_t =1$. Since $(x_t)_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell)$, there are $\\ell$ such indices in ${\\mathbb{T}}(k)$. As before, let us order them as $t^1\\prec\\ldots\\prec t^\\ell$ using the lexicographical ordering and set $$B_{t^1}\\coloneqq \\bar{B}_1,\\ldots, B_{t^\\ell}\\coloneqq \\bar{B}_\\ell$$ and $$B_t\\coloneqq \\emptyset$$ for every $t\\in{\\mathbb{T}}(k){\\!\\setminus\\!}{\\ensuremath{ \\left\\{ t^1,\\ldots,t^\\ell \\right\\} }}$. ",
"Then, let $$A_i\\coloneqq {\\ensuremath{\\left( \\bigcup_{t\\in{\\mathbb{T}}(k)\\colon t_i=c}B_t \\right)}}\\cup B_{\\mathbf{c}}$$ for each $i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ and ${\\mathscr{A}}\\coloneqq (A_1,\\ldots,A_k)$. It is clear that $\\bigcup_{i=1}^k A_i={\\mathcal{N}}$. Moreover, the assumption that $(x_t)_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell)\\subseteq G(k)$ guarantees that $A_i{\\!\\setminus\\!}A_j\\neq\\emptyset$ for every $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$. Finally, by construction of the mapping in , we conclude that $\\mathcal{B}({\\mathscr{A}})=\\mathcal{B}$ and $(x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)}=(x_t)_{t\\in{\\mathbb{T}}(k)}$. This shows that every element of $\\tilde{S}({\\mathcal{N}},\\ell)\\times F(k,\\ell)$ is the value of the mapping in for some ${\\mathscr{A}}\\in C({\\mathcal{N}},\\ell)$ with $(x_t({\\mathscr{A}}))_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell)$.\n\nTherefore, follows. ",
"As an immediate consequence of disjointness, holds as well.",
"\n\n\\[compcor\\] It holds $$|C({\\mathcal{N}},k)|=\\sum_{\\ell=1}^{(2^k-2)\\wedge n}\\ell!\\tilde{s}(n,\\ell) |F(k,\\ell)|.$$\n\nBy in Remark \\[interpretation\\], $|\\tilde{S}(n,\\ell)\\times F(k,\\ell)|=\\ell!\\tilde{s}(n,\\ell) |F(k,\\ell)|$ for each $\\ell\\in{\\ensuremath{ \\left\\{ 1,\\ldots,2^k-2 \\right\\} }}$. ",
"Hence, the corollary follows from Theorem \\[mainthm\\].",
"\n\nNext, we aim to refine the result of Corollary \\[compcor\\] by showing that $F(k,\\ell)$ is the empty set for small values of $\\ell$. To that end, for a subset $T\\subseteq{\\mathbb{T}}(k)$ and $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$, let us define $$u_{ij}(T)\\coloneqq\\sum_{t\\in T}1_{{\\ensuremath{ \\left\\{ c \\right\\} }}}(t_i)1_{{\\ensuremath{ \\left\\{ e \\right\\} }}}(t_j).$$\n\n\\[ell0result\\] Let $$\\ell_0(k)\\coloneqq \\min{\\ensuremath{ \\left\\{ \\abs{T}\\mid u_{ij}(T)\\geq 1\\ \\forall i\\neq j,\\ T\\subseteq{\\mathbb{T}}(k) \\right\\} }}$$ Then, for every $\\ell\\in{\\ensuremath{ \\left\\{ 1,\\ldots,2^k-2 \\right\\} }}$, $$\\ell \\geq \\ell_0(k)\\quad\\Leftrightarrow\\quad F(k,\\ell)\\neq \\emptyset.$$ In particular, $$\\ell_0(k)=\\min{\\ensuremath{ \\left\\{ \\ell\\mid F(k,\\ell)\\neq\\emptyset \\right\\} }}.$$\n\nLet $\\ell\\in{\\ensuremath{ \\left\\{ 1,\\ldots,2^k-2 \\right\\} }}$. ",
"Suppose that $\\ell\\geq\\ell_0(k)$. Let $T^\\ast\\subseteq{\\mathbb{T}}(k)$ such that $|T^\\ast|=\\ell_0(k)$ and $u_{ij}(T^\\ast)\\geq 1$ for every $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$. By adding $\\ell-\\ell_0$ more elements to $T^\\ast$ arbitrarily, one can find a set $T\\subseteq{\\mathbb{T}}(k)$ such that $T^\\ast\\subseteq T$ and $|T|=\\ell$. For each $t\\in{\\mathbb{T}}(k)$, let us define a binary variable $x_t$ by $x_t=1$ if $t\\in T$ and $x_t=0$ if $T\\in{\\mathbb{T}}(k){\\!\\setminus\\!}T$. The assumed properties of $T^\\ast$ ensure that $(x_t)_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell)$. Hence, $F(k,\\ell)\\neq \\emptyset$. In particular, the case $\\ell=\\ell_0$ implies that $\\ell_0(k)\\geq \\min{\\ensuremath{ \\left\\{ \\ell\\mid F(k,\\ell)\\neq\\emptyset \\right\\} }}$.",
"\n\nFor the converse, suppose that $F(k,\\ell)\\neq \\emptyset$. Let $(x_t)_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell)$ and $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$. By the definition of $F(k,\\ell)$, there exists $t(i,j)\\in {\\mathbb{T}}(k)$ such that $x_{t(i,j)}=1$, $t(i,j)_i=c$, $t(i,j)_j=e$. Let $$T={\\ensuremath{ \\left\\{ t(i,j)\\mid i\\neq j \\right\\} }}.$$ Note that $$u_{ij}(T)=\\sum_{t\\in T}1_{{\\ensuremath{ \\left\\{ c \\right\\} }}}(t_i)1_{{\\ensuremath{ \\left\\{ e \\right\\} }}}(t_j)\\geq 1_{{\\ensuremath{ \\left\\{ c \\right\\} }}}(t(i,j)_i)1_{{\\ensuremath{ \\left\\{ e \\right\\} }}}(t(i,j)_j)=1\\cdot 1=1.$$ Hence, $\\ell_0(k)\\leq |T|$. By the definition of $F(k,\\ell)$ again, $$\\ell_0(k)\\leq |T|\\leq \\sum_{i\\neq j}x_{t(i,j)}\\leq \\sum_{t\\in{\\mathbb{T}}(k)}x_t=\\ell.$$ Hence, $\\ell_0(k)\\leq \\ell$. In particular, $\\ell_0(k)\\leq \\min{\\ensuremath{ \\left\\{ \\ell\\mid F(k,\\ell)\\neq\\emptyset \\right\\} }}$.",
"\n\n\\[ell0forcounting\\] It holds $$|C({\\mathcal{N}},k)|=\\sum_{\\ell=\\ell_0(k)}^{(2^k-2)\\wedge n}\\ell!\\tilde{s}(n,\\ell) |F(k,\\ell)|.$$\n\nThis is an immediate consequence of Corollary \\[compcor\\] and Proposition \\[ell0result\\].",
"\n\nPartitioning the sets of labelings {#partitioningsec}\n==================================\n\nBy Theorem \\[mainthm\\] and Corollary \\[ell0forcounting\\] of Section \\[problemdefn\\], we are able to calculate the cardinality of the set $C({\\mathcal{N}}, k)$ of constructive $k$-covers of ${\\mathcal{N}}$ in terms of ISNs $\\tilde{s}(n,\\ell)$ as well as the cardinalities of the sets $F(k,\\ell)$ of $(k,\\ell)$-labelings for a range of $\\ell$ values. ",
"While it is easy to numerically calculate ISNs by and , the calculation of $|F(k,\\ell)|$ by brute force enumeration could be quite difficult even for small values of $k,\\ell$. In this section, we introduce three notions of symmetry for the sets $F(k,\\ell)$, $\\ell\\in{\\ensuremath{ \\left\\{ \\ell_0(k),\\ldots,2^k-2 \\right\\} }}$, which yield an equivalence relation. ",
"It turns out that the equivalence classes of this relation provide substantial reduction in the computational effort to find the cardinalities $|F(k,\\cdot)|$. Let $k\\in{\\mathbb{N}}$. Let us fix a nonempty subset $T$ of ${\\mathbb{T}}(k)$. We call $T$ the *branching set* of index vectors. ",
"Let us define $$\\mathcal{Z}_T(k)\\coloneqq {\\ensuremath{ \\left\\{ y=(y_t)_{t\\in T}\\mid y_t\\in{\\ensuremath{ \\left\\{ 0,1 \\right\\} }}\\ \\forall t\\in T \\right\\} }}.$$ We also fix $\\ell\\in{\\mathbb{N}}$ with $\\ell_0(k)\\leq \\ell\\leq 2^k-2$, where $\\ell_0(k)$ is defined as in Proposition \\[ell0result\\]. ",
"In particular, $F(k,\\ell)\\neq\\emptyset$. We may consider partitioning $F(k,\\ell)$ with respect to the possible ways of assigning the binary variables $x_t$ associated to all $t\\in T$. The next definition formalizes this idea.",
"\n\n\\[DefnOfFm\\] Let $y_t\\in{\\ensuremath{ \\left\\{ 0,1 \\right\\} }}$ for each $t\\in T$. Then, the set of all $(k,\\ell)$-labelings with respect to $y= (y_t)_{t\\in T}$ is defined as $$F_{y}(k,\\ell)\\coloneqq{\\ensuremath{ \\left\\{ (x_t)_{t\\in{\\mathbb{T}}(k)}\\in F(k,\\ell)\\mid x_t = y_t \\ \\forall t\\in T \\right\\} }}.$$\n\nIf $\\sum_{t\\in T}y_t >\\ell$, then $F_{y}(k,\\ell)=\\emptyset$ obviously. ",
"Let us introduce the set $$\\mathcal{Y}_T(k,\\ell)\\coloneqq {\\ensuremath{ \\left\\{ y=(y_t)_{t\\in T}\\in\\mathcal{Z}_T(k)\\mid \\sum_{t\\in T}y_t \\leq \\ell \\right\\} }}.$$\n\nGiven $y\\in {\\mathcal{Y}}_T(k,\\ell)$, depending on the structure of $T$ and $y$, the set $F_y(k,\\ell)$ may still be empty. ",
"Nevertheless, such cases will be detected in the computational procedure presented later in this section and we do not need to distinguish them *a priori* in the theoretical development.",
"\n\nWe begin with a simple result that provides a partitioning of $F(k,\\ell)$ into smaller sets.",
"\n\n\\[PropBranch\\] Let $y,z\\in{\\mathcal{Y}}_T(k,\\ell)$.\n\n(i) $F_{y}(k, \\ell) \\cap F_{z}(k, \\ell) = \\emptyset$ if $y\\neq z$.\n\n(ii) It holds $$F(k,\\ell)=\\bigcup_{y\\in {\\mathcal{Y}}_T(k,\\ell)}F_{y}(k, \\ell).$$\n\nIn particular, $$|F(k, \\ell)| = \\sum_{y\\in {\\mathcal{Y}}_T(k,\\ell)} |F_y(k, \\ell)|.$$\n\n(i) This is an immediate consequence of Definition \\[DefnOfFm\\].",
"\n\n(ii) The $\\supseteq$ part of the equality is obvious since $F_{y}(k, \\ell) \\subseteq F(k, \\ell)$ for each $y\\in {\\mathcal{Y}}_T(k,\\ell)$. For the $\\subseteq$ part, let $(x_t)_{t\\in{\\mathbb{T}}(k)}\\in F(k, \\ell)$. Let us define $y=(y_t)_{t\\in T}$ by setting $y_t\\coloneqq x_t$ for each $t\\in T$. Then, $\\sum_{t\\in T}y_t= \\sum_{t\\in T}x_t\\leq\\sum_{t\\in{\\mathbb{T}}(k)}x_t=\\ell$ so that $y\\in{\\mathcal{Y}}_T(k,\\ell)$. Clearly, we also have $(x_t)_{t\\in {\\mathbb{T}}(k)}\\in F_{y}(k,\\ell)$. Hence, the $\\subseteq$ part of the equality follows.",
"\n\nThe last statement follows directly from (i) and (ii).",
"\n\nWhile Proposition \\[PropBranch\\] partitions $F(k,\\ell)$ into the smaller sets $F_y(k,\\ell)$, $y\\in{\\mathcal{Y}}_T(k,\\ell)$, it may still be computationally expensive to calculate the cardinality of each of these sets by an enumerative method. ",
"By introducing three notions of symmetry below, we show that the cardinalities $|F_y(k,\\ell)|$ are repeated for many $y\\in{\\mathcal{Y}}_T(k,\\ell)$ so that we only need to calculate the distinct values of these cardinalities and the number of times each cardinality value is repeated.",
"\n\nA symmetry based on permutations {#permsym}\n--------------------------------\n\nThe first notion of symmetry we introduce is based on permutations. ",
"To that end, let us denote by $\\mathbb{S}_k$ the symmetric group of ${\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$, that is, the set of all permutations $\\pi\\colon{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}\\to{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$. ",
"Let $\\pi\\in{\\mathbb{S}}_k$. Given $t=(t_1,\\ldots,t_k)\\in {\\ensuremath{ \\left\\{ e,c \\right\\} }}^k$, we may consider $t$ as a function $t\\colon{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}\\to {\\ensuremath{ \\left\\{ e,c \\right\\} }}$ and define the composition $t\\circ \\pi \\colon{\\ensuremath{ \\left\\{ 1,\\ldots, k \\right\\} }}\\to{\\ensuremath{ \\left\\{ e,c \\right\\} }}$ by $$(t\\circ \\pi)(i)=(t\\circ\\pi)_i\\coloneqq t_{\\pi(i)},\\quad i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }},$$ or, we may simply define $t\\circ \\pi$ as the vector $$t\\circ \\pi = ((t\\circ \\pi)_1,\\ldots,(t\\circ\\pi)_k)\\coloneqq (t_{\\pi(1)},\\ldots, t_{\\pi(k)})\\in{\\ensuremath{ \\left\\{ e,c \\right\\} }}^k.$$ From the definition of ${\\mathbb{T}}(k)$ (see ), it is clear that $t\\circ \\pi \\in {\\mathbb{T}}(k)$ if and only if $t\\in{\\mathbb{T}}(k)$. Let us introduce the set $$T^\\pi \\coloneqq {\\ensuremath{ \\left\\{ t\\circ \\pi \\mid t\\in T \\right\\} }}.$$ We call $T$ symmetric with respect to $\\pi$ if $T=T^\\pi$. In particular, it is always the case that ${\\mathbb{T}}(k)$ is symmetric with respect to $\\pi$. We denote by ${\\mathbb{S}}_k^T$ the set of all permutations with respect to which $T$ is symmetric, that is, $${\\mathbb{S}}_k^T \\coloneqq{\\ensuremath{ \\left\\{ \\pi\\in{\\mathbb{S}}_k\\mid T=T^\\pi \\right\\} }}.$$ Note that ${\\mathbb{S}}_k^T\\neq\\emptyset$ as we always have $T=T^\\pi$ when $\\pi$ is the identity permutation.",
"\n\nThe next proposition formulates how the number of $(k,\\ell)$-labelings associated to a vector $y\\in{\\mathcal{Y}}_T(k,\\ell)$ changes under the application of a permutation.",
"\n\n\\[equalityofcard\\] Let $\\pi\\in{\\mathbb{S}}_k^T$ and $y\\in {\\mathcal{Y}}_T(k,\\ell)$. Define $y^\\pi=(y^\\pi_t)_{t\\in T}$ by $$y^\\pi_t \\coloneqq y_{t\\circ \\pi},\\quad t\\in T.$$ Then, $y^\\pi \\in {\\mathcal{Y}}_T(k,\\ell)$ and $|F_y(k,\\ell)|=|F_{y^\\pi}(k,\\ell)|$.\n\nSince $y\\in{\\mathcal{Y}}_T(k,\\ell)$ and $T=T^\\pi$, we have $$\\sum_{t\\in T}y^\\pi_t = \\sum_{t\\in T}y_{t\\circ\\pi}=\\sum_{t\\in T}y_t \\leq \\ell.$$ Hence, $y^\\pi\\in {\\mathcal{Y}}_T(k,\\ell)$.\n\nTo prove that $|F_y(k,\\ell)|=|F_{y^\\pi}(k,\\ell)|$, it is sufficient to establish a bijection from $F_y(k,\\ell)$ into $F_{y^\\pi}(k,\\ell)$. To that end, given $(x_t)_{t\\in {\\mathbb{T}}(k)}\\in F_y(k,\\ell)$, let us define $(x^\\pi_t)_{t\\in {\\mathbb{T}}(k)}$ by $$x^\\pi_t = x_{t\\circ \\pi},\\quad t\\in {\\mathbb{T}}(k).$$ We first show that $(x^\\pi_t)_{t\\in{\\mathbb{T}}(k)}\\in F_{y^\\pi}(k,\\ell)$. Let $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$. Denoting the inverse permuatation of $\\pi$ by $\\pi^{-1}$, we have $$\\begin{aligned}\n\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=e,t_j=c}x^\\pi_t\n&= \\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=e,t_j=c}x_{t\\circ \\pi}\\\\\n&=\\sum_{t\\in{\\mathbb{T}}(k)\\colon (t\\circ\\pi)_{\\pi^{-1}(i)}=e,(t\\circ\\pi)_{\\pi^{-1}(j)}=c}x_{t\\circ \\pi}\\\\\n&=\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_{\\pi^{-1}(i)}=e,t_{\\pi^{-1}(j)}=c}x_{t},\\end{aligned}$$ where we make a change of variables using the fact that ${\\mathbb{T}}(k)=({\\mathbb{T}}(k))^\\pi$ in order to get the last equality. ",
"Since $i\\neq j$, we have $\\pi^{-1}(i)\\neq \\pi^{-1}(j)$. As we also have $(x_t)_{t\\in{\\mathbb{T}}(k)}\\in G(k)$ (see ), it follows that $$\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=e,t_j=c}x^\\pi_t=\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_{\\pi^{-1}(i)}=e,t_{\\pi^{-1}(j)}=c}x_{t}\\geq 1.$$ Similarly, since ${\\mathbb{T}}(k)=({\\mathbb{T}}(k))^\\pi$, $$\\sum_{t\\in{\\mathbb{T}}(k)}x^\\pi_t = \\sum_{t\\in {\\mathbb{T}}(k)}x_{t\\circ\\pi}=\\sum_{t\\in{\\mathbb{T}}(k)}x_t = \\ell.$$ On the other hand, for each $t\\in T$, we have $t\\circ\\pi\\in T$ so that $$x^\\pi_t = x_{t\\circ \\pi} = y_{t\\circ \\pi}=y^\\pi_t.$$ Therefore, $(x^\\pi_t)_{t\\in{\\mathbb{T}}(k)}\\in F_{y^\\pi}(k,\\ell)$.\n\nIt remains to check that the mapping $(x_t)_{t\\in{\\mathbb{T}}(k)}\\mapsto (x_t^\\pi)_{t\\in{\\mathbb{T}}(k)}$ is indeed a bijection from $F_y(k,\\ell)$ into $F_{y^\\pi}(k,\\ell)$. Let $(x_t)_{t\\in {\\mathbb{T}}(k)},$ $(\\bar{x}_t)_{t\\in{\\mathbb{T}}(k)}\\in F_y(k,\\ell)$ such that $x_t^\\pi =\\bar{x}_t^\\pi$ for every $t\\in{\\mathbb{T}}(k)$, that is, $x_{t\\circ \\pi}=\\bar{x}_{t\\circ\\pi}$ for every $t\\in{\\mathbb{T}}(k)$. Since ${\\mathbb{T}}(k)=({\\mathbb{T}}(k))^\\pi$, this is equivalent to having $x_t = \\bar{x}_t$ for every $t\\in{\\mathbb{T}}(k)$. Hence, $(x_t)_{t\\in{\\mathbb{T}}(k)}\\mapsto (x_t^\\pi)_{t\\in{\\mathbb{T}}(k)}$ is injective. ",
"Next, let $(z_t)_{t\\in{\\mathbb{T}}(k)}\\in F_{y^\\pi}(k,\\ell)$. Let us define $(x_t)_{t\\in{\\mathbb{T}}(k)}$ by $$x_t \\coloneqq z^{\\pi^{-1}}_t=z_{t\\circ \\pi^{-1}},\\quad t\\in{\\mathbb{T}}(k).$$ Let $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ such that $i\\neq j$. Hence, we have $\\pi(i)\\neq\\pi(j)$ so that $$\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=e,\\ t_j=c}x_t=\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=e,\\ t_j=c} z_{t\\circ \\pi^{-1}}=\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_{\\pi(i)}=e,\\ t_{\\pi(j)}=c} z_{t}\\geq 1.$$ Next, since ${\\mathbb{T}}(k)=({\\mathbb{T}}(k))^{\\pi^{-1}}$, we have $$\\sum_{t\\in{\\mathbb{T}}(k)}x_t = \\sum_{t\\in{\\mathbb{T}}(k)}z_{t\\circ \\pi^{-1}}=\\sum_{t\\in{\\mathbb{T}}(k)}z_t = \\ell.$$ On the other hand, since $T=T^\\pi$, we also have $T=T^{\\pi^{-1}}$. Hence, for each $t\\in T$, we have $t\\circ\\pi^{-1}\\in T$ so that $$x_t = z_{t\\circ\\pi^{-1}}=y_{t\\circ \\pi^{-1}}^{\\pi}=y_t.$$ Therefore, $(x_t)_{t\\in{\\mathbb{T}}(k)}\\in F_y(k,\\ell)$, that is, $(x_t)_{t\\in{\\mathbb{T}}(k)}\\mapsto (x_t^\\pi)_{t\\in{\\mathbb{T}}(k)}$ is surjective as well.",
"\n\nA symmetry based on taking complements {#compsym}\n--------------------------------------\n\nIn addition to the above notion of permutation-based symmetry, we introduce a second type of symmetry based on taking “complements,” that is, based on changing the roles of $e$ and $c$ in the index vectors. ",
"To be more precise, let us define two mappings $\\alpha_1,\\alpha_2\\colon{\\ensuremath{ \\left\\{ e,c \\right\\} }}\\to{\\ensuremath{ \\left\\{ e,c \\right\\} }}$ by $$\\alpha_1(e)=\\alpha_2(c)=e,\\quad \\alpha_1(c)=\\alpha_2(e)=c.$$ In other words, $\\alpha_1$ is the identity mapping and $\\alpha_2$ switches $e$ and $c$. Let us formally define the set $\\mathbb{A}={\\ensuremath{ \\left\\{ \\alpha_1,\\alpha_2 \\right\\} }}$, which is indeed the symmetric group of ${\\ensuremath{ \\left\\{ e,c \\right\\} }}$. ",
"Let $\\alpha\\in\\mathbb{A}$. Similar to what is done in Section \\[permsym\\], we may regard each $t=(t_1,\\ldots,t_k)\\in{\\ensuremath{ \\left\\{ e,c \\right\\} }}^k$ as a function $t\\colon{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}\\to{\\ensuremath{ \\left\\{ e,c \\right\\} }}$ and define the composition $\\alpha\\circ t\\colon {\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}\\to{\\ensuremath{ \\left\\{ e,c \\right\\} }}$ by $$(\\alpha\\circ t)(i)=(\\alpha\\circ t)_i \\coloneqq \\alpha(t_i),\\quad i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }},$$ or, we define $\\alpha\\circ t$ as the vector $$\\alpha\\circ t = {\\ensuremath{\\left( (\\alpha\\circ t)_1,\\ldots,(\\alpha\\circ t)_k \\right)}}\\coloneqq {\\ensuremath{\\left( \\alpha(t_1),\\ldots,\\alpha(t_k) \\right)}}\\in {\\ensuremath{ \\left\\{ e,c \\right\\} }}^k.$$ Clearly, $\\alpha\\circ t\\in{\\mathbb{T}}(k)$ if and only if $t\\in {\\mathbb{T}}(k)$. Let us also define $$T^\\alpha \\coloneqq {\\ensuremath{ \\left\\{ \\alpha\\circ t\\mid t\\in T \\right\\} }}$$ and $$\\mathbb{A}^T \\coloneqq {\\ensuremath{ \\left\\{ \\alpha\\in \\mathbb{A}\\mid T=T^\\alpha \\right\\} }}.$$ Since $\\alpha_1$ is the identity mapping, we always have $T=T^{\\alpha_1}$ so that $\\mathbb{A}^T \\neq \\emptyset$.\n\nIn the next proposition, we relate the numbers of $(k,\\ell)$-labelings associated to a vector $y\\in{\\mathcal{Y}}_T(k,\\ell)$ before and after taking complements.",
"\n\n\\[equalityofcard2\\] Let $\\alpha\\in \\mathbb{A}^T$ and $y\\in {\\mathcal{Y}}_T(k,\\ell)$. Define ${}^\\alpha y=({}^\\alpha y_t)_{t\\in T}$ by $${}^\\alpha y_t \\coloneqq y_{\\alpha\\circ t},\\quad t\\in T.$$ Then, ${}^\\alpha y\\in {\\mathcal{Y}}_T(k,\\ell)$ and $|F_y(k,\\ell)|=|F_{{}^\\alpha y}(k,\\ell)|$.\n\nThe result is trivial for $\\alpha=\\alpha_1$. Let us assume that $\\alpha=\\alpha_2$. Since $y\\in{\\mathcal{Y}}_T(k,\\ell)$ and $T=T^{\\alpha}$, we have $$\\sum_{t\\in T}{}^\\alpha y_t = \\sum_{t\\in T}y_{\\alpha\\circ t}=\\sum_{t\\in T}y_t \\leq \\ell.$$ Hence, ${}^\\alpha y\\in {\\mathcal{Y}}_T(k,\\ell)$.\n\nTo prove that $|F_y(k,\\ell)|=|F_{{}^\\alpha y}(k,\\ell)|$, we construct a bijection from $F_y(k,\\ell)$ to $F_{{}^\\alpha y}(k,\\ell)$ as follows. ",
"Given $(x_t)_{t\\in{\\mathbb{T}}(k)}\\in F_y(k,\\ell)$, let us define $({}^\\alpha x_t)_{t\\in{\\mathbb{T}}(k)}$ by $${}^\\alpha x_t =x_{\\alpha \\circ t},\\quad t\\in{\\mathbb{T}}(k).$$ Let $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$. Since $(x_t)_{t\\in {\\mathbb{T}}(k)}\\in G(k)$, we have $$\\begin{aligned}\n \\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=e,t_j=c}{}^\\alpha x_t &= \\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=e,t_j=c}x_{\\alpha \\circ t}\\\\\n &= \\sum_{t\\in{\\mathbb{T}}(k)\\colon \\alpha(t_i)=c,\\alpha(t_j)=e}x_{\\alpha \\circ t}\\\\\n &=\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=c,t_j=e}x_t\\geq 1.",
"\n \\end{aligned}$$ Similarly, $$\\sum_{t\\in{\\mathbb{T}}(k)}{}^\\alpha x_t= \\sum_{t\\in{\\mathbb{T}}(k)}x_{\\alpha \\circ t}=\\sum_{t\\in{\\mathbb{T}}(k)}x_t = \\ell$$ and $${}^\\alpha x_t = x_{\\alpha \\circ t}=y_{\\alpha \\circ t}={}^\\alpha y_t,\\quad t\\in T.$$ Hence, $({}^\\alpha x_t)_{t\\in{\\mathbb{T}}(k)}\\in F_{{}^\\alpha y}(k,\\ell)$. Using a similar argument as in the proof of Proposition \\[equalityofcard\\], it can be shown that the mapping $(x_t)_{t\\in{\\mathbb{T}}(k)}\\mapsto ({}^\\alpha x_t)_{t\\in{\\mathbb{T}}(k)}$ is a bijection. ",
"The details are omitted.",
"\n\nA symmetry based on impact sets {#impactsym}\n-------------------------------\n\nIn this subsection, we introduce a third notion of symmetry based on the idea that two binary vectors $y,z\\in\\mathcal{Z}_T(k)$ might impose the same set of constraints in the definition of $G(k)$, see , which we will refer to as the *impact set* of these vectors.",
"\n\nGiven $y=(y_t)_{t\\in T}\\in\\mathcal{Z}_T(k)$, we define the *impact set* ${\\mathcal{D}}_T(y)$ of $y$ as $${\\mathcal{D}}_T(y)\\coloneqq {\\ensuremath{ \\left\\{ (i,j)\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}^2\\mid \\exists t\\in T\\colon (t_i=c\\ \\wedge\\ \\ t_j=e\\ \\wedge\\ y_t=1) \\right\\} }}.$$ The next theorem provides a relationship for the values of $|F_y(k,\\cdot)|$ and $|F_z(k,\\cdot)|$ when $y,z\\in\\mathcal{Z}_T(k)$ have the same impact set.",
"\n\n\\[simeqprop\\] Let $y,z\\in \\mathcal{Z}_T(k)$ be such that ${\\mathcal{D}}_T(y)={\\mathcal{D}}_T(z)$. Let $$w \\coloneqq \\sum_{t\\in T}y_t - \\sum_{t\\in T}z_t.$$ Suppose that $w\\geq 0$. The following results hold.",
"\n\n(i) $|F_y(k,\\ell+w)|=|F_z(k,\\ell)|$ for every $\\ell\\in{\\mathbb{N}}$ such that $\\ell_0(k)\\leq \\ell \\leq \\ell+w\\leq 2^k-2$.\n\n(ii) $|F_y(k,\\ell+w)|=0$ for every $\\ell\\in{\\mathbb{N}}$ such that $\\ell< \\ell_0(k)\\leq \\ell+w$.\n\n(iii) $|F_z(k,\\ell)|=0$ for every $\\ell\\in{\\mathbb{N}}$ such that $\\ell\\leq 2^k-2 <\\ell+w$.\n\nWe consider the sets $F_y(k,\\ell), F_z(k,\\ell)$ defined by for every $\\ell\\in{\\mathbb{N}}$. (Hence, we extend the definition in for $\\ell\\geq 2^k-2$). ",
"Let us fix $\\ell\\in{\\mathbb{N}}$. We establish a bijection from $F_z(k,\\ell)$ to $F_y(k,\\ell+w)$. Given $x=(x_t)_{t\\in{\\mathbb{T}}(k)}\\in F_z(k,\\ell)$, let us define $\\bar{x}=(\\bar{x}_t)_{t\\in{\\mathbb{T}}(k)}$ by $$\\bar{x}_t = \\begin{cases}y_t&\\text{if } t\\in T,\\\\ x_t & \\text{if }t\\notin T.\\end{cases}$$ Let $i,j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ with $i\\neq j$. First, suppose that $(i,j)\\in {\\mathcal{D}}_T(y)={\\mathcal{D}}_T(z)$. Hence, there exists $t^1\\in T$ such that $t^1_i=c$, $t^1_j=e$, $y_{t^1}=1$. So $$\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=c,t_j=e}\\bar{x}_t\\geq \\bar{x}_{t^1}=y_{t^1}=1.$$ Next, suppose that $(i,j)\\notin {\\mathcal{D}}_T(y)={\\mathcal{D}}_T(z)$. Since $x\\in F_z(k,\\ell)$, there exists $t^2\\in {\\mathbb{T}}(k)\\setminus T$ such that $t^2_i=c$, $t^2_j=e$, $x_{t^2}=1$. So $$\\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=c,t_j=e}\\bar{x}_t\\geq \\bar{x}_{t^2}=x_{t^2}=1.$$ Moreover, $$\\sum_{t\\in {\\mathbb{T}}(k)}\\bar{x}_t = \\sum_{t\\in T}y_t +\\sum_{t\\in{\\mathbb{T}}(k)\\setminus T}x_t =\\sum_{t\\in T}y_t +\\ell - \\sum_{t\\in T}x_t=\\sum_{t\\in T}y_t +\\ell - \\sum_{t\\in T}z_t=\\ell+w.$$ Hence, $\\bar{x}\\in F_y(k,\\ell+w)$.\n\nNext, we show that the mapping $x\\mapsto \\bar{x}$ is a bijection from $F_z(k,\\ell)$ into $F_y(k,\\ell+w)$. Let $x^1=(x^1_t)_{t\\in{\\mathbb{T}}(k)}, x^2=(x^2_t)_{t\\in {\\mathbb{T}}(k)}\\in F_z(k,\\ell)$ such that their images are equal, that is, $\\bar{x}^1_t = \\bar{x}^2_t$ for every $t\\in{\\mathbb{T}}(k)$. From the definition of the mapping, it is immediate that $x^1_t=x^2_t$ for every $t\\in {\\mathbb{T}}(k)\\setminus T$. On the other hand, $x^1_t=x^2_t=z_t$ for every $t\\in T$ since $x^1,x^2\\in F_z(k,\\ell)$. Therefore, $x^1=x^2$. This proves that the mapping is injective. ",
"Let $\\tilde{x}=(\\tilde{x}_t)_{t\\in{\\mathbb{T}}(k)}\\in F_y(k,\\ell+w)$. Define $x=(x_t)_{t\\in{\\mathbb{T}}(k)}$ by $$x_t=\\begin{cases}z_t&\\text{if }t\\in T,\\\\ \\tilde{x}_t&\\text{if }t\\notin T.\\end{cases}$$ It is not difficult to check that $x\\in F_z(k,\\ell)$ and $\\bar{x}=\\tilde{x}$, which shows that the mapping is surjective. ",
"Hence, thanks to the bijection, we conclude that $|F_y(k,\\ell+w)|=|F_z(k,\\ell)|$ for every $\\ell\\in{\\mathbb{N}}$. If $\\ell<\\ell_0(k)$, then $F_z(k,\\ell)=\\emptyset$ so that $F_y(k,\\ell+w)=\\emptyset$ as well. ",
"Similarly, if $2^k-2<\\ell+w $, then $F_y(k,\\ell+w)=\\emptyset$ so that $F_z(k,\\ell)=\\emptyset$ as well. ",
"Hence, all three results hold.",
"\n\nEquivalence relation for the symmetries {#equiv1}\n---------------------------------------\n\nGiven $t\\in {\\mathbb{T}}(k)$, $x_t\\in{\\ensuremath{ \\left\\{ e,c \\right\\} }}$, $\\pi\\in{\\mathbb{S}}_k$ and $\\alpha\\in\\mathbb{A}$, note that $$({}^\\alpha x_t)^\\pi = {}^\\alpha (x^\\pi_t)=x_{\\alpha\\circ t\\circ \\pi}.$$ Hence, we simply write ${}^\\alpha x^\\pi_t\\coloneqq x_{\\alpha\\circ t\\circ \\pi}$ for the common value. ",
"On $\\mathcal{Z}_T(k)$, let us define the relation $\\equiv$ by $$\\label{equivalence}\ny\\equiv z\\quad \\Leftrightarrow\\quad \\exists(\\pi,\\alpha)\\in{\\mathbb{S}}_k^T\\times\\mathbb{A}^T\\colon {\\mathcal{D}}_T(z)={\\mathcal{D}}_T({}^\\alpha y^\\pi)$$ for each $y=(y_t)_{t\\in T},z=(z_t)_{t\\in T}\\in\\mathcal{Z}_T(k)$.\n\n\\[equivrel\\] The relation $\\equiv$ defined by is an equivalence relation on $\\mathcal{Z}_T(k)$.\n\nThe reflexivity of $\\equiv$ follows since the identity permutation on ${\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ is always a member of ${\\mathbb{S}}_k^T$. To show that $\\equiv$ is symmetric, let $y,z\\in \\mathcal{Z}_T(k)$ such that $y\\equiv z$. So ${\\mathcal{D}}_T(z)={\\mathcal{D}}_T({}^\\alpha y^\\pi)$ for some $\\pi\\in{\\mathbb{S}}_k^T$ and $\\alpha\\in\\mathbb{A}^T$. Then, $$T^{\\pi^{-1}}={\\ensuremath{ \\left\\{ t\\circ \\pi^{-1}\\mid t\\in T \\right\\} }}={\\ensuremath{ \\left\\{ \\bar{t}\\circ\\pi\\circ\\pi^{-1}\\mid \\bar{t}\\in T \\right\\} }}=T$$ since $T=T^{\\pi}$. So $\\pi^{-1}\\in{\\mathbb{S}}_k^T$. On the other hand, it is easy to see that $\\alpha^{-1}=\\alpha$. We claim that ${\\mathcal{D}}_T(y)={\\mathcal{D}}_T({}^\\alpha z^{\\pi^{-1}})$. To show this, first, let $(i,j)\\in{\\mathcal{D}}_T(y)$. So there exists $t\\in T$ such that $t_i=c$, $t_j=e$, $y_t=1$. Letting $t^\\prime\\coloneqq \\alpha\\circ t\\circ \\pi^{-1}$, we may write $t=\\alpha\\circ t^\\prime\\circ \\pi$. In particular, we have the following:\n\n(i) $t^\\prime_{\\pi(i)}=\\alpha(t_{\\pi^{-1}(\\pi(i))})=\\alpha(t_i)=\\alpha(c)$.\n\n(ii) $t^{\\prime}_{\\pi(j)}=\\alpha(t_{\\pi^{-1}(\\pi(j))})=\\alpha(t_j)=\\alpha(e)$.\n\n(iii) ${}^\\alpha y_{t^\\prime}^{\\pi}=y_{\\alpha\\circ t^{\\prime}\\circ \\pi}=y_t=1$.\n\nIt follows that $(\\pi(i),\\pi(j))\\in{\\mathcal{D}}_T({}^\\alpha y^{\\pi})$ if $\\alpha=\\alpha_1$, and $(\\pi(j),\\pi(i))\\in{\\mathcal{D}}_T({}^\\alpha y^{\\pi})$ if $\\alpha=\\alpha_2$. Let us consider the case $\\alpha=\\alpha_1$. Since $(\\pi(i),\\pi(j))\\in{\\mathcal{D}}_T({}^\\alpha y^{\\pi})={\\mathcal{D}}_T(z)$, there exists $t^{\\prime\\prime}\\in T$ such that $t^{\\prime\\prime}_{\\pi(i)}=c$, $t^{\\prime\\prime}_{\\pi(j)}=e$, $z_{t^{\\prime\\prime}}=1$. Let us define $t^{\\prime\\prime\\prime}\\coloneqq \\alpha\\circ t^{\\prime\\prime}\\circ \\pi$ so that $t^{\\prime\\prime}=\\alpha\\circ t^{\\prime\\prime\\prime}\\circ \\pi^{-1}$. In particular, we have the following:\n\n(i) $t^{\\prime\\prime\\prime}_{i}=\\alpha(t^{\\prime\\prime}_{\\pi(i)})=\\alpha(c)=c$.\n\n(ii) $t^{\\prime\\prime\\prime}_{j}=\\alpha(t^{\\prime\\prime}_{\\pi(j)})=\\alpha(e)=e$.\n\n(iii) ${}^\\alpha z_{t^{\\prime\\prime\\prime}}^{\\pi^{-1}}=z_{\\alpha\\circ t^{\\prime\\prime\\prime}\\circ \\pi^{-1}}=z_{t^{\\prime\\prime}}=1$.\n\nHence, $(i,j)\\in {\\mathcal{D}}_T({}^\\alpha z^{\\pi^{-1}})$. The case $\\alpha=\\alpha_2$ can be treated by similar arguments and we obtain $(i,j)\\in {\\mathcal{D}}_T({}^\\alpha z^{\\pi^{-1}})$ as well. ",
"Hence, ${\\mathcal{D}}_T(y)\\subseteq {\\mathcal{D}}_T({}^\\alpha z^{\\pi^{-1}})$.\n\nConversely, let $(i,j)\\in {\\mathcal{D}}_T({}^\\alpha z^{\\pi^{-1}})$. So there exists $t\\in T$ such that $t_i=c$, $t_j=e$, ${}^\\alpha z^{\\pi^{-1}}_t=1$. Let $t^\\prime\\coloneqq\\alpha\\circ t \\circ \\pi^{-1}$. In a similar way as above, we have $t^\\prime_{\\pi(i)}=\\alpha(c)$, $t^{\\prime}_{\\pi(j)}=\\alpha(e)$, $z_{t^\\prime}=1$, that is, $(\\pi(i),\\pi(j))\\in {\\mathcal{D}}_T(z)$ if ${\\alpha}={\\alpha}_1$, and $(\\pi(j),\\pi(i))\\in {\\mathcal{D}}_T(z)$ if ${\\alpha}={\\alpha}_2$. Suppose that ${\\alpha}={\\alpha}_1$. In this case, since $(\\pi(i),\\pi(j))\\in {\\mathcal{D}}_T(z)={\\mathcal{D}}_T({}^\\alpha y^\\pi)$, there exists $t^{\\prime\\prime}\\in T$ such that $t^{\\prime\\prime}_{\\pi(i)}=c$, $t^{\\prime\\prime}_{\\pi(j)}=e$, ${}^{\\alpha}y^\\pi_{t^{\\prime\\prime}}=1$. Let $t^{\\prime\\prime\\prime}\\coloneqq \\alpha\\circ t^{\\prime\\prime}\\circ \\pi$. Then, we have $t^{\\prime\\prime\\prime}_i={\\alpha}(c)=c$, $t^{\\prime\\prime\\prime}_j={\\alpha}(e)=e$, $y_{t^{\\prime\\prime\\prime}}=1$ so that $(i,j)\\in {\\mathcal{D}}_T(y)$. Similarly, we may show that $(i,j)\\in {\\mathcal{D}}_T(y)$ in the case ${\\alpha}={\\alpha}_2$ as well. ",
"Hence, ${\\mathcal{D}}_T({}^\\alpha z^{\\pi^{-1}})\\subseteq{\\mathcal{D}}_T(y)$. This completes the proof of ${\\mathcal{D}}_T(y)={\\mathcal{D}}_T({}^\\alpha z^{\\pi^{-1}})$. Therefore, $z\\equiv y$.\n\nTo show that $\\equiv$ is transitive, let $y,z,v\\in \\mathcal{Z}_T(k)$ such that $y\\equiv z$ and $z\\equiv v$. So ${\\mathcal{D}}_T(z)={\\mathcal{D}}_T({}^\\alpha y^\\pi)$ and ${\\mathcal{D}}_T(v)={\\mathcal{D}}_T({}^\\beta z^{\\sigma})$ for some $\\pi,\\sigma\\in{\\mathbb{S}}_k^T$ and $\\alpha,\\beta\\in\\mathbb{A}^T$. Since $T^\\pi=T^{\\sigma}=T$, we also have $T^{\\sigma\\circ \\pi}={\\ensuremath{ \\left\\{ t\\circ\\sigma\\circ \\pi\\mid t\\in T \\right\\} }}={\\ensuremath{ \\left\\{ \\bar{t}\\circ \\pi \\mid \\bar{t}\\in T \\right\\} }}=T$ so that $\\sigma\\circ\\pi\\in{\\mathbb{S}}_k^T$. On the other hand, $\\alpha\\circ\\beta $ is either equal to $\\alpha_1$ or to $\\alpha_2$ so that $\\alpha\\circ\\beta\\in\\mathbb{A}^T$. We claim that ${\\mathcal{D}}_T(v)={\\mathcal{D}}_T({}^{\\alpha\\circ\\beta}y^{\\sigma\\circ\\pi})$.\n\nTo prove the claim, let $(i,j)\\in {\\mathcal{D}}_T(v)$. Since ${\\mathcal{D}}_T(v)={\\mathcal{D}}_T({}^\\beta z^{\\sigma})$, there exists $t\\in T$ such that $t_i=c$, $t_j=e$, ${}^\\beta z^\\sigma_t=1$. Letting $t^\\prime=\\beta\\circ t\\circ\\sigma$, we have $t^\\prime_{\\sigma^{-1}(i)}\\coloneqq\\beta(c)$, $t^\\prime_{\\sigma^{-1}(j)}=\\beta(e)$, $z_{t^\\prime}=1$. Hence, $(\\sigma^{-1}(i),\\sigma^{-1}(j))\\in{\\mathcal{D}}_T(z)$ if $\\beta={\\alpha}_1$, and $(\\sigma^{-1}(j),\\sigma^{-1}(i))\\in{\\mathcal{D}}_T(z)$ if $\\beta={\\alpha}_2$. Suppose that $\\beta={\\alpha}_1$. Since $(\\sigma^{-1}(i),\\sigma^{-1}(j))\\in{\\mathcal{D}}_T(z)={\\mathcal{D}}_T({}^\\alpha y^\\pi)$, there exists $t^{\\prime\\prime}\\in T$ such that $t^{\\prime\\prime}_{\\sigma^{-1}(i)}=c$, $t^{\\prime\\prime}_{\\sigma^{-1}(j)}=e$, ${}^\\alpha y^\\pi_{t^{\\prime\\prime}}=1$. Letting $t^{\\prime\\prime\\prime}=\\beta\\circ t^{\\prime\\prime}\\circ\\sigma^{-1}$, we have $t^{\\prime\\prime\\prime}_i=c$, $t^{\\prime\\prime\\prime}_i=e$, ${}^{\\alpha\\circ\\beta}y^{\\sigma\\circ\\pi}_{t^{\\prime\\prime\\prime}}={}^{{\\alpha}}y^{\\pi}_{t^{\\prime\\prime}}=1$. Hence, $(i,j)\\in{\\mathcal{D}}_T({}^{\\alpha\\circ\\beta}y^{\\sigma\\circ\\pi})$. Similarly, we can reach the same conclusion when ${\\beta}={\\alpha}_2$. So ${\\mathcal{D}}_T(v)\\subseteq {\\mathcal{D}}_T({}^{\\alpha\\circ\\beta}y^{\\sigma\\circ\\pi})$. The proof of $ {\\mathcal{D}}_T({}^{\\alpha\\circ\\beta}y^{\\sigma\\circ\\pi})\\subseteq {\\mathcal{D}}_T(v)$ is similar, hence we omit it. ",
"So we have $y\\equiv v$. Therefore, $\\equiv$ is an equivalence relation on $\\mathcal{Z}_T(k)$.\n\nNext, we address the role of Proposition \\[equivrel\\] for computational purposes. ",
"Note that the relation $\\equiv$ partitions $\\mathcal{Z}_T(k)$ into equivalence classes; let us denote them by $\\mathcal{Z}_{T,1}(k),\\ldots,\\mathcal{Z}_{T,A}(k)$, where $A\\in{\\mathbb{N}}$ is the number of distinct classes. ",
"Algorithm \\[alg1\\] shows the precise steps of the main procedure in which these classes are calculated. ",
"The two subroutines of this procedure that are used to find the equivalent elements with respect to $\\equiv$ are given in Algorithm \\[alg2\\] and Algorithm \\[alg3\\]. ",
"Let $a\\in{\\ensuremath{ \\left\\{ 1,\\ldots,A \\right\\} }}$ and let $z^{T,a}$ be a fixed representative element of $\\mathcal{Z}_{T,a}(k)$. For each $y\\in\\mathcal{Z}_{T,a}(k)$, the relationship between $|F_{y}(k,\\cdot)|$ and $|F_{z^{T,a}}(k,\\cdot)|$ is formulated by Theorem \\[simeqprop\\]: indeed, letting $$w(y,a)\\coloneqq \\sum_{t\\in T}y_{t}-\\sum_{t\\in T}z^{T,a}_t,$$ we have $$\\begin{aligned}\n|F_{y}(k,\\ell)|=\\begin{cases}\n|F_{z^{T,a}}(k,\\ell-w(y,a))|&\\text{if }\\ell,\\ell-w(y,a)\\in{\\ensuremath{ \\left\\{ \\ell_0(k),\\ldots,2^{k}-2 \\right\\} }},\\\\ \n0 &\\text{else}.\\end{cases}\\label{shift}\\end{aligned}$$ Therefore, the values $|F_y(k,\\cdot)|$ for a given $y\\in\\mathcal{Z}_{T,a}(k)$ can be calculated by a “shift\" of the values $|F_{z^{T,a}}(k,\\cdot)|$ according to . ",
"This will be illustrated further in Example \\[k=4ex\\] and Example \\[k=5ex\\] in the next section.",
"\n\nLet us introduce some additional notation that will make the presentation of the examples simpler. ",
"First, without loss of generality, we assume that $z^{T,a}$ achieves the minimum possible sum $\\sum_{t\\in T}y_t$ among all $y\\in \\mathcal{Z}_{T,a}(k)$; hence $w(y,a)\\geq 0$ for each $y\\in\\mathcal{Z}_{T,a}(k)$ and $w(z^{T,a},a)=0$. Let ${\\mathcal{W}}(a)$ be the set of all possible values of $w(y,a)$, that is, $${\\mathcal{W}}(a)\\coloneqq{\\ensuremath{ \\left\\{ w(y,a)\\mid y\\in\\mathcal{Z}_{T,a}(k) \\right\\} }},$$ which is a finite subset of ${\\mathbb{Z}}_+={\\ensuremath{ \\left\\{ 0,1,2,\\ldots \\right\\} }}$. ",
"For each $w\\in{\\mathcal{W}}(a)$, let us define $$\\mathcal{Z}_{T,a,w}(k)={\\ensuremath{ \\left\\{ y\\in\\mathcal{Z}_{T,a}(k)\\mid w(y,a)=w \\right\\} }}.$$ Hence, we may partition $\\mathcal{Z}_{T,a}(k)$ as $$\\mathcal{Z}_{T,a}(k)=\\bigcup_{w\\in{\\mathcal{W}}(a)}\\mathcal{Z}_{T,a,w}(k).$$ We fix one representative $z^{T,a,w}\\in \\mathcal{Z}_{T,a,w}(k)$ for each $w\\in{\\mathcal{W}}(a)$ such that $z^{T,a,0}=z^{T,a}$. Hence, in view of Proposition \\[PropBranch\\], we may write $$|F(k,\\ell)|=\\sum_{a=1}^A \\sum_{w\\in{\\mathcal{W}}(a)}|F_{z^{T,a,w}}(k,\\ell)|\\cdot|\\mathcal{Z}_{T,a,w}(k)|$$ for each $\\ell\\in{\\ensuremath{ \\left\\{ \\ell_0(k),\\ldots,2^k-2 \\right\\} }}$. ",
"We will use these notation and reformulations in the examples of the next section.",
"\n\n$\\bar{\\mathcal{D}}_{T} \\gets \\emptyset $ $\\bar{\\mathcal{D}}_{T} \\gets \\bar{\\mathcal{D}}_{T}\\cup \\mathcal{D}_{T}(y) $ $asymmetricMatrices \\gets \\emptyset$ $A \\gets 0$ $symmetryMatrix \\gets \\algvar{generateSymmetryMatrix}(\\bar{\\mathcal{D}}_{T}, y, T)$ $a \\gets \\algvar{findEquivalenceClass}(symmetryMatrix, asymmetricMatrices, \\bar{\\mathcal{D}}_{T} )$ $A\\gets A+1$ $\\mathcal{Z}_{T,A}(k)\\gets \\{y\\}$ $z^{T,A}\\gets y$ $asymmetricMatrices \\gets asymmetricMatrices \\cup {\\ensuremath{ \\left\\{ symmetryMatrix \\right\\} }}$ $\\mathcal{Z}_{T,a}(k)\\gets \\mathcal{Z}_{T,a}(k)\\cup\\{y\\}$ ${\\mathcal{W}}(a) \\gets \\emptyset$ $w \\gets \\sum_{t\\in T}y_t-\\sum_{t\\in T}z^{T,a}_{t}$ $\\mathcal{Z}_{T, a, w} \\gets \\mathcal{Z}_{T, a, w} \\cup \\{y\\}$ ${\\mathcal{W}}(a) \\gets {\\mathcal{W}}(a) \\cup \\{ w \\}$ $\\mathcal{Z}_{T, a, w} \\gets \\{ y \\}$ $z^{T,a,w} \\gets y$ Calculate $|F_{z^{T,a}}(k,\\ell)|$ by no-good cuts. ",
"$|F(k,\\ell)|\\gets 0$ $|F(k,\\ell)|\\gets|F(k,\\ell)|+|F_{z^{T,a}}(k,\\ell-w)|\\cdot|\\mathcal{Z}_{T,a,w}(k)|$\n\n$symmetryMatrix \\gets zeros(|\\bar{\\mathcal{D}}_{T}|, |\\mathbb{S}^T_k|\\cdot|\\mathbb{A}^T|)$ $A \\gets 1$ $B \\gets 1$ $symmetryMatrix(A,B) = 1$ $B \\gets B + 1$ $A \\gets A + 1$ symmetryMatrix\n\n$A \\gets 1$ $A$ $A \\gets A+1$\n\nComputational procedure with no-good cuts {#nogoodsec}\n-----------------------------------------\n\nWith the equivalence relation $\\equiv$ introduced in Section \\[equiv1\\], we calculate the cardinalities $|F(k,\\cdot)|$ through the equivalence classes $\\mathcal{Z}_{T,a}(k)$, $a\\in{\\ensuremath{ \\left\\{ 1,\\ldots,A \\right\\} }}$, and the corresponding $|F_{z^{T,a}}(k,\\cdot)|$ values for a fixed representative $z^{T,a}$ of each class.",
"\n\nIt remains to calculate the number of solutions for each equivalence class (as needed in line 21 of Algorithm \\[alg1\\]). ",
"To that end, let $a\\in{\\ensuremath{ \\left\\{ 1,\\ldots,A \\right\\} }}$ and $z=z^{T,a}$. In order to calculate $|F_z(k,\\ell)|$, we adopt an optimization approach based on the so-called *no-good cuts*. ",
"Given a set $F^\\ast\\subseteq F_z(k,\\ell)$, we consider the following integer-linear optimization problem: $$\\begin{aligned}\n\\text{maximize}& \\qquad 0\\tag{$\\mathscr{P}(z,F^\\ast)$} \\\\\n\\text{subject to}& \\qquad \\sum_{t\\in{\\mathbb{T}}(k)\\colon t_i=c, t_j=e}x_t\\geq 1\\quad \\forall i\\neq j\\ \\label{constraint1} \\\\\n\\emph{}& \\qquad \\sum_{t\\in{\\mathbb{T}}(k)}x_t=\\ell \\label{constraint2} \\\\\n\\emph{}&\\qquad x_t = y_t \\quad \\forall t\\in T\\label{constraint5}\\\\\n\\emph{}& \\qquad \\sum_{t\\in{\\mathbb{T}}(k)\\colon x^*_t=1} (1-x_t) + \\sum_{t\\in{\\mathbb{T}}(k)\\colon x^*_t=0}x_t \\quad \\geq 1 \\quad \\forall (x^*_t)_{t\\in{\\mathbb{T}}(k)} \\in F^* \\label{constraint3} \\\\\n\\emph{}& \\qquad x_t\\in \\{0,1\\} \\quad \\forall t\\in{\\mathbb{T}}(k) \\label{constraint4}\\end{aligned}$$ Note that $(\\mathscr{P}(z,F^\\ast))$ is basically a feasibility problem since we maximize a constant function. ",
"Here, constraints , , are the relations in the definition of $F(k,\\ell)$; constraint is the additional requirement in Definition \\[DefnOfFm\\]. ",
"Constraint is the collection of no-good cuts; it makes sure that the new solution $(x_t)_{t\\in{\\mathbb{T}}(k)}$ to be found is different from each of the solutions $(x_t^\\ast)_{t\\in{\\mathbb{T}}(k)}$ that are already stored in $F^\\ast$. Indeed, it is not difficult to check that the inequality in is equivalent to having $$\\exists t\\in{\\mathbb{T}}(k)\\colon x_t\\neq x^\\ast_t$$ for each $(x^\\ast_t)_{t\\in{\\mathbb{T}}(k)}\\in F^\\ast$. While more general formulations of no-good cuts for continuous variables are nonconvex inequalities, the formulation we use here is for binary variables due to the nature of our problem and it yields a linear inequality. ",
"The reader is referred to [@nogoodcut] for a detailed treatment of no-good cuts.",
"\n\nThe computational procedure is initialized by solving $(\\mathscr{P}(z,F^{(1)}))$ with $F^{(1)}\\coloneqq \\emptyset$. If $F_z(k,\\ell)=\\emptyset$, then this problem terminates by infeasibility. ",
"Otherwise, it yields a $(k,\\ell)$-labeling $(x_t^{(1)})_{t\\in{\\mathbb{T}}(k)}$ in $F_z(k,\\ell)$ as an optimal solution. ",
"For each $u\\in{\\mathbb{N}}$, in the $(u+1)^{\\text{st}}$ iteration, we call $(\\mathscr{P}(z,F^{(u+1)}))$ with $F^{(u+1)}\\coloneqq F^{(u)}\\cup\\{(x_t^{(u)})_{t\\in{\\mathbb{T}}(k)}\\}$. If $|F_z(k,\\ell)|\\leq u$, then the problem terminates by infeasibility. ",
"Otherwise, it yields a $(k,\\ell)$-labeling in $F_z(k,\\ell)$ that is different from each of the points in $F^{(u)}$. The procedure terminates by infeasibility when $u=|F_z(k,\\ell)|$ in which case we have $F_z(k,\\ell) = F^{(u)}\\cup\\{(x_t^{(u)})_{t\\in{\\mathbb{T}}(k)}\\}$. Hence, we find the cardinality of $F_z(k,\\ell)$ by finding all of its elements.",
"\n\nIt should be noted that, as the iteration number increases, the number of no-good cuts in the optimization problem increases and it takes more time to compute a new solution. ",
"Hence, when deciding on the choice of $T$, it is desirable to control $|F_z(k,\\ell)|$ by a reasonable upper bound that depends on $T$. For this purpose, we use the simple upper bound $$|F_z(k,\\ell)|\\leq \\binom{2^k-2-\\bar{z}}{\\ell-\\bar{z}},$$ where $\\bar{z}\\coloneqq\\sum_{t\\in T}z_t$; however, better upper bounds can be obtained by exploiting the structure of $T$.\n\nTo illustrate the computational procedure, in the ‘‘Total\" rows of Table \\[k=4table1\\] and Table \\[k=5table1\\], we present the $|F(k,\\cdot)|$ values for $k=4$ and $k=5$, respectively. ",
"From these tables, it is notable that for fixed $k$, the quantity $|F(k,\\ell)|$ first increases with $\\ell$, then makes a maximum around $\\ell=2^{k-1}-1$ and then decreases with $\\ell$. Detailed explanations on these tables are provided in the following two examples.",
"\n\n\\[k=4ex\\] Suppose that $k=4$. In this case, we have $\\ell_0(k)=4$ and $2^k-2=14$. Hence, we consider the values $\\ell\\in\\{4,\\ldots,14\\}$. As the branching set of index vectors, we select $T=\\{(c,e,e,e),(c,e,c,e),(c,e,e,c),(c,e,c,e)\\}$, which corresponds to the regions $A_1 \\cap \\bar{A}_2 \\cap \\bar{A}_3 \\cap \\bar{A}_4$, $A_1 \\cap \\bar{A}_2 \\cap A_3 \\cap \\bar{A}_4$, $A_1 \\cap \\bar{A}_2 \\cap \\bar{A}_3 \\cap A_4$, $A_1 \\cap \\bar{A}_2 \\cap A_3 \\cap A_4$. Hence, $|\\mathcal{Z}_T(k)|=16$. By Algorithm \\[alg1\\], we find out that $\\equiv$ has $A=6$ equivalence classes. ",
"In the header column of Table \\[k=4table1\\], we use the format $(a,w,s)$ to report the equivalence class index $a$, the value $w\\in{\\mathcal{W}}(a)$ that is fixed for the corresponding row, and the cardinality $s=|\\mathcal{Z}_{T,a,w}(k)|$ that corresponds to $(a,w)$. For instance, the row of $(5,1,2)$ gives the $|F_{y}(4,\\cdot)|$ values for each of the two members of $\\mathcal{Z}_{T,5,1}(4)$. The entries in the ‘‘Total\" row represent the values $|F(k,\\ell)|=\\sum_{a=1}^{6}\\sum_{w\\in{\\mathcal{W}}(a)}|F_{z^{T,a,w}}(k,\\ell)|\\cdot|\\mathcal{Z}_{T,a,w}(k)|$ for all $\\ell\\in{\\ensuremath{ \\left\\{ \\ell_0(k),\\ldots,2^k-2 \\right\\} }}$. ",
"In Table \\[k=4table1\\], the rows corresponding to the same equivalence class are placed consecutively and shaded with the same color; we alternate between two colors as the class index $a$ changes. ",
"The representatives $z^{T,a,w}$, $a\\in{\\ensuremath{ \\left\\{ 1,\\ldots,A \\right\\} }}$, $w\\in{\\mathcal{W}}(a)$, are listed in Table \\[k=4table2\\]. ",
"For instance, the line for $(5,1)$ states that $$z^{T,5,1}_{(c,e,e,e)}=1,\\quad z^{T,5,1}_{(c,e,c,e)}=1, \\quad z^{T,5,1}_{(c,e,e,c)}=1,\\quad z^{T,5,1}_{(c,e,c,e)}=0.$$\n\n\\[k=5ex\\] Suppose that $k=5$. In this case, we have $\\ell_0(k)=4$ and $2^k-2=30$. As the branching set of index vectors, we fix $T={\\ensuremath{ \\left\\{ t^1,\\ldots,t^{15} \\right\\} }}$ and the precise definitions of $t^1,\\ldots,t^{15}$ are given in Table \\[k=5table3\\]. ",
"For instance, $t^7=(c,e,c,e,e)$. We have $|\\mathcal{Z}_T(k)|=2^{15}$ and there are $A=28$ equivalence classes of $\\equiv$. Table \\[k=5table1\\] provides the $|F_{z^{T,a,w}}(5,\\ell)|$ values and it is presented in two pages. ",
"Its structure is the same as that of Table \\[k=4table1\\]. ",
"The definitions of the representatives $z^{T,a,w}$, $a\\in{\\ensuremath{ \\left\\{ 1,\\ldots,28 \\right\\} }}$, $w\\in{\\mathcal{W}}(a)$, are given in Table \\[k=5table2\\].",
"\n\nTable \\[k=5table1\\] illustrates the tremendous reduction in computational effort provided by the symmetries encoded in $\\equiv$. For each value of $a$, we only compute the values $|F_{z^{T,a,w}}(k,\\cdot)|$ for $w=0$, that is, the values in the first row for $a$; then, for $w>0$, the rows are obtained by simple shifts of the row $w=0$. The row of $(a,w)$ is repeated $s=|\\mathcal{Z}_{T,a,w}(k)|$ times in the ultimate value of $|F(k,\\ell)|$. For instance, in a brute-force calculation without using symmetries, the values in the row for $(27,4)$ would have been calculated $s=4055$ times, which is avoided due to the structure provided by $\\equiv$.\n\nApplication to reliability theory {#reliability}\n=================================\n\nIn this section, we illustrate the use of constructive covers in reliability theory.",
"\n\nIn the setting of [@barlow], let us consider a *multi-state coherent system* with $n\\in{\\mathbb{N}}$ components forming a set ${\\mathcal{N}}$. Without loss of generality, let us write ${\\mathcal{N}}={\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$. ",
"Each component $p\\in{\\mathcal{N}}$ has a state variable $z_p$ taking values in the set $\\mathcal{S}\\coloneqq{\\ensuremath{ \\left\\{ 0,1,\\ldots,s \\right\\} }}$, where $s\\in{\\mathbb{N}}$ is fixed for all components. ",
"Then, the states of all components can be expressed as a vector $z=(z_1,\\ldots,z_n)\\in\\mathcal{S}^n$. In classical reliability theory, the typical systems are binary, that is, one takes $\\mathcal{S}={\\ensuremath{ \\left\\{ 0,1 \\right\\} }}$. ",
"In such systems, the state $1$ corresponds to the “functioning\" state and $0$ corresponds to the “failure\" state. ",
"Hence, the general case with $s+1$ states can be used to model varying levels of perfection for how well the components operate.",
"\n\nThe structure of the system is encoded by a function $\\phi\\colon\\mathcal{S}^n\\to\\mathcal{S}$ such that $\\phi(z)=\\phi(z_1,\\ldots,z_n)$ gives the state of the overall system when component $p$ is at state $z_p$ for each $p\\in{\\mathcal{N}}$. We call $\\phi$ the *structure function* of the system. ",
"For instance, a *parallel* system is defined as a system whose structure function is given by $\\phi(z)=\\max{\\ensuremath{ \\left\\{ z_1,\\ldots,z_n \\right\\} }}$ for each $z\\in\\mathcal{S}^n$. Similarly, a *series* system has the structure function $\\phi(z)=\\min{\\ensuremath{ \\left\\{ z_1,\\ldots,z_n \\right\\} }}$ for each $z\\in\\mathcal{S}^n$. In general, a *coherent system* is a system which is built as a nested structure of parallel and series systems. ",
"More precisely, let $k\\in{\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$ and consider distinct sets $P_1,\\ldots,P_k\\subseteq{\\mathcal{N}}$ satisfying the following properties: the sets are not strict subsets of each other, and $\\bigcup_{i=1}^k P_i={\\mathcal{N}}$. Then, the structure function of a coherent system described with these sets is defined by $$\\label{phipath}\n\\phi(z)=\\max_{i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}}\\min_{p\\in P_i}z_p$$ for each $z\\in\\mathcal{S}^n$. The sets $P_1,\\ldots,P_k$ are called the *minimal path sets* of the system.",
"\n\nNote that the above requirements for the minimal path sets of the system are precisely the conditions in the definition of constructive ordered $k$-cover (Definition \\[kcover\\]) except that the order of the sets is not important. ",
"Hence, in view of Remark \\[unordered\\], every constructive unordered $k$-cover of ${\\mathcal{N}}$ corresponds to a system design with $k$ minimal path sets and $n$ components, and vice versa. ",
"By Corollary \\[ell0forcounting\\], the number of such system designs is given by $$\\frac{|C({\\mathcal{N}},k)|}{k!}=\\sum_{\\ell=\\ell_0}^{(2^k-2)\\wedge n}\\frac{\\ell!}{k!}\\tilde{s}(n,\\ell) |F(k,\\ell)|.$$\n\nGiven a coherent system with minimal path sets $P_1,\\ldots,P_k$, by following a certain procedure, one can construct the so-called *minimal cut sets* $C_1,\\ldots,C_r\\subseteq{\\mathcal{N}}$ with $r\\in{\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$ satisfying the following properties: the sets are not strict subsets of each other, $\\bigcup_{j=1}^r C_j={\\mathcal{N}}$ and each minimal cut set has a nonempty intersection with each minimal path set. ",
"It can be shown that [@barlow Proposition 1.1] the structure function of the system can also be computed by the formula $$\\label{phicut}\n\\phi(z)=\\min_{j\\in{\\ensuremath{ \\left\\{ 1,\\ldots,r \\right\\} }}}\\max_{p\\in C_j}z_p$$ for each $z\\in\\mathcal{S}^n$.\n\n[width=1.4,totalheight=0.92-2]{}\n\n[|c|\\*[28]{}[p[1cm]{}|]{}]{} &$4$ & $ 5$ & $ 6$ & $ 7$ & $8$& $9$ & $ 10$ & $11$ & $12$ & $13$ &$14$ & $ 15$ & $ 16$ & $ 17$ & $18$& $19$ & $ 20$ & $21$ & $22$ & $23$ &$24$ & $ 25$ & $ 26$ & $ 27$ & $28$& $29$ & $ 30$\\\n$(1,0,1)$& $0$& $38$& $615$& $2245$& $3900$& $4055$& $2798$& $1345$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(2,0,5)$& $0$& $11$& $193$& $1105$& $2889$& $4350$& $4235$& $2838$& $1349$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(3,0,10)$& $0$& $32$& $324$& $1397$& $3229$& $4578$& $4325$& $2858$& $1351$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(4,0,10)$& $0$& $0$& $48$& $441$& $1685$& $3570$& $4806$& $4415$& $2878$& $1353$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(4,1,10)$& $0$& $0$& $0$& $48$& $441$& $1685$& $3570$& $4806$& $4415$& $2878$& $1353$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(5,0,20)$& $0$& $0$& $39$& $378$& $1538$& $3399$& $4692$& $4370$& $2868$& $1352$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(6,0,30)$& $0$& $2$& $85$& $607$& $2009$& $3923$& $5036$& $4505$& $2898$& $1355$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(7,0,30)$& $0$& $1$& $78$& $596$& $2003$& $3922$& $5036$& $4505$& $2898$& $1355$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(7,1,30)$& $0$& $0$& $1$& $78$& $596$& $2003$& $3922$& $5036$& $4505$& $2898$& $1355$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(8,0,15)$& $2$& $34$& $244$& $990$& $2549$& $4405$& $5313$& $4605$& $2919$& $1357$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(9,0,20)$& $0$& $0$& $3$& $126$& $788$& $2355$& $4288$& $5268$& $4595$& $2918$& $1357$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(9,1,90)$& $0$& $0$& $0$& $3$& $126$& $788$& $2355$& $4288$& $5268$& $4595$& $2918$& $1357$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(9,2,60)$& $0$& $0$& $0$& $0$& $3$& $126$& $788$& $2355$& $4288$& $5268$& $4595$& $2918$& $1357$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(9,3,10)$& $0$& $0$& $0$& $0$& $0$& $3$& $126$& $788$& $2355$& $4288$& $5268$& $4595$& $2918$& $1357$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(10,0,120)$& $0$& $0$& $2$& $102$& $692$& $2179$& $4105$& $5152$& $4550$& $2908$& $1356$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(10,1,60)$& $0$& $0$& $0$& $2$& $102$& $692$& $2179$& $4105$& $5152$& $4550$& $2908$& $1356$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(11,0,30)$& $0$& $2$& $41$& $303$& $1191$& $2905$& $4772$& $5545$& $4695$& $2939$& $1359$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(11,1,30)$& $0$& $0$& $2$& $41$& $303$& $1191$& $2905$& $4772$& $5545$& $4695$& $2939$& $1359$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(12,0,60)$& $0$& $2$& $37$& $270$& $1085$& $2724$& $4588$& $5429$& $4650$& $2929$& $1358$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(13,0,60)$& $0$& $1$& $35$& $290$& $1178$& $2899$& $4771$& $5545$& $4695$& $2939$& $1359$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(13,1,120)$& $0$& $0$& $1$& $35$& $290$& $1178$& $2899$& $4771$& $5545$& $4695$& $2939$& $1359$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(13,2,60)$& $0$& $0$& $0$& $1$& $35$& $290$& $1178$& $2899$& $4771$& $5545$& $4695$& $2939$& $1359$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(14,0,15)$& $0$& $2$& $50$& $375$& $1417$& $3283$& $5149$& $5779$& $4785$& $2959$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(15,0,20)$& $0$& $0$& $22$& $230$& $1033$& $2688$& $4575$& $5427$& $4650$& $2929$& $1358$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(15,1,20)$& $0$& $0$& $0$& $22$& $230$& $1033$& $2688$& $4575$& $5427$& $4650$& $2929$& $1358$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(16,0,60)$& $0$& $2$& $41$& $305$& $1198$& $2914$& $4777$& $5546$& $4695$& $2939$& $1359$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(16,1,180)$& $0$& $0$& $2$& $41$& $305$& $1198$& $2914$& $4777$& $5546$& $4695$& $2939$& $1359$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(16,2,60)$& $0$& $0$& $0$& $2$& $41$& $305$& $1198$& $2914$& $4777$& $5546$& $4695$& $2939$& $1359$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(17,0,30)$& $0$& $7$& $88$& $491$& $1608$& $3472$& $5266$& $5824$& $4795$& $2960$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(17,1,30)$& $0$& $0$& $7$& $88$& $491$& $1608$& $3472$& $5266$& $5824$& $4795$& $2960$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(18,0,40)$& $0$& $0$& $3$& $61$& $410$& $1468$& $3321$& $5163$& $5781$& $4785$& $2959$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(18,1,360)$& $0$& $0$& $0$& $3$& $61$& $410$& $1468$& $3321$& $5163$& $5781$& $4785$& $2959$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(18,2,670)$& $0$& $0$& $0$& $0$& $3$& $61$& $410$& $1468$& $3321$& $5163$& $5781$& $4785$& $2959$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(18,3,540)$& $0$& $0$& $0$& $0$& $0$& $3$& $61$& $410$& $1468$& $3321$& $5163$& $5781$& $4785$& $2959$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(18,4,225)$& $0$& $0$& $0$& $0$& $0$& $0$& $3$& $61$& $410$& $1468$& $3321$& $5163$& $5781$& $4785$& $2959$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(18,5,50)$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $3$& $61$& $410$& $1468$& $3321$& $5163$& $5781$& $4785$& $2959$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(18,6,5)$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $3$& $61$& $410$& $1468$& $3321$& $5163$& $5781$& $4785$& $2959$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$\\\n$(19,0,360)$& $0$& $0$& $2$& $48$& $350$& $1323$& $3110$& $4967$& $5663$& $4740$& $2949$& $1360$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(19,1,660)$& $0$& $0$& $0$& $2$& $48$& $350$& $1323$& $3110$& $4967$& $5663$& $4740$& $2949$& $1360$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(19,2,360)$& $0$& $0$& $0$& $0$& $2$& $48$& $350$& $1323$& $3110$& $4967$& $5663$& $4740$& $2949$& $1360$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(19,3,60)$& $0$& $0$& $0$& $0$& $0$& $2$& $48$& $350$& $1323$& $3110$& $4967$& $5663$& $4740$& $2949$& $1360$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(20,0,20)$& $0$& $0$& $16$& $160$& $740$& $2100$& $4088$& $5776$& $6105$& $4895$& $2981$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n\n[width=1.4,totalheight=0.92-2]{}\n\n[|c|\\*[28]{}[p[1cm]{}|]{}]{} &$4$ & $ 5$ & $ 6$ & $ 7$ & $8$& $9$ & $ 10$ & $11$ & $12$ & $13$ &$14$ & $ 15$ & $ 16$ & $ 17$ & $18$& $19$ & $ 20$ & $21$ & $22$ & $23$ &$24$ & $ 25$ & $ 26$ & $ 27$ & $28$& $29$ & $ 30$\\\n$(20,1,90)$& $0$& $0$& $0$& $16$& $160$& $740$& $2100$& $4088$& $5776$& $6105$& $4895$& $2981$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(20,2,60)$& $0$& $0$& $0$& $0$& $16$& $160$& $740$& $2100$& $4088$& $5776$& $6105$& $4895$& $2981$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(20,3,10)$& $0$& $0$& $0$& $0$& $0$& $16$& $160$& $740$& $2100$& $4088$& $5776$& $6105$& $4895$& $2981$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(21,0,120)$& $0$& $0$& $7$& $97$& $545$& $1749$& $3682$& $5462$& $5942$& $4840$& $2970$& $1362$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(21,1,60)$& $0$& $0$& $0$& $7$& $97$& $545$& $1749$& $3682$& $5462$& $5942$& $4840$& $2970$& $1362$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(22,0,30)$& $0$& $3$& $40$& $245$& $915$& $2331$& $4291$& $5895$& $6150$& $4905$& $2982$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(22,1,210)$& $0$& $0$& $3$& $40$& $245$& $915$& $2331$& $4291$& $5895$& $6150$& $4905$& $2982$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(22,2,330)$& $0$& $0$& $0$& $3$& $40$& $245$& $915$& $2331$& $4291$& $5895$& $6150$& $4905$& $2982$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(22,3,180)$& $0$& $0$& $0$& $0$& $3$& $40$& $245$& $915$& $2331$& $4291$& $5895$& $6150$& $4905$& $2982$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(22,4,30)$& $0$& $0$& $0$& $0$& $0$& $3$& $40$& $245$& $915$& $2331$& $4291$& $5895$& $6150$& $4905$& $2982$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(23,0,120)$& $0$& $1$& $20$& $157$& $690$& $1960$& $3878$& $5580$& $5987$& $4850$& $2971$& $1362$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(23,1,180)$& $0$& $0$& $1$& $20$& $157$& $690$& $1960$& $3878$& $5580$& $5987$& $4850$& $2971$& $1362$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(23,2,60)$& $0$& $0$& $0$& $1$& $20$& $157$& $690$& $1960$& $3878$& $5580$& $5987$& $4850$& $2971$& $1362$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(24,0,20)$& $0$& $2$& $30$& $200$& $795$& $2121$& $4039$& $5685$& $6030$& $4860$& $2972$& $1362$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(24,1,40)$& $0$& $0$& $2$& $30$& $200$& $795$& $2121$& $4039$& $5685$& $6030$& $4860$& $2972$& $1362$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(24,2,20)$& $0$& $0$& $0$& $2$& $30$& $200$& $795$& $2121$& $4039$& $5685$& $6030$& $4860$& $2972$& $1362$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(25,0,120)$& $0$& $1$& $23$& $181$& $775$& $2135$& $4109$& $5783$& $6106$& $4895$& $2981$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(25,1,660)$& $0$& $0$& $1$& $23$& $181$& $775$& $2135$& $4109$& $5783$& $6106$& $4895$& $2981$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(25,2,780)$& $0$& $0$& $0$& $1$& $23$& $181$& $775$& $2135$& $4109$& $5783$& $6106$& $4895$& $2981$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(25,3,360)$& $0$& $0$& $0$& $0$& $1$& $23$& $181$& $775$& $2135$& $4109$& $5783$& $6106$& $4895$& $2981$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(25,4,60)$& $0$& $0$& $0$& $0$& $0$& $1$& $23$& $181$& $775$& $2135$& $4109$& $5783$& $6106$& $4895$& $2981$& $1363$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(26,0,5)$& $0$& $1$& $20$& $155$& $675$& $1911$& $3787$& $5475$& $5910$& $4815$& $2962$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(26,1,5)$& $0$& $0$& $1$& $20$& $155$& $675$& $1911$& $3787$& $5475$& $5910$& $4815$& $2962$& $1361$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(27,0,38)$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(27,1,615)$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(27,2,2245)$& $0$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(27,3,3900)$& $0$& $0$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(27,4,4055)$& $0$& $0$& $0$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(27,5,2798)$& $0$& $0$& $0$& $0$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$\\\n$(27,6,1345)$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$\\\n$(27,7,455)$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$& $0$& $0$\\\n$(27,8,105)$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$& $0$\\\n$(27,9,15)$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$& $0$\\\n$(27,10,1)$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $1$& $15$& $105$& $455$& $1365$& $3003$& $5005$& $6435$& $6435$& $5005$& $3003$& $1365$& $455$& $105$& $15$& $1$\\\n$(28,0,520)$& $0$& $0$& $4$& $50$& $290$& $1035$& $2541$& $4543$& $6105$& $6270$& $4950$& $2992$& $1364$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(28,1,2100)$& $0$& $0$& $0$& $4$& $50$& $290$& $1035$& $2541$& $4543$& $6105$& $6270$& $4950$& $2992$& $1364$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(28,2,3040)$& $0$& $0$& $0$& $0$& $4$& $50$& $290$& $1035$& $2541$& $4543$& $6105$& $6270$& $4950$& $2992$& $1364$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(28,3,2220)$& $0$& $0$& $0$& $0$& $0$& $4$& $50$& $290$& $1035$& $2541$& $4543$& $6105$& $6270$& $4950$& $2992$& $1364$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(28,4,900)$& $0$& $0$& $0$& $0$& $0$& $0$& $4$& $50$& $290$& $1035$& $2541$& $4543$& $6105$& $6270$& $4950$& $2992$& $1364$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$& $0$\\\n$(28,5,200)$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $4$& $50$& $290$& $1035$& $2541$& $4543$& $6105$& $6270$& $4950$& $2992$& $1364$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$& $0$\\\n$(28,6,20)$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $0$& $4$& $50$& $290$& $1035$& $2541$& $4543$& $6105$& $6270$& $4950$& $2992$& $1364$& $455$& $105$& $15$& $1$& $0$& $0$& $0$& $0$\\\n\n------------------------------------------------------------------------\n\n& & & && & & &&&& & & &&& &&&&&& && &&&\\\n\n------------------------------------------------------------------------\n\n[|>P[1.2cm]{}|P[2.4cm]{}|P[2.4cm]{}|P[2.4cm]{}|P[2.4cm]{}|P[2.4cm]{}|]{} &$A_1$& $A_2$& $A_3$& $A_4$&$A_5$\\\n$t^1$&$c$ &$e$ &$e$ &$e$ &$e$\\\n$t^2$&$e$ &$c$ &$e$ &$e$ &$e$\\\n$t^3$&$e$ &$e$ &$c$ &$e$ &$e$\\\n$t^4$&$e$ &$e$ &$e$ &$c$ &$e$\\\n$t^5$&$e$ &$e$ &$e$ &$e$ &$c$\\\n$t^6$&$c$ &$c$ &$e$ &$e$ &$e$\\\n$t^7$&$c$ &$e$ &$c$ &$e$ &$e$\\\n$t^8$&$c$ &$e$ &$e$ &$c$ &$e$\\\n$t^9$&$c$ &$e$ &$e$ &$e$ &$c$\\\n$t^{10}$&$e$ &$c$ &$c$ &$e$ &$e$\\\n$t^{11}$&$e$ &$c$ &$e$ &$c$ &$e$\\\n$t^{12}$&$e$ &$c$ &$e$ &$e$ &$c$\\\n$t^{13}$&$e$ &$e$ &$c$ &$c$ &$e$\\\n$t^{14}$&$e$ &$e$ &$c$ &$e$ &$c$\\\n$t^{15}$&$e$ &$e$ &$e$ &$c$ &$c$\\\n\nLet us comment on the alternative ways of calculating the state of the system given in and . ",
"We observe that the system is in the failure state if there is at least one minimal cut set in which every component is in the failure state, and the system is in a functioning state if there is at least one minimal path set in which every component is in a functioning state. ",
"Indeed, let $z\\in\\mathcal{S}^n$ and $\\bar{s}\\in\\mathcal{S}$. Thanks to , we have $\\phi(z)\\leq \\bar{s}$ if and only if, for every minimal path set $P_i$, there is at least one component $p\\in P_i$ with $z_p \\leq \\bar{s}$. Conversely, thanks to , we have $\\phi(z)>\\bar{s}$ if and only if, for every minimal cut set $C_j$, there is at least one component $p\\in C_j$ with $z_p>\\bar{s}$.\n\nAs mentioned above, the minimal cut sets corresponding to a collection of minimal path sets can be constructed by a certain procedure. ",
"To be able to describe this procedure, we review the notion of minimality next. ",
"Let $\\tilde{\\mathscr{C}}=\\{\\tilde{C}_1,\\ldots,\\tilde{C}_{\\tilde{r}}\\}$ be a collection of distinct subsets of ${\\mathcal{N}}$ with $\\tilde{r}\\in{\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$. ",
"For $i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,\\tilde{r} \\right\\} }}$, the set $\\tilde{C}_i$ is called a *dominated element* of $\\tilde{\\mathscr{C}}$ if there is $i^\\prime\\in{\\ensuremath{ \\left\\{ 1,\\ldots,\\tilde{r} \\right\\} }}{\\!\\setminus\\!}{\\ensuremath{ \\left\\{ i \\right\\} }}$ such that $\\tilde{C}_{i^\\prime}\\subseteq \\tilde{C}_i$; in this case, $\\tilde{C}_i$ is also said to be *dominated by* $\\tilde{C}_{i^\\prime}$. $\\tilde{C}_k$ is called a *minimal element* of $\\tilde{\\mathscr{C}}$ if it is not a dominated element. ",
"Since $\\tilde{\\mathscr{C}}$ is a finite collection, a minimal element of it always exists. ",
"Moreover, it is easy to observe that every dominated element is dominated by at least one minimal element. ",
"It is easy to see that $\\tilde{\\mathscr{C}}$ is an constructive unordered $\\tilde{r}$-cover of ${\\mathcal{N}}$ if and only if every set in $\\tilde{\\mathscr{C}}$ is a minimal element of $\\tilde{\\mathscr{C}}$ and $\\bigcup_{i=1}^{\\tilde{r}} \\tilde{C}_i={\\mathcal{N}}$.\n\nLet $\\mathscr{P}={\\ensuremath{ \\left\\{ P_1,\\ldots,P_k \\right\\} }}$ be a constructive unordered $k$-cover of ${\\mathcal{N}}$. A set $C\\subseteq {\\ensuremath{ \\left\\{ 1,\\ldots,n \\right\\} }}$ is called an *intersector* of $\\mathscr{P}$ if there exists a surjective function $f\\colon{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}\\to C$ such that $f(i)\\in P_i$ for every $i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}.$ In other words, an intersector chooses one component from each set in $\\mathscr{P}$ but the same component can be chosen from multiple sets. ",
"Consequently, for an intersector $C$ of $\\mathscr{P}$, it holds $C\\cap P_i\\neq \\emptyset$ for each $i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$ but the cardinality of such an intersection may exceed one, in general. ",
"Moreover, for every component $p\\in{\\mathcal{N}}$, there exists an intersector $C$ of $\\mathscr{P}$ such that $p\\in C$. ",
"Let us denote by $\\mathscr{C}_0$ the collection of all intersectors of $\\mathscr{P}$ and by $\\mathscr{C}$ the collection of all minimal elements of $\\mathscr{C}_0$. Let us write $$\\label{minint}\n\\mathscr{C}={\\ensuremath{ \\left\\{ C_1,\\ldots,C_r \\right\\} }},$$ where $r=|\\mathscr{C}|$.\n\nThe collection $\\mathscr{C}$ given in is a constructive unordered $r$-cover of ${\\mathcal{N}}$.\n\nWe first note that, by construction, every set in $\\mathscr{C}$ is a minimal element of $\\mathscr{C}_0$, hence it is a minimal element of $\\mathscr{C}$ as well. ",
"It remains to show that $\\bigcup_{j=1}^r C_j ={\\mathcal{N}}$. The $\\subseteq$ part is obvious since $C_1,\\ldots,C_r$ are subsets of ${\\mathcal{N}}$. To prove the $\\supseteq$ part, let us fix $p\\in{\\mathcal{N}}$. Let us denote by $\\mathscr{C}_0(p)$ the collection of all intersectors of $\\mathscr{P}$ containing $p$ as an element and by $\\mathscr{C}(p)$ the collection of all minimal elements of $\\mathscr{C}_0(p)$. Let us write $\\mathscr{C}(p)={\\ensuremath{ \\left\\{ K_1,\\ldots,K_q \\right\\} }}$ with $q\\in{\\mathbb{N}}$ as a collection of distinct sets. ",
"To conclude the proof, it suffices to show that $\\mathscr{C}(p)\\subseteq\\mathscr{C}$. To that end, we let ${\\alpha}\\in{\\ensuremath{ \\left\\{ 1,\\ldots,q \\right\\} }}$ and show that $K_{\\alpha}\\in\\mathscr{C}$. To get a contradiction, suppose that $K_{\\alpha}\\notin\\mathscr{C}$. Note that $\\mathscr{C}(p)\\subseteq\\mathscr{C}_0$. Hence, the supposition is equivalent to that, $K_{\\alpha}$ is a dominated element of $\\mathscr{C}_0$ so that there exists $j({\\alpha})\\in{\\ensuremath{ \\left\\{ 1,\\ldots,r \\right\\} }}$ such that $C_{j({\\alpha})}\\subseteq K_{\\alpha}$. Moreover, such $C_{j({\\alpha})}$ does not contain $p$ as an element as otherwise $C_{j({\\alpha})}$ would be a set in $\\mathscr{C}_0(p)$, which would contradict the minimality of $K_j$ in $\\mathscr{C}_0(p)$. Since $C_{{\\alpha}(j)}$ is an intersector of $\\mathscr{P}$, there exists a surjective function $f\\colon{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}\\to C_{j({\\alpha})}$ such that $f(i)\\in P_i$ for every $i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}$. ",
"Define a function $g\\colon{\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }}\\to {\\mathcal{N}}$ by letting $g(i)=p$ if $p\\in P_{i} $ and $g(i)=f(i)$ if $p\\notin P_i$. Since $\\mathscr{P}$ is constructive, there exists $i^\\prime$ such that $p\\in P_{i^\\prime}$. Consequently, the image $g({\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }})$ of $g$ is an intersector of $\\mathscr{P}$ containing $p$ as an element, $C_{j({\\alpha})}{\\!\\setminus\\!}g({\\ensuremath{ \\left\\{ 1,\\ldots,m \\right\\} }})\\neq \\emptyset$, and $g({\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }})\\subseteq C_{j({\\alpha})}\\cup{\\ensuremath{ \\left\\{ p \\right\\} }}\\subseteq K_j$. Hence, $g({\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }})\\in\\mathscr{C}_0(p)$ and the minimality of $K_j$ in $\\mathscr{C}_0(p)$ implies $C_{j({\\alpha})}\\subseteq K_j=g({\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }})$, which contradicts $C_{j({\\alpha})}{\\!\\setminus\\!}g({\\ensuremath{ \\left\\{ 1,\\ldots,k \\right\\} }})\\neq \\emptyset$. Therefore, $K_j\\in\\mathscr{C}$.\n\nAs an alternative construction, one can start with a constructive unordered $r$-cover $\\{C_1,\\ldots,C_r\\}$ of ${\\mathcal{N}}$ to be used as the collection of the minimal cut sets of the system, that is, the structure function is defined by . ",
"Then, the corresponding minimal path sets can be constructed by the above procedure, which guarantees that each minimal path set has a nonempty intersection with each minimal cut set. ",
"The number of all system designs with $r$ minimal cut sets is given by $$\\frac{|C({\\mathcal{N}},r)|}{r!}=\\sum_{\\ell=\\ell_0(k)}^{(2^r-2)\\wedge n}\\frac{\\ell!}{r!}\\tilde{s}(n,\\ell) |F(r,\\ell)|.$$ We finish this section by providing two exact calculations of the above quantity based on the earlier calculations.",
"\n\nUsing Example\\[k=4ex\\], we calculate the number of all system designs with $n=7$ components and $r=4$ minimal cut sets as $$\\begin{aligned}\n \\frac{|C({\\mathcal{N}},r)|}{r!}&=\\frac{1}{24}\\sum_{\\ell=4}^{7}\\ell!\\tilde{s}(7,\\ell) |F(4,\\ell)|\\\\\n &=\\frac{1}{24}{\\ensuremath{\\left( 4!\\tilde{s}(7,4)|F(4,4)|+5!\\tilde{s}(7,5)|F(4,5)|+6!\\tilde{s}(7,6)|F(4,6)|+7!\\tilde{s}(7,7)|F(4,7)| \\right)}}\\\\\n &=\\frac{1}{24}{\\ensuremath{\\left( 4!\\cdot 1050\\cdot 25+5!\\cdot 266\\cdot 304 + 6!\\cdot 28\\cdot 1165+7!\\cdot 1\\cdot 2188 \\right)}}\\\\\n &=1,868,650.",
"\n \\end{aligned}$$\n\nUsing Example\\[k=5ex\\], we calculate the number of all system designs with $n=9$ components and $r=5$ minimal cut sets as $$\\begin{aligned}\n \\frac{|C({\\mathcal{N}},r)|}{r!}&=\\frac{1}{120}\\sum_{\\ell=4}^{9}\\ell!\\tilde{s}(9,\\ell) |F(5,\\ell)|\\\\\n &=\\frac{1}{120}(4!\\tilde{s}(9,4)|F(5,4)|+5!\\tilde{s}(9,5)|F(5,5)|+6!\\tilde{s}(9,6)|F(5,6)|+7!\\tilde{s}(9,7)|F(5,7)|\\\\\n &\\quad \\quad\\quad +8!\\tilde{s}(9,8)|F(5,8)|+9!\\tilde{s}(9,9)|F(5,9)|)\\\\\n &=\\frac{1}{120}(4!\\cdot42525\\cdot 30 + 5!\\cdot 22827\\cdot 2026+6!\\cdot 5880\\cdot 41430+7!\\cdot 750 \\cdot 376350\\\\\n &\\quad \\quad\\quad +8!\\cdot 45 \\cdot 2003655+9!\\cdot 1 \\cdot 7286000)\\\\\n &=65,691,305,652.",
"\n \\end{aligned}$$\n\nConclusion {#conc}\n==========\n\nIn this paper, we consider the problem of counting the number of ways that one can cover a finite set by a given number of subsets with the additional requirement that every pair of these subsets has a nonempty set difference. ",
"It turns out that this seemingly simple problem requires a deep enumeration argument which results in two auxiliary problems: calculating ISNs and counting certain labelings of the disjoint regions that are induced by a cover. ",
"While the calculation of ISNs can be handled by a simple recursive relation, we solve the labeling problem by a more sophisticated method that exploits certain symmetries available in the set of labelings and uses no-good cuts from optimization literature. ",
"As the numerical examples illustrate, even for small values of $k$, the number of subsets in the cover, one has to calculate very large cardinalities due to exponential growth. ",
"The enhancement of this method for larger values of $k$ as well as the asymptotic analysis of the overall problem are subjects of future research.",
"\n\nAppendix: Proofs of the results in Section \\[prelim\\] {#app}\n=====================================================\n\nUsing binomial expansion, we obtain $$\\begin{aligned}\n \\tilde{s}(n,\\ell)&=\\frac{1}{\\ell!}\\sum_{j=0}^\\ell (-1)^{\\ell-j}\\binom{\\ell}{j}(j+1)^n=\\frac{1}{\\ell!}\\sum_{j=0}^\\ell (-1)^{\\ell-j}\\binom{\\ell}{j}\\sum_{i=0}^n\\binom{n}{i}j^i\\\\\n &=\\frac{1}{\\ell!}\\sum_{i=0}^n\\binom{n}{i}\\sum_{j=0}^\\ell (-1)^{\\ell-j}\\binom{\\ell}{j}j^i=\\frac{1}{\\ell!}\\sum_{i=1}^n\\binom{n}{i}\\sum_{j=0}^\\ell (-1)^{\\ell-j}\\binom{\\ell}{j}j^i=\\sum_{i=1}^n\\binom{n}{i}s(i,\\ell).",
"\n \\end{aligned}$$ Here, to get the penultimate equality, we use the fact that, for $i=0$, $$\\sum_{j=0}^\\ell (-1)^{\\ell-j}\\binom{\\ell}{j}j^i=\\sum_{j=0}^\\ell (-1)^{\\ell-j}(+1)^j\\binom{\\ell}{j}=0.$$ Hence, follows. ",
"If $n<\\ell$, then implies $$\\tilde{s}(n,\\ell)=\\sum_{i=1}^n\\binom{n}{i}s(i,\\ell)=\\sum_{i=1}^n\\binom{n}{i}0=0.$$ On the other hand, if $n\\geq \\ell$, then we have $s(i,\\ell)=0$ for each $i\\in{\\ensuremath{ \\left\\{ 1,\\ldots,\\ell-1 \\right\\} }}$ so that $$\\tilde{s}(n,\\ell)=\\sum_{i=\\ell}^n\\binom{n}{i}s(i,\\ell)=\\sum_{i=0}^{n-\\ell}\\binom{n}{i}s(n-i,\\ell).$$ Hence, follows. ",
"In particular, $\\tilde{s}(n,n)=\\binom{n}{0} s(n,n)=1$. Finally, by together with (i) and (iii), we have $$\\tilde{s}(n,1)=\\sum_{i=1}^n \\binom{n}{i}s(i,1)=\\sum_{i=1}^n \\binom{n}{i}=2^n-1.$$\n\nLet $n\\in{\\mathbb{N}}{\\!\\setminus\\!}{\\ensuremath{ \\left\\{ 1 \\right\\} }}$ and $\\ell\\in{\\ensuremath{ \\left\\{ 2,\\ldots,n \\right\\} }}$. ",
"By elementary calculations, we obtain $$\\begin{aligned}\n &(\\ell+1)\\tilde{s}(n,\\ell)+\\tilde{s}(n,\\ell-1)\\\\\n &=\\frac{\\ell+1}{\\ell!}\\sum_{j=0}^\\ell (-1)^{\\ell-j}\\binom{\\ell}{j}(j+1)^n+\\frac{1}{(\\ell-1)!}\\sum_{j=0}^{\\ell-1} (-1)^{\\ell-1-j}\\binom{\\ell-1}{j}(j+1)^n\\\\\n &=\\frac{\\ell+1}{\\ell!}\\sum_{j=0}^{\\ell-1} (-1)^{\\ell-j}\\binom{\\ell}{j}(j+1)^n+\\frac{\\ell+1}{\\ell!}(\\ell+1)^n+\\frac{1}{(\\ell-1)!}\\sum_{j=0}^{\\ell-1} (-1)^{\\ell-1-j}\\binom{\\ell-1}{j}(j+1)^n\\\\\n &=\\frac{\\ell+1}{\\ell}\\frac{1}{(\\ell-1)!}\\sum_{j=0}^{\\ell-1} (-1)^{\\ell-j}\\binom{\\ell}{j}(j+1)^n+\\frac{\\ell+1}{\\ell!}(\\ell+1)^n+\\frac{(-1)^{-1}}{(\\ell-1)!}\\sum_{j=0}^{\\ell-1} (-1)^{\\ell-j}\\binom{\\ell-1}{j}(j+1)^n\\\\\n &=\\frac{1}{(\\ell-1)!}\\sum_{j=0}^{\\ell-1} (-1)^{\\ell-j}(j+1)^n{\\ensuremath{\\left( \\frac{\\ell+1}{\\ell}\\binom{\\ell}{j}-\\binom{\\ell-1}{j} \\right)}}+\\frac{\\ell+1}{\\ell!}(\\ell+1)^n\\\\\n &=\\frac{1}{(\\ell-1)!}\\sum_{j=0}^{\\ell-1} (-1)^{\\ell-j}(j+1)^n\\binom{\\ell}{j}{\\ensuremath{\\left( \\frac{\\ell+1}{\\ell}-\\frac{\\ell-j}{\\ell} \\right)}}+\\frac{\\ell+1}{\\ell!}(\\ell+1)^n\\\\\n &=\\frac{1}{\\ell!}\\sum_{j=0}^{\\ell-1} (-1)^{\\ell-j}\\binom{\\ell}{j}(j+1)^{n+1}+\\frac{1}{\\ell!}(\\ell+1)^{n+1}=\\frac{1}{\\ell!}\\sum_{j=0}^{\\ell} (-1)^{\\ell-j}\\binom{\\ell}{j}(j+1)^{n+1}=\\tilde{s}(n+1,\\ell),\n \\end{aligned}$$ as desired. ",
"The boundary conditions are given by (iii), (iv) of Proposition \\[workhorse\\].",
"\n\n[99]{}\n\nR. E. Barlow, A. S. Wu, *Coherent systems with multi-state components*, Mathematics of Operations Research, **3**(4): 275–281, 1978.",
"\n\nA. P. Burger, J. H. van Vuuren, *Balanced minimum covers of a finite set*, Discrete Mathematics, **307**: 2853–2860, 2007.",
"\n\nR. J. Clarke, *Covering a set by subsets*, Discrete Mathematics, **81**: 147–152, 1990.",
"\n\nC. D’Ambrosioa, A. Frangionib, L. Libertic, A. Lodia, *On interval-subgradient and no-good cuts*, Operations Research Letters, **38**: 341–345, 2010.",
"\n\nT. Hearne, C. Wagner, *Minimal covers of finite sets*, Discrete Mathematics, **5**: 247–251, 1973.",
"\n\nG. F. Royle, *Counting set covers and split graphs*, Journal of Integer Sequences, **3**: 00.2.6, 2000.",
"\n\nK. L. Collins, A. N. Trenk, *Finding balance: split graphs and related classes*, The Electronic Journal of Combinatorics, **25**(1): P1.73, 2018.",
"\n\n[^1]: Bilkent University, Department of Industrial Engineering, Ankara, Turkey, cararat@bilkent.edu.tr.",
"\n\n[^2]: Bilkent University, Department of Industrial Engineering and Faculty of Business Administration, Ankara, Turkey, ulku@bilkent.edu.tr.",
"\n\n[^3]: Middle East Technical University, Department of Electrical and Electronics Engineering, Ankara, Turkey, emrullah.ildiz@metu.edu.tr.",
"\n"
] | {
"pile_set_name": "ArXiv"
} | [
0,
0,
0.0000046986200674930675,
0,
0,
0.0001512287334593573,
0.000013850415512465373,
0,
0.000027434842249657064,
0.000053863832232117214,
0.00002204148206925434,
0.00006298815822625346,
0.00004565376186997809,
0.000014907350814686723,
0,
0.00004504301608035674,
0,
0,
0,
0,
0,
0,
0,
0.000014792899408284025,
0.0001,
0.00008656509695290859,
0,
0,
0.000006642576256775427,
0,
0,
0,
0.0000980296049406921,
0,
0,
0,
0,
0.000037637848620572846,
0,
0,
0.0000483863163497363,
0,
0.0000026595697525359,
0,
0,
0,
0.0000706164818868724,
0.0000016468983962503416,
0.00008264462809917355,
0,
0,
0,
0.000001626926280716368,
0.0000010650069598204824,
0,
0,
0.00001262594378929825,
0.000010054495364877636,
0.000002176632256529171,
0,
0,
0,
0.000006177396289238048,
0.000004767262256631262,
0.000017580827856068275,
0.000010639769329800929,
0,
0.000006354834917275936,
0.000010679653124866504,
0.0000033543989587945633,
0.000001859504132231405,
0,
0.000005336042620039615,
0.000002317387007106267,
0,
0.000023781212841854935,
0.0003429355281207133,
0.0000026545477712416915,
0.0000016735589402355369,
0.0000049055136747325574,
0.00002047460125714052,
0.000010283780934898524,
0.000007631024693995909,
0,
0,
0,
0,
0,
0,
0,
0.000007846275765208045,
0.000003429355281207133,
0,
0,
0,
0,
0.000015140274644582053,
0.0000015890874188770872,
0,
0.0000014588913592782571,
0.0000031196264434511552,
0.0000027736686390532547,
0,
0,
0,
0.0000038366801973588295,
0.000008417295859532166,
0.000007283957811316356,
0,
0.000008499859752314087,
0.000005049867440979675,
0.00002311390532544379,
0.000013697129081744465,
0.0000017159434136772359,
0,
0.00002333776750916007,
0,
0,
0.000012193263222069807,
5.270074868001093e-7,
7.292664090411533e-7,
5.221378621482945e-7,
0.00006383861597880558,
0,
0,
0,
0.00001218315105018762,
0.00010850694444444444,
0,
0.000007904857139469347,
0.000009555456284981928,
0,
0.0000038044801558315075,
0.00000526292706460243,
0,
0,
0.000004065696230150932,
0.000048902146804244705,
0.0000023595980188815034,
0.00015625,
0,
0,
0,
0.00000825736557008852,
0,
0.000006611570247933884,
0,
0.000003099583415988891,
0.00000500721038295145,
0,
0.000048225308641975306,
0,
0.000020108990729755272,
0,
0,
0.00000148358927721014,
0.000016259105098855357,
0,
0,
0,
0,
0,
0.000009920585711380399,
0,
0,
0.00002712673611111111,
0,
7.039330268337306e-8,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.000009845620667926906,
0,
0,
0,
0.00001054140664530275,
0.00001006319687638369,
0.0000043508149076322,
0,
0,
0,
0,
0,
0.000012530346933980734,
0.000043266630611141155,
0,
0.00001940974951718248,
0.000005484591041468993,
0,
0.00004959333465582226,
0.00013007284079084286,
0.00012624668602449185,
0.00004385772553835358,
0.0001,
0.00009070294784580499,
0.00004627701420704336,
0.00027210884353741496,
0.0001508978421608571,
0.0001035143108534755,
0
] | 0.000017 | 5 |
[
"In-Silico Skin Model: A Multiscale Simulation Study of Drug Transport.",
"\nAccurate in-silico models are required to predict the release of drug molecules through skin in order to supplement the in-vivo experiments for faster development/testing of drugs. ",
"The upper most layer of the skin, stratum corneum (SC), offers the main resistance for permeation of actives. ",
"Most of the SC's molecular level models comprise cholesterol and phospholipids only, which is far from reality. ",
"In this study we have implemented a multiscale modeling framework to obtain the release profile of three drugs, namely, caffeine, fentanyl, and naphthol, through skin SC. ",
"We report for the first time diffusion of drugs through a realistic skin molecular model comprised of ceramides, cholesterol, and free fatty acid. ",
"The diffusion coefficients of drugs in the SC lipid matrix were determined from multiple constrained molecular dynamics simulations. ",
"The calculated diffusion coefficients were then used in the macroscopic models to predict the release profiles of drugs through the SC. ",
"The obtained release profiles were in good agreement with available experimental data. ",
"The partition coefficient exhibits a greater effect on the release profiles. ",
"The reported multiscale modeling framework would provide insight into the delivery mechanisms of the drugs through the skin and shall act as a guiding tool in performing targeted experiments to come up with a suitable delivery system."
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0.0002040816326530612,
0,
0.00008264462809917355,
0.00007971938775510203,
0.00003419855682090216,
0,
0.00005653230821414438,
0.00005406574394463668,
0,
0,
0
] | 0.000046 | 5 |
[
"These sites are ad—free\n\nThis giveaway has ended and the winners are JULIAN and MASON BROSKI.",
"\n\nTerve taas,\n\nI think it’s time for a new giveaway. ",
"Summer is almost here and allergies tormenting people. ",
"So, I’ll giveaway a PSN Gift Card $50 to a one lucky chosen one at June 10th, 2019.",
"\n\nTo participate this giveaway I’d like you to answer to this topic: Have any video game changed your life? ",
"How? (",
"You can also participate just commenting, without answering the topic :] )\n\nI’ll keep this giveaway up until June 10th, 2019 (of Finnish time). ",
"The prize is given via email, or via privnote, as a code. ",
"You can leave your email address when commenting. ",
"This giveaway is open WORLDWIDE.",
"\n\n(I recommend to login or leave an email address when commenting, so I can contact the winner.)"
] | {
"pile_set_name": "OpenWebText2"
} | [
0,
0,
0,
0.0001451589490492089,
0,
0,
0,
0,
0,
0,
0
] | 0.000013 | 5 |
[
"Autologous stem cell transplantation: a possible treatment for refractory juvenile chronic arthritis?",
"\nIn adults, autologous stem cell transplantation (ASCT) has been described recently as a possible treatment for severe autoimmune disease refractory to conventional treatment. ",
"We report here the four first children with severe forms of juvenile chronic arthritis (JCA) treated with ASCT. ",
"We studied three children with systemic JCA and one child with polyarticular JCA. ",
"Unprimed bone marrow was harvested 1 month prior to ASCT. ",
"T-cell depletion of the graft was performed with CD2 and CD3 antibodies. ",
"We used a preparative regimen of antithymocyte globulin (ATG; 20 mg/kg), cyclophosphamide (Cy; 200 mg/kg) and low-dose total body irradiation (TBI; 4 Gy). ",
"Methotrexate (MTX) and cyclosporin A (CsA) were stopped before ASCT; prednisone was tapered after 2 months. ",
"After ASCT, our patients showed an anti-inflammatory-drug-free follow-up of 6-18 months with a marked decrease in joint swelling, pain and morning stiffness. ",
"The erythrocyte sedimentation rate (ESR), C-reactive protein (CRP) and haemoglobin (Hb) returned to near-normal values within 6 weeks. ",
"Despite T-cell depletion, there was a very rapid immune reconstitution. ",
"Two patients developed a limited varicella zoster virus (VZV) eruption which was treated by acyclovir."
] | {
"pile_set_name": "PubMed Abstracts"
} | [
0,
0.00003228305785123967,
0.00015943877551020407,
0.000297441998810232,
0.0005945303210463733,
0,
0.00008324661810613944,
0.00008573388203017832,
0,
0.00010973936899862826,
0,
0.00009611687812379854
] | 0.000122 | 5 |
[
"You can define multimethods with the \"multi\" declarator:\n\n use Class::Multimethods::Pure;\n\n multi collide => ('Bullet', 'Ship') => sub {\n my ($a, $b) = @_; ...\n };\n\n multi collide => ('Ship', 'Asteroid') => sub {\n my ($a, $b) = @_; ...\n };\n\nIt is usually wise to put such declarations within a BEGIN block, so\nthey behave more like Perl treats subs (you can call them without\nparentheses and you can use them before you define them).",
"\n\nWWW: https://metacpan.org/release/Class-Multimethods-Pure\n"
] | {
"pile_set_name": "Github"
} | [
0.0000046447681331747915,
0.0005555555555555556
] | 0.00028 | 5 |
[
"Q:\n\nHigh Side Constant Current Source\n\nI am trying to create a constant current source of 100mA to charge a single cell Li-ion battery. ",
"I see the LM317 thrown around a lot as a solution, but I'm looking for something that does not require a 1.2V drop (Due to the Vref=1.2V for a LM317). ",
"The problem is when I look at more modern LDOs, they tend to have a ground as well as a ADJ pin, and I'm wondering if these can be floated the same way the traditional LM317 regulators could.",
"\nOnce such device I was looking at was a ADP123AU due to it having a Vref of 0.5V. \n\nSo looking at the block diagram they do not mention what the 0.5V is ref to but it would have to be ground as far as I can understand, so if you float ground as shown, would it work? ",
"Or does anyone know another small regulator / specialty IC that can do this?",
"\n\nsimulate this circuit – Schematic created using CircuitLab\nEDIT:\nThanks for the input, it is interesting but I may not have been clear in the initial question. ",
"I am looking to do this as simple as possible, something such as the LM317 with a single resistor. ",
"Multiple op-amps and transistors is something I would like to avoid.",
"\nDoes anyone have an opinion on if what I proposed in my question would work?",
"\n\nA:\n\nYou can use this idea: -\n\nThe voltage across R1 sets the voltage that is forced across R2 by the op-amp's negative feedback. ",
"Let's say that voltage is 0.1 volts and let's say R2 is 1 ohm. ",
"This means that when 0.1 volts is forced across R2 there can only be 100mA flowing through it.",
"\n99%+ of that current flows through the load so it's basically a constant current generator. ",
"Less than 1% flows into the output of the op-amp to drive the base.",
"\nSounds simple but you'll need a rail-to-rail op-amp with inputs capable of getting to within 100mV of the positive rail. ",
"Not too tricky of course. ",
"The voltage across R1 being set to 0.1V won't be stable if the V+ rail moves about so some kind of positive supply referenced shunt regulator can be used and this can be further potted down to provide 0.1 volts across R1.",
"\nSaturation of the PNP might be 100mV so overall, this design could be expected to \"drop\" about 200mV. It's a circuit I use a lot for the excitation of strain gauges.",
"\n\nA:\n\nAny op amp that includes V+ in it's common mode range (ie rail to rail input range)can be used to monitor a high side current sense resistor and to compare the voltage drop with a high side referenced voltage.",
"\nA current mirror is often used in this specific applicatiopn to \"reflect\" a high side referenced voltage to ground (usually with amplification). ",
"Specialist ICs are available to do this task but a pair of well-enough matched transistors can be used for the purpose. ",
"\n\nHigh side voltage sensing with opamps:\nIf using non rail-to-rail opamps the voltages on either side of the reference resistor may be divided down with a resistive divider to get the voltages within the available range.",
"\nHere is an example from fig 3 here - Planet Analog: Understand low-side vs. high-side current sensing\nThey divide the voltages before and after Vsense (Vcommon and say Vs) by 10:1 (9K:1k) but in doing so also reduce the delta voltage across the sense resistor by 10. ",
"Better where the absolute voltage allows is to divide by as little as possible. ",
"eg if the opamp will allow Vin to be within 1.5V of V+ and a 12V supply is used then Vin max = 12-1.5V = 10.5V or 10.5/12 = 0.875 of V+. ",
"To err on the safe side limit Vin max to say 2/3 = 0.66 of Vsupply or 8V in this case.",
"\nHere set R1 = 10k say and R2 = 20K or 22k using E12 resistor values. ",
"They show amplifier A2 with a gain of 250 - rather more than you'd hope to need in most cases. ",
" Amplifier A1 needs to have a low enough input offset voltage to deal with the delta V experienced. ",
"If you set V_Rsense max = 0.5V and want 1% resolution then 1% of Vsense_max = 0.5V x 1% = 5 mV. A1 now sees 2/3 of that due tpo the resistor dividers or about 3 mV per 1% step in Vsense. ",
"Most common op-amps (evenones with otherwise quite good specs) can have Vinput_offset of more than 3 mV - but there are also many available with far far less. ",
"\n\nApplication note from MSU using TI ICs\nHe uses eg the TI INA138 current sense IC - datasheet here\nGains of 1 to 100 from Rsense to Rl may be obrained with a maximum drop across across Rsense of 0.5V (lower OK). ",
"\nFrom the data sheet\n\nExamples of dedicated ICs:\nLTC6101\nOther LT related solutions\n\nA zillion DIY solutions\n\nADP122 datasheet\n\nA:\n\nMy Investigation\nSo, I downloaded LTSpice, and found an appropriate LDO Regulator made my LT that met my specifications of a low dropout and low Vref. ",
"I created the example circuit from above and simulated it.",
"\nSimulation\nAfter testing the circuit shown below with both a small Rload and large Rload (full and empty battery) I discovered that 'any' adjustable regulator even with a ground can be floated as the old LM317 could. ",
"I suspect that this is due to the small Quiescent current that can be sunk by just about any load.",
"\nThe image shows a 20mA current source that is comprised of 2 components, a LDO and resistor.",
"\n\n"
] | {
"pile_set_name": "StackExchange"
} | [
0,
0,
0.000027411529289219047,
0,
0,
0.00007620789513793629,
0.0001020304050607081,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0,
0.000036289737262302225,
0,
0,
0.00006944444444444444,
0,
0,
0,
0.00010655868719697373,
0.00027041644131963225,
0.0002040816326530612,
0,
0.0001,
0,
0,
0.00004408296413850868,
0.000037458327610533285,
0,
0.00006312599949499201,
0,
0.00011562030292519367,
0
] | 0.000033 | 5 |
[
"galaxy-auth\ngalaxy-job-execution\ngalaxy-job-metrics\ngalaxy-tool-util\ngalaxy-web-framework\ngalaxy-web-stack\n"
] | {
"pile_set_name": "Github"
} | [
0
] | 0 | 5 |
[
"Jim,\n\nAttached is our report for WTG 79 which answers the questions posed by \nEickoff. ",
" Please note that we provided more information than we were asked \nfor in anticipation of additional questions from them, yourself and \nengineering. ",
" In the attached report we have provided graphs which cover the \nprevious month (versus the previous week), the production since commissioning \n(through February), and a fault list.",
"\n\nThe gaps in the data occur wherever the SCADA system did not record data or \nit was corrupted in some way. ",
" Please note the fault data is particularly \nsusceptible to data integrity problems but it does appear that we had pretty \ngood data recovery during this period.",
"\n\nIn the graph section we included a graph of Gen rpm/rotor rpm which should \nyield the gearbox gear ratio (a constant). ",
" However, interestingly enough the \nvalues fluctuated from time to time which we cannot explain.",
"\n\nWe will have Trent Mesa WTG #30 for you tomorrow morning.",
"\n\nBest Regards,\nHollis"
] | {
"pile_set_name": "Enron Emails"
} | [
0.0001321178491214163,
0,
0,
0,
0,
0.00006830134553650708,
0,
0,
0
] | 0.000022 | 5 |
[
"₵Ahmed Ali, also known as Palani Baba, murdered in 1997 at Pollachi, India, was founder and leader of the All India Jihad Committee in Tamil Nadu, India.",
"\nOn January 28, 1997, Palani Baba was hacked to death by six persons, five of whom were later sentenced to life imprisonment. ",
"The motive for the slaying was said to be the group called RSS's personal grudge against Palani Baba. ",
"The murder resulted in riots in Coimbatore district, Tamil Nadu.",
"\nLater in 2005 the Madras High Court acquitted the five accused.",
"\nHe was buried near New Ayakudi in Palani Taluk. ",
"His cemetery is located just opposite to the ITO school, in New Ayakudi village.",
"\n\nThis is an excerpt from the article Palani Baba from the Wikipedia free encyclopedia. ",
"A list of authors is available at Wikipedia.",
"\n\nThe article Palani Baba at en.wikipedia.org was accessed 895 times in the last 30 days. (",
"as of: 08/17/2014)\n\nThe lSl had also been trying to make inroads into southern lndia. ",
"The lSl-funded\nand banned lslamic Sevak Sangh, which became very active in neighbouring\nKerala, managed to gain a foothold in Tamil Nadu also due to Palani Baba's\nefforts.",
"\n\nThe book will explore contemporary manifestations of the worship of Siva that have transmigrated to the West. ",
"It explores Hindu vernacular traditions or 'village Hinduism' especially in the context of the Hindu diaspora, where the general assumption is that such forms of Hinduism cannot survive as they lack the infrastructure and the rura...\n\nThe bomb blast in the RSS building in Chennai in August 1993 and the murder of\nHindu Munnani State president P. Rajagopalan in Madurai in October 1994 and\nthat of Jihad Committee chief Palani Baba in January 1997 at Pollachi near ...\n\n14.1 .1.1 Basinal (Palani and Tarjil formations) 14.1.1.1.1 Palani Formation The Palani Formation was defined by Bellen in ... the Palani Formation is only present\nin the Baba dome in the SE of the anticline, and overlies the Avanah Formation.",
"\n\nThe ISI had also been trying to make inroads into southern India. ",
"The ISI-funded\nand banned Islamic Sevak Sangh, which became very active in neighbouring\nKerala, managed to gain a foothold in Tamil Nadu also due to Palani Baba's\nefforts."
] | {
"pile_set_name": "Pile-CC"
} | [
0.00008543722499893203,
0,
0.00009611687812379854,
0.000244140625,
0.000244140625,
0.0004164931278633902,
0,
0.00012913223140495868,
0.0005165289256198347,
0.00012075836251660429,
0,
0.00010259567046270647,
0.00007971938775510203,
0.000015736600776207834,
0.00021626297577854672,
0.00013679422728360863
] | 0.00015 | 5 |