Di Maria loses a hopeful ball out of bounds on the left.
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Pushing the bounds on space requires investments in science, technology, engineering, and math education.
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The park often celebrates creative Disney bounds on Twitter and openly encourages guests to participate.
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There is good reason to hope the court will finally set bounds on partisan gerrymandering.
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She stepped out of bounds on her bread-and-butter floor routine — a big penalty.
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Another guy said that it wasn't goaltending, it just went out of bounds on us.
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But the researchers found a way to put bounds on the possible properties of that theory.
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Structural racism sets bounds on who has access to that food, or healthcare, or clothing, or shelter.
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James stepped out of bounds on a drive to the basket with less than two seconds left.
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Structural racism sets bounds on who has access to that food, or healthcare, or clothing,or shelter.
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He said he began voicing his concerns to leadership on Wednesday and talked to Bounds on Thursday.
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Robinson rumbled down the sideline and was forced out of bounds on the Cardinal 21-yard line.
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On the 27th, Saunders hit his drive out of bounds on the left, incurring a one-stroke penalty.
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Jackson deflected the ball out of bounds on the inbounds, reducing the clock to 0.5 of a second.
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"We're just trying to put some bounds on the testing on the roadways," NTSB chair Robert Sumwalt said.
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He has demeaned the presidency by engaging in name calling that is simply out of bounds on most playgrounds.
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She also had a double bogey after driving out of bounds on the par-4 third and three bogeys.
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Davis was hurt diving into the stands to stop a ball from going out of bounds on the defensive end.
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Whether or not Twitter also struggles to define its bounds on these types of issues will remain to be seen.
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Harry was incorrectly ruled out of bounds on the play and the Patriots had to settle for a field goal.
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And, as mentioned, promotions must be ignored, so these estimates are plausibly upper bounds on the set-top box fees.
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On floor, Alex Naddour fell on his final tumbling pass and Sam Mikulak went out of bounds on his first two.
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Elizabeth Warren still bounds on stage at campaign events like she just heard the starter pistol, often shouting "Woo-hoo" for emphasis.
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Early in the fourth quarter, backup quarterback Austin Kendall suffered an apparent knee injury sliding out of bounds on the Owls' sideline.
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Congress has already passed, and is expected to pass more process changes that put significant bounds on federal regulators overall, including the FCC.
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"As experiments get more sensitive, they put ever more stringent bounds on the interactions of dark matter and the visible particles," Davoudiasl explained.
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" Bosch had effectively removed the historical bounds on crop yields, so much so that he was widely credited with making "bread from air.
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Your optimism knows no bounds on Sunday when Mercury connects with lucky Jupiter, encouraging you to spread a positive mental attitude as far as you can.
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Wilson was stopped short in bounds on a third-down run with 21999 seconds remaining in the second quarter, but the clock stopped when he was flagged.
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Turner missed the free throw, but the ball went out of bounds on the Cavaliers, leaving the Celtics with possession and one final shot to win it.
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Originally, Beasley was called out of bounds on the field, but after review was ruled to have gotten his knee down before his elbows landed out of bounds.
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Going out-of-bounds on the 10th led to another double-bogey, and he dropped two more shots at the 13th, where his tee shot sailed way left.
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Arizona averted a semi-disaster when Wilson apparently hit Siasoi Wilson for an 8-yard touchdown, but after further review Wilson was ruled out of bounds on the catch.
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But Williams went out of bounds on his own and re-entered the field and was called for illegal touching, wiping out what would have been a game-winner.
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First there was the controversial call on wide receiver DeAndre Hopkins, who was ruled out of bounds on what at first appeared to be a 60-yard touchdown run.
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The latter was no gimmie from 45 yards out and had to be done with the clock running, as Antonio Gates was tackled in bounds on the previous play.
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His drive to the basket with 11 seconds remaining made it 116-113, and Monk missed a 3-pointer before Walker lost the ball out of bounds on the sideline.
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His left foot stepped out of bounds on the play, with his knee buckling awkwardly, before he endured hard contact to his upper body on a hit by Steve Nelson.
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Voice recognition still has a way to go but Apple, Amazon, and Google have made leaps and bounds on advancements in voice recognition with Siri, Alexa and Google Assistant, respectively.
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Democrat pressed Bounds on newspaper columns he wrote as a student at Stanford University in the 1990s that they said showed an insensitively toward racial minorities and victims of sexual harassment.
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Chris Paul picked up a technical in the final minute, J.J. Redick fumbled the ball out of bounds on the next possession, and the team left the court in a huff.
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Tim Hardaway Jr. was ruled out of bounds on the ensuing possession and the Knicks lost their third straight game and sixth of eight to fall a season-worst eight games under .
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He had been striving to peak for this tournament, but immediately put himself in a huge deficit, hitting out of bounds on the first hole and finishing it with a quadruple bogey.
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Johnson was a stroke off the lead in the last round of the 2011 British Open at Royal St. George's when he hit a long iron out-of-bounds on a par 5.
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He did not return ... Broncos defensive coordinator Wade Phillips was leveled in a sideline collision late in the second quarter, when Steelers WR Martavis Bryant was driven out of bounds on a reverse.
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Ian Clark came up well short of the rim on a wide-open 3-pointer and Andre Iguodala simply threw the ball out of bounds on a pass that dramatically missed its mark.
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Victor Oladipo threw a pass about five feet above Westbrook's head and out of bounds on the next possession, and Harden made a layup on the other end with about three minutes left.
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But then, in a swirl of black robes, the boyish figure of Judge Jack Durkin, 60, bounds on to the bench, and starts peppering them with questions about how life is treating them.
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As he digs up weeds and bounds on top of anyone who'll dare play with him, he's nothing if not a conversation starter; Amber strikes up chats with every fellow dog owner who passes.
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While many will focus on whether Parks's foot went out of bounds on the return, the Broncos won the game not just because of the return but also because they dominated time of possession.
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Bombarded from all sides, Warren could also sound mildly exasperated at times, a far cry from the joyful Warren of the campaign trail, who bounds on stage, tells personal stories, and poses for selfies.
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Further, the Brady Act even specified that people who suffer from mental illnesses are not designated "mentally defective"; therefore, it becomes more obvious that the VA has stepped out of bounds on this issue.
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His nomination was withdrawn minutes before a floor vote, when Senator Tim Scott of South Carolina, the only African-American Republican in the Senate, announced that he wouldn't vote for Bounds on account of those columns.
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Williams came close to stepping out of bounds on the touchdown catch, but he reached the ball over the pylon to break the plane of the goal line and the play was upheld after a review.
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Battling a kidney stone that she insisted was manageable, Biles fell twice — sitting down her vault in the first rotation and coming off the beam on her third — and stepped out of bounds on the floor exercise.
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At his confirmation hearing in May, Democratic senators pressed Bounds on newspaper columns he wrote as a student at Stanford University in the 1990s that they said showed an insensitively toward racial minorities and victims of sexual harassment.
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It reiterates the rule that US law doesn't apply outside the US …[And] it keeps foreigners' data secure from the US government, which has shown again and again that it's willing to overstep reasonable bounds on its power.
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Though she stepped out of bounds on her third pass, her score of 14.933 was a full point better than that of her teammate Morgan Hurd, who earned her third medal of the meet by finishing with silver.
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Verniaiev was a bit shaky as he went out of bounds on the floor exercise and even took a big hop on his high bar routine to finish second in his group behind Cuba's 2015 silver medalist Manrique Larduet.
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Early in the second quarter, Gamecocks wide receiver Bryan Edwards was ruled out of bounds on a 216-yard catch in the end zone, only for a video review to reveal that he was in fact in, making it 242-227.
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WeWork is uniquely positioned to invest in workplace technology and services, and I look forward to partnering with their team to build more robust products for our clients and create a global platform to help companies push the bounds on our collective potential.
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Testing to failure is a crucial component of the development of any new spacecraft, because it means you can set the real-world bounds on what the spacecraft can withstand, and in actual use scenarios rather than just in simulation or in theory.
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Perhaps it's unfair to make the receiver the scapegoat for the Cowboys loss, though his decision not to run out of bounds on what ended up being the game's final play did cost Dallas a chance for a desperation 63-ish-yard field goal attempt.
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Jerome Travers, an amateur, made the turn in the final round knowing he needed a solid closing nine to win the title, but he began the homestretch with an awful shot, a ball struck by a driving iron sliced out of bounds on the 21915th.
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Tannehill overthrew an open Kenny Stills to open the Dolphins' final drive, which started at the Miami 22-yard line, then Seattle defensive Cassius Marsh forced him to fumble the ball out of bounds on second down, with 2723 seconds left on the clock.
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Justin Thomas, in his debut as the No. 123 player in the world, was trading birdies and bogeys and was making progress until he hit his approach out-of-bounds on the par-212 seventh hole and made double bogey, sending him to a 23.
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It's important to note that while we welcome a multitude of viewpoints, we also believe strongly that people should feel – and be – safe when they use Facebook, and we therefore have Community Standards that define the behavior that we think is out-of-bounds on the platform.
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That she managed to win the all around gold despite making glaring errors on her three strongest apparatus — a wobble on the beam, a tumble out of bounds on the floor and giant hop forward from her Amanar vault landing — was testament to what she can do.
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In the 30th minute of West Ham vs Sunderland, Antonio saved the ball from going out of bounds on the touchline, took on two defenders, then confronted three more as he rocketed off a shot that neatly tucked itself into the corner of the post and net.
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The deconstruction of a Fred Rogers figure would make for an interesting show on its own, but Kidding transcends that premise by leaps and bounds on the strength of Carrey's performance and a determination to make the show just as rough — and riveting — as real life.
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While the Fed may need "more specialized responses" to the use of artificial intelligence or computer algorithms in assessing risk and making credit decisions, he said he was hesitant to impose "bounds" on what institutions can do, rather than develop "milestones" or circuit breakers that would pause any process that was producing bad results.
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The call was reversed in the Patriots' favor, but that was New England's last challenge, which prevented it from challenging a later play in which wide receiver N'Keal Harry was incorrectly ruled out of bounds on his way to the end zone — forcing New England to settle for a field goal on that drive.
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The White House formally withdrew President TrumpDonald John TrumpFacebook releases audit on conservative bias claims Harry Reid: 'Decriminalizing border crossings is not something that should be at the top of the list' Recessions happen when presidents overlook key problems MORE's controversial circuit court nomination for Ryan Bounds on Tuesday, almost a week after Senate Majority Leader Mitch McConnellAddison (Mitch) Mitchell McConnellPelosi, Schumer press for gun screenings as Trump inches away The malware election: Returning to paper ballots only way to prevent hacking First House Republican backs bill banning assault weapons MORE (R-Ky.) announced that his nomination would not make it to a vote due to lack of support.
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The upper bounds on cap sets imply lower bounds on certain types of algorithms for matrix multiplication..
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APOLLO will place much tighter bounds on any such variations.
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In 1902, he derived Bendixson's inequality which puts bounds on the characteristic roots of matrices.
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59 (2001), no. 3, 479–522.Donaldson, S.K. Lower bounds on the Calabi functional. J. Differential Geom.
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The intuition behind the CDF-based approach is that bounds on the CDF of a distribution can be translated into bounds on statistical functionals of that distribution. Given an upper and lower bound on the CDF, the approach involves finding the CDFs within the bounds that maximize and minimize the statistical functional of interest.
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The idea of bounding probability has a very long tradition throughout the history of probability theory. Indeed, in 1854 George Boole used the notion of interval bounds on probability in his The Laws of Thought. Also dating from the latter half of the 19th century, the inequality attributed to Chebyshev described bounds on a distribution when only the mean and variance of the variable are known, and the related inequality attributed to Markov found bounds on a positive variable when only the mean is known. KyburgKyburg, H.E., Jr. (1999).
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In Ramsey theory, graphs constructed using generalized polygons give us some of the best known constructive lower bounds on offdiagonal Ramsey numbers.
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The full statement of Vinogradov's theorem gives asymptotic bounds on the number of representations of an odd integer as a sum of three primes.
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The PSVM minimizes a new objective which ensures theoretical bounds on the generalization error and automatically selects features which are used for classification or regression.
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There are dual interpretations of a p-box. It can be understood as bounds on the cumulative probability associated with any x-value. For instance, in the p-box depicted at right, the probability that the value will be 2.5 or less is between 4% and 36%. A p-box can also be understood as bounds on the x-value at any particular probability level.
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Odlyzko, A. M., Sloane, N. J. A. New bounds on the number of unit spheres that can touch a unit sphere in n dimensions. J. Combin.
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As discussed below, it is also possible to place error bounds on the accuracy of the value of a definite integral estimated using a trapezoidal rule.
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In mathematics, the Poincaré inequality is a result in the theory of Sobolev spaces, named after the French mathematician Henri Poincaré. The inequality allows one to obtain bounds on a function using bounds on its derivatives and the geometry of its domain of definition. Such bounds are of great importance in the modern, direct methods of the calculus of variations. A very closely related result is Friedrichs' inequality.
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Naor's research concerns metric spaces, their properties, and related algorithms, including improved upper bounds on the Grothendieck inequality, applications of this inequality, and research on metrical task systems.
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1901) and Sicci G. Owens (b. 1904). Ella died on May 10, 1908. 2) Lucy H. Bounds on May 19, 1909. They had two children: Murdice L. Owens (b.
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In part because the Shannon capacity is difficult to compute, researchers have looked for other graph invariants that are easy to compute and that provide bounds on the Shannon capacity.
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The Rademacher complexity can be used to derive data-dependent upper-bounds on the learnability of function classes. Intuitively, a function-class with smaller Rademacher complexity is easier to learn.
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Specifically Cook and Reckhow observed that proving proof size lower bounds on stronger and stronger propositional proof systems can be viewed as a step towards separating NP from coNP (and thus P from NP), since the existence of a propositional proof system that admits polynomial size proofs for all tautologies is equivalent to NP=coNP. Contemporary proof complexity research draws ideas and methods from many areas in computational complexity, algorithms and mathematics. Since many important algorithms and algorithmic techniques can be cast as proof search algorithms for certain proof systems, proving lower bounds on proof sizes in these systems implies run time lower bounds on the corresponding algorithms. This connects proof complexity to more applied areas such as SAT solving.
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Behrend's work covered a wide range of topics, and often consisted of "a new approach to questions already deeply studied". He began his research career in number theory, publishing three papers by the age of 23. His doctoral work provided upper and lower bounds on the density of the abundant numbers. He also provided elementary bounds on the prime number theorem, before that problem was solved more completely by Paul Erdős and Atle Selberg in the late 1940s.
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Choie works on various aspects of Jacobi forms. Together with Winfried Kohnen, she has proved upper bounds on the first sign change of Fourier coefficients of cusp forms, generalizing the work of Siegel.
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The upper bound was later improved by Laurent BartholdiLaurent Bartholdi. Lower bounds on the growth of a group acting on the binary rooted tree. International Journal of Algebra and Computation, vol. 11 (2001), no.
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Stein's method is a general method in probability theory to obtain bounds on the distance between two probability distributions with respect to a probability metric. It was introduced by Charles Stein, who first published it in 1972, to obtain a bound between the distribution of a sum of m-dependent sequence of random variables and a standard normal distribution in the Kolmogorov (uniform) metric and hence to prove not only a central limit theorem, but also bounds on the rates of convergence for the given metric.
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Probability bounds analysis (PBA) is a collection of methods of uncertainty propagation for making qualitative and quantitative calculations in the face of uncertainties of various kinds. It is used to project partial information about random variables and other quantities through mathematical expressions. For instance, it computes sure bounds on the distribution of a sum, product, or more complex function, given only sure bounds on the distributions of the inputs. Such bounds are called probability boxes, and constrain cumulative probability distributions (rather than densities or mass functions).
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In this scenario, any bipartite experiment revealing Bell nonlocality can just provide lower bounds on the hidden influence's propagation speed. Quantum experiments with three or more parties can, nonetheless, disprove all such non-local hidden variable models.
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On November 7, Nebraska defeated Michigan State by a score of 39–38. Nebraska ran a 91-yard scoring drive in 38 seconds, capped by Tommy Armstrong Jr.'s 30-yard touchdown pass to Brandon Reilly, leaving 17 seconds left in the fourth quarter. Before the catch, Reilly went out of bounds on his route, making him an ineligible receiver. Replay officials determined that Michigan State cornerback Jermaine Edmondson had forced him out of bounds, although replay footage seemed to show that Reilly had gone out of bounds on his own accord.
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Many of the known lower bounds on Ramsey numbers come from examples of circulant graphs that have small maximum cliques and small maximum independent sets.Small Ramsey Numbers, Stanisław P. Radziszowski, Electronic J. Combinatorics, dynamic survey 1, updated 2014.
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This structure theory has led to new advances in polyhedral combinatorics and new bounds on the chromatic number of claw-free graphs, as well as to new fixed- parameter-tractable algorithms for dominating sets in claw-free graphs.
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Better asymptotic bounds on the time required to multiply matrices have been known since the work of Strassen in the 1960s, but it is still unknown what the optimal time is (i.e., what the complexity of the problem is).
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In probability theory, the Chernoff bound, named after Herman Chernoff but due to Herman Rubin, gives exponentially decreasing bounds on tail distributions of sums of independent random variables. It is a sharper bound than the known first- or second-moment-based tail bounds such as Markov's inequality or Chebyshev's inequality, which only yield power-law bounds on tail decay. However, the Chernoff bound requires that the variates be independent – a condition that neither Markov's inequality nor Chebyshev's inequality require, although Chebyshev's inequality does require the variates to be pairwise independent. It is related to the (historically prior) Bernstein inequalities and to Hoeffding's inequality.
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In mathematics, a univariate polynomial of degree with real or complex coefficients has complex roots, if counted with their multiplicities. They form a set of points in the complex plane. This article concerns the geometry of these points, that is the information about their localization in the complex plane that can be deduced from the degree and the coefficients of the polynomial. Some of these geometrical properties are related to a single polynomial, such as upper bounds on the absolute values of the roots, which define a disk containing all roots, or lower bounds on the distance between two roots.
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Arithmetic and other operations on Dempster–Shafer structures. International Journal of Man-machine Studies 25: 357–366. described the elementary procedures by which bounds on convolutions can be computed under an assumption of independence. At about the same time, Makarov,Makarov, G.D. (1981).
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Lieb–Robinson bounds are used in many areas of mathematical physics. Among the main applications of the bound there is the error bounds on quantum simulation algorithms, the existence of the thermodynamic limit, the exponential decay of correlations and the Lieb–Schultz–Mattis theorem.
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USA Today. August 9, 2012. Retrieved August 14, 2012. In the floor final, Wieber placed seventh with a score of 14.500 after going out of bounds on her second tumbling pass (her score from the team final would've been enough to win the bronze medal).
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Some types of SerDes include encoding/decoding blocks. The purpose of this encoding/decoding is typically to place at least statistical bounds on the rate of signal transitions to allow for easier clock recovery in the receiver, to provide framing, and to provide DC balance.
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In 1969, Jeanne Ferrante received her B.A. from New College at Hofstra University in Natural Sciences, with High Honors in Mathematics. She went on to complete a Ph.D. at MIT and wrote her thesis "Some Upper and Lower Bounds on Decision Procedures in Logic".
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Other results in the generic group model are for instance.Ueli M. Maurer, Stefan Wolf: Lower Bounds on Generic Algorithms in Groups. EUROCRYPT 1998: 72-84 The model can also be extended to other algebraic structures like rings.Divesh Aggarwal, Ueli Maurer: Breaking RSA Generically Is Equivalent to Factoring.
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The inequality can also be used to prove Beck's theorem, that if a finite point set does not have a linear number of collinear points, then it determines a quadratic number of distinct lines.. Similarly, Tamal Dey used it to prove upper bounds on geometric k-sets.
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But every spectrum in the field GF(q^m) and zero at certain components may not have inverse transforms with components in the field GF(q). Such spectrum can not be used as cyclic codes. Following are the few bounds on the spectrum of cyclic codes.
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In 1977 Musgrove married Melanie Ballard. In 2001, while Musgrove was governor, the couple divorced after 24 years of marriage. The results and settlement of the divorce were sealed by the judge at the request of the Musgroves. Musgrove married Dr. Melody Bounds on August 4, 2007.
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The bound on the total number of cliques follows easily from the bounds on triangles and K4 subgraphs, and is also stated explicitly by , who provides an Apollonian network as an example showing that this bound is tight. For generalizations of these bounds to nonplanar surfaces, see .
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As well as developing Jarník's algorithm, he found tight bounds on the number of lattice points on convex curves, studied the relationship between the Hausdorff dimension of sets of real numbers and how well they can be approximated by rational numbers, and investigated the properties of nowhere-differentiable functions.
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When producing bounds on the CDF, we must differentiate between pointwise and simultaneous bands. Illustration of different CDF bounds. This shows CDF bounds generated from a random sample of 30 points. The purple line is the simultaneous DKW bounds which encompass the entire CDF at 95% confidence level.
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Erdős, Rényi, and Szüsz asked for nontrivial bounds on the length of the finite Engel expansion of a rational number x/y; this question was answered by Erdős and Shallit, who proved that the number of terms in the expansion is O(y1/3 + ε) for any ε > 0.; .
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It is also possible to compute interval bounds on the conjunction or disjunction under other assumptions about the dependence between A and B. For instance, one might assume they are positively dependent, in which case the resulting interval is not as tight as the answer assuming independence but tighter than the answer given by the Fréchet inequality. Comparable calculations are used for other logical functions such as negation, exclusive disjunction, etc. When the Boolean expression to be evaluated becomes complex, it may be necessary to evaluate it using the methods of mathematical programming to get best-possible bounds on the expression. A similar problem one presents in the case of probabilistic logic (see for example Gerla 1994).
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In particular, if the number of public bits shared between Alice and Bob are not counted against the communication complexity, it is easy to argue that computing any function has O(1) communication complexity. On the other hand, both models are equivalent if the number of public bits used by Alice and Bob is counted against the protocol's total communication. Though subtle, lower bounds on this model are extremely strong. More specifically, it is clear that any bound on problems of this class immediately imply equivalent bounds on problems in the deterministic model and the private and public coin models, but such bounds also hold immediately for nondeterministic communication models and quantum communication models.
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The length of such a sequence, for a given choice of k, can be only slightly longer than its number of distinct symbols. This phenomenon has been used to prove corresponding near-linear bounds on various problems in discrete geometry, for instance showing that the unbounded face of an arrangement of line segments can have complexity that is only slightly superlinear. The book is about this family of results, both on bounding the lengths of Davenport–Schinzel sequences and on their applications to discrete geometry. The first three chapters of the book provide bounds on the lengths of Davenport–Schinzel sequences whose superlinearity is described in terms of the inverse Ackermann function \alpha(n).
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I Math. 294 (1982), no. 14, bounds for the order of the Tate–Shafarevich groupGoldfeld, Dorian; Szpiro, Lucien Bounds for the order of the Tate–Shafarevich group, Compositio Mathematica 97 (1995), no. 1-2, Goldfeld, Dorian; Lieman, Daniel Effective bounds on the size of the Tate–Shafarevich group. Math. Res. Lett.
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Distance estimates for poisson process approximations of dependent thinnings. Electronic Journal of Probability, 10:165–201, 2005. Stein's method has also been used to derive upper bounds on metrics of Poisson and other processes such as the Cox point process, which is a Poisson process with a random intensity measure.
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These algorithms try to directly optimize the value of one of the above evaluation measures, averaged over all queries in the training data. This is difficult because most evaluation measures are not continuous functions with respect to ranking model's parameters, and so continuous approximations or bounds on evaluation measures have to be used.
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During event finals, Johnson first competed on the balance beam, where she fell on her standing full and on her switch side leap, scoring a 14.475 and finishing last. In floor exercise, she went out-of-bounds on her first tumbling pass, but won the gold with a 15.250, just eclipsing teammate Sacramone.
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Though Occam and PAC learnability are equivalent, the Occam framework can be used to produce tighter bounds on the sample complexity of classical problems including conjunctions, conjunctions with few relevant variables,Haussler, D. (1988). Quantifying inductive bias: AI learning algorithms and Valiant's learning framework . Artificial intelligence, 36(2), 177-221. and decision lists.
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A simplicial line arrangement (left) and a simple line arrangement (right). In geometry an arrangement of lines is the partition of the plane formed by a collection of lines. Bounds on the complexity of arrangements have been studied in discrete geometry, and computational geometers have found algorithms for the efficient construction of arrangements.
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Sixteen fourth powers are always needed to write a number of the form 31·16n. 617597724 is the last number less than 1.3 which requires ten fifth powers, and 51033617 the last number less than 1.3 which requires eleven. The upper bounds on the right with are due to Vaughan and Wooley.
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V. Protasov, R. M. Jungers, and V. D. Blondel. "Joint spectral characteristics of matrices: a conic programming approach." SIAM Journal on Matrix Analysis and Applications, 2008. The advantage of these methods is that they are easy to implement, and in practice, they provide in general the best bounds on the joint spectral radius.
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Thus, the diameter provides a lower bound on the number of steps this method requires. The Hirsch conjecture, now disproved, suggested a strong bound on how large the diameter could be. Weaker (quasi-polynomial) upper bounds on the diameter are known, as well as proofs of the Hirsch conjecture for special classes of polytope.
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Interval valued probabilities. SIPTA Documention on Imprecise Probability. reviewed the history of interval probabilities and traced the development of the critical ideas through the 20th century, including the important notion of incomparable probabilities favored by Keynes. Of particular note is Fréchet's derivation in the 1930s of bounds on calculations involving total probabilities without dependence assumptions.
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The Fisher information has been used to find bounds on the accuracy of neural codes. In that case, X is typically the joint responses of many neurons representing a low dimensional variable θ (such as a stimulus parameter). In particular the role of correlations in the noise of the neural responses has been studied.
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Stochastic effect on aerial image. Due to EUV doses generally being low, the statistical bounds on the image are noticeably large. An individual location within a large feature population could suffer a severe image distortion as depicted here. As light consists of photons, at low doses the image quality ultimately depends on the photon number.
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In the early stage of his career, Colding did impressive work on manifolds with bounds on Ricci curvature. In 1995 he presented this work at the Geometry Festival. He began working with Jeff Cheeger while at NYU. He gave a 45-minute invited address to the ICM on this work in 1998 in Berlin.
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In mathematics, the limit inferior and limit superior of a sequence can be thought of as limiting (i.e., eventual and extreme) bounds on the sequence. They can be thought of in a similar fashion for a function (see limit of a function). For a set, they are the infimum and supremum of the set's limit points, respectively.
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In mathematical analysis, the Chebyshev-Markov-Stieltjes inequalities are inequalities related to the problem of moments that were formulated in the 1880s by Pafnuty Chebyshev and proved independently by Andrey Markov and (somewhat later) by Thomas Jan Stieltjes. Informally, they provide sharp bounds on a measure from above and from below in terms of its first moments.
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After presiding in the exchequer for five years, Smythe was compelled in November 1777 to resign because of bad health. He was granted a pension of £2,400, and on 3 December was sworn a member of the privy council. He died at Old Bounds on 2 November 1778, and was buried at Sutton-at-Hone, Kent.
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The legislature may design some criminal prohibitions to place bounds on the kinds of governmental conduct that can be authorized by the Executive. Or the legislature may enact a criminal prohibition in order to limit the scope of the conduct that the legislature has otherwise authorized the Executive to undertake pursuant to another statute. See, e.g., Nardone v.
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His 2006 season ended when he broke his left ankle in the seventh game against the Carolina Panthers, after being tackled out of bounds on a kickoff return. In 2007, he was declared inactive in 9 games and was not re- signed at the end of the year, after losing his returner job to Miles Austin.
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Weaker adversaries can use this attack in combination with other attacks to cause more issues. Mix networks derive security by changing order of messages they receive to avoid creating significant relation between the incoming and outgoing messages. Mixes create interference between messages. The interference puts bounds on the rate of information leak to an observer of the mix.
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A major open problem in finite semigroup theory is the decidability of complexity: is there an algorithm that will compute the Krohn–Rhodes complexity of a finite semigroup, given its multiplication table? Upper bounds and ever more precise lower bounds on complexity have been obtained (see, e.g. Rhodes & Steinberg, 2009). Rhodes has conjectured that the problem is decidable.
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Interval arithmetic, interval mathematics, interval analysis, or interval computation, is a method developed by mathematicians since the 1950s and 1960s as an approach to putting bounds on rounding errors and measurement errors in mathematical computation and thus developing numerical methods that yield reliable results. Interval arithmetic helps find reliable and guaranteed solutions to equations and optimization problems.
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A maxsum division is not always fair; see the example above. Similarly, a fair division is not always maxsum. One approach to this conflict is to bound the "price of fairness" - calculate upper and lower bounds on the amount of decrease in the sum of utilities, that is required for fairness. For more details, see price of fairness.
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Acyclic coloring. Every graph G with acyclic chromatic number k has \chi_g(G) \le k(k+1). Marking game. For every graph G, \chi_g(G) \le col_g(G), where col_g(G) is the game coloring number of G. Almost every known upper bound for the game chromatic number of graphs are obtained from bounds on the game coloring number.
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The lower courts had used the Court's decision in Burson to assert the Minnesota law was similarly valid. The Court instead ruled 7-2 that unlike Burson, which set narrow bounds on what the state could restrict around polling places (specifically, political campaigning speech), the Minnesota laws was too vague on what was allowed or not, and reversed the decision of lower courts.
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With respect to certain appropriately normalised inequalities, the independence number, Lovász number, and fractional packing number of the graph of an experimental scenario provide tight upper bounds on the degree to which classical theories, quantum theory, and generalised probabilistic theories, respectively, may exhibit contextuality in an experiment of that kind. A more refined framework based on hypergraphs rather than graphs is also used.
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Edmonds received his Bachelors at Waterloo in 1987 and his Ph.D. in 1993 at University of Toronto. His thesis proved lower bounds on time-space tradeoffs. He did his post-doctorate work at the ICSI in Berkeley on secure data transmission over networks for multi-media applications. He joined Department of EECS at Lassonde School of Engineering York University in 1995.
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In mathematics, the Legendre sieve, named after Adrien-Marie Legendre, is the simplest method in modern sieve theory. It applies the concept of the Sieve of Eratosthenes to find upper or lower bounds on the number of primes within a given set of integers. Because it is a simple extension of Eratosthenes' idea, it is sometimes called the Legendre–Eratosthenes sieve.Iwaniec, Henryk.
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The pseudorandom generators used in cryptography and universal algorithmic derandomization have not been proven to exist, although their existence is widely believed. Proofs for their existence would imply proofs of lower bounds on the circuit complexity of certain explicit functions. Such circuit lower bounds cannot be proved in the framework of natural proofs assuming the existence of stronger variants of cryptographic pseudorandom generators.
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He first perform complete calculation of the amplitude of Do-D-o mixing and the analyses of the consequence of Bo-B-o mixing immediately after its discovery. He also derived new bounds on masses and couplings of gauge bosons, exotic fermions and supersymmetric particles using the data from the Large Electron Positron (LEP) collider at CERN and the Tevatron collider at Fermilab.
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This would be an incredible coincidence since WEP and SEP depend on very different and arbitrary properties – the exact composition of the Earth and the Moon, and their self-energies. But this unlikely case cannot be completely ruled out until either other solar system bodies are measured to similar precision, or laboratory experiments reduce the bounds on WEP violations alone.
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In probability theory, the Markov–Krein theorem gives the best upper and lower bounds on the expected values of certain functions of a random variable where only the first moments of the random variable are known. The result is named after Andrey Markov and Mark Krein. The theorem can be used to bound average response times in the M/G/k queueing system.
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The table below is a brief chronology of computed numerical values of, or bounds on, the mathematical constant pi (). For more detailed explanations for some of these calculations, see Approximations of . Graph showing how the record precision of numerical approximations to pi measured in decimal places (depicted on a logarithmic scale), evolved in human history. The time before 1400 is compressed.
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Although her conjecture led to subsequent research in the same area, it has been shown to be inconsistent with the actual average packing density in dimensions two through four. Palásti's results in the theory of random graphs include bounds on the probability that a random graph has a Hamiltonian circuit, and on the probability that a random directed graph is strongly connected.
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A 1902 illustration of the two species The picathartes are large ( long) passerines with crow-like black bills, long neck, tail, and legs. They weigh between . The strong feet and grey legs are adapted to terrestrial movement, and the family progresses through the forest with long bounds on the ground. The wings are long but are seldom used for long flights.
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F. Yang, S. Wang, and C. Deng, "Compressive sensing of image reconstruction using multi-wavelet transform", IEEE 2010 The current smallest upper bounds for any large rectangular matrices are for those of Gaussian matrices.B. Bah and J. Tanner "Improved Bounds on Restricted Isometry Constants for Gaussian Matrices" Web forms to evaluate bounds for the Gaussian ensemble are available at the Edinburgh Compressed Sensing RIC page.
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Also top quark pairs have been examined in the D0 experiment (2012). They showed that the cross section production of these pairs doesn't depend on sidereal time during Earth's rotation. Lorentz violation bounds on Bhabha scattering have been given by Charneski et al. (2012). They showed that differential cross sections for the vector and axial couplings in QED become direction dependent in the presence of Lorentz violation.
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Beavan, Aldermen of London, II, p. 40; Simpson, 'Antiquities', p. 387. A new Lord Mayor's pew was constructed in 1590 (on the south side at the east end), and the "Green Men" had their weapons and shields refurbished. Through the 1590s several dinners are recorded, including those for the parson, curate, wardens and sidesmen at the Visitations, and for beating the bounds on Ascension Day.
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A generalization of the fork- join queueing system is the (n,k) fork-join system where the job exits the system when any k out of n tasks are served. The traditional fork-join queueing system is a special case of the (n,k) system when k = n . Bounds on the mean response time of this generalized system were found by Joshi, Liu and Soljanin.
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9th hole in 2006 The first hole, a short Par-5, is an easy beginning hole. The tee is elevated above the fairway, tempting players to hit driver but out of bounds on the left side and a barranca crossing the fairway make players cautious. Scores range from eagle to double bogey. The second hole is a long par four that plays uphill and into the wind.
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The umpire copped a bit of abuse from the opposition but that was par for the course. It was in the days of the one central umpire. The out of bounds on the full rule had only just been introduced and of course it was applied. Some of the older heads were not too happy but recognized that it had become a law of the game.
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In 1997, ESPN College Gameday broadcast from East Lansing, as No. 5 Michigan defeated No. 15 Michigan State, 23–7. The Wolverines intercepted six Spartan passes, five off Spartan quarterback Todd Schultz. The interceptions included a one-handed catch by eventual 1997 Heisman Trophy winner Charles Woodson after which he managed to get one foot in bounds on the sideline. Marcus Ray had a pair of interceptions.
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Because training sets are finite and the future is uncertain, learning theory usually does not yield guarantees of the performance of algorithms. Instead, probabilistic bounds on the performance are quite common. The bias–variance decomposition is one way to quantify generalization error. For the best performance in the context of generalization, the complexity of the hypothesis should match the complexity of the function underlying the data.
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Excavation was funded by the Heritage Lottery Fund in 2017. Newport appears prominently on a 1578 parish map of Pembrokeshire, and is a former marcher borough. George Owen of Henllys, in 1603, described it as one of five Pembrokeshire boroughs overseen by a portreeve. It retains some of the borough customs such as electing a mayor, who beats the bounds on horseback every August.
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Daniel was a punter for the Tennessee Volunteers in college. In the 2015 season, Daniel executed a punt late in the rivalry game against Georgia that helped set up the Vols' first victory over the Bulldogs in several years. The punt went out of bounds on the Bulldogs' half-yard line. In his four years with the Volunteers, Daniel's average punting average was fifth in the nation.
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The estimate is a specific value of a functional approximation to f(x) = over the interval. Obtaining a better estimate involves either obtaining tighter bounds on the interval, or finding a better functional approximation to f(x). The latter usually means using a higher order polynomial in the approximation, though not all approximations are polynomial. Common methods of estimating include scalar, linear, hyperbolic and logarithmic.
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Bernoulli, 19(4):1243–1267, 2013. There a number of methods that can be used to justify, informally or rigorously, approximating the occurrence of random events or phenomena with suitable Poisson point processes. The more rigorous methods involve deriving upper bounds on the probability metrics between the Poisson and non-Poisson point processes, while other methods can be justified by less formal heuristics.R. Arratia, S. Tavare, et al.
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At the same time, Hoard enforces provable bounds on the total amount of fragmentation. McKinley was a leader of the DaCapo research group, which spanned nine institutions and was funded by an NSF ITR (2000-2006). This project produced a number of innovative virtual machine technologies, open source tools, open source benchmarks, and new methodologies for evaluating managed runtimes. The benchmarking and methodologies efforts were led by Stephen M. Blackburn.
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In the event finals, Amânar had the opportunity to defend her Olympic vault title from four years earlier. However, she stumbled badly while debuting a new vault (a 2 twisting laid-out Yurchenko, which was then named after her), and did not win a medal. She went on to win bronze on floor exercise after losing points for a step out of bounds on her last tumbling pass.
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In probability theory, Popoviciu's inequality, named after Tiberiu Popoviciu, is an upper bound on the variance σ2 of any bounded probability distribution. Let M and m be upper and lower bounds on the values of any random variable with a particular probability distribution. Then Popoviciu's inequality states: : \sigma^2 \le \frac14 ( M - m )^2. This equality holds precisely when half of the probability is concentrated at each of the two bounds.
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The two fields can interact through the interactions of ordinary particles if the energy of the interaction is sufficiently high. These particle interactions would appear to have "missing" energy and momentum that would not be detected by the experimental apparatus. Certain distinct distributions of missing energy would signify the production of unparticle stuff. If such signatures are not observed, bounds on the model can be set and refined.
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In another game, against Richmond, Todd kicked 7 goals and 12 points, as well as kicking out of bounds on the full five times.Atkinson, p. 115. His season tally was the highest in the league and Todd again topped the league in 1939 VFL season, this time finishing with 121 goals. His 1939 finals total of 23 goals was not bettered until Gary Ablett kicked 27 in the 1989 series.
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The upper bounds on proton decay rate can also be satisfied because the squarks are very heavy as well. On the other hand, unlike conventional supersymmetry, split supersymmetry does not solve the hierarchy problem which has been a primary motivation for proposals for new physics beyond the Standard Model since 1979. One proposal is that the hierarchy problem is "solved" by assuming fine-tuning due to anthropic reasons.
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At ICTP, he taught the advanced course of differential equations, Special functions, Upper and lower bounds on Entropy and the Number Theory. In 1988, after researching at ICTP under Abdus Salam, Qadir re-joined Qau and became full professor of Mathematics. In 1989, Qadir published a book on Special relativity through World Scientific. Qadir provided simple representation of details of calculations and its extension into theory of motion.
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In the laboratory, biostratigraphers analyze rock samples from outcrop and drill cores for the fossils found in them. These fossils help scientists to date the core and to understand the depositional environment in which the rock units formed. Geochronologists precisely date rocks within the stratigraphic section to provide better absolute bounds on the timing and rates of deposition. Magnetic stratigraphers look for signs of magnetic reversals in igneous rock units within the drill cores.
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Eric Katz is a mathematician working in combinatorial algebraic geometry and arithmetic geometry. He is currently an associate professor in the Department of Mathematics at Ohio State University. In joint work with Karim Adiprasito and June Huh, he resolved the Heron–Rota–Welsh conjecture on the log-concavity of the characteristic polynomial of matroids. With Joseph Rabinoff and David Zureick-Brown, he has given bounds on rational and torsion points on curves.
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Stein's method is a mathematical technique originally developed for approximating random variables such as Gaussian and Poisson variables, which has also been applied to point processes. Stein's method can be used to derive upper bounds on probability metrics, which give way to quantify how different two random mathematical objects vary stochastically.A. D. Barbour and T. C. Brown. Stein's method and point process approximation. Stochastic Processes and their Applications, 43(1):9–31, 1992.
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This software update enhanced the user interface and allowed the user to set bounds on activations of muscles and actuators relating to static optimization not dynamic optimization. OpenSim 2.4 was released on October 10, 2011. This newest and most recent update includes faster and more robust tools for Inverse Dynamics and Inverse Kinematics, new visualization tools, enhanced access for API users, and many usability improvements. OpenSim 3.2 was released on March 13, 2014.
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In wireless networks, the factors that contribute to the SINR are often random (or appear random) including the signal propagation and the positioning of network transmitters and receivers. Consequently, in recent years this has motivated research in developing tractable stochastic geometry models in order to estimate the SINR in wireless networks. The related field of continuum percolation theory has also been used to derive bounds on the SINR in wireless networks.M. Franceschetti and R. Meester.
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Although earning enough points to compete in the all-around competition, Zmeskal would again falter during her first event, the floor exercise, stepping out of bounds on her final tumbling pass. She finished 10th in the all-around final, and later finished 8th in the vault final and 6th in the floor final. It would later be revealed that Zmeskal was suffering from a stress fracture in her ankle before the Olympics began.
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The idea of comparing the size of proofs can be used for any automated reasoning procedure that generates a proof. Some research has been done about the size of proofs for propositional non-classical logics, in particular, intuitionistic, modal, and non-monotonic logics. Hrubeš (2007-2009) proved exponential lower bounds on size of proofs in Extended Frege system in some modal logics and intuitionistic logic using a version of monotone feasible interpolation.
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Mayo during the 2013 Pro Bowl He was voted a defensive co-captain by his teammates for the fourth straight year. On November 16, 2012, Mayo was fined $10,000 for a late hit out of bounds on Week 10 against C. J. Spiller with the Buffalo Bills. This drew an unnecessary roughness call. Later in the year, he was selected in the 2013 Pro Bowl in recognition of his successful 2012 season.
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A fundamental question in the study of SDR is whether or not an SDR exists. Hall's marriage theorem gives necessary and sufficient conditions for a finite collection sets, some possibly overlapping, to have a transversal. The condition is that, for every integer k, every collection of k sets must contain in common at least k different elements. The following refinement by H. J. Ryser gives lower bounds on the number of such SDRs. Theorem.
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13-27, and independently Miklós AjtaiMiklós Ajtai, "\Sigma^1_1-Formulae on Finite Structures", Annals of Pure and Applied Logic, 24 (1983) 1-48. established super-polynomial lower bounds on the size of constant-depth Boolean circuits for the parity function, i.e., they showed that polynomial-size constant-depth circuits cannot compute the parity function. Similar results were also established for the majority, multiplication and transitive closure functions, by reduction from the parity function.
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The field goal uprights are 9 feet wide, and the crossbar is 18 feet above the playing surface. Unlike Arena football, the ball is not "live" when rebounded off the nets behind the end zone, or their support apparatuses. A player is counted as out of bounds on the sidelines if they come into contact or fall over the boundary wall. Each team fields eight players at a time from a 21-man active roster.
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The second shot is downhill, with out of bounds on the left and in back of the green. The green can be receptive to shots played short right, due to a mound which feeds shots toward the green. The 2nd hole is an uphill par 3, featuring the most severely sloped green on the course. The green slopes considerably from back to front, and has bunkers on the left and right sides.
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The constant can be lowered to , but at the expense of replacing with the worse constant of . The motivation of Leighton in studying crossing numbers was for applications to VLSI design in theoretical computer science. Later, Székely also realized that this inequality yielded very simple proofs of some important theorems in incidence geometry, such as Beck's theorem and the Szemerédi-Trotter theorem, and Tamal Dey used it to prove upper bounds on geometric k-sets.
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Heegaard Floer homology is a homology theory whose Euler characteristic is the Alexander polynomial of the knot. It has been proven effective in deducing new results about the classical invariants. Along a different line of study, there is a combinatorially defined cohomology theory of knots called Khovanov homology whose Euler characteristic is the Jones polynomial. This has recently been shown to be useful in obtaining bounds on slice genus whose earlier proofs required gauge theory.
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The Newton–Fourier method is Joseph Fourier's extension of Newton's method to provide bounds on the absolute error of the root approximation, while still providing quadratic convergence. Assume that is twice continuously differentiable on and that contains a root in this interval. Assume that on this interval (this is the case for instance if , , and , and on this interval). This guarantees that there is a unique root on this interval, call it .
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Victory seemed assured, but Maryland failed to convert a first down and the inexperienced Randall Jones ran out of bounds on third down, which stopped the clock when Virginia had no time-outs. The Cavaliers got the ball on their own 24-yard line. In nine plays and just 46 seconds, Dan Ellis led a 76-yard drive that culminated with a touchdown pass to Billy McMullen to win the game with 26 seconds left.
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The southern tip of the island is, like the Neuer Bessin was therefore classified as conservation zone I of the national park und is out-of-bounds. On the island are two nature reserves, the between Neuendorf and Vitte and the in the north. The Naturschutzgesellschaft Hiddensee und Boddenlandschaft maintains a national park house in Vitte, with a permanent exhibition of fauna and flora. In 1936 the was established on the island.
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These problems were finally settled by ,As previously announced by . who showed that the seven graphs of the Petersen family are the only minimal forbidden minors for these graphs. Therefore, linklessly embeddable graphs and flat embeddable graphs are both the same set of graphs, and are both the same as the graphs that have no Petersen family minor. also asked for bounds on the number of edges and the chromatic number of linkless embeddable graphs.
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In statistics, cumulative distribution function (CDF)-based nonparametric confidence intervals are a general class of confidence intervals around statistical functionals of a distribution. To calculate these confidence intervals, all that is required is an independently and identically distributed (iid) sample from the distribution and known bounds on the support of the distribution. The latter requirement simply means that all the nonzero probability mass of the distribution must be contained in some known interval [a,b].
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At the 2004 Summer Olympics in Athens, Dos Santos qualified for the floor exercise event final and became the first female gymnast to perform a laid-out double Arabian. The skill, now known as the Dos Santos II, was the second to be named after her. However, in the final, she went out of bounds on a tumbling pass and placed fifth. In December 2004, she became the World Cup floor champion, again beating Ponor.
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The scanner listens to the channel for a duration called the scan window, which is periodically repeated every scan interval. The discovery latency is therefore determined by a probabilistic process and depends on the three parameters (viz., the advertising interval, the scan interval and the scan window). The discovery scheme of BLE adopts a periodic-interval based technique, for which upper bounds on the discovery latency can be inferred for most parametrizations.
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35 Despite a much wetter winter than the drought year of 1969, scoring in 1970 was higher than ever before, exceeding 100 points per team per game for the first time, including a record highest losing score. This was largely due to the “out of bounds on the full” rule which the WANFL adopted for the first time after its success in the 1969 VFL season.See ‘Bunton Favours “Hook” Kick’; The West Australian, 7 April 1970, p.
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By using the Goddard–Thorn theorem, Borcherds showed that the homogeneous pieces of the Lie algebra are naturally isomorphic to graded pieces of the Moonshine module, as representations of the monster simple group. Earlier applications include Frenkel's determination of upper bounds on the root multiplicities of the Kac-Moody Lie algebra whose Dynkin diagram is the Leech lattice, and Borcherds's construction of a generalized Kac-Moody Lie algebra that contains Frenkel's Lie algebra and saturates Frenkel's 1/∆ bound.
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Donaghadee Golf Club was founded in 1899 by Stephen Mccausland and is part links and part open parkland. The course has recently undergone a major course refurbishment with the addition of many new bunkers. The 18th hole is a finishing hole with out of bounds on both left and right, while the sea breeze can provide an extra challenge to visitors. This area of the County Down coastline and Donaghadee in particular provides views over the nearby Copeland Islands.
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Vanishing Fiber Diameter (VFD) \- Combination of average stress and strain assumptions that can be visualized as each fiber having a vanishing diameter yet finite volume. Composite Cylinder Assemblage (CCA) \- Composite composed of cylindrical fibers surrounded by cylindrical matrix layer, cylindrical elasticity solution. Analogous method for macroscopically isotropic inhomogeneous materials: Composite Sphere Assemblage (CSA) Hashin-Shtrikman Bounds - Provide bounds on the elastic moduli and tensors of transversally isotropic composites (reinforced, e.g., by aligned continuous fibers) and isotropic composites (reinforced, e.g.
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Finally, when a leaf node is reached, it is expanded and its children are evaluated. The proof and disproof numbers represent lower bounds on the number of nodes to be evaluated to prove (or disprove) certain nodes. By always selecting the most proving (disproving) node to expand, an efficient search is generated. Some variants of proof number search like dfPN, PN2, PDS-PN have been developed to address the quite big memory requirements of the algorithm.
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Microwave and optical cavities have been used to constrain d=4 violations. Microwave experiments have also placed some bounds on nonminimal d=6 and d=8 violations. However, for d>4, the effects of Lorentz violation grow with frequency, so optical cavities provide better sensitivity to nonrenormalizable violations, all else being equal. The geometrical symmetries of the cavity also affect the sensitivity since parity symmetric cavities are only directly sensitive to parity-even coefficients for Lorentz violation.
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Rows not mentioned in an RHS vector would be assumed to have a right-hand-side of zero. The optional BOUNDS section specifies lower and upper bounds on individual variables, if they are not given by rows in the matrix. All the bounds that have a given name in column 5 are taken together as a set. Variables not mentioned in a given BOUNDS set are taken to be non-negative (lower bound zero, no upper bound).
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Uncertainties of the definition, extent, and potential of mixedwood types necessitate the placement of some mensurational bounds on the subject of mixedwood management, especially the distribution and component sub-types, age classes, advance growth, productivity, and rotation ages. A major ecological factor in mixedwood management is the spruce budworm; another is the problem of providing for sufficient white spruce regeneration.Project 07-24-0 analysis, Artificial regeneration of spruce in the spruce–fir forest type of Ontario.
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Similarly, channel pairs that are far apart but exhibit harmonic interference can be removed from the edge set of H. In each case, these simplified models display many of the issues that have to be handled in practice. Constraint satisfaction problems, which generalize graph homomorphism problems, can express various additional types of conditions (such as individual preferences, or bounds on the number of coinciding assignments). This allows the models to be made more realistic and practical.
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These series in 1977, 1978 and 1987 were played by all the VFL clubs. During its history, the Night Series was used to trial rule changes. Two particular rules which were trialled and later introduced were the free kick for kicking out of bounds on the full (trialled in 1966, introduced in the VFL in 1969 and nationally in 1970) and the centre square to control congestion at centre bounces (trialled in 1966, introduced nationally in 1973).
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As soon as he turned it loose, he immediately rushed in for the rebound. He caught the ball in midair as his momentum was carrying him out of bounds on the baseline just right of the lane. In an instant, he switched the ball to his left hand (a right-handed shot would have hit the side of the backboard) and flipped it in the basket. Bird would finish with 18 points, 21 rebounds, and nine assists.
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Davies and Ghahramani proposed Random Forest Kernel and show that it can empirically outperform state-of-art kernel methods. Scornet first defined KeRF estimates and gave the explicit link between KeRF estimates and random forest. He also gave explicit expressions for kernels based on centered random forest and uniform random forest, two simplified models of random forest. He named these two KeRFs Centered KeRF and Uniform KeRF, and proved upper bounds on their rates of consistency.
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Common developmental patterns seen during tropical cyclone development, and their Dvorak-assigned intensities Within the Dvorak satellite strength estimate for tropical cyclones, there are several visual patterns that a cyclone may take on which define the upper and lower bounds on its intensity. The central dense overcast (CDO) pattern is one of those patterns. The central dense overcast utilizes the size of the CDO. The CDO pattern intensities start at T2.5, equivalent to minimal tropical storm intensity, .
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The density of matter in intergalactic space is reasonably well established at about one atom per cubic meter. Assuming this is a typical density near a boundary, the gamma ray luminosity of the boundary interaction zone can be calculated. No such zones have been detected, but 30 years of research have placed bounds on how far they might be. On the basis of such analyses, it is now deemed unlikely that any region within the observable universe is dominated by antimatter.
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The work of Hall, Taunt, and Carter was presented in textbook form in . The focus on soluble A-groups broadened, with the classification of finite simple A-groups in which allowed generalizing Taunt's work to finite groups in . Interest in A-groups also broadened due to an important relationship to varieties of groups discussed in . Modern interest in A-groups was renewed when new enumeration techniques enabled tight asymptotic bounds on the number of distinct isomorphism classes of A-groups in .
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This algorithm was designed by Janez Konc and description was published in 2007. In comparison to earlier algorithms described in the published article Source code the MaxCliqueDyn algorithm is improved by an improved approximate coloring algorithm (ColorSort algorithm) and by applying tighter, more computationally expensive upper bounds on a fraction of the search space. Both improvements reduce time to find maximum clique. In addition to reducing time improved coloring algorithm also reduces the number of steps needed to find a maximum clique.
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Due to conservation of energy, only magnetic monopoles with masses less than half of the center of mass energy of the colliding particles can be produced. Beyond this, very little is known theoretically about the creation of magnetic monopoles in high energy particle collisions. This is due to their large magnetic charge, which invalidates all the usual calculational techniques. As a consequence, collider based searches for magnetic monopoles cannot, as yet, provide lower bounds on the mass of magnetic monopoles.
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Empirical risk minimization (ERM) is a principle in statistical learning theory which defines a family of learning algorithms and is used to give theoretical bounds on their performance. The core idea is that we cannot know exactly how well an algorithm will work in practice (the true "risk") because we don't know the true distribution of data that the algorithm will work on, but we can instead measure its performance on a known set of training data (the "empirical" risk).
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North Carolina's first possession of the second overtime period ended with a turnover, while Kansas missed a long jump shot in theirs. North Carolina's Brennan boxed out Chamberlain who went over him to collect the rebound and was called for over the back. Joe Quigg turned the ball over after traveling, while Chamberlain threw the ball out of bounds on the subsequent possession. Carolina failed to capitalize on Chamberlain's error when Kearns missed the front end of a one-and-one.
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P-boxes are usually merely bounds on possible distributions. The bounds often also enclose distributions that are not themselves possible. For instance, the set of probability distributions that could result from adding random values without the independence assumption from two (precise) distributions is generally a proper subset of all the distributions enclosed by the p-box computed for the sum. That is, there are distributions within the output p-box that could not arise under any dependence between the two input distributions.
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In the 1978 game between Ohio State and Clemson, Ohio State coach Woody Hayes lost his temper after a late game interception by Clemson nose guard Charlie Bauman, who stepped in front of the receiver on a pass from quarterback Art Schlichter. Bauman ran the ball out of bounds on the Ohio State sideline where Hayes struck Bauman with his right forearm. The play sealed the Tigers' 17–15 win over the Buckeyes and Hayes was fired the next day before leaving Jacksonville.
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The primary contributions to M-matrix theory has mainly come from mathematicians and economists. M-matrices are used in mathematics to establish bounds on eigenvalues and on the establishment of convergence criteria for iterative methods for the solution of large sparse systems of linear equations. M-matrices arise naturally in some discretizations of differential operators, such as the Laplacian, and as such are well-studied in scientific computing. M-matrices also occur in the study of solutions to linear complementarity problem.
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A constraint is a condition that must be satisfied in order for the design to be feasible. An example of a constraint in aircraft design is that the lift generated by a wing must be equal to the weight of the aircraft. In addition to physical laws, constraints can reflect resource limitations, user requirements, or bounds on the validity of the analysis models. Constraints can be used explicitly by the solution algorithm or can be incorporated into the objective using Lagrange multipliers.
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However, bowing to social pressure, one early morning she pressed the child against her chest, went out of thevillage and left the child in the hole of a tree. After some time a carder passing by suddenly saw the child lying in the hole of the tree. His joy knew no bounds on seeing the child. He thought, “I have no child of my own; here is God’s gift.” He carried the child home and said to his wife, “Look here.
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Beginning with ,. a number of researchers have investigated the behavior of the longest common subsequence length when the two given strings are drawn randomly from the same alphabet. When the alphabet size is constant, the expected length of the LCS is proportional to the length of the two strings, and the constants of proportionality (depending on alphabet size) are known as the Chvátal–Sankoff constants. Their exact values are not known, but upper and lower bounds on their values have been proven,.
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Even if the parameters such as mean and variance of a distribution are known precisely, the distribution cannot be specified precisely if the distribution family is unknown. In such situations, envelopes of all distributions matching given moments can be constructed from inequalities such as those due to Markov, Chebyshev, Cantelli, or RoweRowe, N.C. (1988). Absolute bounds on the mean and standard deviation of transformed data for constant-sign-derivative transformations. SIAM Journal of Scientific and Statistical Computing 9: 1098–1113.
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He converted the 3-point play to take a 106–103 lead. After a timeout, the Sixers put the ball in the hands of Erving, who tried a spectacular, scooping finger-roll, but missed. Magic got the rebound to seemingly seal the win, but the Lakers tried to force the fast-break and ended up turning the ball over, out-of-bounds. However, the Sixers turned the ball right back over by stepping out of bounds on a desperation 3-point attempt.
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There was a heavily padded wall on each sideline, with the padding placed on top of the hockey dasher boards. The field goal uprights were 9 feet wide, and the crossbar was 18 feet above the playing surface. Unlike Arena football, the ball was not "live" when rebounded off the nets behind the end zone or their support apparatuses. A player was counted as out of bounds on the sidelines if they came into contact or fell over the boundary wall.
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The quidditch pitch is usually marked with cones or with painted lines, and it is where all play occurs (a rectangle of around the pitch). Balls are not allowed to be kicked off the pitch under penalty, nor is play allowed in the spectator zones. Players are asked to return to the pitch when play continues out of bounds. On the edge of the pitch is a penalty box where players who have committed fouls that warrant yellow cards are sent for one minute.
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In cryptography, an adversary's advantage is a measure of how successfully it can attack a cryptographic algorithm, by distinguishing it from an idealized version of that type of algorithm. Note that in this context, the "adversary" is itself an algorithm and not a person. A cryptographic algorithm is considered secure if no adversary has a non-negligible advantage, subject to specified bounds on the adversary's computational resources (see concrete security). "Negligible" usually means "within O(2−p)" where p is a security parameter associated with the algorithm.
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He punted a ball that went out of bounds on the Saint Mary's one-yard line. The punt traveled a total of 97 yards and would (as of 2006) rank as the second longest of college football history if pre-1937 statistics were included in the NCAA record book. Casanova was Santa Clara's team captain in his senior year under coach Adam Walsh, who had played at Notre Dame under Knute Rockne. Casanova graduated in 1927 with a bachelor's degree in philosophy and a minor in history.
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A nested triangles graph with 18 vertices In graph theory, a nested triangles graph with n vertices is a planar graph formed from a sequence of n/3 triangles, by connecting pairs of corresponding vertices on consecutive triangles in the sequence. It can also be formed geometrically, by gluing together n/3 − 1 triangular prisms on their triangular faces. This graph, and graphs closely related to it, have been frequently used in graph drawing to prove lower bounds on the area requirements of various styles of drawings.
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By using a highly sensitive "superconducting quantum interference device" (SQUID) one can, in principle, detect even a single magnetic monopole. According to standard inflationary cosmology, magnetic monopoles produced before inflation would have been diluted to an extremely low density today. Magnetic monopoles may also have been produced thermally after inflation, during the period of reheating. However, the current bounds on the reheating temperature span 18 orders of magnitude and as a consequence the density of magnetic monopoles today is not well constrained by theory.
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Later Huffine got off a successful punt, however the Islanders drove to the Muncie two-yard line, only to fumble. But, when Huffine went into the end zone for yet another punt attempt, Walt Buland broke through to block, and Wyman scored again by falling on the ball in the end zone. As soon as Huffine was called upon to punt again, Shaw and Oke Smith blocked another one. This time Dewey Lyle recovered but stepped out of bounds on the 15-yard line.
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He nearly tied the game later on a rollout with a head-first dive at the pylon with 7:51 left, and the initial ruling on the field was a touchdown. But a replay review determined his foot was out of bounds. On fourth and 1, Edwards was stopped and NMSU took over. Clay and Victor Johnson ground down the clock for the Aggies, and the Gophers didn't get the ball back until 2:09 remained, starting at their own 11-yard line with no timeouts.
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Invariant theory of finite groups has intimate connections with Galois theory. One of the first major results was the main theorem on the symmetric functions that described the invariants of the symmetric group S_n acting on the polynomial ring R[x_1, \ldots, x_n] by permutations of the variables. More generally, the Chevalley–Shephard–Todd theorem characterizes finite groups whose algebra of invariants is a polynomial ring. Modern research in invariant theory of finite groups emphasizes "effective" results, such as explicit bounds on the degrees of the generators.
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Twenty-five minutes into the final quarter and with scores level, Collingwood's Wayne Richardson had a shot at goal on the run but kicked it out of bounds on the full. St Kilda then began to work the ball out of defence after winning the boundary throw-in. A kick from Ian Cooper saw the ball make its way to centre half-forward. Collingwood defender Ted Potter failed to mark the ball low down, and with the players scrummaging for the ball, a bounce was called.
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Tanner graphs were proposed by Michael TannerR. Michael Tanner Professor of Computer Science, School of Engineering University of California, Santa Cruz Testimony before Representatives of the United States Copyright Office February 10, 1999 as a means to create larger error correcting codes from smaller ones using recursive techniques. He generalized the techniques of Elias for product codes. Tanner discussed lower bounds on the codes obtained from these graphs irrespective of the specific characteristics of the codes which were being used to construct larger codes.
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The term physical constant expresses the notion of a physical quantity subject to experimental measurement which is independent of the time or location of the experiment. The constancy (immutability) of any "physical constant" is thus subject to experimental verification. Paul Dirac in 1937 speculated that physical constants such as the gravitational constant or the fine-structure constant might be subject to change over time in proportion of the age of the universe. Experiments conducted since then have put upper bounds on their time-dependence.
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Although queue layouts do not necessarily produce good two-dimensional graph drawings, they have been used for three-dimensional graph drawing. In particular, a graph class X has bounded queue number if and only if for every n-vertex graph G in X, it is possible to place the vertices of G in a three-dimensional grid of dimensions so that no two edges (when drawn straight) cross each other.; ; . See for tighter bounds on the grid dimensions for graphs of small queue number.
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Figure 5. Multiple RINA networks supporting several internetworks. A DIF enables a DAP to allocate flows to one or more DAPs, by just providing the names of the targeted DAPs and the desired QoS parameters such as bounds on data loss and latency, ordered or out-of- order delivery, reliability, and so forth. DAPs may not trust the DIF they are using and may therefore protect their data before writing it to the flow via a SDU protection module, for example by encrypting it.
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More specifically, define the Hajós number of a -chromatic graph to be the minimum number of steps needed to construct from , where each step forms a new graph by combining two previously formed graphs, merging two nonadjacent vertices of a previously formed graph, or adding a vertex or edge to a previously formed graph. They showed that, for an -vertex graph with edges, . If every graph has a polynomial Hajós number, this would imply that it is possible to prove non-colorability in nondeterministic polynomial time, and therefore imply that NP = co-NP, a conclusion considered unlikely by complexity theorists.. However, it is not known how to prove non-polynomial lower bounds on the Hajós number without making some complexity-theoretic assumption, and if such a bound could be proven it would also imply the existence of non-polynomial bounds on certain types of Frege system in mathematical logic. The minimum size of an expression tree describing a Hajós construction for a given graph may be significantly larger than the Hajós number of , because a shortest expression for may re-use the same graphs multiple times, an economy not permitted in an expression tree.
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Head coach Sean Payton officially named him the backup, behind Bell, to begin the regular season. He made his professional regular season debut and first career start in the New Orleans Saints' season-opener at the Minnesota Vikings and recorded five combined tackles in their 29–19 loss. He was credited with his first career tackle on wide receiver Stefon Diggs after pushing him out of bounds on the Vikings' first drive, but drew an unnecessary roughness penalty after hitting Diggs while he was out of bounds. On September 24, 2017, Williams assisted on two tackles, deflected a pass, and made his first career interception off a pass by Cam Newton during a 34–13 win at the Carolina Panthers in Week 3. He was inactive for the Saints' Week 13 victory against the Carolina Panthers, due to a groin injury he sustained the previous week. On December 31, 2017, Williams collected a season-high eight combined tackles, two pass deflections, and made a season-high two interceptions off pass attempts by Jameis Winston in the Saints' 31–24 loss at the Tampa Bay Buccaneers.
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Edward McKendree Bounds was born on August 15, 1835, in Shelbyville, Missouri. He is the son of Thomas Jefferson and Hester A. (née Purnell) Bounds.Bounds on Prayer 2006, pages viii–xiv In the preface to E.M. Bounds on Prayer, published by Hendrickson Christian Classics Series over 90 years after Bounds' death, it is surmised that young Edward was named after the evangelist, William McKendree, who planted churches in western Missouri and served as the fourth bishop of the Methodist Episcopal Church. He was the fifth child, in a family of three sons and three daughters.
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Then in June 2012, it was announced by CERN that the four Gran Sasso experiments OPERA, ICARUS, LVD, and BOREXINO measured neutrino speeds consistent with the speed of light, indicating that the initial OPERA result was due to equipment errors. In addition, Fermilab stated that the detectors for the MINOS project were being upgraded,. Fermilab scientists closely analyzed and placed bounds on the errors in their timing system. On June 8, 2012 MINOS announced that according to preliminary results, the neutrino speed is consistent with the speed of light.
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Circuit complexity goes back to Shannon (1949), who proved that almost all Boolean functions on n variables require circuits of size Θ(2n/n). Despite this fact, complexity theorists have only been able to prove superpolynomial circuit lower bounds on functions explicitly constructed for the purpose of being hard to calculate. More commonly, superpolynomial lower bounds have been proved under certain restrictions on the family of circuits used. The first function for which superpolynomial circuit lower bounds were shown was the parity function, which computes the sum of its input bits modulo 2.
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It is a difficult hole featuring a dogleg left, and a large bunker short of the green, as well as out of bounds on the right side of the fairway. 18th Hole: This finishing hole features the most water on the entire course. The tee shot needs to carry a large pond and a bunker to reach a small patch of fairway that sets the golfer up for an uphill approach shot over another pond of similar size. The green is well protected by mounds on all sides, and the hole measures at 432-yards.
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Again, the difficult part and a great achievement of analytic number theory is obtaining specific upper bounds on the error term E(r). It was shown by Gauss that E(r) = O(r). In general, an O(r) error term would be possible with the unit circle (or, more properly, the closed unit disk) replaced by the dilates of any bounded planar region with piecewise smooth boundary. Furthermore, replacing the unit circle by the unit square, the error term for the general problem can be as large as a linear function of r.
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The initial proposed problem for this project, now called Polymath1 by the Polymath community, was to find a new combinatorial proof to the density version of the Hales–Jewett theorem. As the project took form, two main threads of discourse emerged. The first thread, which was carried out in the comments of Gowers's blog, would continue with the original goal of finding a combinatorial proof. The second thread, which was carried out in the comments of Terence Tao's blog, focused on calculating bounds on density of Hales-Jewett numbers and Moser numbers for low dimensions.
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Since the Diósi–Penrose model predicts deviations from standard quantum mechanics, the model can be tested. The only free parameter of the model is the size of the mass density distribution, given by R_0. All bounds present in the literature are based on an indirect effect of the gravitational-related collapse: a Brownian-like diffusion induced by the collapse on the motion of the particles. This Brownian-like diffusion is a common feature of all objective-collapse theories and, typically, allows to set the strongest bounds on the parameters of these models.
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Every reducible configuration contains a cycle, so for every finite set S of reducible configurations there is a number γ such that all configurations in the set contain a cycle of length at most γ. However, there exist snarks with arbitrarily high girth, that is, with arbitrarily high bounds on the length of their shortest cycle.. A snark G with girth greater than γ cannot contain any of the configurations in the set S, so the reductions in S are not strong enough to rule out the possibility that G might be a minimal counterexample.
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In the mathematical discipline of descriptive set theory, a scale is a certain kind of object defined on a set of points in some Polish space (for example, a scale might be defined on a set of real numbers). Scales were originally isolated as a concept in the theory of uniformization,Kechris and Moschovakis 2008:28 but have found wide applicability in descriptive set theory, with applications such as establishing bounds on the possible lengths of wellorderings of a given complexity, and showing (under certain assumptions) that there are largest countable sets of certain complexities.
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The goal of optimization is therefore either to find the best query plan based on some specification of user preferences provided as input to the optimizer (e.g., users can define weights between different cost metrics to express relative importance or define hard cost bounds on certain metrics) or to generate an approximation of the set of Pareto-optimal query plans (i.e., plans such that no other plan has better cost according to all metrics) such that the user can select the preferred cost tradeoff out of that plan set.
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Malden, MA: Blackwell Science, 2000. The magnitude of the exhumation a rock has been subjected to may be inferred from geobarometry (measuring previous pressure and temperature history of a rock or assemblage). Knowing the pressure and temperature history of a region can yield an estimate of the ambient geothermal gradient and bounds on the exhumation process; however, geobarometric/geothermometric studies do not produce a rate of exhumation (or any other information on time). One can infer exhumation rates from fission tracks and from radiometric ages as long as one has an estimated thermal profile.
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To reflect a preference for higher rather than lower returns, this objective function is increasing in wealth, and to reflect risk aversion it is concave. For realistic utility functions in the presence of many assets that can be held, this approach, while theoretically the most defensible, can be computationally intensive. Harry Markowitz developed the "critical line method", a general procedure for quadratic programming that can handle additional linear constraints and upper and lower bounds on holdings. Moreover, the approach provides a method for determining the entire set of efficient portfolios.
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This article discusses the analysis of parallel algorithms. Like in the analysis of "ordinary", sequential, algorithms, one is typically interested in asymptotic bounds on the resource consumption (mainly time spent computing), but the analysis is performed in the presence of multiple processor units that cooperate to perform computations. Thus, one can determine not only how many "steps" a computation takes, but also how much faster it becomes as the number of processors goes up. The analysis approach works by first suppressing (or abstracting away) the number of processors.
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In 1985, Luca Cardelli and Peter Wegner recognized the advantages of allowing bounds on the type parameters. Many operations require some knowledge of the data types, but can otherwise work parametrically. For example, to check whether an item is included in a list, we need to compare the items for equality. In Standard ML, type parameters of the form ’’a are restricted so that the equality operation is available, thus the function would have the type ’’a × ’’a list → bool and ’’a can only be a type with defined equality.
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Numerical analysis is the study of algorithms that use numerical approximation (as opposed to general symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Modern numerical analysis does not seek exact answers, because exact answers are often impossible to obtain in practice. Instead, much of numerical analysis is concerned with obtaining approximate solutions while maintaining reasonable bounds on errors. Numerical analysis naturally finds applications in all fields of engineering and the physical sciences, but in the 21st century, the life sciences and even the arts have adopted elements of scientific computations.
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The problem is in some ways unique to spin-0 particles (such as the Higgs boson), which can give rise to issues related to quantum corrections that do not affect particles with spin. A number of solutions have been proposed, including supersymmetry, conformal solutions and solutions via extra dimensions such as braneworld models. There are also issues of quantum triviality, which suggests that it may not be possible to create a consistent quantum field theory involving elementary scalar particles. However, if quantum triviality is avoided, triviality constraints may set bounds on the Higgs Boson mass.
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In this version of the problem, it is possible to construct graphs with a non-constant number of linear-sized induced matchings, and this result leads to nearly-tight bounds on the approximation ratio of streaming matching algorithms. The subquadratic upper bound on the Ruzsa–Szemerédi problem was also used to provide an o(3^n) bound on the size of cap sets, before stronger bounds of the form c^n for c<3 were proven for this problem. It also provides the best known upper bound on tripod packing.
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During a game against the Philadelphia Eagles on December 19, 2010, Dodge had a 36-yard punt that was returned by DeSean Jackson for a touchdown as time expired, giving the Eagles a 38−31 win in a game later called the "Miracle at the New Meadowlands". Shortly after the winning touchdown, Dodge was publicly criticized by his head coach, Tom Coughlin, for failing to punt the ball out-of-bounds. On September 3, 2011, Dodge was released from the Giants in favor of former New York Jet punter Steve Weatherford.
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Reserve fullback Robert Newhouse scored the winning points on a 3-yard third-quarter run. The Buccaneers had the ball in the final minute, but Kevin House was ruled out of bounds on a potentially game-winning end-zone reception. Jimmie Giles' fumble on the following play was recovered by Michael Downs at the Dallas 1-yard line with five seconds remaining. Buccaneer players were upbeat after the loss, feeling vindicated that they had been able to play competitively with the Cowboys, as contrasted with their playoff loss of the previous season.
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Within the Dvorak satellite strength estimate for tropical cyclones, there are several visual patterns that a cyclone may take on which define the upper and lower bounds on its intensity. The primary patterns used are curved band pattern (T1.0-T4.5), shear pattern (T1.5-T3.5), central dense overcast (CDO) pattern (T2.5-T5.0), banding eye pattern (T4.0-T4.5), eye pattern (T4.5 – T8.0), and central cold cover (CCC) pattern. Both the central dense overcast and embedded eye pattern utilize the size of the CDO. The CDO pattern intensities start at T2.5, equivalent to minimal tropical storm intensity ().
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Since the gradients of V(\cdot, \cdot) in the incremental gradient descent iterations are also stochastic estimates of the gradient of I_n[w], this interpretation is also related to the stochastic gradient descent method, but applied to minimize the empirical risk as opposed to the expected risk. Since this interpretation concerns the empirical risk and not the expected risk, multiple passes through the data are readily allowed and actually lead to tighter bounds on the deviations I_n[w_t] - I_n[w^\ast_n], where w^\ast_n is the minimizer of I_n[w].
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The noisy-channel coding theorem of Claude Shannon answers the question of how much bandwidth is left for data communication while using the most efficient code that turns the decoding error probability to zero. This establishes bounds on the theoretical maximum information transfer rate of a channel with some given base noise level. However, the proof is not constructive, and hence gives no insight of how to build a capacity achieving code. After years of research, some advanced ECC systems nowadays come very close to the theoretical maximum.
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While football and soccer players deal with similar variations of field surface and stadium covering, the size and shape of their fields are much more standardized. The area out-of-bounds on a football or soccer field does not affect play the way foul territory in baseball does, so variations in that regard are largely insignificant.Puhalla, Krans, and Goatley (2003), p. 207. A New York Yankees batter and a Boston Red Sox catcher at Fenway Park These physical variations create a distinctive set of playing conditions at each ballpark.
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Edelman, Ostrovsky and Schwarz, working under complete information, show that GSP (in the model presented above) always has an efficient locally-envy free equilibrium, i.e., an equilibrium maximizing social welfare, which is measured as SW = \sum_i \alpha_i v_i where bidder i is allocated slot i according to the decreasing bid vector (b_1, \dots, b_n). Further, the expected total revenue in any locally-envy free equilibrium is at least as high as in the (truthful) VCG outcome. Bounds on the welfare at Nash equilibrium are given by Caragiannis et al.
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346, Beginning in 1969 Klarner made significant contributions to the theory of combinatorial enumeration, especially focusing on polyominoesAnother Fine Math You've Got Me Into. . ., By Ian Stewart, Dover Publications (January 15, 2004), p. 21, and box-packing.Packing a rectangle with congruent n-ominoes Journal of Combinatorial Theory, Vol. 7, Issue 2, September 1969, Pages 107-115Klarner systems and tiling boxes with polyominoes by Michael Reid, Journal of Combinatorial Theory, Series A, Vol. 111, Issue 1, July 2005, Pages 89-105 Working with Ronald L. Rivest he found upper bounds on the number of n-ominoes.
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"Last Train to Clarksville" was the debut single by the Monkees. It was released on August 16, 1966, and later included on the group's self-titled album, which was released on October 10, 1966.The Monkees Greatest Hits Rhino Entertainment R2 75785 Liner notes The song, written by Tommy Boyce and Bobby Hart, was recorded at RCA Victor Studio B in Hollywood on July 25, 1966, and was already on the Boss Hit Bounds on August 17, 1966. The song topped the Billboard Hot 100 on November 5, 1966.
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UM drove to the MSU 14 for a first and 10 with under two minutes to play, but MSU defensive end Dustin O'Connell came through for the Bobcats. O'Connell (who had just returned from a severely broken collarbone) and linebacker Jody Owens dropped Reynolds for a one-yard loss on first down. O'Connell then hurried UM quarterback Justin Roper into throwing an incomplete pass on second down, and batted down a pass intended for a wide-open Kavario Middleton on third down. Roper threw the ball out of bounds on fourth down.
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Sewell was born Hazel Bounds on May 1, 1898, and she was one of ten children. She grew up on the Nez Perce Native American Reservation in Lapwai, Idaho, and though poor, her family was described as "happy." Before working for Walt Disney as a young adult, she married her husband Glenn O. Sewell, and they continued to reside in Lapwai. (Glenn Sewell was the brother of Blanche Sewell, a film editor in classic Hollywood.) After her husband found work in Los Angeles, the couple moved there with their only daughter Marjorie Sewell.
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Because a range of child nodes is permitted, B-trees do not need re-balancing as frequently as other self- balancing search trees, but may waste some space, since nodes are not entirely full. The lower and upper bounds on the number of child nodes are typically fixed for a particular implementation. For example, in a 2–3 tree (sometimes referred to as a 2–3 B-tree), each internal node may have only 2 or 3 child nodes. Each internal node of a B-tree contains a number of keys.
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Here no amount of variety recording the patients' average temperature would detect this small signal which might have a big effect. Monitoring is required on individuals thus amplifying variety (see Algedonic alerts in the viable system model or VSM). Beer's work in management cybernetics and VSM is largely based on variety engineering. Further applications involving Ashby's view of state counting include the analysis of digital bandwidth requirements, redundancy and software bloat, the bit representation of data types and indexes, analogue to digital conversion, the bounds on finite state machines and data compression.
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After the publication of Calogero's original paper, "[The] [c]osmic origin of quantization" a response was published by Giuseppe Gaeta of the University of Rome in which he discussed the compatibility of the conjecture with present bounds on variation of fundamental constants, but also outlined his focus on the modification of the relation between redshift and distance, and of the estimations attained from observations of elapsed time from the production of cosmic radiation and implications—both being related also, to the observed blackbody distribution of background cosmic radiation.
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Edwards faced competition from Fitzpatrick and Brian Brohm for the Bills' starting quarterback position in 2010. Edwards won the battle and started in all four of the Bills' preseason games. In their first two games of the regular season, Edwards threw for only 241 yards combined and completed only 29 passes between the two games, and the Bills lost both games. On his final play as a Bill, against Green Bay, Edwards ran out of bounds on a fourth down scramble, 7 yards short of the first down marker with 1:10 to go.
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Upper bounds on the absolute values of polynomial roots are widely used for root-finding algorithms, either for limiting the regions where roots should be searched, or for the computation of the computational complexity of these algorithms. Many such bounds have been given, and the sharper one depends generally of the specific sequence of coefficient that are considered. Most bounds are greater or equal to one, and are thus not sharp for a polynomial which have only roots of absolute values lower than one. However, such polynomials are very rare, as shown below.
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In the all-around, She performed well on her first three rotations: vault, uneven bars and balance beam to lead the competition going into the final rotation, but stepped out of bounds on floor exercise and dropped to fifth place. She went on to win a silver medal on vault behind Romanian Simona Amânar, the first Chinese female gymnast to win a medal on vault at the Olympic/World Championship level. After the 1996 Olympics, she participated in exhibitions and shows in the United States before returning to training. She continued to compete through the 1997 season.
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In the early 1880s, Friedrich Otto Hultsch (1833–1906) and Karl Heinrich Hunrath (b. 1847) noted how the bounds could be found quickly by means of simple binomial bounds on square roots close to a perfect square modelled on Elements II.4, 7; this method is favoured by Thomas Little Heath. Although only one route to the bounds is mentioned, in fact there are two others, making the bounds almost inescapable however the method is worked. But the bounds can also be produced by an iterative geometrical construction suggested by Archimedes' Stomachion in the setting of the regular dodecagon.
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The Hawks scored 7.3 in the quarter to the Saints' three straight goals. Going into the game, Hudson needed four goals to surpass Bob Pratt's record for most goals in a VFL season but only managed to kick three which left him level with Pratt on 150 goals. Late in the game he had a set shot on goal to break the record but kicked the ball into the man on the mark, Barry Lawrence. His last attempt for the record, had Hudson kicking out of bounds on the full after running towards an open goal.
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Letters, 10, (1963), p. 460 Finally, in 1966 he succeeded in demonstrating the validity of the Froissart bound using local field theory, without postulating the Mandelstam representation.A.Martin, « Extension of the axiomatic analyticity domain of scattering amplitudes by unitarity: », Nuovo Cimento, 42, (1966), p. 930 In the meantime, in 1964, he obtains an absolute bound on the pion-pion scattering amplitude,An absolute bound on the pion pion scattering amplitude, Stanford Preprint ITP-1 (1964) non publié this bound was considerably improved later.B. Bonnier, C Lopez et G.Mennessier, « Improved absolute bounds on the π0π0 amplitude », Physics Letters B, 60, (1), 22 December 1975, p.
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A fundamental question of longstanding theoretical interest is to prove lower bounds on the complexity and exact operation counts of fast Fourier transforms, and many open problems remain. It is not rigorously proved whether DFTs truly require Ω(N log N) (i.e., order N log N or greater) operations, even for the simple case of power of two sizes, although no algorithms with lower complexity are known. In particular, the count of arithmetic operations is usually the focus of such questions, although actual performance on modern- day computers is determined by many other factors such as cache or CPU pipeline optimization.
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By providing a provably polynomial-time ε-approximation algorithm, they resolved a long-standing open problem in optimal control. Their first paper considered time-optimal control ("fastest path") of a point mass under Newtonian dynamics, amidst polygonal (2D) or polyhedral (3D) obstacles, subject to state bounds on position, velocity, and acceleration. Later they extended the technique to many other cases, for example, to 3D open-chain kinematic robots under full Lagrangian dynamics. More recently, many practical heuristic algorithms based on stochastic optimization and iterative sampling were developed, by a wide range of authors, to address the kinodynamic planning problem.
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Separately, game theory has played a role in online algorithms; in particular, the -server problem, which has in the past been referred to as games with moving costs and request- answer games. Yao's principle is a game-theoretic technique for proving lower bounds on the computational complexity of randomized algorithms, especially online algorithms. The emergence of the Internet has motivated the development of algorithms for finding equilibria in games, markets, computational auctions, peer-to-peer systems, and security and information markets. Algorithmic game theory and within it algorithmic mechanism design combine computational algorithm design and analysis of complex systems with economic theory.
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Classical provable security primarily aimed at studying the relationship between asymptotically defined objects. Instead, practice-oriented provable security is concerned with concrete objects of cryptographic practice, such as hash functions, block ciphers, and protocols as they are deployed and used. Practice oriented provable security uses concrete security to analyse practical constructions with fixed key sizes. "Exact security" or "concrete security" is the name given to provable security reductions where one quantifies security by computing precise bounds on computational effort, rather than an asymptotic bound which is guaranteed to hold for "sufficiently large" values of the security parameter.
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None of these pixel resolutions are true resolutions, but they are widely referred to as such; they serve as upper bounds on image resolution. Below is an illustration of how the same image might appear at different pixel resolutions, if the pixels were poorly rendered as sharp squares (normally, a smooth image reconstruction from pixels would be preferred, but for illustration of pixels, the sharp squares make the point better). Image:Resolution illustration.png An image that is 2048 pixels in width and 1536 pixels in height has a total of 2048×1536 = 3,145,728 pixels or 3.1 megapixels.
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Lillian Beatrix Pierce is a mathematician whose research connects number theory with harmonic analysis. She was one of the first mathematicians to prove nontrivial upper bounds on the number of elements of finite order in an ideal class group. She won the 2018 Sadosky Prize for research that "spans and connects a broad spectrum of problems ranging from character sums in number theory to singular integral operators in Euclidean spaces" including in particular "a polynomial Carleson theorem for manifolds". She is an associate professor of mathematics at Duke University, and a von Neumann Fellow at the Institute for Advanced Study.
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Much of the strategy used in Wallyball is similar to that used in volleyball. In the traditional three person game it is advantageous to employ one blocker, one person to defend against the dink (short, soft) shot, and the last person to defend shots over the other players' heads but still in bounds. On offense, the widely accepted strategy is of designating one player to receive all second hits to allow for the other players on their team to prepare for the third hit. In addition, varying the number of touches before the ball is hit over the net is crucial.
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Free protons are emitted directly from atomic nuclei in some rare types of radioactive decay. Protons also result (along with electrons and antineutrinos) from the radioactive decay of free neutrons, which are unstable. The spontaneous decay of free protons has never been observed, and protons are therefore considered stable particles according to the Standard Model. However, some grand unified theories (GUTs) of particle physics predict that proton decay should take place with lifetimes between 1031 to 1036 years and experimental searches have established lower bounds on the mean lifetime of a proton for various assumed decay products.
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Tolerance function (turquoise) and interval-valued approximation (red)'' Interval arithmetic (also known as interval mathematics, interval analysis, or interval computation) is a mathematical technique used to put bounds on rounding errors and measurement errors in mathematical computation. Numerical methods using interval arithmetic can guarantee reliable, mathematically correct results. Instead of representing a value as a single number, interval arithmetic represents each value as a range of possibilities. For example, instead of estimating the height of someone as exactly 2.0 metres, using interval arithmetic one might be certain that that person is somewhere between 1.97 and 2.03 metres.
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As different types of algorithms are sometimes considered, ranging from algorithms with specific bounds on their running time to algorithms which may ask questions of an oracle machine, there are different notions of randomness. The most common of these is known as Martin-Löf randomness (K-randomness or 1-randomness), but stronger and weaker forms of randomness also exist. The term "algorithmically random" used to refer to a particular single (finite or infinite) sequence without clarification is usually taken to mean "incompressible" or, in the case the sequence is infinite and prefix algorithmically random (i.e., K-incompressible), "Martin-Löf-Chaitin random".
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To classify the computation time (or similar resources, such as space consumption), it is helpful to demonstrate upper and lower bounds on the maximum amount of time required by the most efficient algorithm to solve a given problem. The complexity of an algorithm is usually taken to be its worst-case complexity, unless specified otherwise. Analyzing a particular algorithm falls under the field of analysis of algorithms. To show an upper bound T(n) on the time complexity of a problem, one needs to show only that there is a particular algorithm with running time at most T(n).
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In 2000, its author Emery Berger benchmarked some famous memory allocators and stated Hoard improves the performance of multithreaded applications by providing fast, scalable memory management functions (malloc and free). In particular, it reduces contention for the heap (the central data structure used in dynamic memory allocation) caused when multiple threads allocate or free memory, and avoids the false sharing that can be introduced by memory allocators. At the same time, Hoard has strict bounds on fragmentation. Hoard continues to be maintained and improved, and is in use by a number of open source and commercial projects.
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She did make a few mistakes that probably cost her team a shot at the gold medal in the team final. After Zamolodchikova fell off the balance beam, Lobaznyuk wanted to get a 10.0 SV (start value) so badly that she included a move not originally in her beam routine and promptly fell off the side of the beam. Dianov remarked afterwards, "It was a noble impulse and so it was impossible to rebuke her for it". In the all-around final, Lobaznyuk stepped out of bounds on her floor routine and misstepped on beam, resulting in a fifth-place result.
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In general, a stronger code induces more redundancy that needs to be transmitted using the available bandwidth, which reduces the effective bit-rate while improving the received effective signal-to-noise ratio. The noisy-channel coding theorem of Claude Shannon answers the question of how much bandwidth is left for data communication while using the most efficient code that turns the decoding error probability to zero. This establishes bounds on the theoretical maximum information transfer rate of a channel with some given base noise level. His proof is not constructive, and hence gives no insight of how to build a capacity achieving code.
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Oberwolfach, 2014 Christine Bachoc (born 1964) is a French mathematician known for her work in coding theory, kissing numbers, lattice theory, and semidefinite programming. She is a professor of mathematics at the University of Bordeaux. Bachoc earned a doctorate in 1989 with the dissertation Réseaux unimodulaires et problèmes de plongement liés à la forme Trace. In 2011, Bachoc and Frank Vallentin won the Society for Industrial and Applied Mathematics Activity Group on Optimization Prize for their work proving upper bounds on high-dimensional kissing numbers by combining methods from semidefinite programming, harmonic analysis, and invariant theory.
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The study of arrangements was begun by Jakob Steiner, who proved the first bounds on the maximum number of features of different types that an arrangement may have.; . An arrangement with n lines has at most n(n − 1)/2 vertices, one per pair of crossing lines. This maximum is achieved for simple arrangements, those in which each two lines has a distinct pair of crossing points. In any arrangement there will be n infinite-downward rays, one per line; these rays separate n + 1 cells of the arrangement that are unbounded in the downward direction.
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Later literature began to accept that there were limits set by temperature, gravity, atmospheric pressure and composition, or the presence of liquids that would set bounds on the possibility of life as we know it existing on other planets. By the 19th century the Moon was given up as an airless desert, incapable of supporting life on its surface (hopes for subsurface life continued until later). Jupiter and the planets beyond were too large, too cold, and had atmospheres composed of poisonous chemicals. Mercury was too close to the Sun and its surface was exposed to extremes of temperature.
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Zeitouni received his bachelor's degree in electrical engineering in 1980 from the Technion. He obtained in 1986 his doctorate in electrical engineering under the supervision of Moshe Zakai with the thesis Bounds on the Conditional Density and Maximum a posteriori Estimators for the Nonlinear Filtering Problem. As a postdoc he was a visiting assistant professor at Brown University and at the Laboratory for Information and Decision Systems at MIT. He joined the Technion in 1989 as senior lecturer, and was promoted in 1991 to associate professor, and in 1997 to full professor in the department of electrical engineering.
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As an alternative to probabilistic methods, heuristic methods exist for performing variant calling on NGS data. Instead of modelling the distribution of the observed data and using Bayesian statistics to calculate genotype probabilities, variant calls are made based on a variety of heuristic factors, such as minimum allele counts, read quality cut-offs, bounds on read depth, etc. Although they have been relatively unpopular in practice in comparison to probabilistic methods, in practice due to their use of bounds and cut-offs they can be robust to outlying data that violate the assumptions of probabilistic models.
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Structural optimization problems consist of two levels of optimization task and are commonly referred as mathematical programming problems with equilibrium constraints (MPEC). The upper level objective in such problems may involve cost minimization or weight minimization subject to bounds on displacements, stresses and contact forces. The decision variables at the upper level usually are shape of the structure, choice of materials, amount of material etc. However, for any given set of upper level variables, the state variables (displacement, stresses and contact forces) can only be figured out by solving the potential energy minimization problem that appears as an equilibrium satisfaction constraint or lower level minimization task to the upper level problem.
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In combinatorics he is known principally for his work with Paul Erdős and János Pach. In discrete geometry he is known for a number of basic concepts and results, jointly with his long-term collaborator, Jacob E. Goodman; of the City College, City University of New York, and some with others. His work with Goodman includes such results as the first nontrivial bounds on the number of order types and polytopes, and a generalization of the Hadwiger transversal theorem to higher dimensions. In real algebraic geometry he is known principally for a series of papers authored jointly with Saugata Basu and Marie-Françoise Roy and for their book.
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Bryson, along with his contemporary, Antiphon, was the first to inscribe a polygon inside a circle, find the polygon's area, double the number of sides of the polygon, and repeat the process, resulting in a lower bound approximation of the area of a circle. "Sooner or later (they figured), ...[there would be] so many sides that the polygon ...[would] be a circle."Blatner, page 16 Bryson later followed the same procedure for polygons circumscribing a circle, resulting in an upper bound approximation of the area of a circle. With these calculations, Bryson was able to approximate π and further place lower and upper bounds on π's true value.
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He was commissioned a Lieutenant-colonel, and participated in the movement of the "Flying Camp" from Philadelphia to New York, where he was engaged in the Battle of Long Island and taken prisoner. He was admitted to parole within certain bounds on April 16, 1777, and exchanged on September 10, 1779. In 1780 he was appointed commissioner of Forage, and whilst serving this appointment he purchased a large amount of supplies for the army, consisting of flour, oats, cattle, sheep, etc. A receipt book of his still extant in 1893, shows receipts for money paid out from August 12, 1780, to December 5, 1781, aggregating $202,033.
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Complexity classes group computational problems by their resource requirements. To do this, computational problems are differentiated by upper bounds on the maximum amount of resources the most efficient algorithm takes to solve them. More particularly, complexity classes are concerned with the rate of growth in resource requirements to solve a computational problem as the input size increases. For example, the amount of time it takes to solve problems in the complexity class P grows relatively slowly as the input size increases, while it grows comparatively quickly for problems in the complexity class EXPTIME (or more accurately, for problems in EXPTIME that are outside of P, since P\subseteqEXPTIME).
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The exercises in this book covered complex numbers, roots of unity, as well as some linear algebra and abstract algebra. In 1959 Brenner generalized propositions by Alexander Ostrowski and G. B. Price on minors of a diagonally dominant matrix. His work is credited with stimulating a reawakening of interest in the permanent of a matrix.Henryk Minc (1978) Permanents, page 13, Encyclopedia of Mathematics and its Applications volume 6, Addison-Wesley One of the challenges in linear algebra is to find the eigenvalues and eigenvectors of a square matrix of complex numbers. In 1931 S. A. Gershgorin described geometric bounds on the eigenvectors in terms of the matrix elements.
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The 1st hole is a short par 4, with a slight dogleg right, with out of bounds on the right hand side. The dogleg is accentuated by a tall fence on the right side of the tee box, which blocks any attempt to drive directly to the green. However, a well placed tee shot which gently moves from left to right will result in a short second shot to a green which is protected by two bunkers short of the green. The 2nd hole is a straight par 4, with a public road which crosses through the hole approximately 140 yards from the green.
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In regression analysis, an interval predictor model (IPM) is an approach to regression where bounds on the function to be approximated are obtained. This differs from other techniques in machine learning, where usually one wishes to estimate point values or an entire probability distribution. Interval Predictor Models are sometimes referred to as a nonparametric regression technique, because a potentially infinite set of functions are contained by the IPM, and no specific distribution is implied for the regressed variables. As a consequence of the theory of scenario optimization, in many cases rigorous predictions can be made regarding the performance of the model at test time .
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Pennfield Parish's boundaries use both metes and bounds: on the north by a line running true west from the southernmost corner of Queens County; on the east by a line running true north from the mouth of the Pocologan River; on the west by a prolongation north and south of the western line of a 1000-acre grant straddling Lake Utopia and then along a line running through the Letang River and Letang Harbour; and on the south by the Bay of Fundy. The parish also includes any islands with two miles (3.2 kilometres) of the shore and The Wolves, a group of islands more than five miles (eight kilometres) offshore.
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Earls Hall Farm Wind Farm, from St Osyth allotments on the east of the village. The wind farm consists of five wind turbines with a total nominal power of 10.25 MW. St Osyth is claimed to be the driest recorded place in the United Kingdom, with an average rainfall of just per year. St Osyth parish extends south from the village to the coast, and includes the smaller villages Point Clear and Lee-over-Sands. Although a significant part of the parish boundary is coastline, which does not need to be "beaten", St Osyth is one parish which maintains the tradition of beating the bounds on Rogation days.
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On floor, however, she went out of bounds on her tucked full- in tumbling pass and fell on her double pike, posting one of the lowest scores of the meet. In a decision that proved controversial, she did not qualify to the 2006 National Championships. She stated that USA Gymnastics officials had told her she would qualify if she attended the national training camp and competed at least one event at the U.S. Classic. But after the Classic, she was told that she had needed a combined score on two events of 28.0 or higher to qualify; her combined score on vault and floor was 27.1.
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One important non-collider effort is the determination of the neutrino masses, since these masses may arise from neutrinos mixing with very heavy particles. In addition, cosmological observations provide many useful constraints on the dark matter, although it may be impossible to determine the exact nature of the dark matter without the colliders. Finally, lower bounds on the very long lifetime of the proton put constraints on Grand Unified Theories at energy scales much higher than collider experiments will be able to probe any time soon. In May 2014, the Particle Physics Project Prioritization Panel released its report on particle physics funding priorities for the United States over the next decade.
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73–79 This method may be used to enumerate either free or fixed polyominoes. A more sophisticated method, described by Redelmeier, has been used by many authors as a way of not only counting polyominoes (without requiring that all polyominoes of order n be stored in order to enumerate those of order n+1), but also proving upper bounds on their number. The basic idea is that we begin with a single square, and from there, recursively add squares. Depending on the details, it may count each n-omino n times, once from starting from each of its n squares, or may be arranged to count each once only.
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The IETF Deterministic Networking (DetNet) Working Group is focusing to define deterministic data paths with high reliability and bounds on latency, loss, and packet delay variation (jitter), such as audio and video streaming, industrial automation, and vehicle control. The goals of Deterministic Networking are to migrate time-critical, high-reliability industrial and audio-video applications from special-purpose Fieldbus networks to IP packet networks. To achieve these goals, DetNet uses resource allocation to manage buffer sizes and transmission rates in order to satisfy end-to-end latency requirements. Service protection against failures with redundancy over multiple paths and explicit routes to reduce packet loss and reordering.
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In 2002, 76-year-old Paterno chased down referee Dick Honig in a dead sprint following a 42–35 overtime home loss to Iowa. Paterno saw Tony Johnson catch a pass for a first down with both feet in bounds on the stadium's video replay board, but the play was ruled an incompletion. This being after Penn State had rallied from a 35–13 deficit with 9 minutes left in the game to tie the score at 35, and were driving on their first possession in overtime (a touchdown would have tied the game at 42). Penn State failed on fourth down and Iowa held on for the win.
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In the example, the 95th percentile is sure to be between 9 and 16. If the left and right bounds of a p-box are sure to enclose the unknown distribution, the bounds are said to be rigorous, or absolute. The bounds may also be the tightest possible such bounds on the distribution function given the available information about it, in which case the bounds are therefore said to be best-possible. It may commonly be the case, however, that not every distribution that lies within these bounds is a possible distribution for the uncertain number, even when the bounds are rigorous and best-possible.
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Fagin's theorem is the oldest result of descriptive complexity theory, a branch of computational complexity theory that characterizes complexity classes in terms of logic-based descriptions of their problems rather than by the behavior of algorithms for solving those problems. The theorem states that the set of all properties expressible in existential second-order logic is precisely the complexity class NP. It was proven by Ronald Fagin in 1973 in his doctoral thesis, and appears in his 1974 paper. The arity required by the second-order formula was improved (in one direction) in Lynch's theorem, and several results of Grandjean have provided tighter bounds on nondeterministic random-access machines.
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It is one of the first rigidity statements in dynamical systems. In the last two decades Katok has been working on other rigidity phenomena, and in collaboration with several colleagues, made contributions to smooth rigidity and geometric rigidity, to differential and cohomological rigidity of smooth actions of higher-rank abelian groups and of lattices in Lie groups of higher rank, to measure rigidity for group actions and to nonuniformly hyperbolic actions of higher-rank abelian groups. Katok's works on topological properties of nonuniformly hyperbolic dynamical systems. It includes density of periodic points and lower bounds on their number as well as exhaustion of topological entropy by horseshoes.
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In mathematics, an Euler system is a collection of compatible elements of Galois cohomology groups indexed by fields. They were introduced by in his work on Heegner points on modular elliptic curves, which was motivated by his earlier paper and the work of . Euler systems are named after Leonhard Euler because the factors relating different elements of an Euler system resemble the Euler factors of an Euler product. Euler systems can be used to construct annihilators of ideal class groups or Selmer groups, thus giving bounds on their orders, which in turn has led to deep theorems such as the finiteness of some Tate-Shafarevich groups.
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Caragiannis et al. and also empirically by Athey and Nekipelov Susan Athey and Denis Nekipelov. A Structural Model of Sponsored Search Advertising Auctions , Ad Auctions Workshop, 2010 discuss the Bayesian version of the game - where players have beliefs about the other players but do not necessarily know the other players' valuations. Gomes and Sweeney prove that an efficient equilibrium might not exist in the partial information setting. Caragiannis et al. consider the welfare loss at Bayes–Nash equilibrium and prove a price of anarchy bound of 2.927. Bounds on the revenue in Bayes–Nash equilibrium are given by Lucier et al. and Caragiannis et al.
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These are particularly useful since they tend to contain very little baryonic matter, reducing the expected background from standard astrophysical processes. Typical indirect searches look for excess gamma rays, which are predicted both as final-state products of annihilation, or are produced as charged particles interact with ambient radiation via inverse Compton scattering. The spectrum and intensity of a gamma ray signal depends on the annihilation products, and must be computed on a model-by-model basis. Experiments that have placed bounds on WIMP annihilation, via the non- observation of an annihilation signal, include the Fermi-LAT gamma ray telescope and the VERITAS ground-based gamma ray observatory.
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Sipser specializes in algorithms and complexity theory, specifically efficient error correcting codes, interactive proof systems, randomness, quantum computation, and establishing the inherent computational difficulty of problems. He introduced the method of probabilistic restriction for proving super-polynomial lower bounds on circuit complexity in a paper joint with Merrick Furst and James B. Saxe. Their result was later improved to be an exponential lower bound by Andrew Yao and Johan Håstad. In an early derandomization theorem, Sipser showed that BPP is contained in the polynomial hierarchy, subsequently improved by Peter Gács and Clemens Lautemann to form what is now known as the Sipser-Gàcs-Lautemann theorem.
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Adaptive control is the control method used by a controller which must adapt to a controlled system with parameters which vary, or are initially uncertain. For example, as an aircraft flies, its mass will slowly decrease as a result of fuel consumption; a control law is needed that adapts itself to such changing conditions. Adaptive control is different from robust control in that it does not need a priori information about the bounds on these uncertain or time-varying parameters; robust control guarantees that if the changes are within given bounds the control law need not be changed, while adaptive control is concerned with control law changing itself.
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For example, see Goemans' and Williamson's semidefinite programming-based Max-Cut approximation algorithm.) The challenge in the first step is to choose a suitable integer linear program. Familiarity with linear programming is required, in particular, familiarity with how to model problems using linear programs and integer linear programs. But, for many problems, there is a natural integer linear program that works well, such as in the Set Cover example below. (The integer linear program should have a small integrality gap; indeed randomized rounding is often used to prove bounds on integrality gaps.) In the second step, the optimal fractional solution can typically be computed in polynomial time using any standard linear programming algorithm.
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Ball's college career will forever be marred with inconsistency. The teams he led "played to the level of the opponent," producing several impressive upsets while losing "easier" games. Although he won several big games for the Jackets including two wins against ranked Auburn University teams and a win against #3 University of Miami on the road in 2005, Ball-led Yellow Jacket teams were 0-4 against the University of Georgia, Georgia Tech's primary rival. Ball's play in these games (including, in 2004, a drive-ending intentional incomplete pass out of bounds on 4th down and earning him the nickname "5th Down Reggie") will always be in question to Georgia Tech fans.
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Each robot builds a map incrementally by matching geometric features (segments and angles between them) in the environment with features previously obtained, The partial maps produced by each robot are then merged again using feature matching. Gini and her authors proposed a method for auctions of tasks to a group of robots. The most distinctive feature is the robustness of the method to robot failures, which is obtained by doing new rounds of auctions every time a task has been completed or a robot has exceeded the time allocated to the task. The paper provides bounds on the cost of the solution achieved, and includes experimental results obtained with real robots and in simulation in a variety of environments.
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Branch and bound (BB or B&B;) is an algorithm design paradigm for discrete and combinatorial optimization problems. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm.
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Stopped short of midfield with less than a minute to play, Tech called its second timeout in order to stop the game clock from ticking down. In college football, the clock stops after a team earns a first down, and because Virginia Tech had not earned a first down on the short run, Tech was forced to call the timeout. Following the timeout, the Hokies ran for a first down, penetrating to the NC State 44-yard line. With 53 seconds remaining, Chapman scrambled out of bounds on a short run. Another short run brought the Hokies to the State 36-yard line, and the Hokies called their final timeout to stop the clock.
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Boston College was the first Big East team to play in the Motor City Bowl and was playing in its fourth straight bowl game. The bowl game MVP was Boston College quarterback Brian St. Pierre, who completed 25 of 35 passes for 342 yards, a personal career high. Boston College scored on its first six possessions, and its 51 points set a Motor City Bowl record which would later be tied in the 2007 Motor City Bowl when the Purdue Boilermakers defeated the Central Michigan Chippewas 51–48. On a sour note two Toledo players were ejected during the game; one for throwing a punch and another for a late hit out of bounds on St. Pierre.
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Human female sexuality encompasses a broad range of behaviors and processes, including female sexual identity and sexual behavior, the physiological, psychological, social, cultural, political, and spiritual or religious aspects of sexual activity. Various aspects and dimensions of female sexuality, as a part of human sexuality, have also been addressed by principles of ethics, morality, and theology. In almost any historical era and culture, the arts, including literary and visual arts, as well as popular culture, present a substantial portion of a given society's views on human sexuality, which include both implicit (covert) and explicit (overt) aspects and manifestations of feminine sexuality and behavior. In most societies and legal jurisdictions, there are legal bounds on what sexual behavior is permitted.
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If the loose ball goes out of bounds on a face- off before either team can pick it up, it is awarded to the team that last touched it and all other players are released when play is restarted. The players facing off may not step on or hold each other's sticks to prevent the other from getting the ball. Nor may they trap the ball beneath their sticks without attempting a "tennis pickup" to prevent anyone from establishing possession, an action normally penalized as withholding the ball from play, another technical foul. If they pick the ball up on the back of their stick but do not immediately flip it into the pocket, it is also considered withholding.
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During the ‘Seventies, Rajaraman extended his research to include particle physics. At that time, high energy hadron scattering was being analysed using S-matrix and Regge pole techniques. Since the Froissart- Martin asymptotic bounds on hadron scattering is not applicable to Weak Interactions, Rajaraman constructed a self-consistent theory of zero-mass neutrinos and showed that ν- ν and ν- ν(bar) scattering total cross sections asymptotically become equal and approach the same constant value. Rajaraman gave the first determination from experimental data of the value of the "Triple Pomeron Vertex" as a function of momentum transfer and also derived the consequences of the vanishing of this vertex on high energy hadron scattering.
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These are the results of the women's individual all-around competition, one of six events for female competitors in artistic gymnastics at the 2000 Summer Olympics in Sydney. The qualification and final rounds took place on September 17 and 21 at the Sydney SuperDome. World all-around silver medalist Viktoria Karpenko led the competition until the last rotation, but was thrown from first place after she stubbed her toe, tripped, and fell out of bounds on floor exercise.IG Online Interview: Viktoria KarpenkoSYDNEY 2000: GYMNASTICS; A Champion Answers Disaster With TriumphKhorkina claims gold at lastSvetlana Khorkina The all-around competition in the discipline of women's artistic gymnastics (WAG) was marred by three separate scandals.
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In the fourth quarter, Longhorns' quarterback James Street couldn't find a receiver and ran 42 yards for a touchdown, then carried over the ball for two to cut the lead to six at 14–8. With 4:47 to play, the Longhorns were on their own 43 on fourth down with three yards to go. Street threw long to Randy Peschel open downfield, who made the catch and fell out of bounds on the 13-yard line. After Ted Koy ran for eleven yards, Jim Bertelsen went over to tie the score, and the extra point kick by Happy Feller gave Texas a 15–14 lead with just under four minutes remaining.
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These experiences may be summed in some sense but can only approximately be shared, even among very similar cognitions with identical DNA. An early explorer of this view was Alan Turing who sought to prove the limits of expressive complexity of human genes in the late 1940s, to put bounds on the complexity of human intelligence and so assess the feasibility of artificial intelligence emerging. Since 2000, Process Psychology has progressed as an independent academic and therapeutic discipline: In 2000, Michel Weber created the Whitehead Psychology Nexus: an open forum dedicated to the cross-examination of Alfred North Whitehead's process philosophy and the various facets of the contemporary psychological field.Cobb, John B., Jr. "Process Psychotherapy: Introduction".
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Symmetry of the distribution decreases the inequality's bounds by a factor of 2 while unimodality sharpens the bounds by a factor of 4/9. Because the mean and the mode in a unimodal distribution differ by at most standard deviations at most 5% of a symmetrical unimodal distribution lies outside (2 + 3)/3 standard deviations of the mean (approximately 3.840 standard deviations). This is sharper than the bounds provided by the Chebyshev inequality (approximately 4.472 standard deviations). These bounds on the mean are less sharp than those that can be derived from symmetry of the distribution alone which shows that at most 5% of the distribution lies outside approximately 3.162 standard deviations of the mean.
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A matching-critical graph is a graph for which the removal of any vertex does not change the size of a maximum matching; by Gallai's characterization, the matching-critical graphs are exactly the graphs in which every connected component is factor-critical.. The complement graph of a critical graph is necessarily matching-critical, a fact that was used by Gallai to prove lower bounds on the number of vertices in a critical graph.. As cited by . Beyond graph theory, the concept of factor-criticality has been extended to matroids by defining a type of ear decomposition on matroids and defining a matroid to be factor-critical if it has an ear decomposition in which all ears are odd..
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The IETF Deterministic Networking (DetNet) Working Group is working to define deterministic data paths with bounds on latency, loss, and packet delay variation (jitter), and high reliability. DetNet shall operate over both Layer 2 bridged segments and Layer 3 routed segments, relying on interoperability with AVB/TSN switches when possible. One of the possible application of DetNet is professional audio/video, such as music and film production, broadcast, cinema, live sound, and large venue (stadiums, halls, conference centers, theme parks, airports, train terminals, etc.) systems for public addressing, media streaming and emergency announcement. The stated goal is to enable geographically distributed, campus/enterprise-wide Intranet for content delivery with bounded low latency (10-15 ms).
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Peppers was double team blocked for the remainder of the Patriots final possession. Peppers was a highly disruptive force all throughout Super Bowl XXXVIII. With 1:08 remaining in the game, and the score tied 29-29, the Patriots were given a short field when Panthers kicker John Kasay kicked the ball out of bounds on the kickoff, giving the Patriots the ball at their own 40 yard line with just over a minute left and three timeouts to use. Brady got the Patriots down the field into field goal range, and Pats kicker Adam Vinatieri kicked a 41 yard field goal through the uprights with 4 seconds remaining for the victory.
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Branch and bound (BB, B&B;, or BnB) is an algorithm design paradigm for discrete and combinatorial optimization problems, as well as mathematical optimization. A branch-and-bound algorithm consists of a systematic enumeration of candidate solutions by means of state space search: the set of candidate solutions is thought of as forming a rooted tree with the full set at the root. The algorithm explores branches of this tree, which represent subsets of the solution set. Before enumerating the candidate solutions of a branch, the branch is checked against upper and lower estimated bounds on the optimal solution, and is discarded if it cannot produce a better solution than the best one found so far by the algorithm.
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Deligne's proof of the Riemann hypothesis over finite fields used the zeta functions of product varieties, whose zeros and poles correspond to sums of zeros and poles of the original zeta function, in order to bound the real parts of the zeros of the original zeta function. By analogy, introduced multiple zeta functions whose zeros and poles correspond to sums of zeros and poles of the Riemann zeta function. To make the series converge he restricted to sums of zeros or poles all with non-negative imaginary part. So far, the known bounds on the zeros and poles of the multiple zeta functions are not strong enough to give useful estimates for the zeros of the Riemann zeta function.
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In mathematics, Wetzel's problem concerns bounds on the cardinality of a set of analytic functions that, for each of their arguments, take on few distinct values. It is named after John Wetzel, a mathematician at the University of Illinois at Urbana–Champaign... Let F be a family of distinct analytic functions on a given domain with the property that, for each x in the domain, the functions in F map x to a countable set of values. In his doctoral dissertation, Wetzel asked whether this assumption implies that F is necessarily itself countable.. As cited by . Paul Erdős in turn learned about the problem at the University of Michigan, likely via Lee Albert Rubel.
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Stein's method can be used not only to prove the central limit theorem, but also to provide bounds on the rates of convergence for selected metrics. The convergence to the normal distribution is monotonic, in the sense that the entropy of Z_n increases monotonically to that of the normal distribution. The central limit theorem applies in particular to sums of independent and identically distributed discrete random variables. A sum of discrete random variables is still a discrete random variable, so that we are confronted with a sequence of discrete random variables whose cumulative probability distribution function converges towards a cumulative probability distribution function corresponding to a continuous variable (namely that of the normal distribution).
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Electroweak vacuum stability landscape as estimated in 2012 Electroweak vacuum stability landscape as estimated in 2018 The stability criteria for the electroweak interaction was first formulated in 1979N. Cabibbo, L. Maiani, G. Parisi and R. Petronzio, Bounds on the Fermions and Higgs Boson Masses in Grand Unified Theories, 1979 as a function of the masses of the theoretical Higgs boson and the heaviest fermion. Discovery of the Top quark in 1995 and the Higgs boson in 2012 have allowed physicists to validate the criteria against experiment, therefore since 2012 Electroweak interaction is considered as the most promising candidate for metastable fundamental force. The corresponding false vacuum hypothesis is called either 'Electroweak vacuum instability' or 'Higgs vacuum instability'.
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However, a key difference is that the dual subgradient algorithm is typically analyzed under restrictive strict convexity assumptions that are needed for the primal variables x(t) to converge. There are many important cases where these variables do not converge to the optimal solution, and never even get near the optimal solution (this is the case for most linear programs, as shown below). On the other hand, the drift-plus- penalty algorithm does not require strict convexity assumptions. It ensures that the time averages of the primals converge to a solution that is within O(1/V) of optimality, with O(V) bounds on queue sizes (it can be shown that this translates into an O(V2) bound on convergence time).
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McPhee will be a free hit at the Dockers, The Roar, Retrieved on 27 November 2009 His first match against his old club Essendon saw him hit the post twice, drop marks and kick out of bounds on the full right in front of Bombers fans who booed him consistently throughout the match. Despite his clangers, Fremantle managed to upset Essendon by 44 points.Dockers break drought by beating Bombers After McPhee's tough start in his return to Fremantle, he improved as the season went on after a change in role. McPhee played his best football for the Dockers towards the end of the season as a run-with player (tagger), a role which requires stopping the influence of the opposition team's most damaging players.
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The motivation for considering completeness properties derives from the great importance of suprema (least upper bounds, joins, "\vee") and infima (greatest lower bounds, meets, "\wedge") to the theory of partial orders. Finding a supremum means to single out one distinguished least element from the set of upper bounds. On the one hand, these special elements often embody certain concrete properties that are interesting for the given application (such as being the least common multiple of a set of numbers or the union of a collection of sets). On the other hand, the knowledge that certain types of subsets are guaranteed to have suprema or infima enables us to consider the computation of these elements as total operations on a partially ordered set.
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The graph removal lemma was later extended to directed graphs and to hypergraphs. An alternative proof, providing stronger bounds on the number of edges that need to be removed as a function of the number of copies of the subgraph, was published by Jacob Fox in 2011. A version for induced subgraphs was proved by Alon, Fischer, Krivelevich, and Szegedy in 2000. It states that for any graph H with h vertices and \epsilon > 0, there exists a constant \delta > 0 such that if an n-vertex graph G has fewer than \delta n^h induced subgraphs isomorphic to H, then it is possible to eliminate all induced copies of H by adding or removing fewer than \epsilon n^2 edges.
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Her uneven bars score would have qualified her in 8th place in that final as well, but she was excluded, as per the rules, after teammates Kocian and Douglas qualified ahead of her. In team finals, she helped the United States team win their third consecutive gold medal at a World Championships event. During the all-around final, Biles performed below her usual standard, taking a large hop on the vault, landing out of bounds on floor (which she stated was a first), and grasping the beam to prevent a fall. However, her final score of 60.399 was more than enough to secure the title with her largest margin of victory yet (over a point ahead of silver medalist Gabby Douglas and bronze medalist Larisa Iordache).
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EPR paradox illustration Roy's research was principally based on pion dynamics and hadron interactions. His work on axiomatic quantum field theory assisted him to develop an exact integral equation which later came to be known as Roy's equations, and many scientists opined that the equation helped in pion–pion data analysis. He furthered the studies of Andre Martin on high-energy bounds and the observations of John Stewart Bell regarding Einstein-Podolsky-Rosen paradox; his work on the former resulted in the development of Roy-Singh bounds (unitarity bounds on high-energy cross sections) and the studies on the latter evolved into Roy-Singh multiparticle Bell inequalities and Auberson-Mahoux-Roy-Singh Bell inequalities. He developed the theme further by proposing Roy's multipartite separability inequalities.
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For proving bounds on this problem, it may be assumed without loss of generality that the inputs are strings over a two-letter alphabet. For, if two strings over a larger alphabet differ then there exists a string homomorphism that maps them to binary strings of the same length that also differ. Any automaton that distinguishes the binary strings can be translated into an automaton that distinguishes the original strings, without any increase in the number of states.. It may also be assumed that the two strings have equal length. For strings of unequal length, there always exists a prime number whose value is logarithmic in the smaller of the two input lengths, such that the two lengths are different modulo .
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Belichick later stated, "With a quarterback like Brady, going for the win is not that dangerous, because he's not going to make a mistake." Brady opened the drive with three dump-off completions to running back J. R. Redmond, who got out of bounds on the last one and moved the ball to their 41-yard line with 33 seconds left. At this point, Madden admitted on the air that he now liked what the Patriots were doing. After an incomplete pass, Brady completed a 23-yard pass underneath the Rams' zone defense to wide receiver Troy Brown—who also got out of bounds—and followed it up with a 6-yard completion to tight end Jermaine Wiggins to advance to the Rams' 30-yard line.
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In the team final, Carey competed on vault and floor exercise, receiving the second highest scores of the day on each, behind Biles, and helping the USA win the gold medal ahead of Russia and Italy. During the vault final Carey performed a Cheng and an Amanar, taking a step out of bounds on the latter, earning an average score of 14.883 and winning the silver medal behind Biles and ahead of Ellie Downie of Great Britain. In November Carey traveled to Zürich, Switzerland to compete at the Swiss Cup, a unique team competition that featured one female gymnast and one male gymnast from the same country going head-to-head with other teams. She was partnered with Allan Bower.
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Froissart mentions "Sir Robert Lauder, a renowned hero" as having been present at the Battle of Otterburn which took place on 19 August 1388.Young, James, Historical References to the Scottish Family of Lauder, Glasgow, 1884: 45 Rymer's Foedera records that Robert de Lawdre was one of the sureties for the Earl of Douglas's bounds on the Middle March during a meeting at 'Haudenstank' between English and Scottish Commissioners on 26 October 1398, to discuss the return of prisoners and ransoms and "the due observance of the truce".Bain, Joseph, FSA (Scot), editor, Calendar of Documents relating to Scotland vol.iv, 1357-1509, Edinburgh, 1888, number 510 Sir Robert Lauder of The Bass took part in the Battle of Nesbit Moor on 22 June 1402, and was captured.
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Optimization algorithms implemented in pSeven allow solving single and multi-objective constrained optimization problems as well as robust and reliability based design optimization problems. Users can solve both engineering optimization problems with cheap to evaluate semi-analytical models and the problems with expensive (in terms of CPU time) objective functions and constraints.F. Gubarev, V. Kunin, A. Pospelov, "Lay-up Optimization of Laminated Composites: Mixed Approach with Exact Feasibility Bounds on Lamination Parameters"Dmitry Khominich, Fedor Gubarev, Alexis Pospelov, "Shape Optimization of Rotating Disks", 20th Conference of the International Federation of Operational Research Societies, 2014 SmartSelection technique automatically and adaptively selects the most suitable optimization algorithm for a given optimization problem from a pool of optimization methods and algorithms in pSeven.
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The editorial board of the Newark newspaper, The Star-Ledger, criticized both the law and its application, arguing that Ravi's crime was not malicious, the law was unconstitutional, and the application of the law against Ravi was a "huge overreach". Washington Post columnist Richard Cohen criticized Ravi for "bullying (via webcam)", but argued that hate crime laws unfairly punish an individual for thought or speech, and therefore erode civil liberties. In a New York Times op-ed piece, journalist Emily Bazelon argued that, while Ravi's invasion of Clementi's privacy "should be out of bounds on a college campus," the punishment he faced was disproportionate to that crime, and that hate crime laws were not intended for these types of actions.
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In this way, the mixing time can be bounded by the time for the two coupled chains to synchronize. Chapter six discusses a technique called "strong stationary times" with which, for some Markov chains, one can prove that choosing a stopping time randomly from a certain distribution will result in a state drawn from the stable distribution. After a chapter on lower bounds on mixing time based on the "bottleneck ratio" and isoperimetric number, the next two chapters of the first part cover two important examples: card shuffling and random walks on graphs. Chapters 10 and 11 consider two more parameters closely related to the mixing time, the hitting time at which the Markov chain first reaches a specified state, and the cover time at which it has first reached all states.
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They can however provide upper bounds on the probability (or cross section) of pair production, as a function of energy. The ATLAS experiment at the Large Hadron Collider currently has the most stringent cross section limits for magnetic monopoles of 1 and 2 Dirac charges, produced through Drell-Yan pair production. A team led by Wendy Taylor searches for these particles based on theories that define them as long lived (they don't quickly decay), as well as being highly ionizing (their interaction with matter is predominantly ionizing). In 2019 the search for magnetic monopoles in the ATLAS detector reported its first results from data collected from the LHC Run 2 collisions at center of mass energy of 13 TeV, which at 34.4 fb−1 is the largest dataset analyzed to date.
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Three major challenges specific to population informatics are: # Preserving privacy of the subjects of the data – due to increasing concerns of privacy and confidentiality sharing or exchanging sensitive data about the subjects across different organizations is often not allowed. Therefore, population informatics need to be applied on encrypted data or in a privacy-preserving setting.Dinusha Vatsalan, Peter Christen, and Vassilios S. Verykios. "A taxonomy of privacy-preserving record linkage techniques." Journal of Information Systems (Elsevier), 38(6): 946-969, 2013. doi: 10.1016/j.is.2012.11.005 # The need for error bounds on the results – since real world data often contain errors and variations error bound need to be used (for approximate matching) so that real decisions that have direct impact on people can be made based on these results.Peter Christen.
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In mathematics, the limit of a sequence of sets A1, A2, ... (subsets of a common set X) is a set whose elements are determined by the sequence in either of two equivalent ways: (1) by upper and lower bounds on the sequence that converge monotonically to the same set (analogous to convergence of real- valued sequences) and (2) by convergence of a sequence of indicator functions which are themselves real-valued. As is the case with sequences of other objects, convergence is not necessary or even usual. More generally, again analogous to real-valued sequences, the less restrictive limit infimum and limit supremum of a set sequence always exist and can be used to determine convergence: the limit exists if the limit infimum and limit supremum are identical. (See below).
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Proton decay is one of the key predictions of the various grand unified theories (GUTs) proposed in the 1970s, another major one being the existence of magnetic monopoles. Both concepts have been the focus of major experimental physics efforts since the early 1980s. To date, all attempts to observe these events have failed; however, these experiments have been able to establish lower bounds on the half-life of the proton. Currently the most precise results come from the Super-Kamiokande water Cherenkov radiation detector in Japan: a 2015 analysis placed a lower bound on the proton's half-life of years via positron decay, and similarly, a 2012 analysis gave a lower bound to the proton's half-life of years via antimuon decay, close to a supersymmetry (SUSY) prediction of 1034–1036 years.
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In March 2019, Uhlenbeck became the first woman to receive the Abel Prize, with the award committee citing the decision for "her pioneering achievements in geometric partial differential equations, gauge theory and integrable systems, and for the fundamental impact of her work on analysis, geometry and mathematical physics." Hans Munthe-Kaas, who chairs the award committee, stated that "Her theories have revolutionised our understanding of minimal surfaces, such as more general minimisation problems in higher dimensions". Uhlenbeck also won the National Medal of Science in 2000,. and the Leroy P. Steele Prize for Seminal Contribution to Research of the American Mathematical Society in 2007, "for her foundational contributions in analytic aspects of mathematical gauge theory", based on her 1982 papers "Removable singularities in Yang–Mills fields" and "Connections with bounds on curvature".
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Several authors have provided additional conditions that classify some graphs as being of class one or class two, but do not provide a complete classification. For instance, if the vertices of the maximum degree in a graph form an independent set, or more generally if the induced subgraph for this set of vertices is a forest, then must be of class one.. showed that almost all graphs are of class one. That is, in the Erdős–Rényi model of random graphs, in which all -vertex graphs are equally likely, let be the probability that an -vertex graph drawn from this distribution is of class one; then approaches one in the limit as goes to infinity. For more precise bounds on the rate at which converges to one, see .
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In computer science, a kernelization is a technique for designing efficient algorithms that achieve their efficiency by a preprocessing stage in which inputs to the algorithm are replaced by a smaller input, called a "kernel". The result of solving the problem on the kernel should either be the same as on the original input, or it should be easy to transform the output on the kernel to the desired output for the original problem. Kernelization is often achieved by applying a set of reduction rules that cut away parts of the instance that are easy to handle. In parameterized complexity theory, it is often possible to prove that a kernel with guaranteed bounds on the size of a kernel (as a function of some parameter associated to the problem) can be found in polynomial time.
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Shortest path algorithms are applied to automatically find directions between physical locations, such as driving directions on web mapping websites like MapQuest or Google Maps. For this application fast specialized algorithms are available. If one represents a nondeterministic abstract machine as a graph where vertices describe states and edges describe possible transitions, shortest path algorithms can be used to find an optimal sequence of choices to reach a certain goal state, or to establish lower bounds on the time needed to reach a given state. For example, if vertices represent the states of a puzzle like a Rubik's Cube and each directed edge corresponds to a single move or turn, shortest path algorithms can be used to find a solution that uses the minimum possible number of moves.
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In mathematics, a transitive reduction of a directed graph D is another directed graph with the same vertices and as few edges as possible, such that if there is a (directed) path from vertex v to vertex w in D, then there is also such a path in the reduction. Transitive reductions were introduced by , who provided tight bounds on the computational complexity of constructing them. More technically, the reduction is a directed graph that has the same reachability relation as D. Equivalently, D and its transitive reduction should have the same transitive closure as each other, and its transitive reduction should have as few edges as possible among all graphs with this property. The transitive reduction of a finite directed acyclic graph (a directed graph without directed cycles) is unique and is a subgraph of the given graph.
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Liukin performed all-around in the qualifying round of competition. She fell on her dismount from the uneven bars, but nevertheless qualified to the all-around final with a score of 62.325, which ranked her just behind Shawn Johnson, her friend and Olympic roommate. Liukin also qualified to three event finals: beam, uneven bars (in spite of the fall) and floor exercise. In the team finals, Liukin performed on three events: beam, bars and floor exercise. Her uneven bars score of 16.900 was the highest mark awarded in the entire Olympic competition. Liukin performed second on balance beam, matching her qualifying score of 15.975. On floor exercise, she stepped out of bounds on her first tumbling pass, incurring a 0.1-point penalty, with a final score of 15.200. The American team earned the silver medal, 2.375 points behind China.
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In information theory and telecommunication engineering, the signal-to- interference-plus-noise ratio (SINR) (also known as the signal-to-noise-plus- interference ratio (SNIR)) is a quantity used to give theoretical upper bounds on channel capacity (or the rate of information transfer) in wireless communication systems such as networks. Analogous to the signal-to-noise ratio (SNR) used often in wired communications systems, the SINR is defined as the power of a certain signal of interest divided by the sum of the interference power (from all the other interfering signals) and the power of some background noise. If the power of noise term is zero, then the SINR reduces to the signal-to-interference ratio (SIR). Conversely, zero interference reduces the SINR to the SNR, which is used less often when developing mathematical models of wireless networks such as cellular networks.
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Most methods for the creation of antimatter (specifically antihydrogen) result in high-energy particles and atoms of high kinetic energy, which are unsuitable for gravity-related study. In recent years, first ALPHA and then ATRAP have trapped antihydrogen atoms at CERN; in 2012 ALPHA used such atoms to set the first free-fall loose bounds on the gravitational interaction of antimatter with matter, measured to within ±7500% of ordinary gravity, not enough for a clear scientific statement about the sign of gravity acting on antimatter. Future experiments need to be performed with higher precision, either with beams of antihydrogen (AEGIS) or with trapped antihydrogen (ALPHA or GBAR). In addition to uncertainty regarding whether antimatter is gravitationally attracted or repulsed from other matter, it is also unknown whether the magnitude of the gravitational force is the same.
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Moreover, Extended Frege is the weakest such system: if another proof system P has this property, then P simulates Extended Frege. An alternative translation between second-order statements and propositional formulas given by Jeff Paris and Alex Wilkie (1985) has been more practical for capturing subsystems of Extended Frege such as Frege or constant-depth Frege. (draft from 2008) While the above mentioned correspondence says that proofs in a theory translate to sequences of short proofs in the corresponding proof system, a form of the opposite implication holds as well. It is possible to derive lower bounds on size of proofs in a proof system P by constructing suitable models of a theory T corresponding to the system P. This allows to prove complexity lower bounds via model-theoretic constructions, an approach known as Ajtai's method.
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In the particular case when k = 3 (that is, for triangle-free circle graphs) the chromatic number is at most five, and this is tight: all triangle-free circle graphs may be colored with five colors, and there exist triangle-free circle graphs that require five colors.See for the upper bound, and for the matching lower bound. and give earlier weaker bounds on the same problem. If a circle graph has girth at least five (that is, it is triangle-free and has no four-vertex cycles) it can be colored with at most three colors.. The problem of coloring triangle-free squaregraphs is equivalent to the problem of representing squaregraphs as isometric subgraphs of Cartesian products of trees; in this correspondence, the number of colors in the coloring corresponds to the number of trees in the product representation.
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Nunavut Parliament building in Iqaluit Government building in Cape Dorset (Kinngait) With all efforts to preserve and cultivate cultural values of the past, the Inuit also want the progress of the modern industrial society. They show concern about the endangering of the environment by technical processes associated with the exploitation of resources, but are also interested in a future of western standards. They have also recognized that they are much better able to influence their conditions of living to their own ideas, when they agree within regional bounds on the goals to be pursued. The Canadian Inuit, just like the other indigenous peoples (First Nations and Métis people) of Canada, grew the demand for collective ethnic rights and a territory of their own, with a government composed of their kind, and Inuktitut as one of the official languages.
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The Lobos began the second half of the game with a kickoff to Navy, and after an unsuccessful drive from each team, the Midshipmen began a drive on their own 25-yard line with 11:30 left in the quarter. With 7:01 left, Polanco scored another rushing touchdown for the Midshipmen, this time for 28 yards. The next Lobos drive began with two penalties from the Midshipmen, moving New Mexico from its own 31-yard line to Navy's 49 before their first snap. The Lobos moved 48 yards over the course of eight plays and almost five minutes of game time, but the team committed a turnover on downs inches away from the goal line when running back D.D. Cox was forced out of bounds on fourth down, preventing the team from scoring any points.
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In essence, the hole is double dogleg in the shape of an elongated and tall S. On the tee, there is out of bounds right and lateral hazard on the left. The ideal tee shot carries to the base of a hill, just to the right of the center of the fairway. The second shot has out of bounds on the whole right side, and well struck second shots will tend to land and bounce left, but the left hand side of the fairway is the preferable angle to play the third shot into a green that has a bunker well short, and one just off the back right, as well as out of bounds over the back of the green. The 6th hole is a par 4 which parallels the 3rd hole, and provides an excellent view of the course and clubhouse.
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These included sitting her Biles vault, falling off the balance beam on her Barani salto, and going out of bounds on her Moors during her floor exercise. Nevertheless, the overwhelming difficulty gap between her and her competitors allowed her to claim the title with a score of 57.491, roughly 1.7 points ahead of silver medalist Mai Murakami of Japan and bronze medalist Morgan Hurd. For example, Biles’ vault had a full point higher in start value compared to the double-twisting Yurchenko vault performed by Hurd and Murakami, and her final skill on the floor exercise, the Silivas, was the opening skill in Hurd and Murakami's routines. Earning her fourth world all-around title, Biles set a new record for most women's World All-Around titles, surpassing the previous record of three held by Svetlana Khorkina.
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A third variation of the problem, still unsolved, is Conway's dead fly problem. John Horton Conway recalled that, as a child, he slept in a room with wallpaper whose flower pattern resembled an array of dead flies, and that he would try to find convex regions that did not have a dead fly in them. In Conway's formulation, the question is whether there exists a Danzer set in which the points of the set (the dead flies) are separated at a bounded distance from each other. Such a set would necessarily also have an upper bound on the distance from each point of the plane to a dead fly (in order to touch all circles of unit area), so it would form a Delone set, a set with both lower and upper bounds on the spacing of the points.
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In theoretical computer science, the algorithmic Lovász local lemma gives an algorithmic way of constructing objects that obey a system of constraints with limited dependence. Given a finite set of bad events {A1, ..., An} in a probability space with limited dependence amongst the Ais and with specific bounds on their respective probabilities, the Lovász local lemma proves that with non-zero probability all of these events can be avoided. However, the lemma is non-constructive in that it does not provide any insight on how to avoid the bad events. If the events {A1, ..., An} are determined by a finite collection of mutually independent random variables, a simple Las Vegas algorithm with expected polynomial runtime proposed by Robin Moser and Gábor Tardos can compute an assignment to the random variables such that all events are avoided.
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For instance, two-dimensional convex hulls can be computed using predicates that test the sign of quadratic polynomials, and therefore may require twice as many bits of precision within these calculations as the input numbers. When integer arithmetic cannot be used (for instance, when the result of a calculation is an algebraic number rather than an integer or rational number), a second method is to use symbolic algebra to perform all computations with exactly represented algebraic numbers rather than numerical approximations to them. A third method, sometimes called a "floating point filter", is to compute numerical predicates first using an inexact method based on floating point arithmetic, but to maintain bounds on how accurate the result is, and repeat the calculation using slower symbolic algebra methods or numerically with additional precision when these bounds do not separate the calculated value from zero.
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Certain disputes during play may also be settled with a ball-up from the point of contention. If the ball is kicked or hit from a ball-up or boundary throw-in over the boundary line or into a behind post without the ball bouncing, a free kick is paid for out of bounds on the full. A free kick is also paid if the ball is deemed by the umpire to have been deliberately carried or directed out of bounds. If the ball travels out of bounds in any other circumstances (for example, contested play results in the ball being knocked out of bounds) a boundary umpire will stand with his back to the infield and return the ball into play with a throw-in, a high backwards toss back into the field of play.
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Common developmental patterns seen during tropical cyclone development, and their Dvorak-assigned intensities The Dvorak technique (developed between 1969 and 1984 by Vernon Dvorak) is a widely used system to estimate tropical cyclone intensity (which includes tropical depression, tropical storm, and hurricane/typhoon/intense tropical cyclone intensities) based solely on visible and infrared satellite images. Within the Dvorak satellite strength estimate for tropical cyclones, there are several visual patterns that a cyclone may take on which define the upper and lower bounds on its intensity. The primary patterns used are curved band pattern (T1.0-T4.5), shear pattern (T1.5–T3.5), central dense overcast (CDO) pattern (T2.5–T5.0), central cold cover (CCC) pattern, banding eye pattern (T4.0–T4.5), and eye pattern (T4.5–T8.0). Both the central dense overcast and embedded eye pattern use the size of the CDO.
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For instance, the length of a Davenport–Schinzel sequence of order three, with n symbols, can be at most \Theta(n\alpha(n)), as the second chapter shows; the third concerns higher orders. The fourth chapter applies this theory to line segments, and includes a proof that the bounds proven using these tools are tight: there exist systems of line segments whose arrangement complexity matches the bounds on Davenport–Schinzel sequence length. The remaining chapters concern more advanced applications of these methods. Three chapters concern arrangements of curves in the plane, algorithms for arrangements, and higher-dimensional arrangements, following which the final chapter (comprising a large fraction of the book) concerns applications of these combinatorial bounds to problems including Voronoi diagrams and nearest neighbor search, the construction of transversal lines through systems of objects, visibility problems, and robot motion planning.
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Zolak resides in Massachusetts with his wife Amy and his three children (Hadley, Samantha, and Brody). His daughter, Samantha, was diagnosed with Type 1 diabetes, and Zolak has since been investigating causes of the disease. After retirement, Zolak became a co-host of a morning sports radio talk show on Rhode Island sportstalk station "The Score" (WSKO/790 & WSKO-FM/99.7) until the show was canceled in 2008. He was also a football analyst for the CBS College Sports Network, as well as on the New England sports program Out of Bounds on the Comcast channel hosted by Gregg Murphy. In addition, Scott was a frequent guest host on The Big Show on WEEI in Boston before joining Gary Tanguay for the midday slot on "The Sports Hub" 98.5FM WBZ-FM, which covers the Boston area.
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The existence of a clique of a given size is a monotone graph property, meaning that, if a clique exists in a given graph, it will exist in any supergraph. Because this property is monotone, there must exist a monotone circuit, using only and gates and or gates, to solve the clique decision problem for a given fixed clique size. However, the size of these circuits can be proven to be a super- polynomial function of the number of vertices and the clique size, exponential in the cube root of the number of vertices.. For earlier and weaker bounds on monotone circuits for the clique problem, see and . Even if a small number of NOT gates are allowed, the complexity remains superpolynomial.. Additionally, the depth of a monotone circuit for the clique problem using gates of bounded fan-in must be at least a polynomial in the clique size.
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In the analysis of algorithms, an enumeration algorithm (i.e., an algorithm for listing a large or infinite collection of structures) is said to have polynomial delay if the time between the output of any one structure and the next is bounded by a polynomial function of the input size, in the worst case.. Polynomial delay implies that the total time used by an algorithm will be polynomial per output item, but is a stronger requirement. This is a desirable property, because it means that any consumer of the stream of outputs will not have to wait idle for a long time from one output to the next. In particular, an algorithm with polynomial delay cannot have a startup phase that takes exponential time before it produces a single output, unlike some algorithms that take polynomial time per output item.. Additionally, unlike bounds on the total time, it is a suitable form of analysis even for algorithms that produce an infinite sequence of outputs.
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The tolerance interval is less widely known than the confidence interval and prediction interval, a situation some educators have lamented, as it can lead to misuse of the other intervals where a tolerance interval is more appropriate. The tolerance interval differs from a confidence interval in that the confidence interval bounds a single-valued population parameter (the mean or the variance, for example) with some confidence, while the tolerance interval bounds the range of data values that includes a specific proportion of the population. Whereas a confidence interval's size is entirely due to sampling error, and will approach a zero-width interval at the true population parameter as sample size increases, a tolerance interval's size is due partly to sampling error and partly to actual variance in the population, and will approach the population's probability interval as sample size increases. The tolerance interval is related to a prediction interval in that both put bounds on variation in future samples.
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The momentum had clearly swung to home underdog Cleveland. Baltimore's Tony Lorick made the bad decision to run the kickoff out of the end zone and was tackled at the Baltimore 11. A clipping penalty moved the Colts back further and they soon had to punt again into the stiff wind. The kick went out of bounds on the Baltimore 39 and Ryan went right back to work. The Browns lost yardage on a broken reverse play, but Ryan dropped back from the 42 and found Collins all alone down the middle at the five; the big flanker waltzed into the end zone and the Browns were up 17–0. Unitas finally got the Colts across midfield against the aroused Browns defense, but running back Lenny Moore fumbled a handoff at the Cleveland 47 and the Browns recovered. Brown rumbled 23 yards with another pitchout to the Colt 14 as the third quarter ended.
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In mathematics, especially potential theory, harmonic measure is a concept related to the theory of harmonic functions that arises from the solution of the classical Dirichlet problem. Harmonic measure is the exit distribution of Brownian motion In probability theory, the harmonic measure of a subset of the boundary of a bounded domain in Euclidean space R^n, n\geq 2 is the probability that a Brownian motion started inside a domain hits that subset of the boundary. More generally, harmonic measure of an Itō diffusion X describes the distribution of X as it hits the boundary of D. In the complex plane, harmonic measure can be used to estimate the modulus of an analytic function inside a domain D given bounds on the modulus on the boundary of the domain; a special case of this principle is Hadamard's three-circle theorem. On simply connected planar domains, there is a close connection between harmonic measure and the theory of conformal maps.
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Separators may be combined into a separator hierarchy of a planar graph, a recursive decomposition into smaller graphs. A separator hierarchy may be represented by a binary tree in which the root node represents the given graph itself, and the two children of the root are the roots of recursively constructed separator hierarchies for the induced subgraphs formed from the two subsets A and B of a separator. A separator hierarchy of this type forms the basis for a tree decomposition of the given graph, in which the set of vertices associated with each tree node is the union of the separators on the path from that node to the root of the tree. Since the sizes of the graphs go down by a constant factor at each level of the tree, the upper bounds on the sizes of the separators also go down by a constant factor at each level, so the sizes of the separators on these paths add in a geometric series to O(√n).
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First, Swift points out that reformers do not appreciate the advantage to them of having such an easy target upon which to practice their criticism and wit with such little risk to their persons in response as the Church and clergy; and rhetorically asks what institution could adequately replace religion in this role. Next, Swift warns that the abolition of Christianity (specifically the Anglican church) could lead to a rise in Presbyterianism, or worse in his mind, Catholicism. Swift's ironic defence of Christianity becomes more earnest and apparent as he finally proposes that if Christianity were to be abolished, all religion should be so banned, so as to fully free men from all bounds on their thinking and behaviour, in order that they may be allowed to freely engage in such vices as prostitution and drunkenness. In conclusion, Swift proposes that if Christianity is to be abolished, it ought not be done until the conclusion of wars in which England was then involved, as many of the country's allies were devoutly Christian, or at least, in the case of Turkey, religious.
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In the preseason poll released on September 24, 1951, Tennessee and Michigan State were ranked first and second, with Tennessee having 60 of the 115 first place votes. MSU had opened its season on the 22nd with a 6-0 win over Oregon State. They were followed by #3 Ohio State, defending champion #4 Oklahoma, and #5 California (which had won its opener against Santa Clara, 34-0). As the regular season progressed, a new poll would be issued on the Monday following the weekend's games. On September 14, the Central Missouri Jules played the Southwestern Moundbuilders in the rejected touchdown game where Southwestern's head coach Harold Hunt "rejected" a touchdown awarded by officials because his player stepped out of bounds. On September 29 #1 Tennessee beat Mississippi State 14-0. #2 Michigan State won at Michigan, 25-0, to take the top spot from the Vols. #3 Ohio State beat visiting SMU 7-0 in a win not deemed good enough to stay in the top five. #4 Oklahoma beat William & Mary 49-7.
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The first game of a major bowl tripleheader (Rose, Orange) on NBC, it kicked off at 1 pm CST. Following morning rains, the game was played on soggy natural turf in clammy temperatures. After a scoreless first quarter, Wyoming drove eighty yards and scored on a one-yard sweep run from halfback Jim Kiick; Jerry DePoyster added field goals of 24 and 49 yards and the Cowboys led at halftime. In the third quarter, LSU running back Glenn Smith came off of the bench and scored on a one-yard touchdown run, making the score In the fourth quarter, Tiger quarterback Nelson Stokley completed touchdown passes of eight and fourteen yards to end Tommy Morel as LSU rallied for a The last score occurred with more than four minutes remaining; quarterback advanced the Cowboys deep into LSU territory, but Wyoming flanker Gene Huey was tackled in-bounds on the five-yard line and Smith, a third-string sophomore, entered the game late in the third quarter and was named the game's most valuable player.
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The root discriminant of a number field, K, of degree n, often denoted rdK, is defined as the n-th root of the absolute value of the (absolute) discriminant of K. The relation between relative discriminants in a tower of fields shows that the root discriminant does not change in an unramified extension. The existence of a class field tower provides bounds on the root discriminant: the existence of an infinite class field tower over Q() where m = 3·5·7·11·19 shows that there are infinitely many fields with root discriminant 2 ≈ 296.276. If we let r and 2s be the number of real and complex embeddings, so that n = r + 2s, put ρ = r/n and σ = 2s/n. Set α(ρ, σ) to be the infimum of rdK for K with (r', 2s') = (ρn, σn). We have (for all n large enough) : \alpha(\rho,\sigma) \ge 60.8^\rho 22.3^\sigma and on the assumption of the generalized Riemann hypothesis : \alpha(\rho,\sigma) \ge 215.3^\rho 44.7^\sigma .
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Euclidean division of polynomials is very similar to Euclidean division of integers and leads to polynomial remainders. Its existence is based on the following theorem: Given two univariate polynomials a(x) and b(x) (where b(x) is a non-zero polynomial) defined over a field (in particular, the reals or complex numbers), there exist two polynomials q(x) (the quotient) and r(x) (the remainder) which satisfy: :a(x) = b(x)q(x) + r(x) where :\deg(r(x)) < \deg(b(x)), where "deg(...)" denotes the degree of the polynomial (the degree of the constant polynomial whose value is always 0 can be defined to be negative, so that this degree condition will always be valid when this is the remainder). Moreover, q(x) and r(x) are uniquely determined by these relations. This differs from the Euclidean division of integers in that, for the integers, the degree condition is replaced by the bounds on the remainder r (non-negative and less than the divisor, which insures that r is unique.) The similarity between Euclidean division for integers and that for polynomials motivates the search for the most general algebraic setting in which Euclidean division is valid.
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The contact graph of an arbitrary finite packing of unit balls is the graph whose vertices correspond to the packing elements and whose two vertices are connected by an edge if the corresponding two packing elements touch each other. The cardinality of the edge set of the contact graph gives the number of touching pairs, the number of 3-cycles in the contact graph gives the number of touching triplets, and the number of tetrahedrons in the contact graph gives the number of touching quadruples (in general for a contact graph associated with a sphere packing in n dimensions that the cardinality of the set of n-simplices in the contact graph gives the number of touching (n + 1)-tuples in the sphere packing). In the case of 3-dimensional Euclidean space, non-trivial upper bounds on the number of touching pairs, triplets, and quadruples were proved by Karoly Bezdek and Samuel Reid at the University of Calgary. The problem of finding the arrangement of n identical spheres that maximizes the number of contact points between the spheres is known as the "sticky-sphere problem".
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A variation of the planar separator theorem involves edge separators, small sets of edges forming a cut between two subsets A and B of the vertices of the graph. The two sets A and B must each have size at most a constant fraction of the number n of vertices of the graph (conventionally, both sets have size at most 2n/3), and each vertex of the graph belongs to exactly one of A and B. The separator consists of the edges that have one endpoint in A and one endpoint in B. Bounds on the size of an edge separator involve the degree of the vertices as well as the number of vertices in the graph: the planar graphs in which one vertex has degree n − 1, including the wheel graphs and star graphs, have no edge separator with a sublinear number of edges, because any edge separator would have to include all the edges connecting the high degree vertex to the vertices on the other side of the cut. However, every planar graph with maximum degree Δ has an edge separator of size O(√(Δn)). proved this result for 2-connected planar graphs, and extended it to all planar graphs.
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At the same conference in October 1938, the ANFC agreed to adopt two of the VFA's other key rules which had a significant effect on gameplay: altering the holding the ball rule to eliminate the provision for a player to drop the ball when tackled; and re-introducing the boundary throw-in whenever the ball went out of bounds, except when put out deliberately. Both rule changes have become fundamental to modern Australian rules football: the modern holding the ball rule, as it applies to a player who has had an opportunity to dispose of the ball prior to being tackled, is practically unchanged from the 1939 interpretation; and other than the introduction in 1970 of a free kick for kicking out of bounds on the full, the boundary throw-in rule remains unchanged. The rules the VFA had introduced to curb rough or time-wasting play were not immediately adopted by the ANFC, but were adopted over the following decades. The ANFC adopted the downfield free kick into its rules in 1945, and it adopted the fifteen-yard penalty for time-wasting or cribbing over the mark in 1954; both rules remain part of modern football, except that the distance of the fifteen-yard penalty was extended to fifty metres in 1988.
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