in programming languages, monomorphization is a compile - time process where polymorphic functions are replaced by many monomorphic functions for each unique instantiation. it is considered beneficial to undergo the mentioned transformation because it results in the output intermediate representation ( ir ) having specific types, which allows for more effective optimization. additionally, many irs are intended to be low - level and do not accommodate polymorphism. the resulting code is generally faster than dynamic dispatch, but may require more compilation time and storage space due to duplicating the function body.


in the us, the ppi was known as the wholesale price index, or wpi, up to 1978. the ppi is one of the oldest continuous systems of statistical data published by the bureau of labor statistics, as well as one of the oldest economic time series compiled by the federal government. the origins of the index can be found in an 1891 u. s. senate resolution authorizing the senate committee on finance to investigate the effects of the tariff laws " upon the imports and exports, the growth, development, production, and prices of agricultural and manufactured articles at home and abroad ".


computations using this algorithm form part of the cryptographic protocols that are used to secure internet communications, and in methods for breaking these cryptosystems by factoring large composite numbers. the euclidean algorithm may be used to solve diophantine equations, such as finding numbers that satisfy multiple congruences according to the chinese remainder theorem, to construct continued fractions, and to find accurate rational approximations to real numbers. finally, it can be used as a basic tool for proving theorems in number theory such as lagrange's four - square theorem and the uniqueness of prime factorizations. the original algorithm was described only for natural numbers and geometric lengths ( real numbers ), but the algorithm was generalized in the 19th century to other types of numbers, such as gaussian integers and polynomials of one variable. this led to modern abstract algebraic notions such as euclidean domains.


in statistics, the ramsey regression equation specification error test ( reset ) test is a general specification test for the linear regression model. more specifically, it tests whether non - linear combinations of the explanatory variables help to explain the response variable. the intuition behind the test is that if non - linear combinations of the explanatory variables have any power in explaining the response variable, the model is misspecified in the sense that the data generating process might be better approximated by a polynomial or another non - linear functional form. the test was developed by james b. ramsey as part of his ph. d. thesis at the university of wisconsin – madison in 1968, and later published in the journal of the royal statistical society in 1969.


in mathematics, an orthodox semigroup is a regular semigroup whose set of idempotents forms a subsemigroup. in more recent terminology, an orthodox semigroup is a regular e - semigroup. the term orthodox semigroup was coined by t. e. hall and presented in a paper published in 1969. certain special classes of orthodox semigroups had been studied earlier. for example, semigroups that are also unions of groups, in which the sets of idempotents form subsemigroups were studied by p. h. h. fantham in 1960.


in the above definition, we are concerned with the number of bits that must be deterministically transmitted between two parties. if both the parties are given access to a random number generator, can they determine the value of f { \ displaystyle f } with much less information exchanged? yao, in his seminal paper answers this question by defining randomized communication complexity. a randomized protocol r { \ displaystyle r } for a function f { \ displaystyle f } has two - sided error.


in the following example the result of the subtraction has fewer digits than x { \ displaystyle x } : 123410 - 123401 using the first method the sum of the nines'complement of x { \ displaystyle x } and y { \ displaystyle y } is 876589 + 123401 — — — — — — — — 999990 the nines'complement of 999990 is 000009. removing the leading zeros gives 9 the desired result. if the subtrahend, y { \ displaystyle y }, has fewer digits than the minuend, x { \ displaystyle x }, leading zeros must be added in the second method. these zeros become leading nines when the complement is taken. for example : 48032 - 391 can be rewritten 48032 - 00391 replacing 00391 with its nines'complement and adding 1 produces the sum : 48032 + 99608 + 1 — — — — — — — 147641 dropping the leading 1 gives the correct answer : 47641.


in order to make an accurate comparison and determine if there is a match, the system requires a shape or points measurement to be compared against the information in the database. this process must be discriminating, quick to compute, concise to store, pose - independent and efficient to match.


in number theory, the padovan sequence is the sequence of integers p ( n ) defined by the initial values p ( 0 ) = p ( 1 ) = p ( 2 ) = 1, { \ displaystyle p ( 0 ) = p ( 1 ) = p ( 2 ) = 1, } and the recurrence relation p ( n ) = p ( n − 2 ) + p ( n − 3 ). { \ displaystyle p ( n ) = p ( n - 2 ) + p ( n - 3 ). } the first few values of p ( n ) are 1, 1, 1, 2, 2, 3, 4, 5, 7, 9, 12, 16, 21, 28, 37, 49, 65, 86, 114, 151, 200, 265,... ( sequence a000931 in the oeis ) a padovan prime is a padovan number that is prime. the first padovan primes are : 2, 3, 5, 7, 37, 151, 3329, 23833, 13091204281, 3093215881333057, 1363005552434666078217421284621279933627102780881053358473, 1558877695141608507751098941899265975115403618621811951868598809164180630185566719,... ( sequence a100891 in the oeis ). the padovan sequence is named after richard padovan who attributed its discovery to dutch architect hans van der laan in his 1994 essay dom.


in mathematics, particularly in computer algebra, abramov's algorithm computes all rational solutions of a linear recurrence equation with polynomial coefficients. the algorithm was published by sergei a. abramov in 1989.


1 _ 01 0 1 _ 0 → 1 _ 01 = 210. 011 1 1 _ 0 → 001 = 1011. 011 200 → 1001 = 1100. 100 011 → 100 = 10000. 1 011 → 100 { \ displaystyle { \ begin { aligned } 211. 0 { \ underline { 1 } } 0 _ { \ phi } = 211 &. { \ underline { 1 } } 01 _ { \ phi } & 0 { \ underline { 1 } } 0 \ rightarrow { \ underline { 1 } } 01 \ \ = 210 &. 011 _ { \ phi } & 1 { \ underline { 1 } } 0 \ rightarrow 001 \ \ = 1011 &. 011 _ { \ phi } & 200 \ rightarrow 1001 \ \ = 1100 &. 100 _ { \ phi } & 011 \ rightarrow 100 \ \ = 10000 &. 1 _ { \ phi } & 011 \ rightarrow 100 \ \ \ end { aligned } } } any positive number with a non - standard terminating base - φ representation can be uniquely standardized in this manner. if we get to a point where all digits are " 0 " or " 1 ", except for the first digit being negative, then the number is negative.


in mathematics, borwein's algorithm is an algorithm devised by jonathan and peter borwein to calculate the value of 1 / π. they devised several other algorithms. they published the book pi and the agm – a study in analytic number theory and computational complexity.


pseudaria, an ancient lost book of false proofs, is attributed to euclid. mathematical fallacies exist in many branches of mathematics. in elementary algebra, typical examples may involve a step where division by zero is performed, where a root is incorrectly extracted or, more generally, where different values of a multiple valued function are equated. well - known fallacies also exist in elementary euclidean geometry and calculus.


there are two common types of mode scramblers : the " step - graded - step " ( s - g - s ) and the " step index with bends ". the s - g - s mode scrambler is actually an assembly, a fusion - spliced concatenation of a step - index profile, a graded - index profile and another step - index profile fiber. typically, each segment is approximately 1 meter long, and may use segments of unconventional size to produce the distribution required according to core size of fiber to be tested.


this can be proved by reduction from planar sat. for the case in which all holes are single points, several constant - factor approximations have been developed : a ( 3 + sqrt ( 3 ) ) approximation in time o ( n 2 ) { \ displaystyle o ( n ^ { 2 } ) } ; a ( 3 + sqrt ( 3 ) ) approximation in time o ( n log n ) { \ displaystyle o ( n \ log { n } ) } ; a 4 approximation in time o ( n log n ) { \ displaystyle o ( n \ log { n } ) } ( more generally, in d dimensions, it is a 2 d { \ displaystyle 2d } approximation in time o ( d n log n ) { \ displaystyle o ( dn \ log { n } ) } ), a 3 approximation in time o ( n 4 ) { \ displaystyle o ( n ^ { 4 } ) } ; a 1. 75 approximation in time o ( n 5 ) { \ displaystyle o ( n ^ { 5 } ) } ( more generally, in d dimensions, it is a 2 d − 4 + 4 / d { \ displaystyle 2d - 4 + 4 / d } approximation in time o ( d n 2 d + 1 ) { \ displaystyle o ( dn ^ { 2d + 1 } ) } ) ; the latter approximation uses a restricted variant of the problem called guillotine partitioning, in which the cuts must be guillotine cuts ( edge - to - edge cuts ). several polynomial - time approximation schemes using sophisticated guillotine cuts.


in this case, the factorization can be done with root - finding algorithms. the case of polynomials with integer coefficients is fundamental for computer algebra. there are efficient computer algorithms for computing ( complete ) factorizations within the ring of polynomials with rational number coefficients ( see factorization of polynomials ).


in some linear optimization problems, even though the number of constraints is exponential, one can still write a custom separation oracle that works in polynomial time. some examples are : the minimum - cost arborescence problem : given a weighted directed graph and a vertex r in it, find a subgraph of minimum cost that contains a directed path from r to any other vertex. the problem can be presented as an lp with a constraint for each subset of vertices, which is an exponential number of constraints.


{ \ displaystyle \ pi \ sigma \ neq \ sigma \ pi. } as a bijection from a set to itself, a permutation is a function that performs a rearrangement of a set, and is not an arrangement itself. an older and more elementary viewpoint is that permutations are the arrangements themselves.


in the japanese kantenji braille, the standard 8 - dot braille patterns 2378, 12378, 23478, and 123478 are the patterns related to braille pattern dots - 1236, since the two additional dots of kantenji patterns 01236, 12367, and 012367 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in mathematics, the probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by paul erdos, for proving the existence of a prescribed kind of mathematical object. it works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is strictly greater than zero. although the proof uses probability, the final conclusion is determined for certain, without any possible error. this method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science ( e. g. randomized rounding ), and information theory.


in the context of program correctness, static analysis can discover vulnerabilities during the development phase of the program. these vulnerabilities are easier to correct than the ones found during the testing phase since static analysis leads to the root of the vulnerability. due to many forms of static analysis being computationally undecidable, the mechanisms for doing it will not always terminate with the right answer – either because they sometimes return a false negative ( " no problems found " when the code does in fact have problems ) or a false positive, or because they never return the wrong answer but sometimes never terminate. despite their limitations, the first type of mechanism might reduce the number of vulnerabilities, while the second can sometimes give strong assurance of the lack of a certain class of vulnerabilities.


in the 1960s, swapping was an early virtual memory technique. an entire program or entire segment would be " swapped out " ( or " rolled out " ) from ram to disk or drum, and another one would be swapped in ( or rolled in ). a swapped - out program would be current but its execution would be suspended while its ram was in use by another program ; a program with a swapped - out segment could continue running until it needed that segment, at which point it would be suspended until the segment was swapped in. a program might include multiple overlays that occupy the same memory at different times.


the purpose of sampling is to reduce the cost and / or the amount of work that it would take to survey the entire target population. a survey that measures the entire target population is called a census. a sample refers to a group or section of a population from which information is to be obtained survey samples can be broadly divided into two types : probability samples and super samples.


in the following description, the terminology used will be particular to the windows nt operating system, but the concepts are applicable to other virtual memory operating systems. when a new application on a 32 - bit os is executed, the process has a 4 gib vas : each one of the memory addresses ( from 0 to 232 − 1 ) in that space can have a single byte as a value. initially, none of them have values ('-'represents no value ). using or setting values in such a vas would cause a memory exception. 0 4 gib vas | - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - | then the application's executable file is mapped into the vas.


ego integrity is the psychological concept of the ego's accumulated assurance of its capacity for order and meaning. ego identity is the accrued confidence that the inner sameness and continuity prepared in the past are matched by the sameness and continuity of one's meaning for others, as evidenced in the promise of a career. body and ego control organ expressions and of the other attributes of the dynamics of a physical system to face the emotions of ego death in circumstances which can summon, sometimes, anti - theonymistic self - abandonment.


the database, where all managed objects are stored, is called management information base. in contrast with a ci, a managed object is " dynamic " and communicates with other network resources that are managed. note : a managed object may represent a physical entity, a network service, or an abstraction of a resource that exists independently of its use in management.


in the united states, the hearing aid compatibility act of 1988 requires that the federal communications commission ( fcc ) ensure that all telephones manufactured or imported for use in the united states after august 1989, and all " essential " telephones, be hearing aid - compatible ( through the use of a telecoil ). " essential " phones are defined as " coin - operated telephones, telephones provided for emergency use, and other telephones frequently needed for use by persons using such hearing aids. " these might include workplace telephones, telephones in confined settings ( like hospitals and nursing homes ), and telephones in hotel and motel rooms. secure telephones, as well as telephones used with public mobile and private radio services, are exempt from the hac act.


in order to use infopath to fill in a form, a designer must develop an infopath template first. according to jean paoli, one of its developers, a key architectural design decision was " to adhere to the xml paradigm of separating the data in a document from the formatting. " a patent filed in 2000 by adriana neagu and jean paoli describes the technology as " authoring xml using dhtml views and xslt. " all the data stored in infopath forms are stored in an xml format, which is referred to as the " data source ".


this is intended to improve readability of the code, by ensuring that statements that are at the same level of nesting within a block are aligned to the same column. other types of secondary notation, however, are not part of the formal notation. for example, when wrapping long lines, every line that is a continuation of a previous line can be indented arbitrarily.


in phrase - based translation, the aim was to reduce the restrictions of word - based translation by translating whole sequences of words, where the lengths may differ. the sequences of words were called blocks or phrases, however, typically they were not linguistic phrases, but phrasemes that were found using statistical methods from corpora. it has been shown that restricting the phrases to linguistic phrases ( syntactically motivated groups of words, see syntactic categories ) decreased the quality of translation. the chosen phrases were further mapped one - to - one based on a phrase translation table, and could be reordered. this table could be learnt based on word - alignment, or directly from a parallel corpus. the second model was trained using the expectation maximization algorithm, similarly to the word - based ibm model.


this replaces the instruction with a jump to a vm - safe equivalent compiled code fragment in hypervisor memory. the guest user - mode code, running in ring 3, generally runs directly on the host hardware in ring 3. in both cases, virtualbox uses csam and patm to inspect and patch the offending instructions whenever a fault occurs. virtualbox also contains a dynamic recompiler, based on qemu to recompile any real mode or protected mode code entirely ( e. g. bios code, a dos guest, or any operating system startup ). using these techniques, virtualbox could achieve performance comparable to that of vmware in its later versions. the feature was dropped starting with virtualbox 6. 1.


in mathematics, euclidean relations are a class of binary relations that formalize " axiom 1 " in euclid's elements : " magnitudes which are equal to the same are equal to each other. "


in order for equation a t a v = a t b { \ displaystyle a ^ { t } av = a ^ { t } b } to be solvable, a t a { \ displaystyle a ^ { t } a } should be invertible, or a t a { \ displaystyle a ^ { t } a }'s eigenvalues satisfy λ 1 ≥ λ 2 > 0 { \ displaystyle \ lambda _ { 1 } \ geq \ lambda _ { 2 } > 0 }. to avoid noise issue, usually λ 2 { \ displaystyle \ lambda _ { 2 } } is required to not be too small. also, if λ 1 / λ 2 { \ displaystyle \ lambda _ { 1 } / \ lambda _ { 2 } } is too large, this means that the point p { \ displaystyle p } is on an edge, and this method suffers from the aperture problem.


in the following code : a = b * c + g ; d = b * c * e ; it may be worth transforming the code to : tmp = b * c ; a = tmp + g ; d = tmp * e ; if the cost of storing and retrieving tmp is less than the cost of calculating b * c an extra time.


in participant governance a network is governed by its members themselves. they call such networks that involve most or all network members interacting on a relatively equal basis in the process of governance " shared participant governance ".


periphrastic hindi verb forms consist of two elements. the first of these two elements is the aspect marker and the second element ( the copula ) is the common tense / mood marker. in literary arabic ( الفصحى al - fusha ) the verb has two aspect - tenses : perfective ( past ), and imperfective ( non - past ).


in the case of k - nearest neighbors regression, when the expectation is taken over the possible labeling of a fixed training set, a closed - form expression exists that relates the bias – variance decomposition to the parameter k : : 37, 223 e = ( f ( x ) − 1 k i = 1 k f ( n i ( x ) ) ) 2 + σ 2 k + σ 2 { \ displaystyle \ operatorname { e } = \ left ( f ( x ) - { \ frac { 1 } { k } } \ sum _ { i = 1 } ^ { k } f ( n _ { i } ( x ) ) \ right ) ^ { 2 } + { \ frac { \ sigma ^ { 2 } } { k } } + \ sigma ^ { 2 } } where n 1 ( x ), …, n k ( x ) { \ displaystyle n _ { 1 } ( x ), \ dots, n _ { k } ( x ) } are the k nearest neighbors of x in the training set. the bias ( first term ) is a monotone rising function of k, while the variance ( second term ) drops off as k is increased. in fact, under " reasonable assumptions " the bias of the first - nearest neighbor ( 1 - nn ) estimator vanishes entirely as the size of the training set approaches infinity.


in probability theory, kolmogorov's zero – one law, named in honor of andrey nikolaevich kolmogorov, specifies that a certain type of event, namely a tail event of independent σ - algebras, will either almost surely happen or almost surely not happen ; that is, the probability of such an event occurring is zero or one. tail events are defined in terms of countably infinite families of σ - algebras. for illustrative purposes, we present here the special case in which each sigma algebra is generated by a random variable x k { \ displaystyle x _ { k } } for k ∈ n { \ displaystyle k \ in \ mathbb { n } }. let f { \ displaystyle { \ mathcal { f } } } be the sigma - algebra generated jointly by all of the x k { \ displaystyle x _ { k } }.


in process improvement efforts, the process performance index is an estimate of the process capability of a process during its initial set - up, before it has been brought into a state of statistical control. formally, if the upper and lower specifications of the process are usl and lsl, the estimated mean of the process is μ ^ { \ displaystyle { \ hat { \ mu } } }, and the estimated variability of the process ( expressed as a standard deviation ) is σ ^ { \ displaystyle { \ hat { \ sigma } } }, then the process performance index is defined as : p ^ p k = min { \ displaystyle { \ hat { p } } _ { pk } = \ min { \ bigg } } σ ^ { \ displaystyle { \ hat { \ sigma } } } is estimated using the sample standard deviation. ppk may be negative if the process mean falls outside the specification limits ( because the process is producing a large proportion of defective output ). some specifications may only be one sided ( for example, strength ). for specifications that only have a lower limit, p ^ p, l o w e r = μ ^ − l s l 3 σ ^ { \ displaystyle { \ hat { p } } _ { p, lower } = { { \ hat { \ mu } } - lsl \ over 3 { \ hat { \ sigma } } } } ; for those that only have an upper limit, p ^ p, u p p e r = u s l − μ ^ 3 σ ^ { \ displaystyle { \ hat { p } } _ { p, upper } = { usl - { \ hat { \ mu } } \ over 3 { \ hat { \ sigma } } } }. practitioners may also encounter p ^ p = u s l − l s l 6 σ ^ { \ displaystyle { \ hat { p } } _ { p } = { \ frac { usl - lsl } { 6 { \ hat { \ sigma } } } } }, a metric that does not account for process performance not exactly centered between the specification limits, and therefore is interpreted as what the process would be capable of achieving if it could be centered and stabilized.


the reinforced concrete will continue to carry the load provided that sufficient reinforcement is present. a typical design problem is to find the smallest amount of reinforcement that can carry the stresses on a small cube ( fig. 1 ). this can be formulated as an optimization problem.


in mathematics, an orientation of a real vector bundle is a generalization of an orientation of a vector space ; thus, given a real vector bundle π : e →b, an orientation of e means : for each fiber ex, there is an orientation of the vector space ex and one demands that each trivialization map ( which is a bundle map ) u : π − 1 ( u ) → u × r n { \ displaystyle \ phi _ { u } : \ pi ^ { - 1 } ( u ) \ to u \ times \ mathbf { r } ^ { n } } is fiberwise orientation - preserving, where rn is given the standard orientation. in more concise terms, this says that the structure group of the frame bundle of e, which is the real general linear group gln ( r ), can be reduced to the subgroup consisting of those with positive determinant. if e is a real vector bundle of rank n, then a choice of metric on e amounts to a reduction of the structure group to the orthogonal group o ( n ). in that situation, an orientation of e amounts to a reduction from o ( n ) to the special orthogonal group so ( n ).


it turned out that descendant trees of a particular kind, the so - called pruned coclass trees whose infinitely many vertices share a common coclass r { \ displaystyle r }, reveal a repeating finite pattern. these two crucial properties of finiteness and periodicity admit a characterization of all members of the tree by finitely many parametrized presentations.


replacing each vertex of the graph by a point and each edge of the graph by a point produces a non - hausdorff space in which the open sets are the sets s { \ displaystyle s } with the property that, if a vertex v { \ displaystyle v } of g { \ displaystyle g } belongs to s { \ displaystyle s }, then so does every edge having v { \ displaystyle v } as one of its endpoints. in either case, every finite subgraph of g { \ displaystyle g } corresponds to a compact subspace of the topological space, and every compact subspace corresponds to a finite subgraph together with, in the hausdorff case, finitely many compact proper subsets of edges. thus, a graph may be covered by a nested sequence of compact sets if and only if it is locally finite, having a finite number of edges at every vertex. if a graph g { \ displaystyle g } is connected and locally finite, then it has a compact cover in which the set κ i { \ displaystyle \ kappa _ { i } } is the set of vertices at distance at most i { \ displaystyle i } from some arbitrarily chosen starting vertex.


in mathematics, and more precisely in semigroup theory, a variety of finite semigroups is a class of semigroups having some nice algebraic properties. those classes can be defined in two distinct ways, using either algebraic notions or topological notions. varieties of finite monoids, varieties of finite ordered semigroups and varieties of finite ordered monoids are defined similarly. this notion is very similar to the general notion of variety in universal algebra.


in symmetric cryptography, the padding oracle attack can be applied to the cbc mode of operation, where the " oracle " ( usually a server ) leaks data about whether the padding of an encrypted message is correct or not. such data can allow attackers to decrypt ( and sometimes encrypt ) messages through the oracle using the oracle's key, without knowing the encryption key.


in statistical hypothesis testing, a type i error is the mistaken rejection of an actually true null hypothesis ( also known as a " false positive " finding or conclusion ; example : " an innocent person is convicted " ), while a type ii error is the failure to reject a null hypothesis that is actually false ( also known as a " false negative " finding or conclusion ; example : " a guilty person is not convicted " ). much of statistical theory revolves around the minimization of one or both of these errors, though the complete elimination of either is a statistical impossibility if the outcome is not determined by a known, observable causal process. by selecting a low threshold ( cut - off ) value and modifying the alpha ( α ) level, the quality of the hypothesis test can be increased. the knowledge of type i errors and type ii errors is widely used in medical science, biometrics and computer science. intuitively, type i errors can be thought of as errors of commission ( i. e., the researcher unluckily concludes that something is the fact ).


in some jurisdictions the law also requires customers to collect the receipt and keep it at least for a short while after leaving the shop, again to check that the shop records sales, so that it cannot evade sales taxes. often cash registers are attached to scales, barcode scanners, checkstands, and debit card or credit card terminals. increasingly, dedicated cash registers are being replaced with general purpose computers with pos software. today, point of sale systems scan the barcode ( usually ean or upc ) for each item, retrieve the price from a database, calculate deductions for items on sale ( or, in british retail terminology, " special offer ", " multibuy " or " buy one, get one free " ), calculate the sales tax or vat, calculate differential rates for preferred customers, actualize inventory, time and date stamp the transaction, record the transaction in detail including each item purchased, record the method of payment, keep totals for each product or type of product sold as well as total sales for specified periods, and do other tasks as well.


it may also result in smoother convergence, as the gradient computed at each step is averaged over more training samples. the convergence of stochastic gradient descent has been analyzed using the theories of convex minimization and of stochastic approximation. briefly, when the learning rates η { \ displaystyle \ eta } decrease with an appropriate rate, and subject to relatively mild assumptions, stochastic gradient descent converges almost surely to a global minimum when the objective function is convex or pseudoconvex, and otherwise converges almost surely to a local minimum. this is in fact a consequence of the robbins – siegmund theorem.


in practice, one can perform multiple stochastic gradient passes ( also called cycles or epochs ) over the data. the algorithm thus obtained is called incremental gradient method and corresponds to an iteration w i = w i − 1 − γ i ∇ v ( ⟨ w i − 1, x t i ⟩, y t i ) { \ displaystyle \ textstyle w _ { i } = w _ { i - 1 } - \ gamma _ { i } \ nabla v ( \ langle w _ { i - 1 }, x _ { t _ { i } } \ rangle, y _ { t _ { i } } ) } the main difference with the stochastic gradient method is that here a sequence t i { \ displaystyle t _ { i } } is chosen to decide which training point is visited in the i { \ displaystyle i } - th step. such a sequence can be stochastic or deterministic.


different from abbreviations, those are universally recognizable across language barriers as distinct and well - defined symbols. at the coding level, prosigns admit any form the morse code can take, unlike abbreviations which have to be sent as a sequence of individual letters, like ordinary text. on the other hand, most prosigns codes are much longer than typical codes for letters and numbers.


table to translate raw ascii values ( a, d, m, s ) to new subroutine index ( 1, 4, 3, 2 ) in constant time using one - dimensional array ( gaps in the range are shown as '..'for this example, meaning'all hex values up to next row '. the first two columns are not part of the array ) in automata - based programming and pseudoconversational transaction processing, if the number of distinct program states is small, a " dense sequence " control variable can be used to efficiently dictate the entire flow of the main program loop. a two byte raw data value would require a minimum table size of 65, 536 bytes – to handle all input possibilities – whilst allowing just 256 different output values. however, this direct translation technique provides an extremely fast validation & conversion to a ( relative ) subroutine pointer if the heuristics, together with sufficient fast access memory, permits its use.


in probability theory, to postselect is to condition a probability space upon the occurrence of a given event. in symbols, once we postselect for an event e { \ displaystyle e }, the probability of some other event f { \ displaystyle f } changes from pr { \ textstyle \ operatorname { pr } } to the conditional probability pr { \ displaystyle \ operatorname { pr } }. for a discrete probability space, pr = pr pr { \ textstyle \ operatorname { pr } = { \ frac { \ operatorname { pr } } { \ operatorname { pr } } } }, and thus we require that pr { \ textstyle \ operatorname { pr } } be strictly positive in order for the postselection to be well - defined. see also postbqp, a complexity class defined with postselection.


regulators and carriers have also been considering blocks of the 300 mhz spectrum which is normally used for television broadcasters. if a company agrees to volunteer their spectrum, the fcc will ask for 120 mhz of it. also, the fcc has been thinking about spectrum sharing which would allow wireless isps to purchase dtv licenses in january 2011, clearwire agreed to sell off its unused spectrum in order to raise money for company spectrum and to seemingly allow other companies to pick up on some unused space.


in the course of its use, the latin alphabet was adapted for use in new languages, sometimes representing phonemes not found in languages that were already written with the roman characters. to represent these new sounds, extensions were therefore created, be it by adding diacritics to existing letters, by joining multiple letters together to make ligatures, by creating completely new forms, or by assigning a special function to pairs or triplets of letters. these new forms are given a place in the alphabet by defining an alphabetical order or collation sequence, which can vary with the particular language.


chip - level multiprocessing ( cmp or multicore ) : integrates two or more processors into one chip, each executing threads independently. any combination of multithreaded / smt / cmp. the key factor to distinguish them is to look at how many instructions the processor can issue in one cycle and how many threads from which the instructions come. for example, sun microsystems'ultrasparc t1 is a multicore processor combined with fine - grain multithreading technique instead of simultaneous multithreading because each core can only issue one instruction at a time.


in mathematics, the concept of groupoid algebra generalizes the notion of group algebra.


denote by c the set of different configurations ( and their number ). for each size s in s and configuration c in c, denote : ns - the number of items of size s. as, c - the number of occurrences of size s in configuration c. xc - a variable denoting the number of bins with configuration c. then, the configuration lp of bin - packing is : minimize c ∈ c x c subject to { \ displaystyle { \ text { minimize } } ~ ~ ~ \ sum _ { c \ in c } x _ { c } ~ ~ ~ { \ text { subject to } } } c ∈ c a s, c x c ≥ n s { \ displaystyle \ sum _ { c \ in c } a _ { s, c } x _ { c } \ geq n _ { s } } for all s in s ( - all ns items of size s are packed ).


1 - d structures such as this are easier to fabricate compared with constructing a rigid 2 - d structure. the symmetrical - ring structure is another classic example. described by the nomenclature these are two rectangular square d type configurations, exactly the same size, lying flat, side by side, in the unit cell. also these are not concentric.


in statistics, principal component regression ( pcr ) is a regression analysis technique that is based on principal component analysis ( pca ). more specifically, pcr is used for estimating the unknown regression coefficients in a standard linear regression model. in pcr, instead of regressing the dependent variable on the explanatory variables directly, the principal components of the explanatory variables are used as regressors. one typically uses only a subset of all the principal components for regression, making pcr a kind of regularized procedure and also a type of shrinkage estimator.


code - based modularity allows developers to reuse and repair parts of the application, but development tools are required to perform these maintenance functions ( e. g. the application may need to be recompiled ). object - based modularity provides the application as a collection of separate executable files that may be independently maintained and replaced without redeploying the entire application ( e. g. microsoft's dynamic - link library ( dll ) ; sun / unix shared object files ). some object messaging capabilities allow object - based applications to be distributed across multiple computers ( e. g. microsoft's component object model ( com ) ).


for all possible assignments of false ( ) or true ( ) to p, q, and r ( columns 1, 3, 5 ), each subformula is evaluated according to the rules for material conditional, the result being shown below its main operator. column 6 shows that the whole formula evaluates to true in every case, i. e. that it is a tautology. in fact, its antecedent ( column 2 ) and its consequent ( column 10 ) are even equivalent.


in recent versions of unix - like operating systems such as linux, openbsd, netbsd, solaris and freebsd, up to 255 - character passphrases can be used.


{ \ displaystyle k ( x, y ; 0 ) = \ delta ( x - y ) ~. } as a fundamental solution, the kernel is additive, d y k ( x, y ; t ) k ( y, z ; t ′ ) = k ( x, z ; t + t ′ ). { \ displaystyle \ int dyk ( x, y ; t ) k ( y, z ; t') = k ( x, z ; t + t') ~. }


the order of a finite field is its number of elements, which is either a prime number or a prime power. for every prime number p and every positive integer k there are fields of order pk, all of which are isomorphic. finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, galois theory, finite geometry, cryptography and coding theory.


a simple solution is to simply avoid taking such unreliable words into account as well. applying again bayes'theorem, and assuming the classification between spam and ham of the emails containing a given word ( " replica " ) is a random variable with beta distribution, some programs decide to use a corrected probability : pr ′ ( s | w ) = s ⋅ pr ( s ) + n ⋅ pr ( s | w ) s + n { \ displaystyle \ pr'( s | w ) = { \ frac { s \ cdot \ pr ( s ) + n \ cdot \ pr ( s | w ) } { s + n } } } where : pr ′ ( s | w ) { \ displaystyle \ pr'( s | w ) } is the corrected probability for the message to be spam, knowing that it contains a given word ; s { \ displaystyle s } is the strength we give to background information about incoming spam ; pr ( s ) { \ displaystyle \ pr ( s ) } is the probability of any incoming message to be spam ; n { \ displaystyle n } is the number of occurrences of this word during the learning phase ; pr ( s | w ) { \ displaystyle \ pr ( s | w ) } is the spamicity of this word. ( demonstration : ) this corrected probability is used instead of the spamicity in the combining formula.


the advantages of salt nitriding are : quick processing time - usually in the order of 4 hours or so to achieve simple operation - heat the salt and workpieces to temperature and submerge until the duration has transpired. the disadvantages are : the salts used are highly toxic - disposal of salts are controlled by stringent environmental laws in western countries and has increased the costs involved in using salt baths. this is one of the most significant reasons the process has fallen out of favor in recent decades. only one process possible with a particular salt type - since the nitrogen potential is set by the salt, only one type of process is possible


linguistic concepts take time to settle in the memory. the learner must use the new concepts frequently after presentation, either by thinking or by speaking, in order to master them. his last observation was that language was learned in sentences with the verb as the most crucial component.


in sentences with subject, object, and verb, any order is possible. however, some orders are more common than others. in a sample of 568 sentences of caesar containing all three elements examined by pinkster, the proportions were : sov : 63 % osv : 21 % ovs : 6 % vos : 5 % svo : 4 % vso : 1 % an example of the typical subject - object - verb ( sov ) word order in caesar is : caesar suas copias in proximum collem subducit.


in knaster's original publication on dendroids, in 1961, he posed the problem of characterizing the dendroids which can be embedded into the euclidean plane. this problem remains open.


in statistics, polynomial regression is a form of regression analysis in which the relationship between the independent variable x and the dependent variable y is modelled as an nth degree polynomial in x. polynomial regression fits a nonlinear relationship between the value of x and the corresponding conditional mean of y, denoted e ( y | x ). although polynomial regression fits a nonlinear model to the data, as a statistical estimation problem it is linear, in the sense that the regression function e ( y | x ) is linear in the unknown parameters that are estimated from the data. for this reason, polynomial regression is considered to be a special case of multiple linear regression. the explanatory ( independent ) variables resulting from the polynomial expansion of the " baseline " variables are known as higher - degree terms. such variables are also used in classification settings.


sensitivity auditing is especially suitable in an adversarial context, where not only the nature of the evidence, but also the degree of certainty and uncertainty associated to the evidence, is the subject of partisan interests. these are the settings considered in post - normal science or in mode 2 science. post - normal science ( pns ) is a concept developed by silvio funtowicz and jerome ravetz, which proposes a methodology of inquiry that is appropriate when “ facts are uncertain, values in dispute, stakes high and decisions urgent ” ( funtowicz and ravetz, 1992 : 251 – 273 ).


in telecommunication, common - channel signaling ( ccs ), or common - channel interoffice signaling ( ccis ), is the transmission of control information ( signaling ) via a separate channel than that used for the messages, the signaling channel usually controls multiple message channels. in the public switched telephone network ( pstn ) one channel of a communications link is typically used for the sole purpose of carrying signaling for establishment and tear down of telephone calls. the remaining channels are used entirely for the transmission of voice messages. in most cases, a single 64 kbit / s channel is sufficient to handle the call setup and call clear - down traffic for numerous bearer ( voice and data ) channels. the technical alternative to ccs is channel - associated signaling ( cas ), in which each bearer channel has a dedicated signaling channel.


the form that a proposition takes depends on the type of logic. the type of logic called propositional, sentential, or statement logic includes only operators and propositional constants as symbols in its language. the propositions in this language are propositional constants, which are considered atomic propositions, and composite ( or compound ) propositions, which are composed by recursively applying operators to propositions.


consequently, descendant trees play a fundamental role in the classification of finite p - groups. by means of kernels and targets of artin transfer homomorphisms, descendant trees can be endowed with additional structure. an important question is how the descendant tree t ( r ) { \ displaystyle { \ mathcal { t } } ( r ) } can actually be constructed for an assigned starting group which is taken as the root r { \ displaystyle r } of the tree. the p - group generation algorithm is a recursive process for constructing the descendant tree of a given finite p - group playing the role of the tree root. this algorithm is implemented in the computational algebra systems gap and magma.


then, someone hands you a huge number of kcbs pentagrams, but at first, all of the colorings are hidden. you're told you can only uncover 2 vertices at most, and only if they share a common edge. so, for each pentagram, you randomly pick an edge and uncover the colors on its vertices.


two years later, sergei adian showed that certain burnside groups are also counterexamples. none of these counterexamples are finitely presented, and for some years it was considered possible that the conjecture held for finitely presented groups.


s + consonant clusters may vary between aspirated and nonaspirated depending upon if the cluster crosses a morpheme boundary or not. for instance, distend has unaspirated since it is not analyzed as two morphemes, but distaste has an aspirated middle because it is analyzed as dis - + taste and the word taste has an aspirated initial t. word - final voiceless stops are sometimes aspirated. voiceless stops in pashto are slightly aspirated prevocalically in a stressed syllable.


in probability theory, a sub - gaussian distribution is a probability distribution with strong tail decay. informally, the tails of a sub - gaussian distribution are dominated by ( i. e. decay at least as fast as ) the tails of a gaussian. this property gives sub - gaussian distributions their name. formally, the probability distribution of a random variable x { \ displaystyle x } is called sub - gaussian if there is a positive constant c such that for every t ≥ 0 { \ displaystyle t \ geq 0 }, p ( | x | ≥ t ) ≤ 2 exp ( − t 2 / c 2 ) { \ textstyle \ operatorname { p } ( | x | \ geq t ) \ leq 2 \ exp { ( - t ^ { 2 } / c ^ { 2 } ) } }.


regarding diagnosis, a proposed taxonomy of service tools is as follows : level 1 : service tool that indicates if a product is functional or not functional. describing computer servers, the states are often referred to as ‘ up ’ or ‘ down ’. this is a binary value.


in number theory, the polya conjecture ( or polya's conjecture ) stated that " most " ( i. e., 50 % or more ) of the natural numbers less than any given number have an odd number of prime factors. the conjecture was set forth by the hungarian mathematician george polya in 1919, and proved false in 1958 by c. brian haselgrove. though mathematicians typically refer to this statement as the polya conjecture, polya never actually conjectured that the statement was true ; rather, he showed that the truth of the statement would imply the riemann hypothesis. for this reason, it is more accurately called " polya's problem ". the size of the smallest counterexample is often used to demonstrate the fact that a conjecture can be true for many cases and still fail to hold in general, providing an illustration of the strong law of small numbers.


in the design of programming languages, an erroneous program is one whose semantics are not well - defined, but where the language implementation is not obligated to signal an error either at compile or at execution time. for example, in ada : in addition to bounded errors, the language rules define certain kinds of errors as leading to erroneous execution. like bounded errors, the implementation need not detect such errors either prior to or during run time. unlike bounded errors, there is no language - specified bound on the possible effect of erroneous execution ; the effect is in general not predictable. defining a condition as " erroneous " means that the language implementation need not perform a potentially expensive check ( e. g. that a global variable refers to the same object as a subroutine parameter ) but may nonetheless depend on a condition being true in defining the semantics of the program. = = notes = =


in the decimal ( base - 10 ) hindu – arabic numeral system, each position starting from the right is a higher power of 10. the first position represents 100 ( 1 ), the second position 101 ( 10 ), the third position 102 ( 10 × 10 or 100 ), the fourth position 103 ( 10 × 10 × 10 or 1000 ), and so on. fractional values are indicated by a separator, which can vary in different locations. usually this separator is a period or full stop, or a comma.


in sequence design, a feedback with carry shift register ( or fcsr ) is the arithmetic or with carry analog of a linear - feedback shift register ( lfsr ). if n > 1 { \ displaystyle n > 1 } is an integer, then an n - ary fcsr of length r { \ displaystyle r } is a finite state device with a state ( a ; z ) = ( a 0, a 1, …, a r − 1 ; z ) { \ displaystyle ( a ; z ) = ( a _ { 0 }, a _ { 1 }, \ dots, a _ { r - 1 } ; z ) } consisting of a vector of elements a i { \ displaystyle a _ { i } } in { 0, 1, …, n − 1 } = s { \ displaystyle \ { 0, 1, \ dots, n - 1 \ } = s } and an integer z { \ displaystyle z }. the state change operation is determined by a set of coefficients q 1, …, q n { \ displaystyle q _ { 1 }, \ dots, q _ { n } } and is defined as follows : compute s = q r a 0 + q r − 1 a 1 + + q 1 a r − 1 + z { \ displaystyle s = q _ { r } a _ { 0 } + q _ { r - 1 } a _ { 1 } + \ dots + q _ { 1 } a _ { r - 1 } + z }. express s as s = a r + n z ′ { \ displaystyle s = a _ { r } + nz'} with a r { \ displaystyle a _ { r } } in s { \ displaystyle s }.


( binary, 6 multiplications ) a 15 = ( 2 × a ) 3 { \ displaystyle a ^ { 15 } = ( ^ { 2 } \ times a ) ^ { 3 } \! } ( shortest addition chain, 5 multiplications ). a 15 = a 3 × ( 2 ) 2 { \ displaystyle a ^ { 15 } = a ^ { 3 } \ times ( ^ { 2 } ) ^ { 2 } \! }


for this purpose several test procedures have been devised. the test procedure due to m. s. e ( mean square error / estimator ) bartlett test is represented here. this test procedure is based on the statistic whose sampling distribution is approximately a chi - square distribution with ( k − 1 ) degrees of freedom, where k is the number of random samples, which may vary in size and are each drawn from independent normal distributions.


in the 1970s the national bureau of standards ( nbs ) defined a set of convenient numbers to ease metrication in the united states. this system of metric values was described as 1 – 2 – 5 series in reverse, with assigned preferences for those numbers which are multiples of 5, 2, and 1 ( plus their powers of 10 ), excluding linear dimensions above 100 mm.


for many modern packet - switched communication systems, even a single uncorrected bit error is enough to cause the loss of a data packet by causing its crc check to fail ; whether that packet loss was caused by a single bit error or a hundred - bit - long error burst is irrelevant. for systems using large amounts of forward error correction, the reverse applies ; a single low - level bit error will almost never occur, since any small errors will almost always be corrected, but any error sufficiently large to cause the forward error correction to fail will almost always result in a large burst error. more specialist and precise definitions of errored seconds exist in standards such as the t1 and ds1 transport systems.


in mathematics, a binary relation on a set may, or may not, hold between two given set members. for example, " is less than " is a relation on the set of natural numbers ; it holds e. g. between 1 and 3 ( denoted as 1 < 3 ), and likewise between 3 and 4 ( denoted as 3 < 4 ), but neither between 3 and 1 nor between 4 and 4. as another example, " is sister of " is a relation on the set of all people, it holds e. g. between marie curie and bronisława dłuska, and likewise vice versa. set members may not be in relation " to a certain degree " - either they are in relation or they are not.


if frame pointers are being used, the prologue will typically set the new value of the frame pointer register from the stack pointer. space on the stack for local variables can then be allocated by incrementally changing the stack pointer. the forth programming language allows explicit winding of the call stack ( called there the " return stack " ).


that may take many clock cycles, since the operand of x may in turn depend on previous instructions that fetch data from main memory. rather than halt while waiting for x to be finished, stage a may guess whether the branch will be taken or not, and fetch the next instruction y based on that guess. if the guess later turns out to be incorrect ( hopefully rarely ), the system would have to backtrack and resume with the correct choice. namely, all the changes that were made to the machine's state by stage a and subsequent stages based on that guess would have to be undone, the instructions following x already in the pipeline would have to be flushed, and stage a would have to restart with the correct instruction pointer. this branch prediction strategy is a special case of speculative execution.


5. clustering we can then cluster different documents based on the features we have generated. see the algorithm section in cluster analysis for different types of clustering methods.


the objective is to achieve the minimum perturbation to the item size vector so that all the items can be packed into the prescribed number of bins. in the maximum resource bin packing problem, the goal is to maximize the number of bins used, such that, for some ordering of the bins, no item in a later bin fits in an earlier bin. in a dual problem, the number of bins is fixed, and the goal is to minimize the total number or the total size of items placed into the bins, such that no remaining item fits into an unfilled bin.


in quantum mechanics, information theory, and fourier analysis, the entropic uncertainty or hirschman uncertainty is defined as the sum of the temporal and spectral shannon entropies. it turns out that heisenberg's uncertainty principle can be expressed as a lower bound on the sum of these entropies. this is stronger than the usual statement of the uncertainty principle in terms of the product of standard deviations. in 1957, hirschman considered a function f and its fourier transform g such that g ( y ) ≈ − ∞ ∞ exp ( − 2 π i x y ) f ( x ) d x, f ( x ) ≈ − ∞ ∞ exp ( 2 π i x y ) g ( y ) d y, { \ displaystyle g ( y ) \ approx \ int _ { - \ infty } ^ { \ infty } \ exp ( - 2 \ pi ixy ) f ( x ) \, dx, \ qquad f ( x ) \ approx \ int _ { - \ infty } ^ { \ infty } \ exp ( 2 \ pi ixy ) g ( y ) \, dy ~, } where the " ≈ " indicates convergence in l2, and normalized so that ( by plancherel's theorem ), − ∞ ∞ | f ( x ) | 2 d x = − ∞ ∞ | g ( y ) | 2 d y = 1.


pell's equation : x 2 − p y 2 = 1, { \ displaystyle \ x ^ { 2 } - py ^ { 2 } = 1, } where p { \ displaystyle p } is a given integer that is not a square number, and in which the variables x { \ displaystyle x } and y { \ displaystyle y } are required to be integers. the equation of pythagorean triples : x 2 + y 2 = z 2, { \ displaystyle x ^ { 2 } + y ^ { 2 } = z ^ { 2 }, } in which the variables x { \ displaystyle x }, y { \ displaystyle y }, and z { \ displaystyle z } are required to be positive integers. the equation of the fermat – catalan conjecture : a m + b n = c k, { \ displaystyle a ^ { m } + b ^ { n } = c ^ { k }, } in which the variables a { \ displaystyle a }, b { \ displaystyle b }, c { \ displaystyle c } are required to be coprime positive integers, and the variables m { \ displaystyle m }, n { \ displaystyle n }, and k { \ displaystyle k } are required to be positive integers satisfying the following equation : 1 m + 1 n + 1 k < 1. { \ displaystyle { \ frac { 1 } { m } } + { \ frac { 1 } { n } } + { \ frac { 1 } { k } } < 1. }


in the case of complete ranks, a commonly used significance test for w against a null hypothesis of no agreement ( i. e. random rankings ) is given by kendall and gibbons ( 1990 ) χ 2 = m ( n − 1 ) w { \ displaystyle \ chi ^ { 2 } = m ( n - 1 ) w } where the test statistic takes a chi - squared distribution with d f = n − 1 { \ displaystyle df = n - 1 } degrees of freedom. in the case of incomplete rankings ( see above ), this becomes χ 2 = λ ( n 2 − 1 ) k + 1 w { \ displaystyle \ chi ^ { 2 } = { \ frac { \ lambda ( n ^ { 2 } - 1 ) } { k + 1 } } w } where again, there are d f = n − 1 { \ displaystyle df = n - 1 } degrees of freedom. legendre compared via simulation the power of the chi - square and permutation testing approaches to determining significance for kendall's w. results indicated the chi - square method was overly conservative compared to a permutation test when m < 20 { \ displaystyle m < 20 }. marozzi extended this by also considering the f test, as proposed in the original publication introducing the w statistic by kendall & babington smith ( 1939 ) : f = w ( m − 1 ) 1 − w { \ displaystyle f = { \ frac { w ( m - 1 ) } { 1 - w } } } where the test statistic follows an f distribution with v 1 = n − 1 − ( 2 / m ) { \ displaystyle v _ { 1 } = n - 1 - ( 2 / m ) } and v 2 = ( m − 1 ) v 1 { \ displaystyle v _ { 2 } = ( m - 1 ) v _ { 1 } } degrees of freedom. marozzi found the f test performs approximately as well as the permutation test method, and may be preferred to when m { \ displaystyle m } is small, as it is computationally simpler.


in telecommunications, a protocol data unit ( pdu ) is a single unit of information transmitted among peer entities of a computer network. it is composed of protocol - specific control information and user data. in the layered architectures of communication protocol stacks, each layer implements protocols tailored to the specific type or mode of data exchange. for example, the transmission control protocol ( tcp ) implements a connection - oriented transfer mode, and the pdu of this protocol is called a segment, while the user datagram protocol ( udp ) uses datagrams as protocol data units for connectionless communication. a layer lower in the internet protocol suite, at the internet layer, the pdu is called a packet, irrespective of its payload type.


in the context of computer programming, instrumentation refers to the measure of a product's performance, in order to diagnose errors and to write trace information. instrumentation can be of two types : source instrumentation and binary instrumentation.


since, for each method of type queue, type stack provides a method with a matching name and signature, this check would succeed. however, clients accessing a stack object through a reference of type queue would, based on queue's documentation, expect fifo behavior but observe lifo behavior, invalidating these clients'correctness proofs and potentially leading to incorrect behavior of the program as a whole. this example violates behavioral subtyping because type stack is not a behavioral subtype of type queue : it is not the case that the behavior described by the documentation of type stack ( i. e. lifo behavior ) complies with the documentation of type queue ( which requires fifo behavior ).


the fact that a map f : x → y { \ displaystyle f : x \ rightarrow y } is an embedding is often indicated by the use of a " hooked arrow " ( u + 21aa rightwards arrow with hook ) ; thus : f : x y. { \ displaystyle f : x \ hookrightarrow y. } ( on the other hand, this notation is sometimes reserved for inclusion maps. )


consequently the proposition became known as a conjecture rather than a theorem. after 358 years of effort by mathematicians, the first successful proof was released in 1994 by andrew wiles and formally published in 1995.


in mathematics education, a number sentence is an equation or inequality expressed using numbers and mathematical symbols. the term is used in primary level mathematics teaching in the us, canada, uk, australia, new zealand and south africa.


in probability theory, a pairwise independent collection of random variables is a set of random variables any two of which are independent. any collection of mutually independent random variables is pairwise independent, but some pairwise independent collections are not mutually independent. pairwise independent random variables with finite variance are uncorrelated. a pair of random variables x and y are independent if and only if the random vector ( x, y ) with joint cumulative distribution function ( cdf ) f x, y ( x, y ) { \ displaystyle f _ { x, y } ( x, y ) } satisfies f x, y ( x, y ) = f x ( x ) f y ( y ), { \ displaystyle f _ { x, y } ( x, y ) = f _ { x } ( x ) f _ { y } ( y ), } or equivalently, their joint density f x, y ( x, y ) { \ displaystyle f _ { x, y } ( x, y ) } satisfies f x, y ( x, y ) = f x ( x ) f y ( y ).


in mathematics, especially in category theory, the codensity monad is a fundamental construction associating a monad to a wide class of functors.


consider the overcategory top / x { \ displaystyle { \ text { top } } / x } of topological spaces over x { \ displaystyle x }, that is, the category of topological spaces together with fixed continuous maps to x { \ displaystyle x }. every object of this category is a continuous map f : y → x { \ displaystyle f : y \ to x }, and a morphism from y → x { \ displaystyle y \ to x } to z → x { \ displaystyle z \ to x } is a continuous map y → z { \ displaystyle y \ to z } that commutes with the two maps to x { \ displaystyle x }. there is a functor γ : top / x → sets { \ displaystyle \ gamma : { \ text { top } } / x \ to { \ text { sets } } } sending an object f : y → x { \ displaystyle f : y \ to x } to f − 1 f ( y ) { \ displaystyle f ^ { - 1 } f ( y ) }.


in mathematics, especially in the area of algebra known as representation theory, the representation ring ( or green ring after j. a. green ) of a group is a ring formed from all the ( isomorphism classes of the ) finite - dimensional linear representations of the group. elements of the representation ring are sometimes called virtual representations. for a given group, the ring will depend on the base field of the representations. the case of complex coefficients is the most developed, but the case of algebraically closed fields of characteristic p where the sylow p - subgroups are cyclic is also theoretically approachable.


the notion of residuated map can be generalized to a binary operator ( or any higher arity ) via component - wise residuation. this approach gives rise to notions of left and right division in a partially ordered magma, additionally endowing it with a quasigroup structure. ( one speaks only of residuated algebra for higher arities ). a binary ( or higher arity ) residuated map is usually not residuated as a unary map.


many other disciplines use similar criteria or have specific measures geared toward the objectives of the field. optimality criteria include maximum likelihood, bayesian, maximum parsimony, sum of squared residuals, least absolute deviations, and many others. = = references = =


calls from mobile phones are usually routed based on the location of the base station rather than the calling party, so these ( along with landline calls to non - emergency telephone numbers ) must be handled manually by the telephone operator or dispatcher, determining whether the caller or incident is within a particular city limit or not so that the proper authorities may be sent. a city's limit may extend into more than one county, which can complicate certain matters of policing and taxation. ( for example, sales tax revenue collected in a city by one county may not be spent in another part of the city outside that county. )


.., a n ⟩ { \ displaystyle q _ { 1 } \ cong \ langle a _ { 1 },..., a _ { n } \ rangle } q 2 ⟨ b 1,.


in mathematics, binary splitting is a technique for speeding up numerical evaluation of many types of series with rational terms. in particular, it can be used to evaluate hypergeometric series at rational points.


hubs have a significantly larger number of links in comparison with other nodes in the network. the number of links ( degrees ) for a hub in a scale - free network is much higher than for the biggest node in a random network, keeping the size n of the network and average degree constant. the existence of hubs is the biggest difference between random networks and scale - free networks. in random networks, the degree k is comparable for every node ; it is therefore not possible for hubs to emerge. in scale - free networks, a few nodes ( hubs ) have a high degree k while the other nodes have a small number of links.


in network science, a hub is a node with a number of links that greatly exceeds the average. emergence of hubs is a consequence of a scale - free property of networks. : 27 while hubs cannot be observed in a random network, they are expected to emerge in scale - free networks. the uprise of hubs in scale - free networks is associated with power - law distribution.


in modern businesses, the design of file servers is complicated by competing demands for storage space, access speed, recoverability, ease of administration, security, and budget. this is further complicated by a constantly changing environment, where new hardware and technology rapidly obsolesces old equipment, and yet must seamlessly come online in a fashion compatible with the older machinery. to manage throughput, peak loads, and response time, vendors may utilize queuing theory to model how the combination of hardware and software will respond over various levels of demand.


in network science, the configuration model is a method for generating random networks from a given degree sequence. it is widely used as a reference model for real - life social networks, because it allows the modeler to incorporate arbitrary degree distributions.


our example is based on a modified post – turing machine model of a turing machine. this model prints only the symbols 0 and 1. the blank tape is considered to be all b's.


in mathematics, a nonlinear eigenproblem, sometimes nonlinear eigenvalue problem, is a generalization of the ( ordinary ) eigenvalue problem to equations that depend nonlinearly on the eigenvalue. specifically, it refers to equations of the form m ( λ ) x = 0, { \ displaystyle m ( \ lambda ) x = 0, } where x = 0 { \ displaystyle x \ neq 0 } is a vector, and m { \ displaystyle m } is a matrix - valued function of the number λ { \ displaystyle \ lambda }. the number λ { \ displaystyle \ lambda } is known as the ( nonlinear ) eigenvalue, the vector x { \ displaystyle x } as the ( nonlinear ) eigenvector, and ( λ, x ) { \ displaystyle ( \ lambda, x ) } as the eigenpair. the matrix m ( λ ) { \ displaystyle m ( \ lambda ) } is singular at an eigenvalue λ { \ displaystyle \ lambda }.


the first few measured and corrected moments about the mean are then related as follows : μ ^ 2 = m 2 − 1 12 c 2 μ ^ 3 = m 3 μ ^ 4 = m 4 − 1 2 m 2 c 2 + 7 240 c 4. { \ displaystyle { \ begin { aligned } { \ hat { \ mu } } _ { 2 } & = m _ { 2 } - { \ frac { 1 } { 12 } } c ^ { 2 } \ \ { \ hat { \ mu } } _ { 3 } & = m _ { 3 } \ \ { \ hat { \ mu } } _ { 4 } & = m _ { 4 } - { \ frac { 1 } { 2 } } m _ { 2 } c ^ { 2 } + { \ frac { 7 } { 240 } } c ^ { 4 }. \ end { aligned } } } when the data come from a normally distributed population, then binning and using the midpoint of the bin as the observed value results in an overestimate of the variance. that is why the correction to the variance is negative.


in post - order we always recursively traverse the current node's left subtree, next we recursively traverse the current node's right subtree and then visit the current node. post - order traversal can be useful to get postfix expression of a binary expression tree.


for example, 21 is the gcd of 252 and 105 ( as 252 = 21 × 12 and 105 = 21 × 5 ), and the same number 21 is also the gcd of 105 and 252 − 105 = 147. since this replacement reduces the larger of the two numbers, repeating this process gives successively smaller pairs of numbers until the two numbers become equal. when that occurs, they are the gcd of the original two numbers.


in statistics and computational geometry, the notion of centerpoint is a generalization of the median to data in higher - dimensional euclidean space. given a set of points in d - dimensional space, a centerpoint of the set is a point such that any hyperplane that goes through that point divides the set of points in two roughly equal subsets : the smaller part should have at least a 1 / ( d + 1 ) fraction of the points. like the median, a centerpoint need not be one of the data points. every non - empty set of points ( with no duplicates ) has at least one centerpoint.


in operating systems, processes are loaded into memory, and wait for their turn to be executed by the central processing unit ( cpu ). cpu scheduling manages process states and decides when a process will be executed next by using the input queue.


instead of sending the caller id in between the first and second ring, some systems ( such as in the uk ) use line reversal to announce the caller id, or caller id signals are simply sent without any announcement. instead of bell 202, the european alternative v. 23 is sometimes used ( without the 75 - baud reverse channel ) or the data is sent using dtmf signalling. in general, cid as transmitted from the origin of the call is only the calling party's full phone number ( including area code, and including international access code and country code if it's an international call ).


if b ∈ a n n ( x − k − 1 b ) = 0 { \ displaystyle \ sum _ { b \ in a } n _ { n } ( x _ { - k } ^ { - 1 } b ) \, = \, 0 }, define p ^ n ( a x − k − 1 ) = 1 / | a | { \ displaystyle { \ hat { p } } _ { n } ( a \ mid x _ { - k } ^ { - 1 } ) \, = \, 1 / | a | }. to i ≥ 1 { \ displaystyle i \ geq 1 }, define λ n ( x − i − 1 ) = 2 y ∈ a a ∈ a n n ( y x − i − 1 a ) log { \ displaystyle \ lambda _ { n } ( x _ { - i } ^ { - 1 } ) \, = \, 2 \, \ sum _ { y \ in a } \ sum _ { a \ in a } n _ { n } ( yx _ { - i } ^ { - 1 } a ) \ log \ left \, } where y x − i − 1 = ( y, x − i, …, x − 1 ) { \ displaystyle yx _ { - i } ^ { - 1 } = ( y, x _ { - i }, \ ldots, x _ { - 1 } ) } and p ^ n ( a x − i − 1 y ) = n n ( y x − i − 1 a ) b ∈ a n n ( y x − i − 1 b ). { \ displaystyle { \ hat { p } } _ { n } ( a \ mid x _ { - i } ^ { - 1 } y ) = { \ frac { n _ { n } ( yx _ { - i } ^ { - 1 } a ) } { \ sum _ { b \ in a } n _ { n } ( yx _ { - i } ^ { - 1 } b ) } }. }


in mathematics, a cocountable subset of a set x is a subset y whose complement in x is a countable set. in other words, y contains all but countably many elements of x. since the rational numbers are a countable subset of the reals, for example, the irrational numbers are a cocountable subset of the reals. if the complement is finite, then one says y is cofinite.


secondly, the fic formulae depend on the specifics of the models used for the observed data and also on how precision is to be measured. the clearest case is where precision is taken to be mean squared error, say r j = b j 2 + τ j 2 { \ displaystyle r _ { j } = b _ { j } ^ { 2 } + \ tau _ { j } ^ { 2 } } in terms of squared bias and variance for the estimator associated with model j { \ displaystyle j }. fic formulae are then available in a variety of situations, both for handling parametric, semiparametric and nonparametric situations, involving separate estimation of squared bias and variance, leading to estimated precision r ^ j { \ displaystyle { \ hat { r } } _ { j } }.


in object - oriented programming languages that do not support higher - order functions, objects can be an effective substitute. an object's methods act in essence like functions, and a method may accept objects as parameters and produce objects as return values. objects often carry added run - time overhead compared to pure functions, however, and added boilerplate code for defining and instantiating an object and its method ( s ). languages that permit stack - based ( versus heap - based ) objects or structs can provide more flexibility with this method. an example of using a simple stack based record in free pascal with a function that returns a function : the function a ( ) takes a txy record as input and returns the integer value of the sum of the record's x and y fields ( 3 + 7 ).


in mobile telecommunications technology, the concept of mobile signature roaming means an access point ( ap ) should be able to get a mobile signature from any end - user, even if the ap and the end - user have not contracted a commercial relationship with the same mssp. otherwise, an ap would have to build commercial terms with as many mssps as possible, and this might be a cost burden. this means that a mobile signature transaction issued by an application provider should be able to reach the appropriate mssp, and this should be transparent for the ap.


in more technical terms, let us assume that we have a theory described by a certain function z { \ displaystyle z } of the state variables { s i } { \ displaystyle \ { s _ { i } \ } } and a certain set of coupling constants { j k } { \ displaystyle \ { j _ { k } \ } }. this function may be a partition function, an action, a hamiltonian, etc. it must contain the whole description of the physics of the system. now we consider a certain blocking transformation of the state variables { s i } → { s ~ i } { \ displaystyle \ { s _ { i } \ } \ to \ { { \ tilde { s } } _ { i } \ } }, the number of s ~ i { \ displaystyle { \ tilde { s } } _ { i } } must be lower than the number of s i { \ displaystyle s _ { i } }.


in the majority of models, sampling fewer taxon with more sites per taxon demonstrated higher accuracy. generally, with the alignment of a relatively equal number of total nucleotide sites, sampling more genes per taxon has higher bootstrapping replicability than sampling more taxa. however, unbalanced datasets within genomic databases make increasing the gene comparison per taxon in uncommonly sampled organisms increasingly difficult.


in some cases, tasks depend on each other. these interdependencies can be illustrated by a directed acyclic graph. intuitively, some tasks cannot begin until others are completed.


in some applications it is useful to be able to compute the bernoulli numbers b0 through bp − 3 modulo p, where p is a prime ; for example to test whether vandiver's conjecture holds for p, or even just to determine whether p is an irregular prime. it is not feasible to carry out such a computation using the above recursive formulae, since at least ( a constant multiple of ) p2 arithmetic operations would be required. fortunately, faster methods have been developed which require only o ( p ( log p ) 2 ) operations ( see big o notation ). david harvey describes an algorithm for computing bernoulli numbers by computing bn modulo p for many small primes p, and then reconstructing bn via the chinese remainder theorem.


in practice, incorrectly received coded data blocks are often stored at the receiver rather than discarded, and when the re - transmitted block is received, the two blocks are combined. this is called hybrid arq with soft combining ( dahlman et al., p. 120 ).


" don't embarrass me with bad pictures " users may have the ability to control which pictures they post on their own facebook page, but they do not have the ability to control what others post. posting and " tagging " unflattering pictures of others may create expectancy violations. " don't mess up my profile " several participants expressed annoyance of others who alter their profiles knowing that their alterations could be perceived negatively, though they did not mention changing their passwords or protecting themselves in other ways.


so f0 is still the truth value of ψ, but the rx value produces a result that is linear in x. also after any q i x i { \ displaystyle { \ mathsf { q } } _ { i } x _ { i } } we add r x 1 … r x i { \ displaystyle \ mathrm { r } _ { x _ { 1 } } \ dots \ mathrm { r } _ { x _ { i } } } in ψ ′ in order to reduce the degree down to 1 after arithmetizing q i { \ displaystyle { \ mathsf { q } } _ { i } }. now let's describe the protocol. if n is the length of ψ, all arithmetic operations in the protocol are over a field of size at least n4 where n is the length of ψ. phase 0 : p → v : p sends f0 to v. v checks that f0 = 1 and rejects if not.


in the chart below, the carian letter for each vowel is followed by the conventional transcription with the greek equivalent in parentheses. an epenthetic schwa to break up clusters may have been unwritten.


in some programming languages, given a two - argument function f ( or a binary operator ), the outer product, f, of two one - dimensional arrays, a and b, is a two - dimensional array c such that c = f ( a, b ). this is syntactically represented in various ways : in apl, as the infix binary operator ∘. f ; in j, as the postfix adverb f / ; in r, as the function outer ( a, b, f ) or the special % o % ; in mathematica, as outer. in matlab, the function kron ( a, b ) is used for this product. these often generalize to multi - dimensional arguments, and more than two arguments.


in tau - square notation from n. bourbaki's theory of sets, the quantifiers are defined as follows : ( x ) a ( x ) ≡ ( τ x ( a ) | x ) a { \ displaystyle ( \ exists x ) a ( x ) \ \ equiv \ ( \ tau _ { x } ( a ) | x ) a } ( x ) a ( x ) ≡ ¬ ( τ x ( ¬ a ) | x ) ¬ a ≡ ( τ x ( ¬ a ) | x ) a { \ displaystyle ( \ forall x ) a ( x ) \ \ equiv \ \ neg ( \ tau _ { x } ( \ neg a ) | x ) \ neg a \ \ equiv \ ( \ tau _ { x } ( \ neg a ) | x ) a } where a is a relation in l, x is a variable, and τ x ( a ) { \ displaystyle \ tau _ { x } ( a ) } juxtaposes a τ { \ displaystyle \ tau } at the front of a, replaces all instances of x with { \ displaystyle \ square }, and links them back to τ { \ displaystyle \ tau }. then let y be an assembly, ( y | x ) a denotes the replacement of all variables x in a with y. this notation is equivalent to the hilbert notation and is read the same. it is used by bourbaki to define cardinal assignment since they do not use the axiom of replacement. defining quantifiers in this way leads to great inefficiencies. for instance, the expansion of bourbaki's original definition of the number one, using this notation, has length approximately 4. 5 × 1012, and for a later edition of bourbaki that combined this notation with the kuratowski definition of ordered pairs, this number grows to approximately 2. 4 × 1054.


in mathematics, the logarithm is the inverse function to exponentiation. that means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. for example, since 1000 = 103, the logarithm base 10 of 1000 is 3, or log10 ( 1000 ) = 3. the logarithm of x to base b is denoted as logb ( x ), or without parentheses, logb x, or even without the explicit base, log x, when no confusion is possible, or when the base does not matter such as in big o notation. the logarithm base 10 is called the decimal or common logarithm and is commonly used in science and engineering.


several models were produced which dispensed with the power transformer, but had circuit features which only allowed operation from ac. some early models were available in both ac - only and ac / dc versions, with the ac / dc versions sometimes slightly more expensive. television receivers were first commercially sold in england in 1936 for the new'television service'broadcast by the british broadcasting corporation. all pre world war ii sets used mains transformers and consequently were ac only.


negative bases are rarely used. in a system with more than | b | { \ displaystyle | b | } unique digits, numbers may have many different possible representations.


in the context of abstract algebra or universal algebra, a monomorphism is an injective homomorphism. a monomorphism from x to y is often denoted with the notation x y { \ displaystyle x \ hookrightarrow y }. in the more general setting of category theory, a monomorphism ( also called a monic morphism or a mono ) is a left - cancellative morphism. that is, an arrow f : x → y such that for all objects z and all morphisms g1, g2 : z → x, f ∘ g 1 = f ∘ g 2 g 1 = g 2.


these simpler expressions make up the majority of redundant, optimizable expressions in programs written in languages other than concatenative languages. an optimizing compiler can only win on redundancies that the programmer could have avoided in the source code. the second way leaves a computed value on the data stack, duplicating it as needed. this uses operations to copy stack entries.


in particular, the convolutional neural network lends itself to eye - tracking, as it is designed for image - centric tasks. with ai, eye - tracking tasks and studies can yield additional information that may not have been detected by human observers. the practice of deep learning also allows for a given neural network to improve at a given task when given enough sample data. this requires a relatively large supply of training data, however. the potential use cases for ai in eye - tracking cover a wide range of topics from medical applications to driver safety to game theory and even education and training applications.


the groups co2 of order 42, 305, 421, 312, 000 = 218 · 36 · 53 · 7 · 11 · 23and co3 of order 495, 766, 656, 000 = 210 · 37 · 53 · 7 · 11 · 23consist of the automorphisms of λ fixing a lattice vector of type 2 and type 3, respectively. as the scalar −1 fixes no non - zero vector, these two groups are isomorphic to subgroups of co1. the inner product on the leech lattice is defined as 1 / 8 the sum of the products of respective co - ordinates of the two multiplicand vectors ; it is an integer.


in mathematics, a function f is cofunction of a function g if f ( a ) = g ( b ) whenever a and b are complementary angles. this definition typically applies to trigonometric functions. the prefix " co - " can be found already in edmund gunter's canon triangulorum ( 1620 ). for example, sine ( latin : sinus ) and cosine ( latin : cosinus, sinus complementi ) are cofunctions of each other ( hence the " co " in " cosine " ) : the same is true of secant ( latin : secans ) and cosecant ( latin : cosecans, secans complementi ) as well as of tangent ( latin : tangens ) and cotangent ( latin : cotangens, tangens complementi ) : these equations are also known as the cofunction identities. this also holds true for the versine ( versed sine, ver ) and coversine ( coversed sine, cvs ), the vercosine ( versed cosine, vcs ) and covercosine ( coversed cosine, cvc ), the haversine ( half - versed sine, hav ) and hacoversine ( half - coversed sine, hcv ), the havercosine ( half - versed cosine, hvc ) and hacovercosine ( half - coversed cosine, hcc ), as well as the exsecant ( external secant, exs ) and excosecant ( external cosecant, exc ) :


during this time the user may be prevented from closing, resizing, or even minimizing the windows of the affected application ( although moving the window is still possible in os x, as well as previously hidden parts of the window which are usually redrawn, even when the application is otherwise unresponsive ). while one application is unresponsive, typically other applications are usable. file system and network delays are another common cause.


{ \ displaystyle \ left. + \ lefte ^ { - ipx } \ right \ }. } thus, ∂ e 1 ( x ) / ∂ x 1 + ∂ e 2 ( x ) / ∂ x 2 + ∂ e 3 ( x ) / ∂ x 3 { \ displaystyle \ partial e _ { 1 } ( x ) / \ partial x _ { 1 } + \ partial e _ { 2 } ( x ) / \ partial x _ { 2 } + \ partial e _ { 3 } ( x ) / \ partial x _ { 3 } } contains terms of the form p 1 1 1 ( p ) + p 2 2 1 ( p ) + p 3 3 1 ( p ) { \ displaystyle p _ { 1 } \ epsilon _ { 1 } ^ { 1 } ( \ mathbf { p } ) + p _ { 2 } \ epsilon _ { 2 } ^ { 1 } ( \ mathbf { p } ) + p _ { 3 } \ epsilon _ { 3 } ^ { 1 } ( \ mathbf { p } ) } which equate to zero by the first of eq. ( 4 ). this gives, ∇ ⋅ e ( x ) = 0, { \ displaystyle \ nabla \ cdot \ mathbf { e } ( x ) = 0, } ∇ ⋅ h ( x ) = 0.


full - text - searching techniques appeared in the 1960s, for example ibm stairs from 1969, and became common in online bibliographic databases in the 1990s. many websites and application programs ( such as word processing software ) provide full - text - search capabilities. some web search engines, such as the former altavista, employ full - text - search techniques, while others index only a portion of the web pages examined by their indexing systems.


it has been demonstrated for the first time in 2011 to enable better training of deeper networks, compared to the widely used activation functions prior to 2011, i. e., the logistic sigmoid ( which is inspired by probability theory ; see logistic regression ) and its more practical counterpart, the hyperbolic tangent. a commonly used variant of the relu activation function is the leaky relu which allows a small, positive gradient when the unit is not active : f ( x ) = { x if x > 0, a x otherwise. { \ displaystyle f ( x ) = { \ begin { cases } x & { \ text { if } } x > 0, \ \ ax & { \ text { otherwise } }. \ end { cases } } } where x is the input to the neuron and a is a small positive constant ( in the original paper the value 0. 01 was used for a ).


in phonology, affricates tend to behave similarly to stops, taking part in phonological patterns that fricatives do not. kehrein ( 2002 ) analyzes phonetic affricates as phonological stops. a sibilant or lateral ( and presumably trilled ) stop can be realized phonetically only as an affricate and so might be analyzed phonemically as a sibilant or lateral stop. in that analysis, affricates other than sibilants and laterals are a phonetic mechanism for distinguishing stops at similar places of articulation ( like more than one labial, coronal, or dorsal place ).


in natural language applications, libraries are a way to cope with thousands of details involved in syntax, lexicon, and inflection. the gf resource grammar library is the standard library for grammatical framework. it covers the morphology and basic syntax for an increasing number of languages, currently including afrikaans, amharic ( partial ), arabic ( partial ), basque ( partial ), bulgarian, catalan, chinese, czech ( partial ), danish, dutch, english, estonian, finnish, french, german, greek ancient ( partial ), greek modern, hebrew ( fragments ), hindi, hungarian ( partial ), interlingua, italian, japanese, korean ( partial ), latin ( partial ), latvian, maltese, mongolian, nepali, norwegian bokmal, norwegian nynorsk, persian, polish, punjabi, romanian, russian, sindhi, slovak ( partial ), slovene ( partial ), somali ( partial ), spanish, swahili ( fragments ), swedish, thai, turkish ( fragments ), and urdu. in addition, 14 languages have wordnet lexicon and large - scale parsing extensions. a full api documentation of the library can be found at the rgl synopsis page. the rgl status document gives the languages currently available in the gf resource grammar library, including their maturity.


( the exception to this is when the first digit is negative one and the next two digits are one, like 1111. 001 = 1. 001. ) this can be converted to the negative of a base - φ representation by negating every digit, standardizing the result, and then marking it as negative. for example, use a minus sign, or some other significance to denote negative numbers.


for k = 1 { \ displaystyle k = 1 } the latter statement can be re - formulated as the # 2 { \ displaystyle _ { 2 } } p - completeness of computing, for a given unitary n×n - matrix u { \ displaystyle u } over a field of characteristic 2, the n×n - matrix h ( u ) { \ displaystyle h ( u ) } whose i, j - th entry is the hamiltonian cycle polynomial of a matrix received from u { \ displaystyle u } via subjecting its rows and columns to any permutation mapping j to 1 and i to 2 and then removing its 1 - st row and 2 - nd column ( i. e. the sum of the products of the arc weights of the corresponding weighted digraph's hamiltonian paths from vertex i to vertex j ) for i = j and zero for i = j. this matrix satisfies the matrix equation u ( h ( u ) ) t = h ( u ) u t { \ displaystyle u ( h ( u ) ) ^ { t } = h ( u ) u ^ { t } }, while ham ( u u a a t 1 ) = ( a 1 2 +..


in public policy, access control to restrict access to systems ( " authorization " ) or to track or monitor behavior within systems ( " accountability " ) is an implementation feature of using trusted systems for security or social control.


in reduced - circumference polar coordinates the spatial metric has the form d σ 2 = d r 2 1 − k r 2 + r 2 d ω 2, where d ω 2 = d θ 2 + sin 2 θ d 2. { \ displaystyle \ mathrm { d } \ mathbf { \ sigma } ^ { 2 } = { \ frac { \ mathrm { d } r ^ { 2 } } { 1 - kr ^ { 2 } } } + r ^ { 2 } \ mathrm { d } \ mathbf { \ omega } ^ { 2 }, \ quad { \ text { where } } \ mathrm { d } \ mathbf { \ omega } ^ { 2 } = \ mathrm { d } \ theta ^ { 2 } + \ sin ^ { 2 } \ theta \, \ mathrm { d } \ phi ^ { 2 }. } k is a constant representing the curvature of the space. there are two common unit conventions : k may be taken to have units of length−2, in which case r has units of length and a ( t ) is unitless.


in the er model, the network generated is homogeneous, meaning each node has the same number of links. this is considered to be an exponential network. when comparing the connectivity of the er model when it undergoes random failures vs directed attacks, we are shown that the exponential network reacts the same way to a random failure as it does to a directed attack. this is due to the homogeneity of the network, making it so that it does not matter whether a random node is selected or one is specifically targeted.


in probability theory, an f { \ displaystyle f } - divergence is a function d f ( p ‖ q ) { \ displaystyle d _ { f } ( p \ | q ) } that measures the difference between two probability distributions p { \ displaystyle p } and q { \ displaystyle q }. many common divergences, such as kl - divergence, hellinger distance, and total variation distance, are special cases of f { \ displaystyle f } - divergence.


pr ( s ) { \ displaystyle \ pr ( s ) } can again be taken equal to 0. 5, to avoid being too suspicious about incoming email. 3 is a good value for s, meaning that the learned corpus must contain more than 3 messages with that word to put more confidence in the spamicity value than in the default value. this formula can be extended to the case where n is equal to zero ( and where the spamicity is not defined ), and evaluates in this case to p r ( s ) { \ displaystyle pr ( s ) }.


in most - idle hunting, calls are always delivered to whichever line has been idle the longest. this considers the length of time that the calltaker has been busy versus available. this is typically used in call centers where the calls are being answered by people, to distribute the load evenly.


in statistical inference, the conditional probability is an update of the probability of an event based on new information. the new information can be incorporated as follows : let a, the event of interest, be in the sample space, say ( x, p ). the occurrence of the event a knowing that event b has or will have occurred, means the occurrence of a as it is restricted to b, i. e. a ∩ b { \ displaystyle a \ cap b }. without the knowledge of the occurrence of b, the information about the occurrence of a would simply be p ( a ) the probability of a knowing that event b has or will have occurred, will be the probability of a ∩ b { \ displaystyle a \ cap b } relative to p ( b ), the probability that b has occurred.


in the following transcriptions, diacritics may be used to distinguish between apical and laminal. the commonality of cross - linguistically is 2 % in a phonological analysis of 2155 languages


if the paging unit is enabled, addresses in a segment are now virtual addresses, rather than physical addresses as they were on the 80286. that is, the segment starting address, the offset, and the final 32 - bit address the segmentation unit derived by adding the two are all virtual ( or logical ) addresses when the paging unit is enabled. when the segmentation unit generates and validates these 32 - bit virtual addresses, the enabled paging unit finally translates these virtual addresses into physical addresses.


the compounding corresponds to a polya urn scheme. it is frequently encountered in bayesian statistics, machine learning, empirical bayes methods and classical statistics as an overdispersed multinomial distribution. it reduces to the categorical distribution as a special case when n = 1. it also approximates the multinomial distribution arbitrarily well for large α. the dirichlet - multinomial is a multivariate extension of the beta - binomial distribution, as the multinomial and dirichlet distributions are multivariate versions of the binomial distribution and beta distributions, respectively.


the feedback vertex set problem has applications in vlsi chip design. another application is in complexity theory. some computational problems on graphs are np - hard in general, but can be solved in polynomial time for graphs with bounded fvs number. some examples are graph isomorphism and the path reconfiguration problem.


in mathematics, the characteristic of a ring r, often denoted char ( r ), is defined to be the smallest number of times one must use the ring's multiplicative identity ( 1 ) in a sum to get the additive identity ( 0 ). if this sum never reaches the additive identity the ring is said to have characteristic zero. that is, char ( r ) is the smallest positive number n such that : ( p 198, thm. 23. 14 ) 1 + + 1 n summands = 0 { \ displaystyle \ underbrace { 1 + \ cdots + 1 } _ { n { \ text { summands } } } = 0 } if such a number n exists, and 0 otherwise.


in mathematics, a negative number represents an opposite. in the real number system, a negative number is a number that is less than zero. negative numbers are often used to represent the magnitude of a loss or deficiency. a debt that is owed may be thought of as a negative asset.


in some languages, morphological features separate verbs based on their transitivity, which suggests this is a salient linguistic feature. for example, in japanese : however, the definition of transitive verbs as those with one object is not universal, and is not used in grammars of many languages.


bot accounts on twitter accelerate true and fake news at the same rate. misinformation spread by bots has been difficult for social media platforms to address.


an implementation vulnerable to sema attacks will perform a different operation depending on whether the bit of the key is 0 or 1, which will use different amounts of power and / or different chip components. this method is prevalent in many different types of side - channel attacks, in particular, power analysis attacks. thus, the attacker can observe the entire computation of encryption and can deduce the key.


in telecommunication, the term electromagnetic environment ( eme ) has the following meanings : for a telecommunications system, the spatial distribution of electromagnetic fields surrounding a given site. the electromagnetic environment may be expressed in terms of the spatial and temporal distribution of electric field strength ( volts per metre ), irradiance ( watts per square metre ), or energy density ( joules per cubic metre ). the resulting product of the power and time distribution, in various frequency ranges, of the radiated or conducted electromagnetic emission levels that may be encountered by a military force, system, or platform when performing its assigned mission in its intended operational environment. it is the sum of electromagnetic interference ; electromagnetic pulse ; hazards of electromagnetic radiation to personnel, ordnance, and volatile materials ; and natural phenomena effects of lightning and p - static. all electromagnetic phenomena observable in a given location.


in the fields of chemistry and cheminformatics, the circuit rank of a molecular graph ( the number of rings in the smallest set of smallest rings ) is sometimes referred to as the frerejacque number.


most mainstream statically - typed languages, such as c + +, c #, and java, are manifestly typed. complete type inference has traditionally been associated with functional languages such as haskell and ml. however, many manifestly - typed languages support partial type inference ; for example, c + +, java, and c # all infer types in certain limited cases.


in monolithic kernels, a driver can write to any word of memory and thus accidentally corrupt user programs. in minix 3, when a user expects data from, for example, the file system, it builds a descriptor telling who has access and at what addresses. it then passes an index to this descriptor to the file system, which may pass it to a driver. the file system or driver then asks the kernel to write via the descriptor, making it impossible for them to write to addresses outside the buffer.


in the it industry, deployment refers to post - sales process of guiding a client from purchase to use of the software or hardware that was purchased. this includes requirements analysis, scope analysis, customisations, systems integrations, user policies, user training and delivery. these steps are often overseen by a project manager using project management methodologies. software deployment involves several professionals that are relatively new to the knowledge based economy such as business analysts, software implementation specialists, solutions architects, and project managers.


in some applications, it is not sufficient to extract only one type of feature to obtain the relevant information from the image data. instead two or more different features are extracted, resulting in two or more feature descriptors at each image point. a common practice is to organize the information provided by all these descriptors as the elements of one single vector, commonly referred to as a feature vector.


in mathematics, an ordered semigroup is a semigroup ( s, • ) together with a partial order ≤ that is compatible with the semigroup operation, meaning that x ≤ y implies z • x ≤ z • y and x • z ≤ y • z for all x, y, z in s. an ordered monoid and an ordered group are, respectively, a monoid or a group that are endowed with a partial order that makes them ordered semigroups. the terms posemigroup, pogroup and pomonoid are sometimes used, where " po " is an abbreviation for " partially ordered ". the positive integers, the nonnegative integers and the integers form respectively a posemigroup, a pomonoid, and a pogroup under addition and the natural ordering. every semigroup can be considered as a posemigroup endowed with the trivial ( discrete ) partial order " = ". a morphism or homomorphism of posemigroups is a semigroup homomorphism that preserves the order ( equivalently, that is monotonically increasing ).


in mathematical optimization, a quadratically constrained quadratic program ( qcqp ) is an optimization problem in which both the objective function and the constraints are quadratic functions. it has the form minimize 1 2 x t p 0 x + q 0 t x subject to 1 2 x t p i x + q i t x + r i ≤ 0 for i = 1, …, m, a x = b, { \ displaystyle { \ begin { aligned } & { \ text { minimize } } & & { \ tfrac { 1 } { 2 } } x ^ { \ mathrm { t } } p _ { 0 } x + q _ { 0 } ^ { \ mathrm { t } } x \ \ & { \ text { subject to } } & & { \ tfrac { 1 } { 2 } } x ^ { \ mathrm { t } } p _ { i } x + q _ { i } ^ { \ mathrm { t } } x + r _ { i } \ leq 0 \ quad { \ text { for } } i = 1, \ dots, m, \ \ & & & ax = b, \ end { aligned } } } where p0, …, pm are n - by - n matrices and x ∈ rn is the optimization variable. if p0, …, pm are all positive semidefinite, then the problem is convex. if these matrices are neither positive nor negative semidefinite, the problem is non - convex. if p1, …, pm are all zero, then the constraints are in fact linear and the problem is a quadratic program.