in mathematical statistics, the kullback – leibler divergence ( also called relative entropy and i - divergence ), denoted d kl ( p q ) { \ displaystyle d _ { \ text { kl } } ( p \ parallel q ) }, is a type of statistical distance : a measure of how one probability distribution p is different from a second, reference probability distribution q. a simple interpretation of the kl divergence of p from q is the expected excess surprise from using q as a model when the actual distribution is p. while it is a distance, it is not a metric, the most familiar type of distance : it is not symmetric in the two distributions ( in contrast to variation of information ), and does not satisfy the triangle inequality. instead, in terms of information geometry, it is a type of divergence, a generalization of squared distance, and for certain classes of distributions ( notably an exponential family ), it satisfies a generalized pythagorean theorem ( which applies to squared distances ). in the simple case, a relative entropy of 0 indicates that the two distributions in question have identical quantities of information. relative entropy is a nonnegative function of two distributions or measures. it has diverse applications, both theoretical, such as characterizing the relative ( shannon ) entropy in information systems, randomness in continuous time - series, and information gain when comparing statistical models of inference ; and practical, such as applied statistics, fluid mechanics, neuroscience and bioinformatics.


are a sheik ” e. n. for, “ he flees ” another example can be found from ket : femba. di, “ i am a tungus ” dɨ. fen, “ i am standing ” in turkic, and a few uralic and australian aboriginal languages, predicative adjectives and copular complements take affixes that are identical to those used on predicative verbs, but their negation is different. for example, in turkish : kos. u. yor. sun “ you are running ” cavus. sun “ you are a sergeant ” under negation, that becomes ( negative affixes in bold ) : kos. mu. yor. sun “ you are not running ” cavus degil. sin “ you are not a sergeant ” therefore, the person agreement affixes used with predicative adjectives and nominals in turkic languages are considered to be nonverbal in character. in some analyses, they are viewed as a form of verbal takeover by a copular strategy.


in the context of building simulation models, error refers to the discrepancy between simulation results and the actual measured performance of the building. there are normally occurring uncertainties in building design and building assessment, which generally stem from approximations in model inputs, such as occupancy behavior. calibration refers to the process of " tuning " or adjusting assumed simulation model inputs to match observed data from the utilities or building management system ( bms ). the number of publications dealing with accuracy in building modeling and simulation increased significantly over the past decade. many papers report large gaps between simulation results and measurements, while other studies show that they can match very well.


during the course of developing a particular formalization of type theory, the type theorist may look back over the rules for types, say c, which have been introduced hitherto and perform the step of recognizing that they are valid according to martin - lof ’ s informal semantics of meaning explanation. this act of ‘ introspection ’ is an attempt to become aware of the conceptions which have governed our constructions in the past. it gives rise to a “ reflection principle which roughly speaking says whatever we are used to doing with types can be done inside a universe ” ( martin - lof 1975, 83 ). on the formal level, this leads to an extension of the existing formalization of type theory in that the type forming capacities of c become enshrined in a type universe uc mirroring c.


in mathematics, a refinement monoid is a commutative monoid m such that for any elements a0, a1, b0, b1 of m such that a0 + a1 = b0 + b1, there are elements c00, c01, c10, c11 of m such that a0 = c00 + c01, a1 = c10 + c11, b0 = c00 + c10, and b1 = c01 + c11. a commutative monoid m is said to be conical if x + y = 0 implies that x = y = 0, for any elements x, y of m.


in the early 2000s, the concept of " disclosure " became increasingly popular in the ufo conspiracy community : that the government had classified and withheld information on alien contact and full disclosure was needed, and was pursued by activist lobbying groups. in 1993, steven m. greer founded the disclosure project to promote the concept. in may 2001, greer held a press conference at the national press club in washington, d. c. that demanded congress hold hearings on " secret u. s.


more abstractly, the logistic function is the natural parameter for the bernoulli distribution, and in this sense is the " simplest " way to convert a real number to a probability. in particular, it maximizes entropy ( minimizes added information ), and in this sense makes the fewest assumptions of the data being modeled ; see § maximum entropy.


continuity is one of the core concepts of calculus and mathematical analysis, where arguments and values of functions are real and complex numbers. the concept has been generalized to functions between metric spaces and between topological spaces. the latter are the most general continuous functions, and their definition is the basis of topology.


in mathematics, near sets are either spatially close or descriptively close. spatially close sets have nonempty intersection. in other words, spatially close sets are not disjoint sets, since they always have at least one element in common. descriptively close sets contain elements that have matching descriptions.


in statistics, canonical - correlation analysis ( cca ), also called canonical variates analysis, is a way of inferring information from cross - covariance matrices. if we have two vectors x = ( x1,..., xn ) and y = ( y1,..., ym ) of random variables, and there are correlations among the variables, then canonical - correlation analysis will find linear combinations of x and y which have maximum correlation with each other. t. r. knapp notes that " virtually all of the commonly encountered parametric tests of significance can be treated as special cases of canonical - correlation analysis, which is the general procedure for investigating the relationships between two sets of variables. " the method was first introduced by harold hotelling in 1936, although in the context of angles between flats the mathematical concept was published by jordan in 1875.


in quantum mechanics, the expectation value is the probabilistic expected value of the result ( measurement ) of an experiment. it can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement ; indeed the expectation value may have zero probability of occurring ( e. g. measurements which can only yield integer values may have a non - integer mean ). it is a fundamental concept in all areas of quantum physics.


in mathematics, a reciprocity law is a generalization of the law of quadratic reciprocity to arbitrary monic irreducible polynomials f ( x ) { \ displaystyle f ( x ) } with integer coefficients. recall that first reciprocity law, quadratic reciprocity, determines when an irreducible polynomial f ( x ) = x 2 + a x + b { \ displaystyle f ( x ) = x ^ { 2 } + ax + b } splits into linear terms when reduced mod p { \ displaystyle p }. that is, it determines for which prime numbers the relation f ( x ) ≡ f p ( x ) = ( x − n p ) ( x − m p ) ( mod p ) { \ displaystyle f ( x ) \ equiv f _ { p } ( x ) = ( x - n _ { p } ) ( x - m _ { p } ) { \ text { } } ( { \ text { mod } } p ) } holds. for a general reciprocity lawpg 3, it is defined as the rule determining which primes p { \ displaystyle p } the polynomial f p { \ displaystyle f _ { p } } splits into linear factors, denoted spl { f ( x ) } { \ displaystyle { \ text { spl } } \ { f ( x ) \ } }.


the singular values are the absolute values of the eigenvalues of a normal matrix a, because the spectral theorem can be applied to obtain unitary diagonalization of a { \ displaystyle a } as a = u λ u ∗ { \ displaystyle a = u \ lambda u ^ { * } }. therefore, a ∗ a = u λ ∗ λ u ∗ = u | λ | u ∗ { \ textstyle { \ sqrt { a ^ { * } a } } = { \ sqrt { u \ lambda ^ { * } \ lambda u ^ { * } } } = u \ left | \ lambda \ right | u ^ { * } }. most norms on hilbert space operators studied are defined using s - numbers.


it is minimal, because each of its edges belongs to a cycle with the hamiltonian path edges that is disjoint from all other such cycles. in a tournament, it may be the case that the minimum feedback arc set and maximum acyclic subgraph are both close to half the edges. more precisely, every tournament graph has a feedback arc set of size ( n 2 ) / 2 − ω ( n 3 / 2 ) { \ displaystyle { \ tbinom { n } { 2 } } / 2 - \ omega ( n ^ { 3 / 2 } ) }, and some tournaments require size ( n 2 ) / 2 − o ( n 3 / 2 ) { \ displaystyle { \ tbinom { n } { 2 } } / 2 - o ( n ^ { 3 / 2 } ) }.


in mathematics and computer science, optimal addition - chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal number of multiplications. using the form of the shortest addition chain, with multiplication instead of addition, computes the desired exponent ( instead of multiple ) of the base. ( this corresponds to oeis sequence a003313 ( length of shortest addition chain for n ). ) each exponentiation in the chain can be evaluated by multiplying two of the earlier exponentiation results.


such a procedure adds a link from every sink, dangling state a { \ displaystyle a } to every other node. now by the construction the sum of all elements in any column of matrix s is equal to unity. in this way the matrix s is mathematically well defined and it belongs to the class of markov chains and the class of perron - frobenius operators. that makes s suitable for the pagerank algorithm.


during this operation, each column is transformed using a fixed matrix ( matrix left - multiplied by column gives new value of column in the state ) : = 0 ≤ j ≤ 3 { \ displaystyle { \ begin { bmatrix } b _ { 0, j } \ \ b _ { 1, j } \ \ b _ { 2, j } \ \ b _ { 3, j } \ end { bmatrix } } = { \ begin { bmatrix } 2 & 3 & 1 & 1 \ \ 1 & 2 & 3 & 1 \ \ 1 & 1 & 2 & 3 \ \ 3 & 1 & 1 & 2 \ end { bmatrix } } { \ begin { bmatrix } a _ { 0, j } \ \ a _ { 1, j } \ \ a _ { 2, j } \ \ a _ { 3, j } \ end { bmatrix } } \ qquad 0 \ leq j \ leq 3 } matrix multiplication is composed of multiplication and addition of the entries. entries are bytes treated as coefficients of polynomial of order x 7 { \ displaystyle x ^ { 7 } }. addition is simply xor.


often a distinction is made between the suffixes / - ak / ('you ', masc. ) and / - ik / ('you ', fem.


in mathematics, the hessian matrix, hessian or ( less commonly ) hesse matrix is a square matrix of second - order partial derivatives of a scalar - valued function, or scalar field. it describes the local curvature of a function of many variables. the hessian matrix was developed in the 19th century by the german mathematician ludwig otto hesse and later named after him. hesse originally used the term " functional determinants ".


if the original curve is a line then the inverse curve will pass through the center of inversion. if the original curve passes through the center of inversion then the inverted curve will be a line. the inverted curve will be the same as the original exactly when the curve intersects the circle of inversion at right angles.


in the beginning linkers gave users very limited control over the arrangement of generated output object files. as the target systems became complex with different memory requirements such as embedded systems, it became necessary to give users control to generate output object files with their specific requirements such as defining base addresses'of segments. linkers control scripts were used for this.


in organic chemistry, gm2 is a type of ganglioside. g refers to ganglioside, the m is for monosialic ( as in it has one sialic acid ), and 2 refers to the fact that it was the second monosialic ganglioside discovered. it is associated with gm2 gangliosidoses such as tay – sachs disease.


" grade of service " sometimes means a measure of inbound call center traffic to verify adherence to conditions to measure the success of customers served. on the other hand, the quality of service which a single circuit is designed or conditioned to provide, e. g. voice grade or program grade is called the quality of service. quality criteria for such circuits may include equalization for amplitude over a specified band of frequencies, or in the case of digital data transported via analogue circuits, may include equalization for phase. criteria for mobile quality of service in cellular telephone circuits include the probability of abnormal termination of the call.


in mathematics ( linear algebra ), the faddeev – leverrier algorithm is a recursive method to calculate the coefficients of the characteristic polynomial p a ( λ ) = det ( λ i n − a ) { \ displaystyle p _ { a } ( \ lambda ) = \ det ( \ lambda i _ { n } - a ) } of a square matrix, a, named after dmitry konstantinovich faddeev and urbain le verrier. calculation of this polynomial yields the eigenvalues of a as its roots ; as a matrix polynomial in the matrix a itself, it vanishes by the cayley – hamilton theorem. computing the characteristic polynomial directly from the definition of the determinant is computationally cumbersome insofar as it introduces a new symbolic quantity λ { \ displaystyle \ lambda } ; by contrast, the faddeev - le verrier algorithm works directly with coefficients of matrix a { \ displaystyle a }. the algorithm has been independently rediscovered several times in different forms.


in phonology, a natural class is a set of phonemes in a language that share certain distinctive features. a natural class is determined by participation in shared phonological processes, described using the minimum number of features necessary for descriptive adequacy.


in instruction pipelines, this technique is called out - of - order execution. guess and backtrack : one important example of item - to - item dependency is the handling of a conditional branch instruction x by an instruction pipeline. the first stage a of the pipeline, that fetches the next instruction y to be executed, cannot perform its task until x has fetched its operand and determined whether the branch is to be taken or not.


in signal processing, a filter is a device or process that removes some unwanted components or features from a signal. filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal. most often, this means removing some frequencies or frequency bands. however, filters do not exclusively act in the frequency domain ; especially in the field of image processing many other targets for filtering exist.


in mathematical logic, the intersection type discipline is a branch of type theory encompassing type systems that use the intersection type constructor ( ∩ ) { \ displaystyle ( \ cap ) } to assign multiple types to a single term. in particular, if a term m { \ displaystyle m } can be assigned both the type φ 1 { \ displaystyle \ varphi _ { 1 } } and the type φ 2 { \ displaystyle \ varphi _ { 2 } }, then m { \ displaystyle m } can be assigned the intersection type φ 1 ∩ φ 2 { \ displaystyle \ varphi _ { 1 } \ cap \ varphi _ { 2 } } ( and vice versa ). therefore, the intersection type constructor can be used to express finite heterogeneous ad hoc polymorphism ( as opposed to parametric polymorphism ). for example, the λ - term λ x.


standard examples of each, all of which are linear classifiers, are : generative classifiers : naive bayes classifier and linear discriminant analysis discriminative model : logistic regressionin application to classification, one wishes to go from an observation x to a label y ( or probability distribution on labels ). one can compute this directly, without using a probability distribution ( distribution - free classifier ) ; one can estimate the probability of a label given an observation, p ( y | x = x ) { \ displaystyle p ( y | x = x ) } ( discriminative model ), and base classification on that ; or one can estimate the joint distribution p ( x, y ) { \ displaystyle p ( x, y ) } ( generative model ), from that compute the conditional probability p ( y | x = x ) { \ displaystyle p ( y | x = x ) }, and then base classification on that. these are increasingly indirect, but increasingly probabilistic, allowing more domain knowledge and probability theory to be applied. in practice different approaches are used, depending on the particular problem, and hybrids can combine strengths of multiple approaches.


in telecommunication, a virtual call capability, sometimes called a virtual call facility, is a service feature in which : a call set - up procedure and a call disengagement procedure determine the period of communication between two dtes in which user data are transferred by a packet switched network end - to - end transfer control of packets within the network is required data may be delivered to the network by the call originator before the call access phase is completed, but the data are not delivered to the call receiver if the call attempt is unsuccessful the network delivers all the user data to the call receiver in the same sequence in which the data are received by the network multi - access dtes may have several virtual calls in progress at the same time. an alternative approach to virtual calls is connectionless communication using datagrams. in the 1970s, the " virtual call " concept was used in the british epss and enhanced by remi despres as " virtual circuits " in the french rcp.


in the c and c + + programming languages, an # include guard, sometimes called a macro guard, header guard or file guard, is a particular construct used to avoid the problem of double inclusion when dealing with the include directive. the c preprocessor processes directives of the form # include in a source file by locating the associated file on disk and transcluding ( " including " ) its contents into a copy of the source file known as the translation unit, replacing the include directive in the process. the files included in this regard are generally header files, which typically contain declarations of functions and classes or structs. if certain c or c + + language constructs are defined twice, the resulting translation unit is invalid.


in probability theory, the expected value ( also called expectation, expectancy, expectation operator, mathematical expectation, mean, average, or first moment ) is a generalization of the weighted average. informally, the expected value is the arithmetic mean of a large number of independently selected outcomes of a random variable. the expected value of a random variable with a finite number of outcomes is a weighted average of all possible outcomes. in the case of a continuum of possible outcomes, the expectation is defined by integration.


these threads sit on a run queue in the operating system until processor time is available for them to perform processing for the interrupt. slihs may have a long - lived execution time, and thus are typically scheduled similarly to threads and processes. in linux, flihs are called upper half, and slihs are called lower half or bottom half. this is different from naming used in other unix - like systems, where both are a part of bottom half.


these include its relationship to ridge regression and best subset selection and the connections between lasso coefficient estimates and so - called soft thresholding. it also reveals that ( like standard linear regression ) the coefficient estimates do not need to be unique if covariates are collinear. though originally defined for linear regression, lasso regularization is easily extended to other statistical models including generalized linear models, generalized estimating equations, proportional hazards models, and m - estimators. lasso's ability to perform subset selection relies on the form of the constraint and has a variety of interpretations including in terms of geometry, bayesian statistics and convex analysis. the lasso is closely related to basis pursuit denoising.


in mathematics, carmichael's totient function conjecture concerns the multiplicity of values of euler's totient function φ ( n ), which counts the number of integers less than and coprime to n. it states that, for every n there is at least one other integer m = n such that φ ( m ) = φ ( n ). robert carmichael first stated this conjecture in 1907, but as a theorem rather than as a conjecture. however, his proof was faulty, and in 1922, he retracted his claim and stated the conjecture as an open problem.


in the event that a study requires the shoreline position from before aerial photographs, or if the location has poor photographic coverage, historical maps provide an alternative. many errors are associated with early maps and charts. such errors may be associated with scale, datum changes, distortions from uneven shrinkage, stretching, creases, tears and folds, different surveying standards, different publication standards and projection errors. the severity of these errors depends on the accuracy of the map and the physical changes that occurred after it was made.


tables of logarithms prepared by john napier in 1614 and 1619 used the period ( full stop ) as the decimal separator, which was then adopted by henry briggs in his influential 17th century work. in france, the full stop was already in use in printing to make roman numerals more readable, so the comma was chosen. many other countries, such as italy, also chose to use the comma to mark the decimal units position. it has been made standard by the iso for international blueprints. however, english - speaking countries took the comma to separate sequences of three digits. in some countries, a raised dot or dash ( upper comma ) may be used for grouping or decimal separator ; this is particularly common in handwriting.


in the case of an approximation of an extremely large number, the relative error may be large, yet there may still be a sense in which one wants to consider the numbers as " close in magnitude ". for example, consider 10 10 { \ displaystyle 10 ^ { 10 } } and 10 9 { \ displaystyle 10 ^ { 9 } } the relative error is 1 − 10 9 10 10 = 1 − 1 10 = 90 % { \ displaystyle 1 - { \ frac { 10 ^ { 9 } } { 10 ^ { 10 } } } = 1 - { \ frac { 1 } { 10 } } = 90 \ % } a large relative error. however, one can also consider the relative error in the logarithms ; in this case, the logarithms ( to base 10 ) are 10 and 9, so the relative error in the logarithms is only 10 %. the point is that exponential functions magnify relative errors greatly – if a and b have a small relative error, 10 a { \ displaystyle 10 ^ { a } } and 10 b { \ displaystyle 10 ^ { b } } the relative error is larger, and 10 10 a { \ displaystyle 10 ^ { 10 ^ { a } } } and 10 10 b { \ displaystyle 10 ^ { 10 ^ { b } } } will have an even larger relative error.


for example, there are methods to locate a gene within a sequence, to predict protein structure and / or function, and to cluster protein sequences into families of related sequences. the primary goal of bioinformatics is to increase the understanding of biological processes. what sets it apart from other approaches is its focus on developing and applying computationally intensive techniques to achieve this goal. examples include : pattern recognition, data mining, machine learning algorithms, and visualization.


for this conclusion to be valid, only very mild assumptions in the theory of computational complexity have to be invoked. in this sense, quantum random sampling schemes can have the potential to show quantum supremacy. a notable property of quantum supremacy is that it can be feasibly achieved by near - term quantum computers, since it does not require a quantum computer to perform any useful task or use high - quality quantum error correction, both of which are long - term goals. consequently, researchers view quantum supremacy as primarily a scientific goal, with relatively little immediate bearing on the future commercial viability of quantum computing. due to unpredictable possible improvements in classical computers and algorithms, quantum supremacy may be temporary or unstable, placing possible achievements under significant scrutiny.


for hockett, morphemes are " meaning elements ", not " form elements ". for him, there is a morpheme plural using allomorphs such as - s, - en and - ren. within much morpheme - based morphological theory, the two views are mixed in unsystematic ways so a writer may refer to " the morpheme plural " and " the morpheme - s " in the same sentence.


in mathematics, particularly in algebra, the injective hull ( or injective envelope ) of a module is both the smallest injective module containing it and the largest essential extension of it. injective hulls were first described in ( eckmann & schopf 1953 ).


in mathematics, a quantaloid is a category enriched over the category sup of suplattices. in other words, for any objects a and b the morphism object between them is not just a set but a complete lattice, in such a way that composition of morphisms preserves all joins : ( i f i ) ∘ ( j g j ) = i, j ( f i ∘ g j ) { \ displaystyle ( \ bigvee _ { i } f _ { i } ) \ circ ( \ bigvee _ { j } g _ { j } ) = \ bigvee _ { i, j } ( f _ { i } \ circ g _ { j } ) } the endomorphism lattice h o m ( x, x ) { \ displaystyle \ mathrm { hom } ( x, x ) } of any object x { \ displaystyle x } in a quantaloid is a quantale, whence the name. = = references = =


in order to make any use of unlabeled data, some relationship to the underlying distribution of data must exist. semi - supervised learning algorithms make use of at least one of the following assumptions :


in the double - tap technique, after the first round is fired, the shooter quickly reacquires the sights for a fast second shot. this skill can be practiced by firing two shots at a time, taking time between the shots to reacquire the sights. with practice, the time between shots becomes briefer and briefer until it seems to an observer as if the shooter is just pulling the trigger twice very quickly. according to a u. s.


in mathematics a stack or 2 - sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. stacks are used to formalise some of the main constructions of descent theory, and to construct fine moduli stacks when fine moduli spaces do not exist. descent theory is concerned with generalisations of situations where isomorphic, compatible geometrical objects ( such as vector bundles on topological spaces ) can be " glued together " within a restriction of the topological basis. in a more general set - up the restrictions are replaced with pullbacks ; fibred categories then make a good framework to discuss the possibility of such gluing.


in the united kingdom, personal data is protected by the data protection act 1998. the act covers all personal data which an organization may hold, including names, birthday and anniversary dates, addresses, and telephone numbers. under english law ( which extends to wales but not to northern ireland or scotland ), the deception offences under the theft act 1968 increasingly contend with identity theft situations.


it is also possible to construct universal graphs for planar graphs that have n1 + o ( 1 ) vertices. sumner's conjecture states that tournaments are universal for polytrees, in the sense that every tournament with 2n − 2 vertices contains every polytree with n vertices as a subgraph. a family f of graphs has a universal graph of polynomial size, containing every n - vertex graph as an induced subgraph, if and only if it has an adjacency labelling scheme in which vertices may be labeled by o ( log n ) - bit bitstrings such that an algorithm can determine whether two vertices are adjacent by examining their labels. for, if a universal graph of this type exists, the vertices of any graph in f may be labeled by the identities of the corresponding vertices in the universal graph, and conversely if a labeling scheme exists then a universal graph may be constructed having a vertex for every possible label. in older mathematical terminology, the phrase " universal graph " was sometimes used to denote a complete graph. the notion of universal graph has been adapted and used for solving mean payoff games.


in mathematics, burnside's theorem in group theory states that if g is a finite group of order p a q b { \ displaystyle p ^ { a } q ^ { b } } where p and q are prime numbers, and a and b are non - negative integers, then g is solvable. hence each non - abelian finite simple group has order divisible by at least three distinct primes.


at this point, both the parent and offspring rules are returned to. the lcs genetic algorithm is highly elitist since each learning iteration, the vast majority of the population is preserved. rule discovery may alternatively be performed by some other method, such as an estimation of distribution algorithm, but a ga is by far the most common approach. evolutionary algorithms like the ga employ a stochastic search, which makes lcs a stochastic algorithm. lcs seeks to cleverly explore the search space, but does not perform an exhaustive search of rule combinations, and is not guaranteed to converge on an optimal solution.


in recent years project management software has moved to mobile devices. in 2015 there are more cell phones than computers in the world, therefore the move of saas applications to the mobile devices makes perfect sense. this migration has had the additional benefit of enabling the users to view and update project details on the go.


in order to evaluate automatic systems on lexical substitution, a task was organized at the semeval - 2007 evaluation competition held in prague in 2007. a semeval - 2010 task on cross - lingual lexical substitution has also taken place.


despite the large qa infrastructure most publishers have, many developers retain a small group of testers to provide on - the - spot qa. now most game developers rely on their highly technical and game savvy testers to find glitches and'bugs'in either the programming code or graphic layers. game testers usually have a background playing a variety of different games on a multitude of platforms.


in statistics the optimistic knowledge gradient is a approximation policy proposed by xi chen, qihang lin and dengyong zhou in 2013. this policy is created to solve the challenge of computationally intractable of large size of optimal computing budget allocation problem in binary / multi - class crowd labeling where each label from the crowd has a certain cost.


in mathematics, exponential equivalence of measures is how two sequences or families of probability measures are " the same " from the point of view of large deviations theory.


in telecommunications and data communication systems, an errored second is an interval of a second during which any error whatsoever has occurred, regardless of whether that error was a single bit error or a complete loss of communication for that entire second. the type of error is not important for the purpose of counting errored seconds. in communication systems with very low uncorrected bit error rates, such as modern fiber optic transmission systems, or systems with higher low - level error rates that are corrected using large amounts of forward error correction, errored seconds are often a better measure of the effective user - visible error rate than the raw bit error rate.


in the japanese kantenji braille, the standard 8 - dot braille patterns 236, 1236, 2346, and 12346 are the patterns related to braille pattern dots - 125, since the two additional dots of kantenji patterns 0125, 1257, and 01257 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


assuming that the required time for each of the tasks is known in advance, an optimal execution order must lead to the minimization of the total execution time. although this is an np - hard problem and therefore can be difficult to be solved exactly. there are algorithms, like job scheduler, that calculate optimal task distributions using metaheuristic methods.


in mathematics, a linearised polynomial ( or q - polynomial ) is a polynomial for which the exponents of all the constituent monomials are powers of q and the coefficients come from some extension field of the finite field of order q. we write a typical example as where each a i { \ displaystyle a _ { i } } is in f q m ( = gf ( q m ) ) { \ displaystyle f _ { q ^ { m } } ( = \ operatorname { gf } ( q ^ { m } ) ) } for some fixed positive integer m { \ displaystyle m }. this special class of polynomials is important from both a theoretical and an applications viewpoint. the highly structured nature of their roots makes these roots easy to determine.


in the u. s. telephone network, the 12 - channel carrier system was an early frequency - division multiplexing system standard, used to carry multiple telephone calls on a single twisted pair of wires, mostly for short to medium distances. in this system twelve voice channels are multiplexed in a high frequency carrier and passed through a balanced pair trunk line similar to those used for individual voice frequency connections. the original system is obsolete today, but the multiplexing of voice channels in units of 12 or 24 channels in modern digital trunk lines such as t - 1 is a legacy of the system.


the undesired components are filtered out using regularization : if σ λ n { \ displaystyle \ sigma \ gg \ lambda n }, then 1 σ i + n λ 1 σ i { \ displaystyle { \ frac { 1 } { \ sigma _ { i } + n \ lambda } } \ sim { \ frac { 1 } { \ sigma _ { i } } } }. if σ λ n { \ displaystyle \ sigma \ ll \ lambda n }, then 1 σ i + n λ 1 λ n { \ displaystyle { \ frac { 1 } { \ sigma _ { i } + n \ lambda } } \ sim { \ frac { 1 } { \ lambda n } } }. the filter function for tikhonov regularization is therefore defined as : g λ ( σ ) = 1 σ + n λ. { \ displaystyle g _ { \ lambda } ( \ sigma ) = { \ frac { 1 } { \ sigma + n \ lambda } }. }


in natural language processing ( nlp ), a text graph is a graph representation of a text item ( document, passage or sentence ). it is typically created as a preprocessing step to support nlp tasks such as text condensationterm disambiguation ( topic - based ) text summarization, relation extraction and textual entailment.


for instance, consider a study where researchers compare a drug with a placebo. if the patients who are given the drug get better than the patients given the placebo by chance, it may appear that the drug is effective, but in fact the conclusion is incorrect. in reverse, type ii errors are errors of omission.


in process improvement efforts, quality costs or cost of quality is a means to quantify the total cost of quality - related efforts and deficiencies. it was first described by armand v. feigenbaum in a 1956 harvard business review article. prior to its introduction, the general perception was that higher quality requires higher costs, either by buying better materials or machines or by hiring more labor. furthermore, while cost accounting had evolved to categorize financial transactions into revenues, expenses, and changes in shareholder equity, it had not attempted to categorize costs relevant to quality, which is especially important given that most people involved in manufacturing never set hands on the product. by classifying quality - related entries from a company's general ledger, management and quality practitioners can evaluate investments in quality based on cost improvement and profit enhancement.


the number of colors required to color unit distance graphs is also unknown ( the hadwiger – nelson problem ) : some unit distance graphs require five colors, and every unit distance graph can be colored with seven colors. for every algebraic number there is a unit distance graph with two vertices that must be that distance apart. according to the beckman – quarles theorem, the only plane transformations that preserve all unit distance graphs are the isometries.


in the japanese kantenji braille, the standard 8 - dot braille patterns 238, 1238, 2348, and 12348 are the patterns related to braille pattern dots - 126, since the two additional dots of kantenji patterns 0126, 1267, and 01267 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


members of the class of brandt semigroups are required to satisfy not just one condition but a set of additional properties. a large collection of special classes of semigroups have been defined though not all of them have been studied equally intensively.


in order to demonstrate the use of some of the indicative verb tenses in louisiana french, take the example of manger, meaning " to eat " : some minor simplification of tenses is exhibited in the conjugation of the verb manger, namely of the plural first and second person conjugations which are inflected identically to the third person singular. not only this, but the inflection of the third person plural verb form has diverged between the form identical to standard french and the use of - ont in for all verbs. the elision that is common in many aspects of french is accelerated in louisiana french with the schwa in je often omitted regardless of the presence of a following vowel as well as the regular use of t'es ( tu es ) and t'as ( tu as ) as opposed to such avoidance in standard french. the present progressive tense of louisiana french initially appears alien as compared to standard french but apres / ape possesses the same function signified by en train de.


it is commonly stated as : in a given instance of the stable - roommates problem ( srp ), each of 2n participants ranks the others in strict order of preference. a matching is a set of n disjoint pairs of participants. a matching m in an instance of srp is stable if there are no two participants x and y, each of whom prefers the other to their partner in m. such a pair is said to block m, or to be a blocking pair with respect to m.


in the dart language, used in the flutter sdk, the conventions are similar to those of java, except that constants are written in lowercamelcase. dart imposes the syntactic rule that non - local identifiers beginning with an underscore ( _ ) are treated as private ( since the language does not have explicit keywords for public or private access ). additionally, source file names do not follow java's " one public class per source file, name must match " rule, instead using snake _ case for filenames.


in the bittorrent file distribution system, a torrent file or meta - info file is a computer file that contains metadata about files and folders to be distributed, and usually also a list of the network locations of trackers, which are computers that help participants in the system find each other and form efficient distribution groups called swarms. a torrent file does not contain the content to be distributed ; it only contains information about those files, such as their names, folder structure, sizes, and cryptographic hash values for verifying file integrity. torrent files are normally named with the extension ". torrent ". a torrent file acts like a table of contents ( index ) that allows computers to find information through the use of a bittorrent client.


in planar graphs, colorings with k { \ displaystyle k } distinct colors are dual to nowhere - zero flows over the ring z k { \ displaystyle \ mathbb { z } _ { k } } of integers modulo k { \ displaystyle k }. in this duality, the difference between the colors of two adjacent regions is represented by a flow value across the edge separating the regions. in particular, the existence of nowhere - zero 4 - flows is equivalent to the four color theorem. the snark theorem generalizes this result to nonplanar graphs. = = references = =


in the first half of the 20th century, various formalisms were proposed to capture the informal concept of a computable function, with μ - recursive functions, turing machines and the lambda calculus possibly being the best - known examples today. the surprising fact that they are essentially equivalent, in the sense that they are all encodable into each other, supports the church - turing thesis. another shared feature is more rarely commented on : they all are most readily understood as models of sequential computation. the subsequent consolidation of computer science required a more subtle formulation of the notion of computation, in particular explicit representations of concurrency and communication.


in the apple darwin operating system, and in the macos and ios operating systems built on top of it, the path of the dynamic linker that should be used is embedded at link time into one of the mach - o load commands in the executable image. in those systems, dynamically loaded shared libraries can be identified either by the filename suffix. dylib or by their placement inside the bundle for a framework. the dynamic linker not only links the target executable to the shared libraries but also places machine code functions at specific address points in memory that the target executable knows about at link time. when an executable wishes to interact with the dynamic linker, it simply executes the machine - specific call or jump instruction to one of those well - known address points.


which is equivalent to f a x ⇒ x ∈ a ]. { \ displaystyle \ forall { \ mathcal { f } } \, \ exists a \ forall x \ rightarrow x \ in a ]. } compared to the axiom stated at the top of this section, this variation asserts only one direction of the implication, rather than both directions.


in more advanced mathematics, the partial sums of the harmonic series 1 + 1 2 + 1 3 + 1 4 + 1 5 + { \ displaystyle 1 + { \ frac { 1 } { 2 } } + { \ frac { 1 } { 3 } } + { \ frac { 1 } { 4 } } + { \ frac { 1 } { 5 } } + \ cdots } grow logarithmically. in the design of computer algorithms, logarithmic growth, and related variants, such as log - linear, or linearithmic, growth are very desirable indications of efficiency, and occur in the time complexity analysis of algorithms such as binary search. logarithmic growth can lead to apparent paradoxes, as in the martingale roulette system, where the potential winnings before bankruptcy grow as the logarithm of the gambler's bankroll. it also plays a role in the st.


notationally : x, x ′ ∈ x, f ( x ) = f ( x ′ ) x = x ′, { \ displaystyle \ forall x, x'\ in x, f ( x ) = f ( x') \ implies x = x ', } or, equivalently ( using logical transposition ), x, x ′ ∈ x, x = x ′ f ( x ) = f ( x ′ ). { \ displaystyle \ forall x, x'\ in x, x \ neq x'\ implies f ( x ) \ neq f ( x'). } the function is surjective, or onto, if each element of the codomain is mapped to by at least one element of the domain.


in natural language processing, semantic compression is a process of compacting a lexicon used to build a textual document ( or a set of documents ) by reducing language heterogeneity, while maintaining text semantics. as a result, the same ideas can be represented using a smaller set of words. in most applications, semantic compression is a lossy compression, that is, increased prolixity does not compensate for the lexical compression, and an original document cannot be reconstructed in a reverse process.


\ matches any single character surrounded by " " since the brackets are escaped, for example : " ", " ", " ", " ", " ] ", and " " ( bracket space bracket ). s. * matches s followed by zero or more characters, for example : " s ", " saw ", " seed ", " s3w96. 7 ", and " s6 # h % ( > > > m n mq ".


in population dynamics the growth of human population is sometimes supposed to be double exponential. varfolomeyev and gurevich experimentally fit n ( y ) = 375. 6 ⋅ 1. 00185 1. 00737 y − 1000 { \ displaystyle n ( y ) = 375. 6 \ cdot 1. 00185 ^ { 1. 00737 ^ { y - 1000 } } \, } where n ( y ) is the population in millions in year y.


the gdp deflator index, or real gdp, measures the level of prices of all - new, domestically produced, final goods and services in an economy. market performance indices include the labour market index / job index and proprietary stock market index investment instruments offered by brokerage houses. some indices display market variations.


in mathematics, a binary relation r on a set x is reflexive if it relates every element of x to itself. an example of a reflexive relation is the relation " is equal to " on the set of real numbers, since every real number is equal to itself. a reflexive relation is said to have the reflexive property or is said to possess reflexivity. along with symmetry and transitivity, reflexivity is one of three properties defining equivalence relations.


in mathematical logic, fixed - point logics are extensions of classical predicate logic that have been introduced to express recursion. their development has been motivated by descriptive complexity theory and their relationship to database query languages, in particular to datalog.


other references are given in the references below. the basic definitions in this article are contained within the first few chapters of any of these books. any monoid can be understood as a special sort of category ( with a single object whose self - morphisms are represented by the elements of the monoid ), and so can any preorder.


the complement is a determiner phrase ( or noun phrase, depending on analytical scheme followed ). determiner phrase : the head of a determiner phrase ( dp ) is a determiner. dps were proposed under generative syntax ; not all theories of syntax agree that they exist. complementizer phrase : the head of a complementizer phrase ( cp ) is a complementizer, like that in english. in some cases the c head is covert ( not overtly present ). the complement of c is generally agreed to be a tense phrase ( tp ). tense phrase : the head of a tense phrase ( tp ) is tense ; these are phrases in which the head is an abstract category representing tense ; the complement is a verb phrase. aspect phrase : the head of an aspect phrase ( aspp ) is aspect ; these are phrases in which the head is an abstract syntactic category representing aspect. in more traditional analysis the entire phrase ( including any elements denoting tense or aspect ) is considered to be simply a verb phrase.


in telecommunications, a femtocell is a small, low - power cellular base station, typically designed for use in a home or small business. a broader term which is more widespread in the industry is small cell, with femtocell as a subset. it connects to the service provider's network via broadband ( such as dsl or cable ) ; current designs typically support four to eight simultaneously active mobile phones in a residential setting depending on version number and femtocell hardware, and eight to sixteen mobile phones in enterprise settings. a femtocell allows service providers to extend service coverage indoors or at the cell edge, especially where access would otherwise be limited or unavailable.


marking a causal process modifies it, a mark not transmitted by a pseudo process. meanwhile, causal forks are " the means by which causal structure is generated and modified ". others have found salmon's theory of mark transmission to have shortcomings, however, whereby it can fail to discern causal processes from pseudo processes.


the need for information sharing has led to the need to depart from the rigidity of mac in favor of balancing need to protect with need to share. when the ‘ balance ’ is decided at the discretion of users, the access control is called discretionary access control ( dac ) that is more tolerant of actions that manage risk where mac requires risk avoidance. allowing users and systems to manage the risk of sharing information is in some way contrary to the original motivation for mac.


in query by example, the element used to search is a multimedia content ( image, audio, video ). in other words, the query is a media. often, it's used audiovisual indexing. it will be necessary to choose the criteria we are going to use for creating metadata.


in the context of free and open - source software, proprietary software only available as a binary executable is referred to as a blob or binary blob. the term usually refers to a device driver module loaded into the kernel of an open - source operating system, and is sometimes also applied to code running outside the kernel, such as system firmware images, microcode updates, or userland programs. the term blob was first used in database management systems to describe a collection of binary data stored as a single entity. when computer hardware vendors provide complete technical documentation for their products, operating system developers are able to write hardware device drivers to be included in the operating system kernels.


scheinerman also conjectured that segments with only three directions would be sufficient to represent 3 - colorable graphs, and west ( 1991 ) conjectured that analogously every planar graph could be represented using four directions. if a graph is represented with segments having only k directions and no two segments belong to the same line, then the graph can be colored using k colors, one color for each direction. therefore, if every planar graph can be represented in this way with only four directions, then the four color theorem follows.


in the following pseudocode algorithm, dist is an array that contains the current distances from the source to other vertices, i. e. dist is the current distance from the source to the vertex u. the prev array contains pointers to previous - hop nodes on the shortest path from source to the given vertex ( equivalently, it is the next - hop on the path from the given vertex to the source ). the code u ← vertex in q with min dist, searches for the vertex u in the vertex set q that has the least dist value. graph. edges ( u, v ) returns the length of the edge joining ( i. e. the distance between ) the two neighbor - nodes u and v. the variable alt on line 14 is the length of the path from the root node to the neighbor node v if it were to go through u. if this path is shorter than the current shortest path recorded for v, that current path is replaced with this alt path. 1 function dijkstra ( graph, source ) : 2 3 for each vertex v in graph. vertices : 4 dist ← infinity 5 prev ← undefined 6 add v to q 7 dist ← 0 8 9 while q is not empty : 10 u ← vertex in q with min dist 11 remove u from q 12 13 for each neighbor v of u still in q : 14 alt ← dist + graph. edges ( u, v ) 15 if alt < dist : 16 dist ← alt 17 prev ← u 18 19 return dist, prev if we are only interested in a shortest path between vertices source and target, we can terminate the search after line 10 if u = target.


prominent intersection type systems include the coppo – dezani type assignment system, the barendregt - coppo – dezani type assignment system, and the essential intersection type assignment system. most strikingly, intersection type systems are closely related to ( and often exactly characterize ) normalization properties of λ - terms under β - reduction. in programming languages, such as typescript and scala, intersection types are used to express ad hoc polymorphism.


in mathematics, in the field of group theory, a metanilpotent group is a group that is nilpotent by nilpotent. in other words, it has a normal nilpotent subgroup such that the quotient group is also nilpotent. in symbols, g { \ displaystyle g } is metanilpotent if there is a normal subgroup n { \ displaystyle n } such that both n { \ displaystyle n } and g / n { \ displaystyle g / n } are nilpotent. the following are clear : every metanilpotent group is a solvable group. every subgroup and every quotient of a metanilpotent group is metanilpotent.


in physics, a dynamical system evolving in time may be described in a phase space, that is by the evolution in time of some variables. if this variables are bounded, that is having a minimum and a maximum, for a theorem due to liouville, a measure can be defined in the space, having a measure space where the lemma applies. as a consequence, given a configuration of the system ( a point in the phase space ) the average return period close to this configuration ( in the neighbourhood of the point ) is inversely proportional to the considered size of volume surrounding the configuration. normalizing the measure space to 1, it becomes a probability space and the measure p ( a ) { \ displaystyle p ( a ) } of its set a { \ displaystyle a } represents the probability of finding the system in the states represented by the points of that set. in this case the lemma implies that the smaller is the probability to be in a certain state ( or close to it ), the longer is the time of return near that state. in formulas, if a { \ displaystyle a } is the region close to the starting point and t r { \ displaystyle t _ { r } } is the return period, its average value is : ⟨ t r ⟩ = τ / p ( a ) { \ displaystyle \ langle t _ { r } \ rangle = \ tau / p ( a ) } where τ { \ displaystyle \ tau } is a characteristic time of the system in question. note that since the volume of a { \ displaystyle a }, therefore p ( a ) { \ displaystyle p ( a ) }, depends exponentially on the n { \ displaystyle n } variables in the system ( a = n { \ displaystyle a = \ epsilon ^ { n } }, with { \ displaystyle \ epsilon } infinitesimal side, therefore less than 1, of the volume in n { \ displaystyle n } dimensions ), p ( a ) { \ displaystyle p ( a ) } decreases very rapidly as the variables of the system increase and consequently the return period increases exponentially. in practice, as the variables needed to describe the system increase, the return period increases rapidly.


removing stop words and punctuation some tokens are less important than others. for instance, common words such as " the " might not be very helpful for revealing the essential characteristics of a text. so usually it is a good idea to eliminate stop words and punctuation marks before doing further analysis.


in mathematics, economics and computer science, particularly in the fields of combinatorics, game theory and algorithms, the stable - roommate problem ( srp ) is the problem of finding a stable matching for an even - sized set. a matching is a separation of the set into disjoint pairs ( " roommates " ). the matching is stable if there are no two elements which are not roommates and which both prefer each other to their roommate under the matching. this is distinct from the stable - marriage problem in that the stable - roommates problem allows matches between any two elements, not just between classes of " men " and " women ".


{ \ displaystyle c. } also, recall that a hermitian ( or real symmetric ) matrix has real eigenvalues. it can be shown that, for a given matrix, the rayleigh quotient reaches its minimum value λ min { \ displaystyle \ lambda _ { \ min } } ( the smallest eigenvalue of m ) when x { \ displaystyle \ mathbf { x } } is v min { \ displaystyle \ mathbf { v } _ { \ min } } ( the corresponding eigenvector ).


in software engineering, code coverage is a percentage measure of the degree to which the source code of a program is executed when a particular test suite is run. a program with high test coverage has more of its source code executed during testing, which suggests it has a lower chance of containing undetected software bugs compared to a program with low test coverage. many different metrics can be used to calculate test coverage.


in physical geography, a channel is a type of landform consisting of the outline of a path of relatively shallow and narrow body of water or of other fluids ( e. g., lava ), most commonly the confine of a river, river delta or strait. the word often refers to a natural body of water, while the cognate term canal denotes a similar artificial structure. channels are important for the functionality of ports and other bodies of water used for navigability for shipping.


much of the system's core, including the lwkt subsystem, the ipi messaging subsystem and the new kernel memory allocator, are lockless, meaning that they work without using mutexes, with each process operating on a single cpu. critical sections are used to protect against local interrupts, individually for each cpu, guaranteeing that a thread currently being executed will not be preempted. serializing tokens are used to prevent concurrent accesses from other cpus and may be held simultaneously by multiple threads, ensuring that only one of those threads is running at any given time. blocked or sleeping threads therefore do not prevent other threads from accessing the shared resource unlike a thread that is holding a mutex.


in some languages, the grammatical expression of past tense is combined with the expression of other categories such as grammatical aspect ( see tense – aspect ). thus a language may have several types of past tense form, their use depending on what aspectual or other additional information is to be encoded. french, for example, has a compound past ( passe compose ) for expressing completed events, and imperfect for continuous or repetitive events. some languages that grammaticalise for past tense do so by inflecting the verb, while others do so periphrastically using auxiliary verbs, also known as " verbal operators " ( and some do both, as in the example of french given above ).


in mathematics, an addition chain for computing a positive integer n can be given by a sequence of natural numbers starting with 1 and ending with n, such that each number in the sequence is the sum of two previous numbers. the length of an addition chain is the number of sums needed to express all its numbers, which is one less than the cardinality of the sequence of numbers.


in proving results in combinatorics several useful combinatorial rules or combinatorial principles are commonly recognized and used. the rule of sum, rule of product, and inclusion – exclusion principle are often used for enumerative purposes. bijective proofs are utilized to demonstrate that two sets have the same number of elements.


in mathematics, particularly graph theory, and computer science, a directed acyclic graph ( dag ) is a directed graph with no directed cycles. that is, it consists of vertices and edges ( also called arcs ), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. a directed graph is a dag if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions. dags have numerous scientific and computational applications, ranging from biology ( evolution, family trees, epidemiology ) to information science ( citation networks ) to computation ( scheduling ). directed acyclic graphs are sometimes instead called acyclic directed graphs or acyclic digraphs.


the pps sampling results in a fixed sample size n ( as opposed to poisson sampling which is similar but results in a random sample size with expectancy of n ). when selecting items with replacement the selection procedure is to just draw one item at a time ( like getting n draws from a multinomial distribution with n elements, each with their own p i { \ displaystyle p _ { i } } selection probability ). if doing a without - replacement sampling, the schema can become more complex. : 93


in programming language theory, flow - sensitive typing ( also called flow typing or occurrence typing ) is a type system where the type of an expression depends on its position in the control flow. in statically typed languages, a type of an expression is determined by the types of the sub - expressions that compose it. however, in flow - sensitive typing, an expression's type may be updated to a more specific type if it follows an operation that validates its type. validating operations can include type predicates, imperative updates, and control flow.


this automorphism group permutes the three 8 - dimensional irreducible representations of spin ( 8 ) ; these being the vector representation and two chiral spin representations. these automorphisms do not project to automorphisms of so ( 8 ). the vector representation — the natural action of so ( 8 ) ( hence spin ( 8 ) ) on f8 — consists over the real numbers of euclidean 8 - vectors and is generally known as the " defining module ", while the chiral spin representations are also known as " half - spin representations ", and all three of these are fundamental representations.


the most common choice is the initial ordinal in that class. this is usually taken as the definition of cardinal number in axiomatic set theory. assuming the axiom of choice, the cardinalities of the infinite sets are denoted 0 < 1 < 2 < …. { \ displaystyle \ aleph _ { 0 } < \ aleph _ { 1 } < \ aleph _ { 2 } < \ ldots. }


consider a segment that begins at n = kl + m, for any integer k, and define : x k { x, 1 ≤ n ≤ l + m − 1 0, otherwise. { \ displaystyle x _ { k } \ \ triangleq { \ begin { cases } x, & 1 \ leq n \ leq l + m - 1 \ \ 0, & { \ textrm { otherwise } }. \ end { cases } } } y k x k ∗ h = m = 1 m h ⋅ x k. { \ displaystyle y _ { k } \ \ triangleq \ x _ { k } * h = \ sum _ { m = 1 } ^ { m } h \ cdot x _ { k }. }


the challenge remains to search large indices or popular query lists in under a few milliseconds so that the user sees results pop up while typing. autocomplete can have an adverse effect on individuals and businesses when negative search terms are suggested when a search takes place. autocomplete has now become a part of reputation management as companies linked to negative search terms such as scam, complaints and fraud seek to alter the results. google in particular have listed some of the aspects that affect how their algorithm works, but this is an area that is open to manipulation.


& & for short - circuit logical and. ( 4 & & 2 ) is true. in c, c + +, and go, a prefix & is a unary operator denoting the address in memory of the argument, e. g. & x, & func, & a. in c + + and php, unary prefix & before a formal parameter of a function denotes pass - by - reference. in pascal, the & as the first character of an identifier prevents the compiler from treating it as a keyword, thus escaping it. in fortran, the ampersand forces the compiler to treat two lines as one.


some of the most basic are the percentage of program subroutines and the percentage of program statements called during execution of the test suite. test coverage was among the first methods invented for systematic software testing. the first published reference was by miller and maloney in communications of the acm, in 1963.


similar definitions exist for digraphs, in terms of directed cycles. finding a vertex - disjoint cycle cover of a directed graph can also be performed in polynomial time by a similar reduction to perfect matching. however, adding the condition that each cycle should have length at least 3 makes the problem np - hard.


later macs could also read and write 1. 44 mb hd disks in pc format with fixed rotation speed. higher capacities were similarly achieved by acorn's risc os ( 800 kb for dd, 1, 600 kb for hd ) and amigaos ( 880 kb for dd, 1, 760 kb for hd ). all 3½ - inch disks have a rectangular hole in one corner which, if obstructed, write - enables the disk.


they > completely < forgot me! i had _ nothing _ to do with it. ( commonly interpreted as underlining, which is an alternative to italics. )


" the theorem appears in a 1922 publication of ernst steinitz, after whom it is named. it can be proven by mathematical induction ( as steinitz did ), by finding the minimum - energy state of a two - dimensional spring system and lifting the result into three dimensions, or by using the circle packing theorem. several extensions of the theorem are known, in which the polyhedron that realizes a given graph has additional constraints ; for instance, every polyhedral graph is the graph of a convex polyhedron with integer coordinates, or the graph of a convex polyhedron all of whose edges are tangent to a common midsphere.


in machine learning, specifically empirical risk minimization, mse may refer to the empirical risk ( the average loss on an observed data set ), as an estimate of the true mse ( the true risk : the average loss on the actual population distribution ). the mse is a measure of the quality of an estimator. as it is derived from the square of euclidean distance, it is always a positive value that decreases as the error approaches zero.


the algorithm takes its name from the fact that, when this rewriting is done and the resulting proof is displayed as a dag ( directed acyclic graph ), the unit node η { \ displaystyle \ eta } appears lower ( i. e., closer to the root ) than it used to appear in the original proof. a naive implementation exploiting theorem would require the proof to be traversed and fixed after each unit node is lowered. it is possible, however, to do better by first collecting and removing all the unit nodes in a single traversal, and afterwards fixing the whole proof in a single second traversal.


brief instructional blocks can be recorded for review by students — they will see the exact presentation that occurred in the classroom with the teacher's audio input. this can help transform learning and instruction. many companies and projects now focus on creating supplemental instructional materials specifically designed for interactive whiteboards. one recent use of the iwb is in shared reading lessons. mimic books, for instance, allow teachers to project children's books onto the interactive whiteboard with book - like interactivity.


in number theory, a branch of mathematics, dickson's conjecture is the conjecture stated by dickson ( 1904 ) that for a finite set of linear forms a1 + b1n, a2 + b2n,..., ak + bkn with bi ≥ 1, there are infinitely many positive integers n for which they are all prime, unless there is a congruence condition preventing this ( ribenboim 1996, 6. i ). the case k = 1 is dirichlet's theorem. two other special cases are well - known conjectures : there are infinitely many twin primes ( n and 2 + n are primes ), and there are infinitely many sophie germain primes ( n and 1 + 2n are primes ). dickson's conjecture is further extended by schinzel's hypothesis h.


in several studies, participants read a list of high or low frequency words along with nonwords ( or pseudowords ). they were tasked with pronouncing the words or nonwords as fast as possible. high frequency words were read aloud faster than low frequency words. participants read the nonwords the slowest. more errors were made when pronouncing the low frequency words than the high frequency words.


in fact, all square roots of natural numbers, other than of perfect squares, are irrational. like all real numbers, irrational numbers can be expressed in positional notation, notably as a decimal number. in the case of irrational numbers, the decimal expansion does not terminate, nor end with a repeating sequence. for example, the decimal representation of π starts with 3. 14159, but no finite number of digits can represent π exactly, nor does it repeat.


for general closed convex sets, the limit point need not be the projection. classical work on the case of two closed convex sets shows that the rate of convergence of the iterates is linear. there are now extensions that consider cases when there are more than two sets, or when the sets are not convex, or that give faster convergence rates.


this chain of extensions canonically embeds the natural numbers in the other number systems. properties of the natural numbers, such as divisibility and the distribution of prime numbers, are studied in number theory. problems concerning counting and ordering, such as partitioning and enumerations, are studied in combinatorics.


the term cone of uncertainty is used in software development where the technical and business environments change very rapidly. however, the concept, under different names, is a well - established basic principle of cost engineering. most environments change so slowly that they can be considered static for the duration of a typical project, and traditional project management methods therefore focus on achieving a full understanding of the environment through careful analysis and planning.


in mathematics, sperner's lemma is a combinatorial result on colorings of triangulations, analogous to the brouwer fixed point theorem, which is equivalent to it. it states that every sperner coloring ( described below ) of a triangulation of an n { \ displaystyle n } - dimensional simplex contains a cell whose vertices all have different colors. the initial result of this kind was proved by emanuel sperner, in relation with proofs of invariance of domain. sperner colorings have been used for effective computation of fixed points and in root - finding algorithms, and are applied in fair division ( cake cutting ) algorithms.


therefore, the dyadic product is linear in both of its operands. in general, two dyadics can be added to get another dyadic, and multiplied by numbers to scale the dyadic. however, the product is not commutative ; changing the order of the vectors results in a different dyadic.


the hid descriptor is a hard coded array of bytes that describes the device's data packets. this includes : how many packets the device supports, the size of the packets, and the purpose of each byte and bit in the packet. for example, a keyboard with a calculator program button can tell the host that the button's pressed / released state is stored as the 2nd bit in the 6th byte in data packet number 4 ( note : these locations are only illustrative and are device - specific ).


in mathematics, the plethystic exponential is a certain operator defined on ( formal ) power series which, like the usual exponential function, translates addition into multiplication. this exponential operator appears naturally in the theory of symmetric functions, as a concise relation between the generating series for elementary, complete and power sums homogeneous symmetric polynomials in many variables. its name comes from the operation called plethysm, defined in the context of so - called lambda rings. in combinatorics, the plethystic exponential is a generating function for many well studied sequences of integers, polynomials or power series, such as the number of integer partitions. it is also an important technique in the enumerative combinatorics of unlabelled graphs, and many other combinatorial objects. in geometry and topology, the plethystic exponential of a certain geometric / topologic invariant of a space, determines the corresponding invariant of its symmetric products.


in mathematical logic, the paris – harrington theorem states that a certain combinatorial principle in ramsey theory, namely the strengthened finite ramsey theorem, which is expressible in peano arithmetic, is not provable in this system. the combinatorial principle is however provable in slightly stronger systems. this result has been described by some ( such as the editor of the handbook of mathematical logic in the references below ) as the first " natural " example of a true statement about the integers that could be stated in the language of arithmetic, but not proved in peano arithmetic ; it was already known that such statements existed by godel's first incompleteness theorem.


if the cpu guesses wrong, all of these instructions and their context need to be flushed and the correct ones loaded, which takes time. this has led to increasingly complex instruction - dispatch logic that attempts to guess correctly, and the simplicity of the original reduced instruction set computing ( risc ) designs has been eroded. vliw lacks this logic, and thus lacks its energy use, possible design defects, and other negative aspects.


in the case where the compact set k { \ displaystyle k } is also convex, the above theorem has as a corollary the first part of the next theorem, which is also often called the krein – milman theorem. the convex hull of the extreme points of k { \ displaystyle k } forms a convex subset of k { \ displaystyle k } so the main burden of the proof is to show that there are enough extreme points so that their convex hull covers all of k. { \ displaystyle k. } for this reason, the following corollary to the above theorem is also often called the krein – milman theorem.


in the international phonetic alphabet ( ipa ), aspirated consonants are written using the symbols for voiceless consonants followed by the aspiration modifier letter ⟨ ⟩, a superscript form of the symbol for the voiceless glottal fricative ⟨ h ⟩. for instance, ⟨ p ⟩ represents the voiceless bilabial stop, and ⟨ pʰ ⟩ represents the aspirated bilabial stop. voiced consonants are seldom actually aspirated. symbols for voiced consonants followed by ⟨ ⟩, such as ⟨ bʰ ⟩, typically represent consonants with murmured voiced release ( see below ).


on the other hand, genuine quantifiers ( e. g.,'every professor') bear scope. an'every - np'triggers the introduction of a complex condition of the form k1 → k2, where k1 and k2 are sub - drss representing the restriction and the scope of the quantification respectively. unlike true quantifiers, indefinite noun phrases just contribute a new dr ( together with some descriptive material in terms of conditions on the dr ), which is placed in a larger structure. this larger structure can be the top - level drs or some sub - drs according to the sentence - internal environment of the analyzed noun phrase — in other words, a level that is accessible to an anaphor that comes later.


in some machine translation and natural language processing systems, written texts in human languages are parsed by computer programs. human sentences are not easily parsed by programs, as there is substantial ambiguity in the structure of human language, whose usage is to convey meaning ( or semantics ) amongst a potentially unlimited range of possibilities but only some of which are germane to the particular case. so an utterance " man bites dog " versus " dog bites man " is definite on one detail but in another language might appear as " man dog bites " with a reliance on the larger context to distinguish between those two possibilities, if indeed that difference was of concern. it is difficult to prepare formal rules to describe informal behaviour even though it is clear that some rules are being followed. in order to parse natural language data, researchers must first agree on the grammar to be used.


some explosives, e. g. anfo, show reduced sensitivity under pressure. a transient pressure wave from a nearby detonation may compress the explosive sufficiently to make its initiation fail. this can be prevented by introducing sufficient delays into the firing sequence. a sympathetic detonation during mine blasting may influence the seismic signature of the blast, by boosting the p - wave amplitude without significantly amplifying the surface wave.


under a montagovian approach, the indefinite a donkey, which is assumed to be inherently an existential quantifier, ends up becoming a universal quantifier, an unwelcome result because the change in quantificational force cannot be accounted for in any principled way. drt avoids this problem by assuming that indefinites introduce discourse referents ( drs ), which are stored in the mental representation and are accessible ( or not, depending on the conditions ) to expressions like pronouns and other anaphoric elements. furthermore, they are inherently non - quantificational, and pick up quantificational force depending upon the context.


minnan also has words consisting of a consonant followed by a syllabic nasal, such as png " cooked rice ". so far, all of these syllabic consonants, at least in the lexical words, have been sonorants, such as,,, and, which have a voiced quality similar to vowels. ( they can carry tone, for example. )


p ( a | b ) ( the conditional probability of a given b ) typically differs from p ( b | a ). for example, if a person has dengue fever, the person might have a 90 % chance of being tested as positive for the disease. in this case, what is being measured is that if event b ( having dengue ) has occurred, the probability of a ( tested as positive ) given that b occurred is 90 %, simply writing p ( a | b ) = 90 %.


in operations on numerical values, problems can arise that result in unexpected output, slowing of a process, or crashing. these can be from a lack of awareness of the qualities of the data storage such as a loss of precision due to rounding, numerically unstable algorithms, arithmetic overflow and underflow, or from lack of awareness of how calculations are handled by different software coding languages such as division by zero which in some languages may throw an exception, and in others may return a special value such as nan or infinity.


some consider " inter - city " service to be that which operates as an express service between two main city stations, bypassing intermediate stations. however, this term is used in australia ( sydney for example ) to describe the regional trains operating beyond the boundaries of the suburban services, even though some of these " inter - city " services stop all stations similar to german regional services. in this regard, the german service delineations and naming conventions are clearer and better used for academic purposes.


in the concept discovery step, terms are grouped to meaning bearing units, which correspond to an abstraction of the world and therefore to concepts. the grouped terms are these domain - specific terms and their synonyms, which were identified in the domain terminology extraction step.


in the following the majority judgment winner for the normal ballots is determined. the sorted ratings would be as follows : result : the median of a is between " good " and " poor " and thus is rounded down to " poor ". the median of b is " fair ". thus, b is elected majority judgment winner.


this phenomenon is closely related to the coupon collector's problem : in order to be connected, a random graph needs enough edges for each vertex to be incident to at least one edge. more precisely, if random edges are added one by one to a graph, then with high probability the first edge whose addition connects the whole graph touches the last isolated vertex. for different models including the random subgraphs of grid graphs, the connected components are described by percolation theory. a key question in this theory is the existence of a percolation threshold, a critical probability above which a giant component ( or infinite component ) exists and below which it does not.


in recursion theory, the kleene – brouwer order may be applied to the computation trees of implementations of total recursive functionals. a computation tree is well - founded if and only if the computation performed by it is total recursive. each state x { \ displaystyle x } in a computation tree may be assigned an ordinal number | | x | | { \ displaystyle | | x | | }, the supremum of the ordinal numbers 1 + | | y | | { \ displaystyle 1 + | | y | | } where y { \ displaystyle y } ranges over the children of x { \ displaystyle x } in the tree. in this way, the total recursive functionals themselves can be classified into a hierarchy, according to the minimum value of the ordinal at the root of a computation tree, minimized over all computation trees that implement the functional. the kleene – brouwer order of a well - founded computation tree is itself a recursive well - ordering, and at least as large as the ordinal assigned to the tree, from which it follows that the levels of this hierarchy are indexed by recursive ordinals.


there is no penalty for incorrect answers. the final song of each round is designated as the " fast track " and is played at double value. during the season finale, this song is played as a " fast track challenge, " in which the teams must respond within the time needed for shazam to identify it. no multiple - choice answers are offered, and only the first team to buzz in is given a chance to name the song and win the money for it.


when compared to shipping boxes and printing user manuals, the pace and efficiency provided by the app store is profound and has changed software distribution forever. during the early development of the electronic appwrapper, it became the first commercial software distribution catalog to allow digital data encryption and provide digital rights management for apps, music and data. this was a tremendous advance for the independent developers who could not possibly access the financial resources to publish software boxes across the country and the world, in order to reach their audience.


in the u. s. and canada, dissemination of flood warnings is covered by specific area message encoding ( same ) code flw, which is used by the u. s. emergency alert system and noaa weather radio network and in canada's weatheradio canada network. " flood statements " are issued by the national weather service to inform the public of flooding along major streams in which there is not a serious threat to life or property. they may also follow a flood warning to give later information.


for our example key matrix : | 6 24 1 13 16 10 20 17 15 | = 6 ( 16 ⋅ 15 − 10 ⋅ 17 ) − 24 ( 13 ⋅ 15 − 10 ⋅ 20 ) + 1 ( 13 ⋅ 17 − 16 ⋅ 20 ) = 441 ≡ 25 ( mod 26 ) { \ displaystyle { \ begin { vmatrix } 6 & 24 & 1 \ \ 13 & 16 & 10 \ \ 20 & 17 & 15 \ end { vmatrix } } = 6 ( 16 \ cdot 15 - 10 \ cdot 17 ) - 24 ( 13 \ cdot 15 - 10 \ cdot 20 ) + 1 ( 13 \ cdot 17 - 16 \ cdot 20 ) = 441 \ equiv 25 { \ pmod { 26 } } } so, modulo 26, the determinant is 25. since 25 = 5 2 { \ displaystyle 25 = 5 ^ { 2 } } and 26 = 2 × 13 { \ displaystyle 26 = 2 \ times 13 }, 25 has no common factors with 26, and this matrix can be used for the hill cipher. the risk of the determinant having common factors with the modulus can be eliminated by making the modulus prime. consequently, a useful variant of the hill cipher adds 3 extra symbols ( such as a space, a period and a question mark ) to increase the modulus to 29.


in standard truth - functional propositional logic, association, or associativity are two valid rules of replacement. the rules allow one to move parentheses in logical expressions in logical proofs. the rules ( using logical connectives notation ) are : and where " { \ displaystyle \ leftrightarrow } " is a metalogical symbol representing " can be replaced in a proof with ".


the time it takes to organise teams and have them cooperate can be time - consuming. additionally, there is a potential risk of having a free - rider problem, where individuals within a team can get away with no contribution to the work and still be compensated the same amount as their peers. however, free - riding can be eliminated by organising set protocols. this allows for easier communication and decision - making, giving each member of the team responsibilities and requirements that are agreed upon.


in mathematics, the theory of linear systems is the basis and a fundamental part of linear algebra, a subject used in most modern mathematics. computational algorithms for finding the solutions are an important part of numerical linear algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. a system of non - linear equations can often be approximated by a linear system ( see linearization ), a helpful technique when making a mathematical model or computer simulation of a relatively complex system.


in register machines, a common subexpression ( a subexpression which is used multiple times with the same result value ) can be evaluated just once and its result saved in a fast register. the subsequent reuses have no time or code cost, just a register reference. this optimization speeds simple expressions ( for example, loading variable x or pointer p ) as well as less - common complex expressions.


by isolating the kernel from concurrency, many parts of the kernel no longer need to be modified to support smp. however, as in giant - lock smp systems only one processor can run the kernel code at a time, performance for applications spending significant amounts of time in the kernel is not much improved. accordingly, the giant - lock approach is commonly seen as a preliminary means of bringing smp support to an operating system, yielding benefits only in user space. most modern operating systems use a fine - grained locking approach.


every job j { \ displaystyle j } consists of m { \ displaystyle m } operations o i j { \ displaystyle o _ { ij } } for i = 1, …, m { \ displaystyle i = 1, \ ldots, m }, to be scheduled in the given order. operation o i j { \ displaystyle o _ { ij } } must be processed for p i j { \ displaystyle p _ { ij } } units on machine i { \ displaystyle i }. j : job - shop problem. every job j { \ displaystyle j } consists of n j { \ displaystyle n _ { j } } operations o k j { \ displaystyle o _ { kj } } for k = 1, …, n j { \ displaystyle k = 1, \ ldots, n _ { j } }, to be scheduled in that order. operation o k j { \ displaystyle o _ { kj } } must be processed for p k j { \ displaystyle p _ { kj } } units on a dedicated machine μ k j { \ displaystyle \ mu _ { kj } } with μ k j = μ k ′ j { \ displaystyle \ mu _ { kj } \ neq \ mu _ { k'j } } for k = k ′ { \ displaystyle k \ neq k'}.


in strongly typed programming languages, each parameter's type must be specified in the procedure declaration. languages using type inference attempt to discover the types automatically from the function's body and usage. dynamically typed programming languages defer type resolution until run - time. weakly typed languages perform little to no type resolution, relying instead on the programmer for correctness. some languages use a special keyword ( e. g. void ) to indicate that the subroutine has no parameters ; in formal type theory, such functions take an empty parameter list ( whose type is not void, but rather unit ).


in mathematics, low - rank approximation is a minimization problem, in which the cost function measures the fit between a given matrix ( the data ) and an approximating matrix ( the optimization variable ), subject to a constraint that the approximating matrix has reduced rank. the problem is used for mathematical modeling and data compression. the rank constraint is related to a constraint on the complexity of a model that fits the data. in applications, often there are other constraints on the approximating matrix apart from the rank constraint, e. g., non - negativity and hankel structure. low - rank approximation is closely related to numerous other techniques, including principal component analysis, factor analysis, total least squares, latent semantic analysis, orthogonal regression, and dynamic mode decomposition.


in terms of machine learning and pattern classification, the labels of a set of random observations can be divided into 2 or more classes. each observation is called an instance and the class it belongs to is the label. the bayes error rate of the data distribution is the probability an instance is misclassified by a classifier that knows the true class probabilities given the predictors. for a multiclass classifier, the expected prediction error may be calculated as follows : e p e = e x { \ displaystyle epe = e _ { x } } where x is the instance, e { \ displaystyle e } the expectation value, ck is a class into which an instance is classified, p ( ck | x ) is the conditional probability of label k for instance x, and l ( ) is the 0 – 1 loss function : l ( x, y ) = 1 − δ x, y = { 0 if x = y 1 if x = y, { \ displaystyle l ( x, y ) = 1 - \ delta _ { x, y } = { \ begin { cases } 0 & { \ text { if } } x = y \ \ 1 & { \ text { if } } x \ neq y \ end { cases } }, } where δ x, y { \ displaystyle \ delta _ { x, y } } is the kronecker delta.


the set as a subspace of r { \ displaystyle \ mathbb { r } } is both open and closed, whereas as a subset of r { \ displaystyle \ mathbb { r } } it is only closed. as a subspace of r { \ displaystyle \ mathbb { r } }, ∪ is composed of two disjoint open subsets ( which happen also to be closed ), and is therefore a disconnected space. let s = [ 0, 1 ) be a subspace of the real line r { \ displaystyle \ mathbb { r } }.


in software engineering, secure coding aims to guard against the accidental introduction of security vulnerabilities. it is also possible to create software designed from the ground up to be secure. such systems are secure by design. beyond this, formal verification aims to prove the correctness of the algorithms underlying a system ; important for cryptographic protocols for example.


in the domain of logical frameworks, the term higher - order abstract syntax is usually used to refer to a specific representation that uses the binders of the meta - language to encode the binding structure of the object language. for instance, the logical framework lf has a λ - construct, which has arrow ( → ) type. as an example, consider we wanted to formalize a very primitive language with untyped expressions, a built - in set of variables, and a let construct ( let = in ), which allows to bind variables var with definition exp in expressions exp '. in twelf syntax, we could do as follows : here, exp is the type of all expressions and var the type of all built - in variables ( implemented perhaps as natural numbers, which is not shown ).


boxes present the advantage of being very easily manipulated by computers, as they form the heart of interval analysis. many interval algorithms naturally provide solutions that are regular subpavings. in computation, a well - known application of subpaving in r² is the quadtree data structure. in image tracing context and other applications is important to see x⁻ as topological interior, as illustrated.


in the 2010s, as social media gained prominence, russia then began to use platforms such as facebook, twitter, and youtube to spread disinformation. russian web brigades and bots, typically operated by russia's internet research agency ( ira ), were commonly used to disseminate disinformation throughout these social media channels. as of late 2017, facebook believed that as many as 126 million of its users had seen content from russian disinformation campaigns on its platform. twitter stated that it had found 36, 000 russian bots spreading tweets related to the 2016 u. s.


all ten rotors were interchangeable in any part of either maze. using rotors to control the stepping of other rotors was a feature of an earlier cipher machine, the us ecm mark ii. mercury also used double - wired rotors, consisting of " inside and outside scrambled wheels ", the outer wheels being settable in a number of positions with respect to the inner wheels.


in mathematics, a euclidean distance matrix is an n×n matrix representing the spacing of a set of n points in euclidean space. for points x 1, x 2, …, x n { \ displaystyle x _ { 1 }, x _ { 2 }, \ ldots, x _ { n } } in k - dimensional space ℝk, the elements of their euclidean distance matrix a are given by squares of distances between them. that is a = ( a i j ) ; a i j = d i j 2 = ‖ x i − x j ‖ 2 { \ displaystyle { \ begin { aligned } a & = ( a _ { ij } ) ; \ \ a _ { ij } & = d _ { ij } ^ { 2 } \ ; = \ ; \ lvert x _ { i } - x _ { j } \ rvert ^ { 2 } \ end { aligned } } } where ‖ ⋅ ‖ { \ displaystyle \ | \ cdot \ | } denotes the euclidean norm on ℝk. a = { \ displaystyle a = { \ begin { bmatrix } 0 & d _ { 12 } ^ { 2 } & d _ { 13 } ^ { 2 } & \ dots & d _ { 1n } ^ { 2 } \ \ d _ { 21 } ^ { 2 } & 0 & d _ { 23 } ^ { 2 } & \ dots & d _ { 2n } ^ { 2 } \ \ d _ { 31 } ^ { 2 } & d _ { 32 } ^ { 2 } & 0 & \ dots & d _ { 3n } ^ { 2 } \ \ \ vdots & \ vdots & \ vdots & \ ddots & \ vdots & \ \ d _ { n1 } ^ { 2 } & d _ { n2 } ^ { 2 } & d _ { n3 } ^ { 2 } & \ dots & 0 \ \ \ end { bmatrix } } } in the context of ( not necessarily euclidean ) distance matrices, the entries are usually defined directly as distances, not their squares.


in network theory, a giant component is a connected component of a given random graph that contains a significant fraction of the entire graph's vertices. more precisely, in graphs drawn randomly from a probability distribution over arbitrarily large graphs, a giant component is a connected component whose fraction of the overall number of vertices is bounded away from zero. in sufficiently dense graphs distributed according to the erdos – renyi model, a giant component exists with high probability.


however, it demonstrates a general technique that has since been used in a wide range of proofs, including the first of godel's incompleteness theorems and turing's answer to the entscheidungsproblem. diagonalization arguments are often also the source of contradictions like russell's paradox and richard's paradox. : 27


sekiro : shadows die twice as the sword wielded by the divine dragon. elden ring as a spear greatly resembling the seven - branced sword called the death ritual spear. monster hunter series as a greatsword crafted from electric monster kirin, king thundersword.


the conjecture was significant, because if true, it would have implied the four color theorem : as tait described, the four - color problem is equivalent to the problem of finding 3 - edge - colorings of bridgeless cubic planar graphs. in a hamiltonian cubic planar graph, such an edge coloring is easy to find : use two colors alternately on the cycle, and a third color for all remaining edges. alternatively, a 4 - coloring of the faces of a hamiltonian cubic planar graph may be constructed directly, using two colors for the faces inside the cycle and two more colors for the faces outside.


in the buffer layer, between 5 wall units and 30 wall units, neither law holds, such that : for 5 < y + < 30 { \ displaystyle 5


in telecommunications, in - band signaling is the sending of control information within the same band or channel used for data such as voice or video. this is in contrast to out - of - band signaling which is sent over a different channel, or even over a separate network. in - band signals may often be heard by telephony participants, while out - of - band signals are inaccessible to the user. the term is also used more generally, for example of computer data files that include both literal data, and metadata and / or instructions for how to process the literal data.


this is most conspicuous in uppercase and lowercase characters : uppercase characters are in columns 4 ( 100 ) and 5 ( 101 ), while the corresponding lowercase characters are in columns 6 ( 110 ) and 7 ( 111 ), requiring only toggling the 6th bit ( 2nd high bit ) to switch case ; as there are only 26 letters, the remaining 6 points in each column were occupied by symbols or, in one case, a control character ( del, in 127 ). this is also present, but less precisely, in the organization of digits and symbols in columns 2 ( 010 ) and 3 ( 011 ) – this discrepancy is the source of bit - paired layouts. ideally the characters would have been ordered so that unshifted and shifted values of a typewriter key were in adjacent columns, allowing shifting to be implemented by toggling the 5th bit ( 1st high bit ).


in statistical mechanics, the gibbs algorithm, introduced by j. willard gibbs in 1902, is a criterion for choosing a probability distribution for the statistical ensemble of microstates of a thermodynamic system by minimizing the average log probability ⟨ ln p i ⟩ = i p i ln p i { \ displaystyle \ langle \ ln p _ { i } \ rangle = \ sum _ { i } p _ { i } \ ln p _ { i } \, } subject to the probability distribution pi satisfying a set of constraints ( usually expectation values ) corresponding to the known macroscopic quantities. in 1948, claude shannon interpreted the negative of this quantity, which he called information entropy, as a measure of the uncertainty in a probability distribution. in 1957, e. t. jaynes realized that this quantity could be interpreted as missing information about anything, and generalized the gibbs algorithm to non - equilibrium systems with the principle of maximum entropy and maximum entropy thermodynamics. physicists call the result of applying the gibbs algorithm the gibbs distribution for the given constraints, most notably gibbs's grand canonical ensemble for open systems when the average energy and the average number of particles are given.


the other constraints are that the measurements of the function are given constants up to order n { \ displaystyle n }. the entropy attains an extremum when the functional derivative is equal to zero : δ j δ p ( p ) = ln p ( x ) + 1 − η 0 − j = 1 n λ j f j ( x ) = 0 { \ displaystyle { \ frac { \ delta j } { \ delta p } } \ left ( p \ right ) = \ ln { p ( x ) } + 1 - \ eta _ { 0 } - \ sum _ { j = 1 } ^ { n } \ lambda _ { j } f _ { j } ( x ) = 0 } therefore, the extremal entropy probability distribution in this case must be of the form ( λ 0 : = η 0 − 1 { \ displaystyle \ lambda _ { 0 } : = \ eta _ { 0 } - 1 } ), p ( x ) = e − 1 + η 0 ⋅ e j = 1 n λ j f j ( x ) = exp ( j = 0 n λ j f j ( x ) ), { \ displaystyle p ( x ) = e ^ { - 1 + \ eta _ { 0 } } \ cdot e ^ { \ sum _ { j = 1 } ^ { n } \ lambda _ { j } f _ { j } ( x ) } = \ exp \ left ( \ sum _ { j = 0 } ^ { n } \ lambda _ { j } f _ { j } ( x ) \ right ) \ ;, } remembering that f 0 ( x ) = 1 { \ displaystyle f _ { 0 } ( x ) = 1 }. it can be verified that this is the maximal solution by checking that the variation around this solution is always negative.


in natural time domain each event is characterized by two terms, the " natural time " χ, and the energy qk. χ is defined as k / n, where k is a natural number ( the k - th event ) and n is the total number of events in the time sequence of data. a related term, pk, is the ratio qk / qtotal, which describes the fractional energy released. the term κ1 is the variance in natural time : κ 1 = k = 1 n p k ( χ k ) 2 − ( k = 1 n p k χ k ) 2 { \ displaystyle \ kappa _ { 1 } = \ sum _ { k = 1 } ^ { n } p _ { k } ( \ chi _ { k } ) ^ { 2 } - { \ bigl ( } \ sum _ { k = 1 } ^ { n } p _ { k } \ chi _ { k } { \ bigr ) } ^ { 2 } } where χ k = k / n { \ displaystyle \ textstyle \ chi _ { k } = k / n } and p k = q k n = 1 n q n { \ displaystyle \ textstyle \ p _ { k } = { \ frac { q _ { k } } { \ sum _ { n = 1 } ^ { n } q _ { n } } } }