in number theory, the fermat quotient of an integer a with respect to an odd prime p is defined as q p ( a ) = a p − 1 − 1 p, { \ displaystyle q _ { p } ( a ) = { \ frac { a ^ { p - 1 } - 1 } { p } }, } or δ p ( a ) = a − a p p { \ displaystyle \ delta _ { p } ( a ) = { \ frac { a - a ^ { p } } { p } } }. this article is about the former ; for the latter see p - derivation. the quotient is named after pierre de fermat. if the base a is coprime to the exponent p then fermat's little theorem says that qp ( a ) will be an integer. if the base a is also a generator of the multiplicative group of integers modulo p, then qp ( a ) will be a cyclic number, and p will be a full reptend prime.


the challenge is to reduce the number of colors from n to, e. g., δ + 1. the more colors are employed, e. g. o ( δ ) instead of δ + 1, the fewer communication rounds are required. a straightforward distributed version of the greedy algorithm for ( δ + 1 ) - coloring requires θ ( n ) communication rounds in the worst case − information may need to be propagated from one side of the network to another side. the simplest interesting case is an n - cycle.


in the 1993 film jurassic park, connection machines ( non - functioning dummies ) are visible in the park's control room, programmer dennis nedry mentions " eight connection machines " and a video about dinosaur cloning mentions " thinking machines supercomputers ". in the 1996 film mission impossible, luther stickell asks franz krieger for " thinking machine laptops " to help hack into the cia's langley supercomputer. tom clancy's novel rainbow six speaks of the nsa's " star machine from a company gone bankrupt, the super - connector from thinking machines, inc., of cambridge, massachusetts " in the nsa's basement. in addition, in the bear and the dragon says the national security agency could crack nearly any book or cipher with one of three custom operating systems designed for a thinking machines supercomputer. in the 2008 video game fallout 3, it is mentioned that the pre - war firm that made the computer systems for vaults is called think machine.


in set theory, the cardinality of the continuum is the cardinality or " size " of the set of real numbers r { \ displaystyle \ mathbb { r } }, sometimes called the continuum. it is an infinite cardinal number and is denoted by c { \ displaystyle { \ mathfrak { c } } } ( lowercase fraktur " c " ) or | r | { \ displaystyle | \ mathbb { r } | }. the real numbers r { \ displaystyle \ mathbb { r } } are more numerous than the natural numbers n { \ displaystyle \ mathbb { n } }. moreover, r { \ displaystyle \ mathbb { r } } has the same number of elements as the power set of n. { \ displaystyle \ mathbb { n }. }


in mathematics, a godel numbering for sequences provides an effective way to represent each finite sequence of natural numbers as a single natural number. while a set theoretical embedding is surely possible, the emphasis is on the effectiveness of the functions manipulating such representations of sequences : the operations on sequences ( accessing individual members, concatenation ) can be " implemented " using total recursive functions, and in fact by primitive recursive functions. it is usually used to build sequential “ data types ” in arithmetic - based formalizations of some fundamental notions of mathematics. it is a specific case of the more general idea of godel numbering. for example, recursive function theory can be regarded as a formalization of the notion of an algorithm, and can be regarded as a programming language to mimic lists by encoding a sequence of natural numbers in a single natural number.


in mathematical finite group theory, the uniqueness case is one of the three possibilities for groups of characteristic 2 type given by the trichotomy theorem. the uniqueness case covers groups g of characteristic 2 type with e ( g ) ≥ 3 that have an almost strongly p - embedded maximal 2 - local subgroup for all primes p whose 2 - local p - rank is sufficiently large ( usually at least 3 ). aschbacher ( 1983a, 1983b ) proved that there are no finite simple groups in the uniqueness case.


however, since only alice knows b { \ displaystyle b }, it makes it virtually impossible for either bob or eve to distinguish the states of the qubits. also, after bob has received the qubits, we know that eve cannot be in possession of a copy of the qubits sent to bob, by the no - cloning theorem, unless she has made measurements. her measurements, however, risk disturbing a particular qubit with probability ½ if she guesses the wrong basis.


in regards to issues with connectivity, it is important to consider the musical score of composite films. much like visual repetition or thematic similarities, the score offers another medium through which stories can be linked. rather than leaving viewers with content to process, decode, intellectualize and then react to, the film score can produce emotional reactions immediately, before viewers have a chance to analyze their own responses. there are three main categories of composite film scores :


in other words, a " sum " s 1 { \ displaystyle s _ { 1 } } with only one term evaluates to that one term, while a " sum " s 0 { \ displaystyle s _ { 0 } } with no terms evaluates to 0. allowing a " sum " with only 1 or 0 terms reduces the number of cases to be considered in many mathematical formulas.


in mathematics, a weighing matrix of order n { \ displaystyle n } and weight w { \ displaystyle w } is a matrix w { \ displaystyle w } with entries from the set { 0, 1, − 1 } { \ displaystyle \ { 0, 1, - 1 \ } } such that : w w t = w i n { \ displaystyle ww ^ { \ mathsf { t } } = wi _ { n } } where w t { \ displaystyle w ^ { \ mathsf { t } } } is the transpose of w { \ displaystyle w } and i n { \ displaystyle i _ { n } } is the identity matrix of order n { \ displaystyle n }. the weight w { \ displaystyle w } is also called the degree of the matrix. for convenience, a weighing matrix of order n { \ displaystyle n } and weight w { \ displaystyle w } is often denoted by w ( n, w ) { \ displaystyle w ( n, w ) }. weighing matrices are so called because of their use in optimally measuring the individual weights of multiple objects. when the weighing device is a balance scale, the statistical variance of the measurement can be minimized by weighing multiple objects at once, including some objects in the opposite pan of the scale where they subtract from the measurement.


for example, a model might be selected by maximizing its performance on some set of training data, and yet its suitability might be determined by its ability to perform well on unseen data ; then over - fitting occurs when a model begins to " memorize " training data rather than " learning " to generalize from a trend. as an extreme example, if the number of parameters is the same as or greater than the number of observations, then a model can perfectly predict the training data simply by memorizing the data in its entirety. ( for an illustration, see figure 2. )


in number theory, carmichael's theorem, named after the american mathematician r. d. carmichael, states that, for any nondegenerate lucas sequence of the first kind un ( p, q ) with relatively prime parameters p, q and positive discriminant, an element un with n = 1, 2, 6 has at least one prime divisor that does not divide any earlier one except the 12th fibonacci number f ( 12 ) = u12 ( 1, −1 ) = 144 and its equivalent u12 ( −1, −1 ) = −144. in particular, for n greater than 12, the nth fibonacci number f ( n ) has at least one prime divisor that does not divide any earlier fibonacci number. carmichael ( 1913, theorem 21 ) proved this theorem. recently, yabuta ( 2001 ) gave a simple proof.


in the context of primitive recursive functions, it is convenient to have a means to represent finite sequences of natural numbers as single natural numbers. one such method, godel's encoding, represents a sequence of positive integers ⟨ n 0, n 1, n 2, …, n k ⟩ { \ displaystyle \ langle n _ { 0 }, n _ { 1 }, n _ { 2 }, \ ldots, n _ { k } \ rangle } as i = 0 k p i n i { \ displaystyle \ prod _ { i = 0 } ^ { k } p _ { i } ^ { n _ { i } } }, where pi represent the ith prime. it can be shown that, with this representation, the ordinary operations on sequences are all primitive recursive. these operations include determining the length of a sequence, extracting an element from a sequence given its index, concatenating two sequences. using this representation of sequences, it can be seen that if h ( m ) is primitive recursive then the function f ( n ) = h ( ⟨ f ( 0 ), f ( 1 ), f ( 2 ), …, f ( n − 1 ) ⟩ ) { \ displaystyle f ( n ) = h ( \ langle f ( 0 ), f ( 1 ), f ( 2 ), \ ldots, f ( n - 1 ) \ rangle ) }. is also primitive recursive. when the sequence ⟨ n 0, n 1, n 2, …, n k ⟩ { \ displaystyle \ langle n _ { 0 }, n _ { 1 }, n _ { 2 }, \ ldots, n _ { k } \ rangle } is allowed to include zeros, it is instead represented as i = 0 k p i ( n i + 1 ) { \ displaystyle \ prod _ { i = 0 } ^ { k } p _ { i } ^ { ( n _ { i } + 1 ) } }, which makes it possible to distinguish the codes for the sequences ⟨ 0 ⟩ { \ displaystyle \ langle 0 \ rangle } and ⟨ 0, 0 ⟩ { \ displaystyle \ langle 0, 0 \ rangle }.


in the following example, statement b explicitly negates statement a : statements can also be mutually exclusive, without explicitly negating each other as in the following example :


in the classic problem the fuel in the jeep and at fuel dumps is treated as a continuous quantity. more complex variations on the problem have been proposed in which the fuel can only be left or collected in discrete amounts. in the camel and bananas problem, the merchant has n units of bananas. the camel can carry at most 1 unit of bananas at any time, and can travel 1 unit of distance on 1 unit of bananas. the market is at m units of distance away.


another square - difference - free set is obtained by doubling the moser – de bruijn sequence. the best known upper bound on the size of a square - difference - free set of numbers up to n { \ displaystyle n } is only slightly sublinear, but the largest known sets of this form are significantly smaller, of size ≈ n 0. 733412 { \ displaystyle \ approx n ^ { 0. 733412 } }. closing the gap between these upper and lower bounds remains an open problem. the sublinear size bounds on square - difference - free sets can be generalized to sets where certain other polynomials are forbidden as differences between pairs of elements.


in signal processing, pre - emphasis is a technique to protect against anticipated noise. the idea is to boost ( and hence distort ) the frequency range that is most susceptible to noise beforehand, so that after a noisy process ( transmission over cable, tape recording... ) more information can be recovered from that frequency range. removal of the distortion caused by pre - emphasis is called de - emphasis, making the output accurately reproduce the original input. emphasis is commonly used in fm broadcasting ( preemphasis improvement ) and vinyl ( e. g. lp ) records. for example, high - frequency signal components may be emphasized to produce a more equal modulation index for a transmitted frequency spectrum, and therefore a better signal - to - noise ratio for the entire frequency range.


in protected mode, the segment _ part is replaced by a 16 - bit selector, in which the 13 upper bits ( bit 3 to bit 15 ) contain the index of an entry inside a descriptor table. the next bit ( bit 2 ) specifies whether the operation is used with the gdt or the ldt. the lowest two bits ( bit 1 and bit 0 ) of the selector are combined to define the privilege of the request, where the values of 0 and 3 represent the highest and the lowest privilege, respectively. this means that the byte offset of descriptors in the descriptor table is the same as the 16 - bit selector, provided the lower three bits are zeroed. the descriptor table entry defines the real linear address of the segment, a limit value for the segment size, and some attribute bits ( flags ).


{ \ displaystyle x | ( y \ mid ( x \ mid z ) ) = ( ( z \ mid y ) \ mid y ) \ mid x. } in 1973, padmanabhan and quackenbush demonstrated a method that, in principle, would yield a 1 - basis for boolean algebra.


in mathematics, the rational sieve is a general algorithm for factoring integers into prime factors. it is a special case of the general number field sieve. while it is less efficient than the general algorithm, it is conceptually simpler. it serves as a helpful first step in understanding how the general number field sieve works.


in mathematics, numerical analysis, and numerical partial differential equations, domain decomposition methods solve a boundary value problem by splitting it into smaller boundary value problems on subdomains and iterating to coordinate the solution between adjacent subdomains. a coarse problem with one or few unknowns per subdomain is used to further coordinate the solution between the subdomains globally. the problems on the subdomains are independent, which makes domain decomposition methods suitable for parallel computing. domain decomposition methods are typically used as preconditioners for krylov space iterative methods, such as the conjugate gradient method, gmres, and lobpcg.


in neural networks, each neuron receives input from some number of locations in the previous layer. in a convolutional layer, each neuron receives input from only a restricted area of the previous layer called the neuron's receptive field. typically the area is a square ( e. g. 5 by 5 neurons ). whereas, in a fully connected layer, the receptive field is the entire previous layer.


according to kunegis, blattner, and moser several online networks follow a non - linear preferential attachment model. communication networks and online contact networks are sub - linear while interaction networks are super - linear. the co - author network among scientists also shows the signs of sub - linear preferential attachment.


in social systems, deterministic chaos is infrequent, because the elements of the system include individuals whose values, awareness, will, foresight, and fallibility, affect the dynamic behavior of the system. however, this does not completely exclude any notional possibility of deterministic chaos in social systems. in fact some authorities argue an increase in the development of nonlinear dynamics and instabilities of social systems.


the classification efficiency is usually indicated by receiver operating characteristics. in the original simca method, the ends of the hyper - plane of each class are closed off by setting statistical control limits along the retained principal components axes ( i. e., score value between plus and minus 0. 5 times score standard deviation ). more recent adaptations of the simca method close off the hyper - plane by construction of ellipsoids ( e. g. hotelling's t2 or mahalanobis distance ). with such modified simca methods, classification of an object requires both that its orthogonal distance from the model and its projection within the model ( i. e. score value within the region defined by the ellipsoid ) are not significant.


this is not to say that all software data ought to be manipulated as graphs, but rather that they can be exchanged as graphs. it can be used to represent instance data as well as schemas for describing the structure of the data. moreover, the schema can be explicitly stated along with instance data.


in the hindley – milner type system, expressions can be given multiple types through parametric polymorphism. but naively giving multiple types to references breaks type safety. the following are typing rules for references and related operators in ml - like languages. r e f : α.


in markup languages and the digital humanities, overlap occurs when a document has two or more structures that interact in a non - hierarchical manner. a document with overlapping markup cannot be represented as a tree. this is also known as concurrent markup. overlap happens, for instance, in poetry, where there may be a metrical structure of feet and lines ; a linguistic structure of sentences and quotations ; and a physical structure of volumes and pages and editorial annotations.


in number theory, a kth root of unity modulo n for positive integers k, n ≥ 2, is a root of unity in the ring of integers modulo n ; that is, a solution x to the equation ( or congruence ) x k ≡ 1 ( mod n ) { \ displaystyle x ^ { k } \ equiv 1 { \ pmod { n } } }. if k is the smallest such exponent for x, then x is called a primitive kth root of unity modulo n. see modular arithmetic for notation and terminology. the roots of unity modulo n are exactly the integers that are coprime with n. in fact, these integers are roots of unity modulo n by euler's theorem, and the other integers cannot be roots of unity modulo n, because they are zero divisors modulo n. a primitive root modulo n, is a generator of the group of units of the ring of integers modulo n. there exist primitive roots modulo n if and only if λ ( n ) = φ ( n ), { \ displaystyle \ lambda ( n ) = \ varphi ( n ), } where λ { \ displaystyle \ lambda } and φ { \ displaystyle \ varphi } are respectively the carmichael function and euler's totient function. a root of unity modulo n is a primitive kth root of unity modulo n for some divisor k of λ ( n ), { \ displaystyle \ lambda ( n ), } and, conversely, there are primitive kth roots of unity modulo n if and only if k is a divisor of λ ( n ). { \ displaystyle \ lambda ( n ). }


in number theory, a wieferich prime is a prime number p such that p2 divides 2p − 1 − 1, therefore connecting these primes with fermat's little theorem, which states that every odd prime p divides 2p − 1 − 1. wieferich primes were first described by arthur wieferich in 1909 in works pertaining to fermat's last theorem, at which time both of fermat's theorems were already well known to mathematicians. since then, connections between wieferich primes and various other topics in mathematics have been discovered, including other types of numbers and primes, such as mersenne and fermat numbers, specific types of pseudoprimes and some types of numbers generalized from the original definition of a wieferich prime. over time, those connections discovered have extended to cover more properties of certain prime numbers as well as more general subjects such as number fields and the abc conjecture. as of april 2023, the only known wieferich primes are 1093 and 3511 ( sequence a001220 in the oeis ).


very often, and in this article, the coefficients of the equations are real or complex numbers and the solutions are searched in the same set of numbers, but the theory and the algorithms apply for coefficients and solutions in any field. for solutions in an integral domain like the ring of the integers, or in other algebraic structures, other theories have been developed, see linear equation over a ring. integer linear programming is a collection of methods for finding the " best " integer solution ( when there are many ). grobner basis theory provides algorithms when coefficients and unknowns are polynomials. also tropical geometry is an example of linear algebra in a more exotic structure.


in simple terms, software verification is : " assuming we should build x, does our software achieve its goals without any bugs or gaps? " on the other hand, software validation is : " was x what we should have built? does x meet the high - level requirements? "


a bijective proof. two sets are shown to have the same number of members by exhibiting a bijection, i. e. a one - to - one correspondence, between them. the term " combinatorial proof " may also be used more broadly to refer to any kind of elementary proof in combinatorics. however, as glass ( 2003 ) writes in his review of benjamin & quinn ( 2003 ) ( a book about combinatorial proofs ), these two simple techniques are enough to prove many theorems in combinatorics and number theory.


supercritical p > ( 1 + ε ) / n { \ displaystyle p > ( 1 + \ varepsilon ) / n } there is a single giant component containing a linear number of vertices. for large values of p { \ displaystyle p } its size approaches the whole graph : | c 1 | ≈ y n { \ displaystyle | c _ { 1 } | \ approx yn } where y { \ displaystyle y } is the positive solution to the equation e − p n y = 1 − y { \ displaystyle e ^ { - pny } = 1 - y }. the remaining components are small, with logarithmic size. in the same model of random graphs, there will exist multiple connected components with high probability for values of p { \ displaystyle p } below a significantly higher threshold, p < ( 1 − ε ) ( log n ) / n { \ displaystyle p < ( 1 - \ varepsilon ) ( \ log n ) / n }, and a single connected component for values above the threshold, p > ( 1 + ε ) ( log n ) / n { \ displaystyle p > ( 1 + \ varepsilon ) ( \ log n ) / n }.


for example, if x 5 { \ displaystyle x _ { 5 } } is non - basic and its coefficient in r { \ displaystyle r } is positive, then increasing it above 0 may make z { \ displaystyle z } larger. if it is possible to do so without violating other constraints, then the increased variable becomes basic ( it " enters the basis " ), while some basic variable is decreased to 0 to keep the equality constraints and thus becomes non - basic ( it " exits the basis " ). if this process is done carefully, then it is possible to guarantee that z { \ displaystyle z } increases until it reaches an optimal bfs.


the concept is not unlike the limited licensing approach for computer software, which places rigid restrictions on resale and reproduction. the intent is to make users understand that the content of any textbook is the intellectual property of the author and / or the publisher, and that as such, subject to copyright. obviously, this idea is completely opposed to the millennia - old tradition of the sale of used books, and would make that entire industry illegal.


{ \ displaystyle m ^ { \ text { t } } \ omega m = \ omega. } under a change of basis, represented by a matrix a, we have ω ↦ a t ω a { \ displaystyle \ omega \ mapsto a ^ { \ text { t } } \ omega a } m ↦ a − 1 m a. { \ displaystyle m \ mapsto a ^ { - 1 } ma. } one can always bring ω { \ displaystyle \ omega } to either the standard form given in the introduction or the block diagonal form described below by a suitable choice of a.


in personality pathology, dimensional models of personality disorders ( also known as the dimensional approach to personality disorders, dimensional classification, and dimensional assessments ) conceptualize personality disorders as quantitatively rather than qualitatively different from normal personality. they consist of extreme, maladaptive levels of certain personality characteristics ( these characteristics are commonly described as facets within broader personality factors or traits ). within the context of personality psychology, a " dimension " refers to a continuum on which an individual can have various levels of a characteristic, in contrast to the dichotomous categorical approach in which an individual does or does not possess a characteristic.


in mathematics, a map or mapping is a function in its general sense. these terms may have originated as from the process of making a geographical map : mapping the earth surface to a sheet of paper. the term map may be used to distinguish some special types of functions, such as homomorphisms. for example, a linear map is a homomorphism of vector spaces, while the term linear function may have this meaning or it may mean a linear polynomial.


in mathematics, euclid numbers are integers of the form en = pn # + 1, where pn # is the nth primorial, i. e. the product of the first n prime numbers. they are named after the ancient greek mathematician euclid, in connection with euclid's theorem that there are infinitely many prime numbers.


in the japanese encodings iso 646 - jp ( a 7 - bit code based on ascii ), jis x 0201 ( an 8 - bit code ), and shift jis ( a multi - byte encoding which is 8 - bit for ascii ), the code point 0x5c that would be used for backslash in ascii is instead rendered as a yen sign ¥. due to extensive use of the 005c code point to represent the yen sign, even today some fonts such as ms mincho render the backslash character as a ¥, so the characters at unicode code points 00a5 ( ¥ ) and 005c ( \ ) both render as ¥ when these fonts are selected. computer programs still treat 005c as a backslash in these environments but display it as a yen sign, causing confusion, especially in ms - dos filenames. several other iso 646 versions also replace backslash with other characters, including ₩ ( korean ), o ( german, swedish ), ø ( danish, norwegian ), c ( french ) and n ( spanish ), leading to similar problems, though with less lasting impact compared to the yen sign. in 1991, rfc 1345 suggested / / as a unique two - character mnemonic that might be used in internet standards as " a practical way of identifying character, without reference to a coded character set and its code in coded character set ". consequently, this style may be seen in early internet engineering task force documents.


in most computer programming languages a do while loop is a control flow statement that executes a block of code and then either repeats the block or exits the loop depending on a given boolean condition. the do while construct consists of a process symbol and a condition. first the code within the block is executed. then the condition is evaluated.


in the 1980s, the graphical kernel system ( gks ) library, based on a 1970s specification with a similar basic geometry and command structure to naplps, was widely implemented on microcomputers, and became the basis of digital research's gsx graphics system used in their gem gui. gks was later extended into a 3d version, and additions to this resulted in phigs ( programmer's hierarchical interactive graphics system ), a competitor to opengl.


as a result, it is often considered to be a more intuitive, but a less systematic approach to divisions – where the efficiency is highly dependent upon one's numeracy skills. to calculate the whole number quotient of dividing a large number by a small number, the student repeatedly takes away " chunks " of the large number, where each " chunk " is an easy multiple ( for example 100×, 10×, 5× 2×, etc. ) of the small number, until the large number has been reduced to zero – or the remainder is less than the small number itself.


and symmetrically ( when xk is a sub - martingale ) : p ( x n − x 0 ≤ − ) ≤ exp ( − 2 2 k = 1 n c k 2 ). { \ displaystyle { \ text { p } } ( x _ { n } - x _ { 0 } \ leq - \ epsilon ) \ leq \ exp \ left ( { - \ epsilon ^ { 2 } \ over 2 \ sum _ { k = 1 } ^ { n } c _ { k } ^ { 2 } } \ right ). } if x is a martingale, using both inequalities above and applying the union bound allows one to obtain a two - sided bound : p ( | x n − x 0 | ≥ ) ≤ 2 exp ( − 2 2 k = 1 n c k 2 ). { \ displaystyle { \ text { p } } ( | x _ { n } - x _ { 0 } | \ geq \ epsilon ) \ leq 2 \ exp \ left ( { - \ epsilon ^ { 2 } \ over 2 \ sum _ { k = 1 } ^ { n } c _ { k } ^ { 2 } } \ right ). }


as in discrete percolation, a common research focus of continuum percolation is studying the conditions of occurrence for infinite or giant components. other shared concepts and analysis techniques exist in these two types of percolation theory as well as the study of random graphs and random geometric graphs. continuum percolation arose from an early mathematical model for wireless networks, which, with the rise of several wireless network technologies in recent years, has been generalized and studied in order to determine the theoretical bounds of information capacity and performance in wireless networks. in addition to this setting, continuum percolation has gained application in other disciplines including biology, geology, and physics, such as the study of porous material and semiconductors, while becoming a subject of mathematical interest in its own right.


in mathematics, light's associativity test is a procedure invented by f. w. light for testing whether a binary operation defined in a finite set by a cayley multiplication table is associative. the naive procedure for verification of the associativity of a binary operation specified by a cayley table, which compares the two products that can be formed from each triple of elements, is cumbersome. light's associativity test simplifies the task in some instances ( although it does not improve the worst - case runtime of the naive algorithm, namely o ( n 3 ) { \ displaystyle { \ mathcal { o } } \ left ( n ^ { 3 } \ right ) } for sets of size n { \ displaystyle n } ).


for example, the proton spin puzzle, the emc effect, the distributions of electric charges inside the nucleons, as found by hofstadter in 1956, and the ad hoc ckm matrix elements. when the term " preon " was coined, it was primarily to explain the two families of spin - 1 / 2 fermions : quarks and leptons. more recent preon models also account for spin - 1 bosons, and are still called " preons ". each of the preon models postulates a set of fewer fundamental particles than those of the standard model, together with the rules governing how those fundamental particles combine and interact. based on these rules, the preon models try to explain the standard model, often predicting small discrepancies with this model and generating new particles and certain phenomena which do not belong to the standard model.


in the 20th century, following the development of formal logic, the ampersand became a commonly used logical notation for the binary operator or sentential connective and. this usage was adopted in computing. many languages with syntax derived from c, including c + +, perl, and more differentiate between : & for bitwise and. ( 4 & 2 ) is zero, ( 4 & 5 ) is 4.


in the us, the cdc recommends essential components of ams programs ( asp ) for acute care hospitals, small and critical access hospitals, resource - limited facilities, long - term care facilities, and outpatient facilities. as of 2014, thirteen internet - based institutional asp resources in us academic medical centers had been published. an asp has the following tasks, in line with quality improvement theory :


an arrow from the node representing a candidate x to the one representing a candidate y is labelled with d. to avoid cluttering the diagram, an arrow has only been drawn from x to y when d > d ( i. e. the table cells with light green background ), omitting the one in the opposite direction ( the table cells with light red background ). one example of computing the strongest path strength is p = 33 : the strongest path from b to d is the direct path ( b, d ) which has strength 33. but when computing p, the strongest path from a to c is not the direct path ( a, c ) of strength 26, rather the strongest path is the indirect path ( a, d, c ) which has strength min ( 30, 28 ) = 28.


in mathematical logic, a formal theory is a set of sentences expressed in a formal language. a formal system ( also called a logical calculus, or a logical system ) consists of a formal language together with a deductive apparatus ( also called a deductive system ). the deductive apparatus may consist of a set of transformation rules, which may be interpreted as valid rules of inference, or a set of axioms, or have both.


these directories contain files with names such as " abcd1234. jpg " that consist of four alphanumeric characters ( often " 100 _ ", " dsc0 ", " dscf ", " img _ ", " mov _ ", or " p000 " ), followed by a number. handling of directories with possibly user - created duplicate numbers may vary among camera firmwares. dcf 2. 0 adds support for dcf optional files recorded in an optional color space ( that is, adobe rgb rather than srgb ). such files must be indicated by a leading " _ " ( as in " _ dsc " instead of " 100 _ " or " dsc0 " ).


in structure mining, a graph kernel is a kernel function that computes an inner product on graphs. graph kernels can be intuitively understood as functions measuring the similarity of pairs of graphs. they allow kernelized learning algorithms such as support vector machines to work directly on graphs, without having to do feature extraction to transform them to fixed - length, real - valued feature vectors. they find applications in bioinformatics, in chemoinformatics ( as a type of molecule kernels ), and in social network analysis. concepts of graph kernels have been around since the 1999, when d. haussler introduced convolutional kernels on discrete structures.


in statistical analysis of binary classification, the f - score or f - measure is a measure of a test's accuracy. it is calculated from the precision and recall of the test, where the precision is the number of true positive results divided by the number of all positive results, including those not identified correctly, and the recall is the number of true positive results divided by the number of all samples that should have been identified as positive. precision is also known as positive predictive value, and recall is also known as sensitivity in diagnostic binary classification.


in order to measure the information of a string relative to another there is the need to rely on relative semi - distances ( nrc ). these are measures that do not need to respect symmetry and triangle inequality distance properties. although the ncd and the nrc seem very similar, they address different questions. the ncd measures how similar both strings are, mostly using the information content, while the nrc indicates the fraction of a target string that cannot be constructed using information from another string. for a comparison, with application to the evolution of primate genomes, see.


according to the curry – howard isomorphism, lambda calculus on its own can express theorems in intuitionistic logic only, and several classical logical theorems can't be written at all. however with these new operators one is able to write terms that have the type of, for example, peirce's law. semantically these operators correspond to continuations, found in some functional programming languages.


in mathematics, a binary relation associates elements of one set, called the domain, with elements of another set, called the codomain. a binary relation over sets x and y is a new set of ordered pairs ( x, y ) consisting of elements x in x and y in y. it is a generalization of the more widely understood idea of a unary function. it encodes the common concept of relation : an element x is related to an element y, if and only if the pair ( x, y ) belongs to the set of ordered pairs that defines the binary relation. a binary relation is the most studied special case n = 2 of an n - ary relation over sets x1,..., xn, which is a subset of the cartesian product x 1 × × x n.


unlike schoof's algorithm, the sea algorithm is typically implemented as a probabilistic algorithm ( of the las vegas type ), so that root - finding and other operations can be performed more efficiently. its computational complexity is dominated by the cost of computing the modular polynomials ψ ℓ ( x, y ) { \ displaystyle \ psi _ { \ ell } ( x, y ) }, but as these do not depend on e { \ displaystyle e }, they may be computed once and reused. under the heuristic assumption that there are sufficiently many small elkies primes, and excluding the cost of computing modular polynomials, the asymptotic running time of the sea algorithm is o ( n 2 m ( n 2 ) / log n ) = o ( n 4 + o ( 1 ) ) { \ displaystyle o ( n ^ { 2 } m ( n ^ { 2 } ) / \ log { n } ) = o ( n ^ { 4 + o ( 1 ) } ) }, where n = log q { \ displaystyle n = \ log { q } }. its space complexity is o ( n 3 log n ) { \ displaystyle o ( n ^ { 3 } \ log { n } ) }, but when precomputed modular polynomials are used this increases to o ( n 4 ) { \ displaystyle o ( n ^ { 4 } ) }.


in order to test plastic welds, there are several requirements for both the inspector as well as the test method. furthermore, there are two different types of testing weld quality. these two types are destructive and non - destructive testing. destructive testing serves to qualify and quantify the weld joint whereas nondestructive testing serves to identify anomalies, discontinuities, cracks, and / or crevices.


in most of these cases the oems are open about their use of such software and fulfil the requirements of their free software licenses, such as the gnu general public license ( gpl ), but in a small number of cases this use is masked, either deliberately or through professed ignorance or misunderstanding. violators are usually found through public records, where they may be forced to declare their implementations, or through their own advertising, for example " embedded software engineers with mandatory linux experience required " on their careers pages, and yet their site or product documentation offers no source download or offer to supply the software source as required by the license gpl. organizations such as gpl - violations. org, the free software foundation ( fsf ) and the software freedom law center ( sflc ) are now more organized at pursuing such violators and obtaining compliance. usually, they seek voluntary compliance as a first step and only enter legal proceedings when blocked. when notified of violations they confirm them by asking the supplier, examining available product samples, or even going so far as to make blind purchases of the product through front companies.


the interpretation commonly taken, however, is that an underlying morpheme | - i | palatalizes the consonant and is subsequently deleted. palatalization may also occur as a morphological feature. for example, although russian makes phonemic contrasts between palatalized and unpalatalized consonants, alternations across morpheme boundaries are normal : ответ ('answer') vs. ответить ('to answer') несу ('carry') vs. несет ('carries') голод ('hunger') vs. голоден ('hungry'masc. )


when p = 1 / 2 { \ displaystyle p = 1 / 2 }, the uncertainty is at a maximum ; if one were to place a fair bet on the outcome in this case, there is no advantage to be gained with prior knowledge of the probabilities. in this case, the entropy is maximum at a value of 1 bit. intermediate values fall between these cases ; for instance, if p = 1 / 4 { \ displaystyle p = 1 / 4 }, there is still a measure of uncertainty on the outcome, but one can still predict the outcome correctly more often than not, so the uncertainty measure, or entropy, is less than 1 full bit.


in mathematics, hall's marriage theorem, proved by philip hall ( 1935 ), is a theorem with two equivalent formulations. in each case, the theorem gives a necessary and sufficient condition for an object to exist : the combinatorial formulation answers whether a finite collection of sets has a transversal — that is, whether an element can be chosen from each set without repetition. hall's condition is that for any group of sets from the collection, the total unique elements they contain is at least as large as the number of sets in the group. the graph theoretic formulation answers whether a finite bipartite graph has a perfect matching — that is, a way to match each vertex from one group uniquely to an adjacent vertex from the other group. hall's condition is that any subset of vertices from one group has a neighbourhood of equal or greater size.


in natural language processing, language identification or language guessing is the problem of determining which natural language given content is in. computational approaches to this problem view it as a special case of text categorization, solved with various statistical methods.


in numerical analysis, the peano kernel theorem is a general result on error bounds for a wide class of numerical approximations ( such as numerical quadratures ), defined in terms of linear functionals. it is attributed to giuseppe peano.


in mathematics, the interval chromatic number x < ( h ) of an ordered graph h is the minimum number of intervals the ( linearly ordered ) vertex set of h can be partitioned into so that no two vertices belonging to the same interval are adjacent in h.


in mathematical combinatorics, the transylvania lottery is a lottery where players selected three numbers from 1 - 14 for each ticket, and then three numbers are chosen randomly. a ticket wins if two of the numbers match the random ones. the problem asks how many tickets the player must buy in order to be certain of winning. ( javier martinez, gloria gutierrez & pablo cordero et al. 2008, p. 85 ) ( mazur 2010, p. 280 problem 15 ) an upper bound can be given using the fano plane with a collection of 14 tickets in two sets of seven.


the question is : how should we choose the prior parameters ( s, g 0 ) { \ displaystyle \ left ( s, g _ { 0 } \ right ) } of the dp, in particular the infinite dimensional one g 0 { \ displaystyle g _ { 0 } }, in case of lack of prior information? to address this issue, the only prior that has been proposed so far is the limiting dp obtained for s → 0 { \ displaystyle s \ rightarrow 0 }, which has been introduced under the name of bayesian bootstrap by rubin ; in fact it can be proven that the bayesian bootstrap is asymptotically equivalent to the frequentist bootstrap introduced by bradley efron. the limiting dirichlet process s → 0 { \ displaystyle s \ rightarrow 0 } has been criticized on diverse grounds.


in software engineering, syntactic methods are techniques for developing correct software programs. the techniques attempt to detect, and thus prevent, certain kinds of defects ( bugs ) by examining the structure of the code being produced at its syntactic rather than semantic level.


in statistics, the power of a binary hypothesis test is the probability that the test correctly rejects the null hypothesis ( h 0 { \ displaystyle h _ { 0 } } ) when a specific alternative hypothesis ( h 1 { \ displaystyle h _ { 1 } } ) is true. it is commonly denoted by 1 − β { \ displaystyle 1 - \ beta }, and represents the chances of a true positive detection conditional on the actual existence of an effect to detect. statistical power ranges from 0 to 1, and as the power of a test increases, the probability β { \ displaystyle \ beta } of making a type ii error by wrongly failing to reject the null hypothesis decreases.


in order to speed up web server responses by lowering average http response times and hardware resources used, many popular web servers implement one or more content caches, each one specialized in a content category. content is usually cached by its origin, e. g. : static content : file cache ; dynamic content : dynamic cache ( module / program output ).


, fn ), and let q { \ displaystyle \ mathbb { q } } denote an equivalent martingale measure. let u = ( u0, u1,..


defining child - related operationsthere are two design variants for defining and implementing child - related operations like adding / removing a child component to / from the container ( add ( child ) / remove ( child ) ) and accessing a child component ( getchild ( ) ) : design for uniformity : child - related operations are defined in the component interface. this enables clients to treat leaf and composite objects uniformly. but type safety is lost because clients can perform child - related operations on leaf objects.


in mathematical cryptography, a kleinian integer is a complex number of the form m + n 1 + − 7 2 { \ displaystyle m + n { \ frac { 1 + { \ sqrt { - 7 } } } { 2 } } }, with m and n rational integers. they are named after felix klein. the kleinian integers form a ring called the kleinian ring, which is the ring of integers in the imaginary quadratic field q ( − 7 ) { \ displaystyle \ mathbb { q } ( { \ sqrt { - 7 } } ) }. this ring is a unique factorization domain.


in some jurisdictions, false statement is a crime similar to perjury.


each array contains 140 ( one for each priority level ) pointers to doubly linked lists, which in turn reference all processes with the given priority. the scheduler selects the next process from the active array with highest priority. when a process'quantum expires, it is placed into the expired array with some priority.


in the context of electrical modeling of transformers and transmission lines, shunt components that provide paths of least resistance in certain models are generally specified in terms of their admittance. each side of most transformer models contains shunt components which model magnetizing current and core losses. these shunt components can be referenced to the primary or secondary side. for simplified transformer analysis, admittance from shunt elements can be neglected.


the problem with this lp is that, in the bin - covering problem, handling small items is problematic, since small items may be essential for the optimal solution. with small items allowed, the number of configurations may be too large even for the technique of karmarkar and karp. csirik, johnson and kenyon present an alternative lp.


this in turn permits a somewhat unified analysis of arithmetic objects through their automorphic functions. simply put, the langlands philosophy allows a general analysis of structuring the abstractions of numbers. naturally, this description is at once a reduction and over - generalization of the program's proper theorems, but these mathematical analogues provide the basis of its conceptualization.


although such evidence is not seen as conclusive, researchers may sometimes regard it as an invitation to more rigorous scientific study of the phenomenon in question. for instance, one study found that 35 of 47 anecdotal reports of drug side - effects were later sustained as " clearly correct. " anecdotal evidence is considered the least certain type of scientific information.


the most promising solution is the decoy states in which alice randomly sends some of her laser pulses with a lower average photon number. these decoy states can be used to detect a pns attack, as eve has no way to tell which pulses are signal and which decoy. using this idea the secure key rate scales as t { \ displaystyle t }, the same as for a single photon source. this idea has been implemented successfully first at the university of toronto, and in several follow - up qkd experiments, allowing for high key rates secure against all known attacks.


in the grammatical tradition of sanskrit, aspirated consonants are called voiceless aspirated, and breathy - voiced consonants are called voiced aspirated. there are no dedicated ipa symbols for degrees of aspiration and typically only two degrees are marked : unaspirated ⟨ k ⟩ and aspirated ⟨ kʰ ⟩. an old symbol for light aspiration was ⟨ ʻ ⟩, but this is now obsolete.


these relations will need to be slowly and consistently established in order to truly unify any kind of information policy and decision - making. if information policy can be established and guided on a semi - national level, the degree of communication and cooperation throughout the world will increase dramatically. as information policy continues to shape many aspects of society, these international relations will become vital ( harpham, 2011 ).


in statistics, a k - statistic is a minimum - variance unbiased estimator of a cumulant.


in statistics, sufficient dimension reduction ( sdr ) is a paradigm for analyzing data that combines the ideas of dimension reduction with the concept of sufficiency. dimension reduction has long been a primary goal of regression analysis. given a response variable y and a p - dimensional predictor vector x { \ displaystyle { \ textbf { x } } }, regression analysis aims to study the distribution of y x { \ displaystyle y \ mid { \ textbf { x } } }, the conditional distribution of y { \ displaystyle y } given x { \ displaystyle { \ textbf { x } } }. a dimension reduction is a function r ( x ) { \ displaystyle r ( { \ textbf { x } } ) } that maps x { \ displaystyle { \ textbf { x } } } to a subset of r k { \ displaystyle \ mathbb { r } ^ { k } }, k < p, thereby reducing the dimension of x { \ displaystyle { \ textbf { x } } }.


when using dilated layers, the number of pixels in the receptive field remains constant, but the field is more sparsely populated as its dimensions grow when combining the effect of several layers. to manipulate the receptive field size as desired, there are some alternatives to the standard convolutional layer. for example, atrous or dilated convolution expands the receptive field size without increasing the number of parameters by interleaving visible and blind regions. moreover, a single dilated convolutional layer can comprise filters with multiple dilation ratios, thus having a variable receptive field size.


the code rate of a convolutional code is commonly modified via symbol puncturing. for example, a convolutional code with a'mother'code rate n / k = 1 / 2 { \ displaystyle n / k = 1 / 2 } may be punctured to a higher rate of, for example, 7 / 8 { \ displaystyle 7 / 8 } simply by not transmitting a portion of code symbols. the performance of a punctured convolutional code generally scales well with the amount of parity transmitted. the ability to perform economical soft decision decoding on convolutional codes, as well as the block length and code rate flexibility of convolutional codes, makes them very popular for digital communications.


that is, if the testing process were repeated with a group of test takers, essentially the same results would be obtained. various kinds of reliability coefficients, with values ranging between 0. 00 ( much error ) and 1. 00 ( no error ), are usually used to indicate the amount of error in the scores. " for example, measurements of people's height and weight are often extremely reliable.


thus for some rational number β. { \ displaystyle \ beta. } the uniqueness of the decomposition over 1 and c { \ displaystyle { \ sqrt { c } } } implies thus that the considered equation is equivalent with it follows by vieta's formulas that x and y must be roots of the quadratic equation its δ = a 2 − c = d 2 > 0 { \ displaystyle ~ \ delta = a ^ { 2 } - c = d ^ { 2 } > 0 ~ } ( = 0, otherwise c would be the square of a ), hence x and y must be and a − a 2 − c 2.


moreover, " push to talk " services offer the instant connectivity of sms and are typically unlimited. the integration between competing providers and technologies necessary for cross - network text messaging was not initially available. some providers originally charged extra for texting, reducing its appeal.


sweep and prune exploits temporal coherence as it is likely that solids do not move significantly between two simulation steps. because of that, at each step, the sorted lists of bounding volume starts and ends can be updated with relatively few computational operations. sorting algorithms which are fast at sorting almost - sorted lists, such as insertion sort, are particularly good for this purpose.


in practice, however, a quadratic nonresidue of p is found via a modified euclid's algorithm and taken as the value of a, since if a is a quadratic nonresidue modulo p then the converse is also true, and the test is conclusive. for such an a the legendre symbol is ( a p ) = − 1. { \ displaystyle \ left ( { \ frac { a } { p } } \ right ) = - 1. }


in mathematics and computer science, the bit predicate, sometimes written bit ( i, j ) { \ displaystyle { \ text { bit } } ( i, j ) }, is a predicate that tests whether the j { \ displaystyle j } th bit of the number i { \ displaystyle i } ( starting from the least significant digit ) is 1, when i { \ displaystyle i } is written as a binary number. its mathematical applications include modeling the membership relation of hereditarily finite sets, and defining the adjacency relation of the rado graph. in computer science, it is used for efficient representations of set data structures using bit vectors, in defining the private information retrieval problem from communication complexity, and in descriptive complexity theory to formulate logical descriptions of complexity classes.


it could thus be thought of as a boolean, i. e., a truth value represented as the numerical value 0 or 1 ( as is sometimes done in computer programming ). dummy variables may be extended to more complex cases.


in quantum information theory, the idea of a typical subspace plays an important role in the proofs of many coding theorems ( the most prominent example being schumacher compression ). its role is analogous to that of the typical set in classical information theory.


vector processors use this technique with one additional trick. because the data layout is in a known format — a set of numbers arranged sequentially in memory — the pipelines can be tuned to improve the performance of fetches. on the receipt of a vector instruction, special hardware sets up the memory access for the arrays and stuffs the data into the processor as fast as possible.


it became the basis of a modern international system that divides clouds into five physical forms which can be further divided or classified into altitude levels to derive ten basic genera. the main representative cloud types for each of these forms are stratiform, cumuliform, stratocumuliform, cumulonimbiform, and cirriform.


also it is sufficient to assume p is a polynomial over q { \ displaystyle \ mathbb { q } } and multiply p by the appropriate denominators to yield integer coefficients. however, whether quantification over rationals can also be substituted for quantification over the integers is a notoriously hard open problem. the mrdp theorem ( so named for the initials of the four principal contributors to its solution ) states that a set of integers is diophantine if and only if it is computably enumerable. a set of integers s is computably enumerable if and only if there is an algorithm that, when given an integer, halts if that integer is a member of s and runs forever otherwise.


the addition of virtual memory into the atlas also eliminated a looming programming problem : planning and scheduling data transfers between main and secondary memory and recompiling programs for each change of size of main memory. the first atlas was commissioned in 1962 but working prototypes of paging had been developed by 1959. : 2 in 1961, the burroughs corporation independently released the first commercial computer with virtual memory, the b5000, with segmentation rather than paging. ibm developed the concept of hypervisors in their cp - 40 and cp - 67, and in 1972 provided it for the s / 370 as virtual machine facility / 370. ibm introduced the start interpretive execution ( sie ) instruction as part of 370 - xa on the 3081, and vm / xa versions of vm to exploit it.


because fuzzy clustering allows genes to belong to more than one cluster, it allows for the identification of genes that are conditionally co - regulated or co - expressed. for example, one gene may be acted on by more than one transcription factor, and one gene may encode a protein that has more than one function. thus, fuzzy clustering is more appropriate than hard clustering.


in statistics, the displaced poisson, also known as the hyper - poisson distribution, is a generalization of the poisson distribution. the probability mass function is p ( x = n ) = { e − λ λ n + r ( n + r )! ⋅ 1 i ( r, λ ), n = 0, 1, 2, … if r ≥ 0 e − λ λ n + r ( n + r )! ⋅ 1 i ( r + s, λ ), n = s, s + 1, s + 2, … otherwise { \ displaystyle p ( x = n ) = { \ begin { cases } e ^ { - \ lambda } { \ dfrac { \ lambda ^ { n + r } } { \ left ( n + r \ right )!


in surveying, an initial point is a datum ( a specific point on the surface of the earth ) that marks the beginning point for a cadastral survey. the initial point establishes a local geographic coordinate system for the surveys that refer to that point. an initial point is defined by the intersection of a principal meridian and a base line.


in the unix operating system, most types of input and output operations are considered to be streams of bytes read from a device or written to a device. this stream of bytes model is used for file i / o, socket i / o, and terminal i / o in order to provide device independence. in order to read and write to a device at the application level, the program calls a function to open the device, which may be a real device such as a terminal or a virtual device such as a network port or a file in a file system. the device's physical characteristics are mediated by the operating system which in turn presents an abstract interface that allows the programmer to read and write bytes from / to the device. the operating system then performs the actual transformation needed to read and write the stream of bytes to the device.


in mathematics, the language of ordered abelian groups has one constant symbol 0, one unary function symbol −, one binary function symbol +, and one binary relation symbol ≤. then : the expressions + ( x, y ) and + ( x, + ( y, − ( z ) ) ) are terms. these are usually written as x + y and x + y − z. the expressions + ( x, y ) = 0 and ≤ ( + ( x, + ( y, − ( z ) ) ), + ( x, y ) ) are atomic formulas. these are usually written as x + y = 0 and x + y − z ≤ x + y. the expression ( x y { \ displaystyle ( \ forall x \ forall y \, } is a formula, which is usually written as x y ( x + y ≤ z ) → x y ( x + y = 0 ).


one sampling unit from each set is then selected ( based on the observed ranks ) for subsequent measurement using a more accurate and reliable ( hence, more expensive ) method for the contaminant of interest. relative to simple random sampling, this design results in more representative samples and so leads to more precise estimates of the population parameters. ranked set sampling is useful when the cost of locating and ranking locations in the field is low compared to laboratory measurements. it is also appropriate when an inexpensive auxiliary variable ( based on expert knowledge or measurement ) is available to rank population units with respect to the variable of interest. to use this design effectively, it is important that the ranking method and analytical method are strongly correlated.


in software engineering, an entity – relationship model ( erm ) is an abstract and conceptual representation of data. entity – relationship modeling is a database modeling method, used to produce a type of conceptual schema or semantic data model of a system, often a relational database, and its requirements in a top - down fashion. diagrams created by this process are called entity - relationship diagrams, er diagrams, or erds. entity – relationship models have had wide application in the building of information systems intended to support activities involving objects and events in the real world. in these cases they are models that are conceptual. however, this modeling method can be used to build computer games or a family tree of the greek gods, in these cases it would be used to model concepts.


the army began issuing an improved stanag magazine in march 2009. according to the army, the m4 only suffered 296 stoppages and said that the high number reported could be attributed to discrepancies in the scoring process. the army testing command stated that, if the number of stoppages caused by a broken part met some threshold, they would be eliminated from the final report pending redesign of the part. the methodology of the test has been debated, as many of the m4s in the test had already seen use, whereas the other rifles were brand new, and that the wide variance in results between summer and fall showed that the test was not accurate, as it was not repeatable with consistent results.


one type is a subtype of another if and only if it contains all the features of the base type, or subtypes thereof. the subtype may contain added features, such as members not present in the base type, or stronger invariants. a distinction exists between structural substitution for inferred and non - inferred polymorphism.


in the java programming language, the try... catch block is used often to catch exceptions. all potentially dangerous code is placed inside the block and, if an exception occurred, is stopped, or caught.


at the end of the process, the approximate best cover will be either h 1 { \ displaystyle h _ { 1 } } or h 2 { \ displaystyle h _ { 2 } }. this algorithm achieves an approximation ratio of 1 − 1 e { \ displaystyle 1 - { 1 \ over e } } for values of k ≥ 3 { \ displaystyle k \ geq 3 }. this is the best possible approximation ratio unless n p ⊆ d t i m e ( n o ( log log n ) ) { \ displaystyle np \ subseteq dtime ( n ^ { o ( \ log \ log n ) } ) }.


in mathematics, two square matrices a and b over a field are called congruent if there exists an invertible matrix p over the same field such that ptap = bwhere " t " denotes the matrix transpose. matrix congruence is an equivalence relation. matrix congruence arises when considering the effect of change of basis on the gram matrix attached to a bilinear form or quadratic form on a finite - dimensional vector space : two matrices are congruent if and only if they represent the same bilinear form with respect to different bases. note that halmos defines congruence in terms of conjugate transpose ( with respect to a complex inner product space ) rather than transpose, but this definition has not been adopted by most other authors.


. { \ displaystyle \ exp ^ { * } ( x ) = \ delta _ { 0 } + \ sum _ { n = 1 } ^ { \ infty } { \ frac { x ^ { * n } } { n! } }. } it is not generally possible to extend this definition to arbitrary distributions, although a class of distributions on which this series still converges in an appropriate weak sense is identified by ben chrouda, el oued & ouerdiane ( 2002 ).


in rendezvous hashing, also called highest random weight ( hrw ) hashing, all clients use the same hash function h ( ) { \ displaystyle h ( ) } ( chosen ahead of time ) to associate a key to one of the n available servers. each client has the same list of identifiers { s1, s2,..., sn }, one for each server. given some key k, a client computes n hash weights w1 = h ( s1, k ), w2 = h ( s2, k ),..., wn = h ( sn, k ). the client associates that key with the server corresponding to the highest hash weight for that key. a server with id s x { \ displaystyle s _ { x } } owns all the keys k m { \ displaystyle k _ { m } } for which the hash weight h ( s x, k m ) { \ displaystyle h ( s _ { x }, k _ { m } ) } is higher than the hash weight of any other node for that key.


in the early days of computing, computer applications directly communicated to the hardware and there was no operating system. as applications grew larger encompassing various domains, oses were invented. they served as middleware providing hardware abstractions to applications.


in the bin packing problem, the size of the bins is fixed and their number can be enlarged ( but should be as small as possible ). in contrast, in the multiway number partitioning problem, the number of bins is fixed and their size can be enlarged. the objective is to find a partition in which the bin sizes are as nearly equal is possible ( in the variant called multiprocessor scheduling problem or minimum makespan problem, the goal is specifically to minimize the size of the largest bin ). in the inverse bin packing problem, both the number of bins and their sizes are fixed, but the item sizes can be changed.


in phrase structure grammars, such as generalised phrase structure grammar, head - driven phrase structure grammar and lexical functional grammar, a feature structure is essentially a set of attribute – value pairs. for example, the attribute named number might have the value singular. the value of an attribute may be either atomic, e. g. the symbol singular, or complex ( most commonly a feature structure, but also a list or a set ). a feature structure can be represented as a directed acyclic graph ( dag ), with the nodes corresponding to the variable values and the paths to the variable names.


in mathematics, more specifically field theory, the degree of a field extension is a rough measure of the " size " of the field extension. the concept plays an important role in many parts of mathematics, including algebra and number theory — indeed in any area where fields appear prominently.


in mathematics, the prime number theorem ( pnt ) describes the asymptotic distribution of the prime numbers among the positive integers. it formalizes the intuitive idea that primes become less common as they become larger by precisely quantifying the rate at which this occurs. the theorem was proved independently by jacques hadamard and charles jean de la vallee poussin in 1896 using ideas introduced by bernhard riemann ( in particular, the riemann zeta function ). the first such distribution found is π ( n ) ~ n / log ( n ), where π ( n ) is the prime - counting function ( the number of primes less than or equal to n ) and log ( n ) is the natural logarithm of n. this means that for large enough n, the probability that a random integer not greater than n is prime is very close to 1 / log ( n ).


after the primary finishes its update, the update is forwarded to other replicas and all perform the update locally. this non - blocking approach can lead to an improvement. the diagram of the local - write protocol depicts the local - write approach in primary - based protocols. a process requests a write operation in a data item x. the current server is considered as the new primary for a data item x. the write operation is performed and when the request is finished, the primary sends an update request to other backup servers. each backup sends an acknowledgment to the primary after finishing the update operation.


yet godel proved that, for any consistent recursively enumerable axiomatic system powerful enough to describe the arithmetic of the natural numbers, there are ( model - theoretically ) true propositions about the natural numbers that cannot be proved from the axioms. such propositions are known as formally undecidable propositions. for example, the continuum hypothesis is undecidable in the zermelo – fraenkel set theory as shown by cohen.


calculate an − 1 modulo n. if the result is not 1, then n is composite. if the result is 1, then n is likely to be prime ; n is then called a probable prime to base a. a weak probable prime to base a is an integer that is a probable prime to base a, but which is not a strong probable prime to base a ( see below ). for a fixed base a, it is unusual for a composite number to be a probable prime ( that is, a pseudoprime ) to that base. for example, up to 25 × 109, there are 11, 408, 012, 595 odd composite numbers, but only 21, 853 pseudoprimes base 2. : 1005 the number of odd primes in the same interval is 1, 091, 987, 404.


in microeconomics, value added may be defined as the market value of aggregate output of a transformation process, minus the market value of aggregate input ( or aggregate inputs ) of a transformation process. one may describe value added with the help of ulbo de sitter's design theory for production synergies. he divides transformation processes into two categories, parts and aspects.


in numerical linear algebra, the gauss – seidel method, also known as the liebmann method or the method of successive displacement, is an iterative method used to solve a system of linear equations. it is named after the german mathematicians carl friedrich gauss and philipp ludwig von seidel, and is similar to the jacobi method. though it can be applied to any matrix with non - zero elements on the diagonals, convergence is only guaranteed if the matrix is either strictly diagonally dominant, or symmetric and positive definite. it was only mentioned in a private letter from gauss to his student gerling in 1823. a publication was not delivered before 1874 by seidel.


in terms of the hilbert symbol, hilbert's reciprocity law for an algebraic number field states that v ( a, b ) v = 1 { \ displaystyle \ prod _ { v } ( a, b ) _ { v } = 1 } where the product is over all finite and infinite places. over the rational numbers this is equivalent to the law of quadratic reciprocity. to see this take a and b to be distinct odd primes. then hilbert's law becomes ( p, q ) ∞ ( p, q ) 2 ( p, q ) p ( p, q ) q = 1 { \ displaystyle ( p, q ) _ { \ infty } ( p, q ) _ { 2 } ( p, q ) _ { p } ( p, q ) _ { q } = 1 } but ( p, q ) p is equal to the legendre symbol, ( p, q ) ∞ is 1 if one of p and q is positive and – 1 otherwise, and ( p, q ) 2 is ( – 1 ) ( p – 1 ) ( q – 1 ) / 4. so for p and q positive odd primes hilbert's law is the law of quadratic reciprocity.


scientific technologies, similarly, often require the development of a full experimental system to go from a viable concept to a technique that works in practice on a usefully consistent basis. for example, the invention of the polymerase chain reaction ( pcr ) is generally attributed to kary mullis, who came up with the concept in 1983, but the process of development of pcr into the revolutionary technology it became by the early 1990s took years of work by others at cetus corporation — and the basic components of the system had been known since the 1960s dna synthesis work of har gobind khorana — making " who invented pcr? " a complicated question.


in the above formulation, if the bit rate constraint is neglected by setting λ { \ displaystyle \ lambda } equal to 0, or equivalently if it is assumed that a fixed - length code ( flc ) will be used to represent the quantized data instead of a variable - length code ( or some other entropy coding technology such as arithmetic coding that is better than an flc in the rate – distortion sense ), the optimization problem reduces to minimization of distortion d { \ displaystyle d } alone. the indices produced by an m { \ displaystyle m } - level quantizer can be coded using a fixed - length code using r = log 2 m { \ displaystyle r = \ lceil \ log _ { 2 } m \ rceil } bits / symbol. for example, when m = { \ displaystyle m = } 256 levels, the flc bit rate r { \ displaystyle r } is 8 bits / symbol. for this reason, such a quantizer has sometimes been called an 8 - bit quantizer.


the processor could still address 4 gb in this mode, but could not execute anything above address 0x3fffffc ( 64 mb ). this mode was used by risc os running on the acorn risc pc to utilise the new processors while retaining compatibility with existing software. arm architecture version 4 made the support of the 26 - bit addressing modes optional, and arm architecture version 5 onwards has removed them entirely.


the mind doesn't work that way, a reaction to steven pinker's how the mind works, is devoted to this subject. fodor ( 1983 ) states that modular systems must — at least to " some interesting extent " — fulfill certain properties : domain specificity : modules only operate on certain kinds of inputs — they are specialised obligatory firing : modules process in a mandatory manner limited accessibility : what central processing can access from input system representations is limited fast speed : probably due to the fact that they are encapsulated ( thereby needing only to consult a restricted database ) and mandatory ( time need not be wasted in determining whether or not to process incoming input ) informational encapsulation : modules need not refer to other psychological systems in order to operate shallow outputs : the output of modules is very simple specific breakdown patterns characteristic ontogeny : there is a regularity of development fixed neural architecture. pylyshyn ( 1999 ) has argued that while these properties tend to occur with modules, one — information encapsulation — stands out as being the real signature of a module ; that is the encapsulation of the processes inside the module from both cognitive influence and from cognitive access. one example is that conscious awareness that the muller - lyer illusion is an illusion does not correct visual processing.


{ \ displaystyle p ^ { - 1 } ( a') = { \ begin { cases } mn - 1 & { \ text { if } } a'= mn - 1, \ \ ma'{ \ bmod { ( } } mn - 1 ) & { \ text { otherwise } }. \ end { cases } } } ( this is just a consequence of the fact that the inverse of an n×m transpose is an m×n transpose, although it is also easy to show explicitly that p−1 composed with p gives the identity. ) as proved by cate & twigg ( 1977 ), the number of fixed points ( cycles of length 1 ) of the permutation is precisely 1 + gcd ( n−1, m−1 ), where gcd is the greatest common divisor. for example, with n = m the number of fixed points is simply n ( the diagonal of the matrix ).


what protection level is implemented and does it adhere to compliance regulations? when implemented it provides a bridge between it professionals and process or application owners. it staff are informed about the data value and management ( usually application owners ) understands better which part of the data centre needs to be invested in to keep operations running effectively. this can be of particular importance in risk management, legal discovery, and compliance with government regulations. data classification is typically a manual process ; however, there are many tools from different vendors that can help gather information about the data. data classification needs to take into account the following : regulatory requirements strategic or proprietary worth organization specific policies ethical and privacy considerations contractual agreements


a group - specific method further decomposes each latent factor into two additive parts : one part corresponds to each item ( and / or each user ), while the other part is shared among items within each item group ( e. g., a group of movies could be movies of the same genre ). then once a new item arrives, we can assign a group label to it, and approximates its latent factor by the group - specific part ( of the corresponding item group ). therefore, although the individual part of the new item is not available, the group - specific part provides an immediate and effective solution. the same applies for a new user, as if some information is available for them ( e. g. age, nationality, gender ) then his / her latent factors can be estimated via an embedding function or a group - specific latent factor.


in the field of distributed algorithms, graph coloring is closely related to the problem of symmetry breaking. the current state - of - the - art randomized algorithms are faster for sufficiently large maximum degree δ than deterministic algorithms. the fastest randomized algorithms employ the multi - trials technique by schneider et al. in a symmetric graph, a deterministic distributed algorithm cannot find a proper vertex coloring.


in telecommunication, a message base station is a predetermined or prescribed spatial or time - sequential arrangement of the parts of a message that is recorded in or on a data storage medium. at one time, messages prepared for electrical transmission were composed on a printed blank form with spaces for each part of the message and for administrative entries. this article incorporates public domain material from federal standard 1037c. general services administration. archived from the original on 2022 - 01 - 22.


galois rings were studied by krull ( 1924 ), and independently by janusz ( 1966 ) and by raghavendran ( 1969 ), who both introduced the name galois ring. they are named after evariste galois, similar to galois fields, which is another name for finite fields. galois rings have found applications in coding theory, where certain codes are best understood as linear codes over z / 4 z { \ displaystyle \ mathbb { z } / 4 \ mathbb { z } } using galois rings gr ( 4, r ).


these machines placed the operands on a push - down ( last - in, first out ) stack. the instruction set was supplemented with a few instructions to fetch and store memory.


constraints may be added to the causes and effects. these are represented as edges labeled with the constraint symbol using a dashed line. for causes, valid constraint symbols are e ( exclusive ), o ( one and only one ), i ( at least one ), and r ( requires ).


for example, giving the structure of the simply - typed λ - calculus at the type level requires binding, or higher - order, type operators. these binding type operators correspond to the 2nd axis of the λ - cube, and type theories such as the simply - typed λ - calculus with type operators, λω. combining type operators with the polymorphic λ - calculus ( system f ) yields system fω.


for example, the failure to read a company's privacy policy regarding communications on their platform could lead one to assume that their communication is protected when it is in fact not. additionally, companies frequently have been known to lack transparency in how they use information, which can be both intentional and unintentional. discussion of communication privacy necessarily requires consideration of technological methods of protecting information / communication in digital mediums, the effectiveness and ineffectiveness of such methods / systems, and the development / advancement of new and current technologies.


in probability theory, kolmogorov's two - series theorem is a result about the convergence of random series. it follows from kolmogorov's inequality and is used in one proof of the strong law of large numbers.


this amounts to choosing, uniformly at random, an edge of the graph ( representing a pair of friends ) and an endpoint of that edge ( one of the friends ), and again calculating the degree of the selected endpoint. the probability of a certain vertex v { \ displaystyle v } to be chosen is d ( v ) | e | 1 2. { \ displaystyle { \ frac { d ( v ) } { | e | } } { \ frac { 1 } { 2 } }. }


in mathematics, a ramanujan prime is a prime number that satisfies a result proven by srinivasa ramanujan relating to the prime - counting function.


in a liquid medium with few or no expected organisms, from an area that is normally sterile ( such as csf, blood inside the circulatory system ) centrifugation, decanting the supernatant and using only the sediment will increase the chance to grow and isolate bacteria or the usually cell - associated viruses. if one expects or looks for a particularly fastidious organism, the microbiological culture and isolation techniques will have to be geared towards that microbe. for example, a bacterium that dies when exposed to air, can only be isolated if the sample is carried and processed under airless or anaerobic conditions. a bacterium that dies when exposed to room temperature ( thermophilic ) requires a pre - warmed transport container, and a microbe that dries and dies when carried on a cotton swab will need a viral transport medium before it can be cultured successfully.


in some cases the computer may not be able to programatically ( via programmed i / o ) acquire position information with adequate timing precision. for example, the computer may be unable to demand samples on a timely periodic schedule ( e. g., for speed measurement ) due to software timing variability. also, in some applications it is necessary to demand samples upon the occurrence of external events, and the computer may be unable to do so in a timely manner. at higher encoder speeds and resolutions, position measurement errors can occur even when interrupts are used to demand samples, because the encoder may move between the time the irq is signaled and the sample demand is issued by the interrupt handler.


eight registers ( l0 through l7 ) are local to the current procedure level, and eight registers ( o0 through o7 ) are the outputs from the current procedure level to the next level called. when a procedure is called, the register window shifts by sixteen registers, hiding the old input registers and old local registers and making the old output registers the new input registers. the common registers ( old output registers and new input registers ) are used for parameter passing.


for example, the finite element method may be recast as a multigrid method. in these cases, multigrid methods are among the fastest solution techniques known today.


on the other hand equation ( 4 ) introduces a way of weighting the movement from the previous step in the iteration. note that if this term was not present in ( 5 ) then the algorithm would output a movement in the estimation even if m = e ( x ^ o l d ) { \ displaystyle \ mathbf { m } = e ( { \ hat { \ mathbf { x } } } _ { old } ) }. it's worth noting that the only strategy used here is to maximize the likelihood at all cost, so artifacts on the image can be introduced. it is worth noting that no prior knowledge on the shape of the ground truth x { \ displaystyle \ mathbf { x } } is used in this derivation.


in the following example, the lexical entry is associated with a lemma clergyman and two inflected forms clergyman and clergymen. the language coding is set for the whole lexical resource. the language value is set for the whole lexicon as shown in the following uml instance diagram. the elements lexical resource, global information, lexicon, lexical entry, lemma, and word form define the structure of the lexicon.


in the germanic languages, weak verbs are by far the largest group of verbs, and are therefore often regarded as the norm ( the regular verbs ). they are distinguished from the germanic strong verbs by the fact that their past tense form is marked by an inflection containing a / t /, / d /, or / ð / sound ( as in english i walk ~ i walked ) rather than by changing the verb's root vowel ( as in english i rise ~ i rose ). whereas the strong verbs are the oldest group of verbs in germanic, originating in indo - european, the weak verbs arose as an innovation in proto - germanic. originally the weak verbs consisted of new verbs coined from pre - existing nouns ( for example the noun name was turned into the verb to name ), or coined from strong verbs to express the sense of causing the action denoted by that strong verb ( for example the strong verb to rise was turned into the weak verb to raise ).


second, is a more complex model better? third, what contribution do individual predictors make to the model? in order to assess models, different model fit statistics would be examined.


in the case of simply typed lambda calculus, a type has an inhabitant if and only if its corresponding proposition is a tautology of minimal implicative logic. similarly, a system f type has an inhabitant if and only if its corresponding proposition is a tautology of intuitionistic second - order logic. girard's paradox shows that type inhabitation is strongly related to the consistency of a type system with curry – howard correspondence. to be sound, such a system must have uninhabited types.


the univac 418 ( aka 1219 ) was an 18 - bit word core memory machine. over the three different models, more than 392 systems were manufactured. the univac 490 was a 30 - bit word core memory machine with 16k or 32k words ; 4. 8 microsecond cycle time.


additionally, minimize the maximal load of all remaining links, but now without the bottleneck links of the first layer. this second iteration further refines the path diversity. next, we determine the bottleneck links of the 2nd network layer.


, x 1 ) { \ displaystyle x ^ { i } = ( x _ { i }, x _ { i - 1 }, x _ { i - 2 },..., x _ { 1 } ) } and the channel become p ( y i | x i, y i − 1 ). { \ displaystyle p ( y _ { i } | x ^ { i }, y ^ { i - 1 } ). }. in such a case the capacity is given by the mutual information rate when there is no feedback available and the directed information rate in the case that either there is feedback or not ( if there is no feedback the directed information equals the mutual information ).


in mathematics invariant theory, the bracket ring is the subring of the ring of polynomials k generated by the d - by - d minors of a generic d - by - n matrix ( xij ). the bracket ring may be regarded as the ring of polynomials on the image of a grassmannian under the plucker embedding. for given d ≤ n we define as formal variables the brackets with the λ taken from { 1,..., n }, subject to = − and similarly for other transpositions. the set λ ( n, d ) of size ( n d ) { \ displaystyle { \ binom { n } { d } } } generates a polynomial ring k over a field k. there is a homomorphism φ ( n, d ) from k to the polynomial ring k in nd indeterminates given by mapping to the determinant of the d by d matrix consisting of the columns of the xi, j indexed by the λ. the bracket ring b ( n, d ) is the image of φ. the kernel i ( n, d ) of φ encodes the relations or syzygies that exist between the minors of a generic n by d matrix. the projective variety defined by the ideal i is the ( n−d ) d dimensional grassmann variety whose points correspond to d - dimensional subspaces of an n - dimensional space. to compute with brackets it is necessary to determine when an expression lies in the ideal i ( n, d ). this is achieved by a straightening law due to young ( 1928 ).


the following week, " gangnam style " descended to number 18 on the chart but achieved the milestone of 3 million downloads sold in the country, becoming the first and only k - pop song to reach the mark. for the week of january 12, 2013, powered by consumers purchasing some of 2012's most buzzworthy hits and radio airplay recounting the same in year - end retrospectives, the song resurged from number 19 to number six with its best weekly total 400, 000 downloads sold, returning to the hot 100's top ten after three weeks out of the top ten. the track dropped to number 14 in its 18th week, ending a 12 - week in the top 10, and number 22 in its 19th week, despite staying in the top ten of digital songs chart with 192, 000 and 105, 000 copies sold, respectively.


in predictive coding, optimising model parameters through a gradient descent on the time integral of free energy ( free action ) reduces to associative or hebbian plasticity and is associated with synaptic plasticity in the brain.


it should be apparent now that falsely equating the two probabilities can lead to various errors of reasoning, which is commonly seen through base rate fallacies. while conditional probabilities can provide extremely useful information, limited information is often supplied or at hand. therefore, it can be useful to reverse or convert a conditional probability using bayes'theorem : p ( a b ) = p ( b a ) p ( a ) p ( b ) { \ displaystyle p ( a \ mid b ) = { { p ( b \ mid a ) p ( a ) } \ over { p ( b ) } } }. another option is to display conditional probabilities in a conditional probability table to illuminate the relationship between events.


in order to overcome the limits of basic boolean searches, information systems have attempted to classify case laws and statutes into more computer friendly structures. usually, this results in the creation of an ontology to classify the texts, based on the way a legal professional might think about them. these attempt to link texts on the basis of their type, their value, and / or their topic areas. most major legal search providers now implement some sort of classification search, such as westlaw's “ natural language ” or lexisnexis'headnote searches.


in mathematics, a cardinal number, or cardinal for short, is what is commonly called the number of elements of a set. in the case of a finite set, its cardinal number, or cardinality is therefore a natural number. for dealing with the case of infinite sets, the infinite cardinal numbers have been introduced, which are often denoted with the hebrew letter { \ displaystyle \ aleph } ( aleph ) marked with subscript indicating their rank among the infinite cardinals. cardinality is defined in terms of bijective functions.


in software, telemetry is used to gather data on the use and performance of applications and application components, e. g. how often certain features are used, measurements of start - up time and processing time, hardware, application crashes, and general usage statistics and / or user behavior. in some cases, very detailed data is reported like individual window metrics, counts of used features, and individual function timings. this kind of telemetry can be essential to software developers to receive data from a wide variety of endpoints that can't possibly all be tested in - house, as well as getting data on the popularity of certain features and whether they should be given priority or be considered for removal. due to concerns about privacy since software telemetry can easily be used to profile users, telemetry in user software is often user choice, commonly presented as an opt - in feature ( requiring explicit user action to enable it ) or user choice during the software installation process.


the applications of model theory to algebraic and diophantine geometry reflect this proximity to classical mathematics, as they often involve an integration of algebraic and model - theoretic results and techniques. consequently, proof theory is syntactic in nature, in contrast to model theory, which is semantic in nature. the most prominent scholarly organization in the field of model theory is the association for symbolic logic.


in mathematics, a square is the result of multiplying a number by itself. the verb " to square " is used to denote this operation. squaring is the same as raising to the power 2, and is denoted by a superscript 2 ; for instance, the square of 3 may be written as 32, which is the number 9. in some cases when superscripts are not available, as for instance in programming languages or plain text files, the notations x ^ 2 ( caret ) or x * * 2 may be used in place of x2.


in order for any concept to have meaning, it must be related to sense perception. the 12 categories, or a priori concepts, are related to phenomenal appearances through schemata. each category has a schema. it is a connection through time between the category, which is an a priori concept of the understanding, and a phenomenal a posteriori appearance.


in statistics, the term analysis may refer to any method used for data analysis. among the many such methods, some are : analysis of variance ( anova ) – a collection of statistical models and their associated procedures which compare means by splitting the overall observed variance into different parts boolean analysis – a method to find deterministic dependencies between variables in a sample, mostly used in exploratory data analysis cluster analysis – techniques for finding groups ( called clusters ), based on some measure of proximity or similarity factor analysis – a method to construct models describing a data set of observed variables in terms of a smaller set of unobserved variables ( called factors ) meta - analysis – combines the results of several studies that address a set of related research hypotheses multivariate analysis – analysis of data involving several variables, such as by factor analysis, regression analysis, or principal component analysis principal component analysis – transformation of a sample of correlated variables into uncorrelated variables ( called principal components ), mostly used in exploratory data analysis regression analysis – techniques for analysing the relationships between several predictive variables and one or more outcomes in the data scale analysis ( statistics ) – methods to analyse survey data by scoring responses on a numeric scale sensitivity analysis – the study of how the variation in the output of a model depends on variations in the inputs sequential analysis – evaluation of sampled data as it is collected, until the criterion of a stopping rule is met spatial analysis – the study of entities using geometric or geographic properties time - series analysis – methods that attempt to understand a sequence of data points spaced apart at uniform time intervals


some phonological theories use'doubling'as a synonym for gemination, while others describe two distinct phenomena. consonant length is a distinctive feature in certain languages, such as arabic, berber, danish, estonian, finnish, hindi, hungarian, italian, japanese, kannada, malayalam, punjabi, polish and turkish. other languages, such as english, do not have word - internal phonemic consonant geminates. consonant gemination and vowel length are independent in languages like arabic, japanese, finnish and estonian ; however, in languages like italian, norwegian and swedish, vowel length and consonant length are interdependent. for example, in norwegian and swedish, a geminated consonant is always preceded by a short vowel, while an ungeminated consonant is preceded by a long vowel. a clear example are the norwegian words tak ('ceiling or roof'of a building ), and takk ('thanks').


in software applications that modify information stored on disk, this generally involves flushing any outstanding writes ; see buffering. with telecom applications, this generally involves allowing existing callers to finish their call but preventing new calls from initiating.


another example, in c + +, uses the " angle bracket " characters < and > in the syntax for template specialization, but two consecutive > characters are interpreted as the right - shift operator > >. prior to c + + 11, the following code would produce a parse error, because the right - shift operator token is encountered instead of two right - angle - bracket tokens : the c + + 11 standard adopted in august 2011 amended the grammar so that a right - shift token is accepted as synonymous with a pair of right angle brackets ( as in java ), which complicates the grammar but allows the continued use of the maximal munch principle. an exception to the maximal munch rule had to be added anyway to deal with the sequence < : : which can appear in templates. in that case, unless the sequence is followed by : or > the character < is interpreted as its own token instead of part of the token < :.


in the semantic web and in knowledge representation, a metaclass is a class whose instances can themselves be classes. similar to their role in programming languages, metaclasses in semantic web languages can have properties otherwise applicable only to individuals, while retaining the same class's ability to be classified in a concept hierarchy. this enables knowledge about instances of those metaclasses to be inferred by semantic reasoners using statements made in the metaclass. metaclasses thus enhance the expressivity of knowledge representations in a way that can be intuitive for users.


in the assessment and prediction of software reliability, we use the reliability growth model. during operation of the software, any data about its failure is stored in statistical form and is given as input to the reliability growth model. using this data, the reliability growth model can evaluate the reliability of software.


the operations can be scheduled in any order. operation o i j { \ displaystyle o _ { ij } } must be processed for p i j { \ displaystyle p _ { ij } } units on machine i { \ displaystyle i }. f : flow - shop problem.


the ability of a mobile phone to connect to a base station depends on the strength of the signal. that may be boosted by higher power transmissions, better antennas, taller antenna masts or alternative solutions like in - building picocells. normal macro - cell signals need to be boosted to pass through buildings, which is a particular problem designing networks for large metropolitan areas with modern skyscrapers, hence the current drive for small cells and micro and pico cells. signals also do not travel deep underground, so specialized transmission solutions are used to deliver mobile phone coverage into areas such as underground parking garages and subway trains.


in the field of machine learning, the goal of statistical classification is to use an object's characteristics to identify which class ( or group ) it belongs to. a linear classifier achieves this by making a classification decision based on the value of a linear combination of the characteristics. an object's characteristics are also known as feature values and are typically presented to the machine in a vector called a feature vector. such classifiers work well for practical problems such as document classification, and more generally for problems with many variables ( features ), reaching accuracy levels comparable to non - linear classifiers while taking less time to train and use.


that is, the method derandomizes the proof. the basic idea is to replace each random choice in a random experiment by a deterministic choice, so as to keep the conditional probability of failure, given the choices so far, below 1. the method is particularly relevant in the context of randomized rounding ( which uses the probabilistic method to design approximation algorithms ). when applying the method of conditional probabilities, the technical term pessimistic estimator refers to a quantity used in place of the true conditional probability ( or conditional expectation ) underlying the proof.


this results in a faster comparison loop, as one comparison is eliminated per iteration, while it requires only one more iteration on average. hermann bottenbruch published the first implementation to leave out this check in 1962. set l { \ displaystyle l } to 0 { \ displaystyle 0 } and r { \ displaystyle r } to n − 1 { \ displaystyle n - 1 }. while l = r { \ displaystyle l \ neq r }, set m { \ displaystyle m } ( the position of the middle element ) to the ceiling of l + r 2 { \ displaystyle { \ frac { l + r } { 2 } } }, which is the least integer greater than or equal to l + r 2 { \ displaystyle { \ frac { l + r } { 2 } } }.


in optimal ls spca ( uspca, uncorrelated spca ) the orthogonality constraints require that the cardinality of the solutions is not smaller than the order of the component, these constraints may also create numerical problems when computing components of order larger than two. correlated spca ( cspca, correlated spca ) is a variant of ls spca in which the orthogonality constraints are relaxed and the solutions are obtained iteratively by minimizing the norm of the approximation error from residuals orthogonal to the previously computed spcs. even though the resulting components are correlated ( usually very mildly ), they have lower cardinality and in many cases explain more variance than the corresponding uspca solutions.


exactly where the boundary is drawn between proper values and data structures masquerading as such is often hard to predict. in c, an array ( of which strings are special cases ) is a data structure but the name of an array is treated as ( has as value ) the reference to the first element of the array, while a struct variable's name refers to a value even if it has fields that are vectors. in maple, a vector is a special case of a table and therefore a data structure, but a list ( which gets rendered and can be indexed in exactly the same way ) is a value.