the uml sequence diagram shows the run - time interactions. in this example, a mediator1 object mediates ( controls and coordinates ) the interaction between colleague1 and colleague2 objects. assuming that colleague1 wants to interact with colleague2 ( to update / synchronize its state, for example ), colleague1 calls mediate ( this ) on the mediator1 object, which gets the changed data from colleague1 and performs an action2 ( ) on colleague2. thereafter, colleague2 calls mediate ( this ) on the mediator1 object, which gets the changed data from colleague2 and performs an action1 ( ) on colleague1.


on the week of september 12, 2012, the song debuted at number seven on the top 20 digital tracks chart, based on nielsen soundscan data. the following week it topped the chart and spent four weeks at the top spot before giving the summit to " i knew you were trouble " by taylor swift. " gangnam style, " however, was back on top of the chart for the week of october 24, and grabbed the number one position for another four straight weeks, tallying a total of eight nonconsecutive weeks atop the chart. on november 16, 2012, the track was certified 4× platinum by music canada, and as of january 2013 had sold more than 476, 000 copies in the country.


in the bulgarian language the vowels а, ъ, о and е can be partially or fully reduced, depending on the dialect, when unstressed to,, and, respectively. the most prevalent is >, > and >, which, in its partial form, is considered correct in literary speech. the reduction > is prevalent in the eastern dialects of the language and is not considered formally correct.


in the context of information security, and especially network security, a spoofing attack is a situation in which a person or program successfully identifies as another by falsifying data, to gain an illegitimate advantage.


let g = per ( 3 ) { \ displaystyle g = { \ text { per } } ( 3 ) } be the permutation groups in three elements. let ρ : per ( 3 ) → gl 5 ( c ) { \ displaystyle \ rho : { \ text { per } } ( 3 ) \ to { \ text { gl } } _ { 5 } ( \ mathbb { c } ) } be a linear representation of per ( 3 ) { \ displaystyle { \ text { per } } ( 3 ) } defined on the generating elements as follows : ρ ( 1, 2 ) = ( − 1 2 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0 0 1 ), ρ ( 1, 3 ) = ( 1 2 1 2 0 0 0 1 2 − 1 0 0 0 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 ), ρ ( 2, 3 ) = ( 0 − 2 0 0 0 − 1 2 0 0 0 0 0 0 1 0 0 0 0 0 0 1 0 0 0 1 0 ). { \ displaystyle \ rho ( 1, 2 ) = { \ begin { pmatrix } - 1 & 2 & 0 & 0 & 0 \ \ 0 & 1 & 0 & 0 & 0 \ \ 0 & 0 & 0 & 1 & 0 \ \ 0 & 0 & 1 & 0 & 0 \ \ 0 & 0 & 0 & 0 & 1 \ end { pmatrix } }, \ quad \ rho ( 1, 3 ) = { \ begin { pmatrix } { \ frac { 1 } { 2 } } & { \ frac { 1 } { 2 } } & 0 & 0 & 0 \ \ { \ frac { 1 } { 2 } } & - 1 & 0 & 0 & 0 \ \ 0 & 0 & 0 & 0 & 1 \ \ 0 & 0 & 0 & 1 & 0 \ \ 0 & 0 & 1 & 0 & 0 \ end { pmatrix } }, \ quad \ rho ( 2, 3 ) = { \ begin { pmatrix } 0 & - 2 & 0 & 0 & 0 \ \ - { \ frac { 1 } { 2 } } & 0 & 0 & 0 & 0 \ \


thus, a { \ displaystyle { \ stackrel { \, \ longrightarrow } { a } } } ⋅ b { \ displaystyle { \ stackrel { \, \ longrightarrow } { b } } } = | a { \ displaystyle { \ stackrel { \, \ longrightarrow } { a } } } | | b { \ displaystyle { \ stackrel { \, \ longrightarrow } { b } } } | cos θmore generally, a bilinear product in an algebra over a field. cross product – also known as the " vector product ", a binary operation on two vectors that results in another vector. the cross product of two vectors in 3 - space is defined as the vector perpendicular to the plane determined by the two vectors whose magnitude is the product of the magnitudes of the two vectors and the sine of the angle between the two vectors.


2 ) multiple losses : x { \ displaystyle x } and y { \ displaystyle y } are both considered losses. here, we see that v a l u e ( − x ) + v a l u e ( − y ) < v a l u e ( − ( x + y ) ) { \ displaystyle value ( - x ) + value ( - y ) v a l u e ( x − y ) { \ displaystyle value ( x ) + value ( - y ) > value ( x - y ) }.


but one really requires average numbers. these average numbers can be obtained by the darwin – fowler method. of course, for systems in the thermodynamic limit ( large number of particles ), as in statistical mechanics, the results are the same as with maximization.


principle 3 : an audit trail or other record of all processes applied to digital evidence should be created and preserved. an independent third party should be able to examine those processes and achieve the same result. principle 4 : the person in charge of the investigation has overall responsibility for ensuring that the law and these principles are adhered to. these guidelines are widely accepted in courts of england and scotland, but they do not constitute a legal requirement and their use is voluntary. it is arguable that whilst voluntary, non adherence is almost certain to lead to the exclusion of evidence that does not comply subject to the provisions of s 78 police and criminal evidence act 1984 ( power to exclude evidence obtained unfairly )


this division requires quotient digit estimation and correction. the montgomery form, in contrast, depends on a constant r > n which is coprime to n, and the only division necessary in montgomery multiplication is division by r. the constant r can be chosen so that division by r is easy, significantly improving the speed of the algorithm. in practice, r is always a power of two, since division by powers of two can be implemented by bit shifting.


in matroid theory, a sylvester matroid is a matroid in which every pair of elements belongs to a three - element circuit ( a triangle ) of the matroid.


the equipment would descramble the signal so that it can be viewed by the subscriber. it also is addressable, meaning that it can be remotely controlled by the company's technical staff. the first major case covered by the media was when 317 subscribers were caught in 1991 when the company they subscribed sent a " bullet " ( a video signal that turns off the equipment ) to their cable boxes. the boxes were modified, but possibly belonged to the cable company.


therefore, the use of production means is scheduled in advance in order to respond to load profiles. the load corresponds to the total electricity consumption over the area of interest. load profiles are usually given by load forecasts which are of high accuracy.


accordingly, the subclass relation makes the collection of all classes into a boolean lattice, which the subset relation does not do for the collection of all sets. instead, the collection of all sets is an ideal in the collection of all classes. ( of course, the collection of all classes is something larger than even a class! ) = = references = =


in the area of mathematics known as semigroup theory, an e - semigroup is a semigroup in which the idempotents form a subsemigroup. certain classes of e - semigroups have been studied long before the more general class, in particular, a regular semigroup that is also an e - semigroup is known as an orthodox semigroup. weipoltshammer proved that the notion of weak inverse ( the existence of which is one way to define e - inversive semigroups ) can also be used to define / characterize e - semigroups as follows : a semigroup s is an e - semigroup if and only if, for all a and b ∈ s, w ( ab ) = w ( b ) w ( a ), where w ( a ) { x ∈ s | xax = x } is the set of weak inverses of a. = = references = =


russell and whitehead's notation for building up types from other types is rather cumbersome, and the notation here is due to church. in the ramified type theory of pm all objects are elements of various disjoint ramified types. ramified types are implicitly built up as follows.


each agent, in turn, claims any item that was not allocated to an agent with a higher priority ( " claims " means that the agent assigns " 1 " to the corresponding variable ). after an agent has assigned all its variables ( either 1 or 0 ), it sends the resulting assignment to the next agent in the lexicographic order. the agents send to each other messages with their envy evaluation of the current assignment. after receiving envy evaluations from other agents, the agent may decide to backtrack on a variable ; if there are no more variables to backtrack, the agent may backtrack to a previous agent. once the first agent backtracks its first variable, the search has ended and the optimal allocation has been found.


among other things, this may permit a single variable to refer to values of different types at different points in the program execution. however, type errors cannot be automatically detected until a piece of code is actually executed, potentially making debugging more difficult. lisp, smalltalk, perl, python, javascript, and ruby are all examples of dynamically - typed languages.


in a library supporting data structures, for example, a class modeling linear structures effects universal quantification with a function for _ all of type boolean that accepts an agent, an instance of function, as an argument. so, in the following example, my _ action is executed only if all members of my _ list contain the character '!


in number theory, a pillai prime is a prime number p for which there is an integer n > 0 such that the factorial of n is one less than a multiple of the prime, but the prime is not one more than a multiple of n. to put it algebraically, n! ≡ − 1 mod p { \ displaystyle n! \ equiv - 1 \ mod p } but p ≡ 1 mod n { \ displaystyle p \ not \ equiv 1 \ mod n }. the first few pillai primes are 23, 29, 59, 61, 67, 71, 79, 83, 109, 137, 139, 149, 193,... ( sequence a063980 in the oeis ) pillai primes are named after the mathematician subbayya sivasankaranarayana pillai, who studied these numbers. their infinitude has been proved several times, by subbarao, erdos, and hardy & subbarao.


to undo this, one adds 7 to the input, then divides the result by 5. therefore, the inverse of f is the function f − 1 : r → r { \ displaystyle f ^ { - 1 } \ colon \ mathbb { r } \ to \ mathbb { r } } defined by f − 1 ( y ) = y + 7 5. { \ displaystyle f ^ { - 1 } ( y ) = { \ frac { y + 7 } { 5 } }. }


in the above example, the result of applying the schensted insertion to successively insert 1, 3, 3, 2, 2, 1, 2 into an initially empty tableau results in a tableau p, and an additional standard tableau q0 recoding the successive shapes, given by p = 1 1 2 2 2 3 3, q 0 = 1 2 3 7 4 5 6, { \ displaystyle p \ quad = \ quad { \ begin { matrix } 1 & 1 & 2 & 2 \ \ 2 & 3 \ \ 3 \ end { matrix } }, \ qquad q _ { 0 } \ quad = \ quad { \ begin { matrix } 1 & 2 & 3 & 7 \ \ 4 & 5 \ \ 6 \ end { matrix } }, } and after replacing the entries 1, 2, 3, 4, 5, 6, 7 in q0 successively by 1, 1, 1, 2, 2, 3, 3 one obtains the pair of semistandard tableaux p = 1 1 2 2 2 3 3, q = 1 1 1 3 2 2 3. { \ displaystyle p \ quad = \ quad { \ begin { matrix } 1 & 1 & 2 & 2 \ \ 2 & 3 \ \ 3 \ end { matrix } }, \ qquad q \ quad = \ quad { \ begin { matrix } 1 & 1 & 1 & 3 \ \ 2 & 2 \ \ 3 \ end { matrix } }. }


quantitative pcr, however, offers an accurate and rapid alternative to traditional pcr. quantitative pcr offers the researcher the opportunity to amplify and analyze the product in a single tube using fluorescent dyes. this is known as homogeneous pcr.


traditional approaches in statistical physics studied the limit of intensive properties as the size of a finite system approaches infinity ( the thermodynamic limit ). when the energy function can be written as a sum of terms that each involve only variables from a finite subsystem, the notion of a gibbs measure provides an alternative approach. gibbs measures were proposed by probability theorists such as dobrushin, lanford, and ruelle and provided a framework to directly study infinite systems, instead of taking the limit of finite systems.


in mathematics, for example in the study of statistical properties of graphs, a null model is a type of random object that matches one specific object in some of its features, or more generally satisfies a collection of constraints, but which is otherwise taken to be an unbiasedly random structure. the null model is used as a term of comparison, to verify whether the object in question displays some non - trivial features ( properties that wouldn't be expected on the basis of chance alone or as a consequence of the constraints ), such as community structure in graphs. an appropriate null model behaves in accordance with a reasonable null hypothesis for the behavior of the system under investigation. one null model of utility in the study of complex networks is that proposed by newman and girvan, consisting of a randomized version of an original graph g { \ displaystyle g }, produced through edges being rewired at random, under the constraint that the expected degree of each vertex matches the degree of the vertex in the original graph. the null model is the basic concept behind the definition of modularity, a function which evaluates the goodness of partitions of a graph into clusters.


in most jurisdictions, prison inmates are forbidden from possessing mobile phones due to their ability to communicate with the outside world and other security issues. mobile phones are one of the most smuggled items into prisons. they provide inmates the ability to make and receive unauthorized phone calls, send email and text messages, use social media, and follow news pertaining to their case, among other forbidden uses.


the generic algorithm has a strongly polynomial o ( v 2e ) time complexity, which is asymptotically more efficient than the o ( ve 2 ) edmonds – karp algorithm. specific variants of the algorithms achieve even lower time complexities. the variant based on the highest label node selection rule has o ( v 2√e ) time complexity and is generally regarded as the benchmark for maximum flow algorithms. subcubic o ( velog ( v 2 / e ) ) time complexity can be achieved using dynamic trees, although in practice it is less efficient. the push – relabel algorithm has been extended to compute minimum cost flows. the idea of distance labels has led to a more efficient augmenting path algorithm, which in turn can be incorporated back into the push – relabel algorithm to create a variant with even higher empirical performance.


there are several different ways to express reciprocity laws. the early reciprocity laws found in the 19th century were usually expressed in terms of a power residue symbol ( p / q ) generalizing the quadratic reciprocity symbol, that describes when a prime number is an nth power residue modulo another prime, and gave a relation between ( p / q ) and ( q / p ). hilbert reformulated the reciprocity laws as saying that a product over p of hilbert norm residue symbols ( a, b / p ), taking values in roots of unity, is equal to 1.


the first five examples are in fact birationally equivalent. that is, for example, a cubic surface has a function field isomorphic to that of the projective plane, being the rational functions in two indeterminates. the cartesian product of two curves also provides examples.


in some computers, the machine code of the architecture is implemented by an even more fundamental underlying layer called microcode, providing a common machine language interface across a line or family of different models of computer with widely different underlying dataflows. this is done to facilitate porting of machine language programs between different models. an example of this use is the ibm system / 360 family of computers and their successors.


instead, virtual memory pages in both processes may refer to the same pages of physical memory until one of them writes to such a page : then it is copied. this optimization is important in the common case where fork is used in conjunction with exec to execute a new program : typically, the child process performs only a small set of actions before it ceases execution of its program in favour of the program to be started, and it requires very few, if any, of its parent's data structures.


files ( or links to files ) can be located in directories. however, more generally, a directory can contain either a list of files or a list of links to files. within this definition, it is of paramount importance that the term " file " includes directories.


but notice that if we are given a particular subset, we can efficiently verify whether the subset sum is zero, by summing the integers of the subset. if the sum is zero, that subset is a proof or witness for the answer is " yes ". an algorithm that verifies whether a given subset has sum zero is a verifier.


{ \ displaystyle \ sum _ { k = 0 } ^ { \ infty } \ left | \ pr ( s _ { n } = k ) - { \ lambda _ { n } ^ { k } e ^ { - \ lambda _ { n } } \ over k! } \ right | < 2 \ left ( 1 \ wedge { \ frac { 1 } { \ lambda } } _ { n } \ right ) \ left ( \ sum _ { i = 1 } ^ { n } p _ { i } ^ { 2 } \ right ). }, where ∧ { \ displaystyle \ wedge } represents the min { \ displaystyle \ min } operator. it is also possible to weaken the independence requirement.


in probability theory, a tree diagram may be used to represent a probability space. a tree diagram may represent a series of independent events ( such as a set of coin flips ) or conditional probabilities ( such as drawing cards from a deck, without replacing the cards ). each node on the diagram represents an event and is associated with the probability of that event. the root node represents the certain event and therefore has probability 1.


in telecommunications, structured cabling is building or campus cabling infrastructure that consists of a number of standardized smaller elements ( hence structured ) called subsystems. structured cabling components include twisted pair and optical cabling, patch panels and patch cables.


it is a decentralized, distributed, self - organizing network of individual fusion centers and their respective partners within each center's area of responsibility. the process is a method of managing the flow of information and intelligence across levels and sectors of government to integrate information for analysis. fusion centers rely on the active involvement of state, local, tribal, and federal law enforcement agencies — and sometimes on non – law enforcement agencies — to provide intelligence for their analysis.


the function sscg ( k ) denotes that length for simple subcubic graphs. the function scg ( k ) denotes that length for ( general ) subcubic graphs. the scg sequence begins scg ( 0 ) = 6, but then explodes to a value equivalent to fε2 * 2 in the fast - growing hierarchy.


in pure mathematics, there are several notational methods for representing large numbers by which the magnitude of a googolplex could be represented, such as tetration, hyperoperation, knuth's up - arrow notation, steinhaus – moser notation, or conway chained arrow notation.


therefore, we can see how important guard digits can be. an example of the error caused by floating point roundoff is illustrated in the following c code. it appears that the program should not terminate.


to " measure " is to place a shorter measuring length s successively ( q times ) along longer length l until the remaining portion r is less than the shorter length s. in modern words, remainder r = l − q×s, q being the quotient, or remainder r is the " modulus ", the integer - fractional part left over after the division. for euclid's method to succeed, the starting lengths must satisfy two requirements : ( i ) the lengths must not be zero, and ( ii ) the subtraction must be " proper " ; i. e., a test must guarantee that the smaller of the two numbers is subtracted from the larger ( or the two can be equal so their subtraction yields zero ). euclid's original proof adds a third requirement : the two lengths must not be prime to one another. euclid stipulated this so that he could construct a reductio ad absurdum proof that the two numbers'common measure is in fact the greatest. while nicomachus'algorithm is the same as euclid's, when the numbers are prime to one another, it yields the number " 1 " for their common measure. so, to be precise, the following is really nicomachus'algorithm.


in mathematical optimization, the klee – minty cube is an example that shows the worst - case computational complexity of many algorithms of linear optimization. it is a deformed cube with exactly 2d corners in dimension d. klee and minty showed that dantzig's simplex algorithm visits all corners of a ( perturbed ) cube in dimension d in the worst case. modifications of the klee – minty construction showed similar exponential time complexity for other pivoting rules of simplex type, which maintain primal feasibility, such as bland's rule. another modification showed that the criss - cross algorithm, which does not maintain primal feasibility, also visits all the corners of a modified klee – minty cube. like the simplex algorithm, the criss - cross algorithm visits all 8 corners of the three - dimensional cube in the worst case.


in software development xrx is a web application architecture based on xforms, rest and xquery. xrx applications store data on both the web client and on the web server in xml format and do not require a translation between data formats. xrx is considered a simple and elegant application architecture due to the minimal number of translations needed to transport data between client and server systems. the xrx architecture is also tightly coupled to w3c standards ( css, xhtml 2. 0, xpath, xml schema ) to ensure xrx applications will be robust in the future. because xrx applications leverage modern declarative languages on the client and functional languages on the server they are designed to empower non - developers who are not familiar with traditional imperative languages such as javascript, java or. net.


however, in 2003, alexander ol'shanskii and mark sapir exhibited a collection of finitely - presented groups which do not satisfy the conjecture. in 2013, nicolas monod found an easy counterexample to the conjecture. given by piecewise projective homeomorphisms of the line, the group is remarkably simple to understand.


in modern x11 systems ( or utilities such as wincompose on windows systems ), the double acute can be typed by pressing the compose key followed by = ( the equal sign ) and desired letter ( o or u ).


in software engineering, profiling ( " program profiling ", " software profiling " ) is a form of dynamic program analysis that measures, for example, the space ( memory ) or time complexity of a program, the usage of particular instructions, or the frequency and duration of function calls. most commonly, profiling information serves to aid program optimization, and more specifically, performance engineering. profiling is achieved by instrumenting either the program source code or its binary executable form using a tool called a profiler ( or code profiler ). profilers may use a number of different techniques, such as event - based, statistical, instrumented, and simulation methods.


in the field of digital and interactive television, nested context language ( ncl ) is a declarative authoring language for hypermedia documents. ncl documents do not contain multimedia elements such as audio or video content ; rather they function as a " glue " language that specifies how multimedia components are related. in particular, ncl documents specify how these components are synchronized relative to each other and how the components are composed together into a unified document. among its main facilities, it treats hypermedia relations as first - class entities through the definition of hypermedia connectors, and it can specify arbitrary semantics for a hypermedia composition using the concept of composite templates.


consider a sequence { a k } { \ displaystyle \ { \ mathbf { a } _ { k } \ } } of fixed self - adjoint matrices that satisfy ( h ( z 1, …, z k, …, z n ) − h ( z 1, …, z k ′, …, z n ) ) 2 a k 2, { \ displaystyle \ left ( \ mathbf { h } ( z _ { 1 }, \ ldots, z _ { k }, \ ldots, z _ { n } ) - \ mathbf { h } ( z _ { 1 }, \ ldots, z'_ { k }, \ ldots, z _ { n } ) \ right ) ^ { 2 } \ preceq \ mathbf { a } _ { k } ^ { 2 }, } where z i { \ displaystyle z _ { i } } and z i ′ { \ displaystyle z'_ { i } } range over all possible values of z i { \ displaystyle z _ { i } } for each index i { \ displaystyle i }. compute the variance parameter σ 2 = ‖ k a k 2 ‖. { \ displaystyle \ sigma ^ { 2 } = { \ bigg \ vert } \ sum _ { k } \ mathbf { a } _ { k } ^ { 2 } { \ bigg \ vert }. }


as indicated by the accent marks, the stress is always on the last syllable, which is unlike the dative - case forms with the same spelling. a few feminine nouns that end with the soft sign, such as дверь and пыль, also have a locative form that differs from the prepositional in that the stress shifts to the final syllable : " на двери ", na dveri ( " on the door " ), but " при двери ", pri dveri ( " by the door " ). these distinct feminine forms are sometimes referenced as " second locative " or " new locative ", because they developed independently from the true locative case, which existed in old russian. with some words, such as дом, dom ( house ), the second locative form is used only in certain idiomatic expressions, while the prepositional is used elsewhere. for example, " на дому ", na domu ( " at the house " or " at home " ) would be used to describe activity that is performed at home, while " на доме " ( " on the house " ) would be used to specify the location of the roof.


from this principle the error rules of summation, multiplication etc. are derived, e. g. : that is to say, in multiplication, the total relative error is the sum of the relative errors of the parameters. to illustrate how this depends on the function considered, consider the case where the function is f ( a, b ) = a ln b { \ displaystyle f ( a, b ) = a \ ln b } instead. then, it can be computed that the error estimate is with an extra'ln b'factor not found in the case of a simple product. this additional factor tends to make the error smaller, as ln b is not as large as a bare b.


in other scenarios, a dispatched object immediately loses its full or partial value, if a certain number of consumers ca have already received the object. in a function, the ordinate value takes on zero, if value x representing cn, has received the value. it draws a dramatic knee on the function's graph. this scenario is prevalent.


in number theory, a probable prime ( prp ) is an integer that satisfies a specific condition that is satisfied by all prime numbers, but which is not satisfied by most composite numbers. different types of probable primes have different specific conditions. while there may be probable primes that are composite ( called pseudoprimes ), the condition is generally chosen in order to make such exceptions rare. fermat's test for compositeness, which is based on fermat's little theorem, works as follows : given an integer n, choose some integer a that is not a multiple of n ; ( typically, we choose a in the range 1 < a < n − 1 ).


in statistics, the weighted geometric mean is a generalization of the geometric mean using the weighted arithmetic mean. given a sample x = ( x 1, x 2 …, x n ) { \ displaystyle x = ( x _ { 1 }, x _ { 2 } \ dots, x _ { n } ) } and weights w = ( w 1, w 2, …, w n ) { \ displaystyle w = ( w _ { 1 }, w _ { 2 }, \ dots, w _ { n } ) }, it is calculated as : x = ( i = 1 n x i w i ) 1 / i = 1 n w i = exp ( i = 1 n w i ln x i i = 1 n w i ) { \ displaystyle { \ bar { x } } = \ left ( \ prod _ { i = 1 } ^ { n } x _ { i } ^ { w _ { i } } \ right ) ^ { 1 / \ sum _ { i = 1 } ^ { n } w _ { i } } = \ quad \ exp \ left ( { \ frac { \ sum _ { i = 1 } ^ { n } w _ { i } \ ln x _ { i } } { \ sum _ { i = 1 } ^ { n } w _ { i } \ quad } } \ right ) } the second form above illustrates that the logarithm of the geometric mean is the weighted arithmetic mean of the logarithms of the individual values. if all the weights are equal, the weighted geometric mean simplifies to the ordinary unweighted geometric mean.


without knowledge of the pepper, other passwords in the database will be far more difficult to extract from their hashed values, as the attacker would need to guess the password as well as the pepper. a pepper adds security to a database of salts and hashes because unless the attacker is able to obtain the pepper, cracking even a single hash is intractable, no matter how weak the original password. even with a list of ( salt, hash ) pairs, an attacker must also guess the secret pepper in order to find the password which produces the hash. the nist specification for a secret salt suggests using a password - based key derivation function ( pbkdf ) with an approved pseudorandom function such as hmac with sha - 3 as the hash function of the hmac. the nist recommendation is also to perform at least 1000 iterations of the pbkdf, and a further minimum 1000 iterations using the secret salt in place of the non - secret salt.


formally, a vertex conflict happens when π i = π j { \ displaystyle \ pi _ { i } = \ pi _ { j } }. edge conflict : an edge conflict occurs whenever two agents cross the same edge in the same direction at the same time, that is π i = π j { \ displaystyle \ pi _ { i } = \ pi _ { j } } and π i = π j { \ displaystyle \ pi _ { i } = \ pi _ { j } }. if vertex conflicts are not allowed, then edge conflicts cannot exist.


the hits computation is performed only on this focused subgraph. according to kleinberg the reason for constructing a base set is to ensure that most ( or many ) of the strongest authorities are included. authority and hub values are defined in terms of one another in a mutual recursion.


a stochastic process { z n, n = 1, 2, … } { \ displaystyle \ { z _ { n }, n = 1, 2, \ ldots \ } } is said to be a threshold geometric process ( threshold gp ), if there exists real numbers a i > 0, i = 1, 2, …, k { \ displaystyle a _ { i } > 0, i = 1, 2, \ ldots, k } and integers { 1 = m 1 < m 2 < < m k < m k + 1 = ∞ } { \ displaystyle \ { 1 = m _ { 1 } 0 { \ displaystyle h ( k ) > 0 } for natural number k { \ displaystyle k }, then { x k, k = 1, 2, … } { \ displaystyle \ { x _ { k }, k = 1, 2, \ ldots \ } } is called a doubly geometric process ( dgp ). the semi - geometric process. given a sequence of non - negative random variables { x k, k = 1, 2, … } { \ displaystyle \ { x _ { k }, k = 1, 2, \ dots \ } }, if p { x k < x | x k − 1 = x k − 1, …, x 1 = x 1 } = p { x k < x | x k − 1 = x k − 1 } { \ displaystyle p \ { x _ { k }


0 7 2 9 4 11 6 1 8 3 10 5 ( 0 + 0 5 10 3 8 1 6 11 4 9 2 7 ( 0 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ = 0 0 0 0 0 0 0 0 0 0 0 0 ( 0 the two cycles may also be aligned as pairs of sum 7 or sum 5 dyads. all together these pairs of cycles form a set complex, " any cyclic set of the set complex may be uniquely identified by its two adjacency sums, " and as such the example above shows p0p7 and i5i0. = = references = =


in neuroscience, predictive coding ( also known as predictive processing ) is a theory of brain function which postulates that the brain is constantly generating and updating a " mental model " of the environment. according to the theory, such a mental model is used to predict input signals from the senses that are then compared with the actual input signals from those senses. with the rising popularity of representation learning, the theory is being actively pursued and applied in machine learning and related fields. the phrase'predictive coding'is also used in several other disciplines such as signal - processing technologies and law in loosely - related or unrelated senses.


( reflexivity ). ( here, id { \ displaystyle \ operatorname { id } } denotes the identity function on x { \ displaystyle x }. ) r = r − 1 { \ displaystyle r = r ^ { - 1 } } ( symmetry ). r r ⊆ r { \ displaystyle rr \ subseteq r } ( transitivity ).


in relation to audiovisual content, according to the meaning given by the canadian radio - television and telecommunications commission ( crtc ) for the purpose of its 2016 discoverability summit, discoverability can be summed up to the intrinsic ability of given content to " stand out of the lot ", or to position itself so as to be easily found and discovered. a piece of audiovisual content can be a movie, a tv series, music, a book ( ebook ), an audio book or podcast. when audiovisual content such as a digital file for a tv show, movie, or song, is made available online, if the content is " tagged " with identifying information such as the names of the key artists ( e. g., actors, directors and screenwriters for tv shows and movies ; singers, musicians and record producers for songs ) and the genres ( for movies genres, music genres, etc. ). when users interact with online content, algorithms typically determine what types of content the user is interested in, and then a computer program suggests " more like this ", which is other content that the user may be interested in.


in standard nmf, matrix factor w ∈ r + m × k ， i. e., w can be anything in that space. convex nmf restricts the columns of w to convex combinations of the input data vectors ( v 1, …, v n ) { \ displaystyle ( v _ { 1 }, \ dots, v _ { n } ) }. this greatly improves the quality of data representation of w. furthermore, the resulting matrix factor h becomes more sparse and orthogonal.


in the computer era, spacing between sentences is handled in several different ways by various software packages. some systems accept whatever the user types, while others attempt to alter the spacing or use the user input as a method of detecting sentences. computer - based word processors and typesetting software such as troff and tex allow users to arrange text in a manner previously only available to professional typesetters. the text - editing environment in emacs uses a double space following a period to identify the end of sentences unambiguously ; the double - space convention prevents confusion with periods within sentences that signify abbreviations. how emacs recognizes the end of a sentence is controlled by the settings sentence - end - double - space and sentence - end. the unix typesetter program troff uses two spaces to mark the end of a sentence.


in mathematics there is a close link between map coloring and graph coloring, since every map showing different areas has a corresponding graph. by far the most famous result in this area is the four color theorem, which states that any planar map can be colored with at most four colors.


in order to preserve the precise meaning and enable accurate parsing of complex udc expressions, a number of connecting symbols are made available to relate and extend udc numbers. these are :


the item - and - process and word - and - paradigm approaches usually address fusional languages. as there is very little fusion involved in word formation, classical typology mostly applies to inflectional morphology. depending on the preferred way of expressing non - inflectional notions, languages may be classified as synthetic ( using word formation ) or analytic ( using syntactic phrases ).


in mathematics, the fourier transform on finite groups is a generalization of the discrete fourier transform from cyclic to arbitrary finite groups.


lucky numbers share some properties with primes, such as asymptotic behaviour according to the prime number theorem ; also, a version of goldbach's conjecture has been extended to them. there are infinitely many lucky numbers. twin lucky numbers and twin primes also appear to occur with similar frequency. however, if ln denotes the n - th lucky number, and pn the n - th prime, then ln > pn for all sufficiently large n. because of their apparent similarities with the prime numbers, some mathematicians have suggested that some of their common properties may also be found in other sets of numbers generated by sieves of a certain unknown form, but there is little theoretical basis for this conjecture.


in the binary tree representation, a successful search can be represented by a path from the root to the target node, called an internal path. the length of a path is the number of edges ( connections between nodes ) that the path passes through. the number of iterations performed by a search, given that the corresponding path has length l { \ displaystyle l }, is l + 1 { \ displaystyle l + 1 } counting the initial iteration. the internal path length is the sum of the lengths of all unique internal paths.


it has been conjectured that infinitely many wilson primes exist, and that the number of wilson primes in an interval { \ displaystyle } is about log log x y { \ displaystyle \ log \ log _ { x } y }. several computer searches have been done in the hope of finding new wilson primes. the ibercivis distributed computing project includes a search for wilson primes. another search was coordinated at the great internet mersenne prime search forum.


in mathematics and theoretical physics, a large diffeomorphism is an equivalence class of diffeomorphisms under the equivalence relation where diffeomorphisms that can be continuously connected to each other are in the same equivalence class. for example, a two - dimensional real torus has a sl ( 2, z ) group of large diffeomorphisms by which the one - cycles a, b { \ displaystyle a, b } of the torus are transformed into their integer linear combinations. this group of large diffeomorphisms is called the modular group. more generally, for a surface s, the structure of self - homeomorphisms up to homotopy is known as the mapping class group. it is known ( for compact, orientable s ) that this is isomorphic with the automorphism group of the fundamental group of s. this is consistent with the genus 1 case, stated above, if one takes into account that then the fundamental group is z2, on which the modular group acts as automorphisms ( as a subgroup of index 2 in all automorphisms, since the orientation may also be reverse, by a transformation with determinant −1 ).


the book the art of the metaobject protocol explains the implementation and use of clos generic functions in detail. one of the early object - oriented programming extensions to lisp is flavors. it used the usual message sending paradigm influenced by smalltalk.


the analysis, which is written in the experimental protocol before the experiment is conducted, is examined in grant applications and administrative review boards. besides the power analysis, there are less formal methods for selecting the number of experimental units. these include graphical methods based on limiting the probability of false negative errors, graphical methods based on an expected variation increase ( above the residuals ) and methods based on achieving a desired confidence interval.


in systems as multiprocessor system, multi - core and numa system, where a dedicated cache for each processor, core or node is used, a consistency problem may occur when a same data is stored in more than one cache. this problem arises when a data is modified in one cache. this problem can be solved in two ways : invalidate all the copies on other caches ( broadcast - invalidate ) update all the copies on other caches ( write - broadcasting ), while the memory may be updated ( write through ) or not updated ( write - back ). note : coherency generally applies only to data ( as operands ) and not to instructions ( see self - modifying code ). the schemes can be classified based on : snoopy scheme vs directory scheme and vs shared caches write through vs write - back ( ownership - based ) protocol update vs invalidation protocol intervention vs not intervention dirty - sharing vs not - dirty - sharing protocol ( moesi vs mesi ) three approaches are adopted to maintain the coherency of data. bus watching or snooping – generally used for bus - based smp – symmetric multiprocessor system / multi - core systems directory - based – message - passing – may be used in all systems but typically in numa system and in large multi - core systems shared cache – generally used in multi - core systems


in mathematics, the nth taxicab number, typically denoted ta ( n ) or taxicab ( n ), also called the nth ramanujan – hardy number, is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. the most famous taxicab number is 1729 = ta ( 2 ) = 13 + 123 = 93 + 103. the name is derived from a conversation in about 1919 involving mathematicians g. h. hardy and srinivasa ramanujan.


invertibility : for every permutation π ∈ s n { \ displaystyle \ pi \ in s _ { n } }, there exists an inverse permutation π − 1 ∈ s n { \ displaystyle \ pi ^ { - 1 } \ in s _ { n } }, so that π π − 1 = π − 1 π = id. { \ displaystyle \ pi \ pi ^ { - 1 } = \ pi ^ { - 1 } \ pi = \ operatorname { id }. } in general, composition of two permutations is not commutative, that is, π σ = σ π.


it relies on k - mer graphs, which performs well with vast quantities of short reads. greedy graph - based approach, which may also use one of the olc or dbg approaches.


in the early days of the development of k - triviality, attention was paid to separation of k - trivial sets and computable sets. chaitin in his 1976 paper mainly studied sets such that there exists b ∈ n { \ displaystyle \ mathbb { n } } with n c ( a n ) ≤ c ( n ) + b { \ displaystyle \ forall nc ( a \ upharpoonright n ) \ leq c ( n ) + b } where c denotes the plain kolmogorov complexity. these sets are known as c - trivial sets. chaitin showed they coincide with the computable sets.


: 201 - 202 : 1 - 2 several reasons were given for the choice of 31 bits instead of 32 bits : the desire to retain the high - order bit as a " control or escape bit. " : 201 in particular, the standard subroutine calling convention marked the final parameter word by setting its high bit.


in 1940 alonzo church ( re ) formulated it as simply typed lambda calculus. and examined by godel in 1944. a survey of these developments is found in collins ( 2012 ).


sweep and prune is also known as sort and sweep, referred to this way in david baraff's ph. d. thesis in 1992. later works like the 1995 paper about i - collide by jonathan d. cohen et al. refer to the algorithm as sweep and prune.


if a group is finite, then its coset enumeration must terminate eventually, although it may take arbitrarily long and use an arbitrary amount of memory, even if the group is trivial. depending on the algorithm used, it may happen that making small changes to the presentation that do not change the group nevertheless have a large impact on the amount of time or memory needed to complete the enumeration. these behaviours are a consequence of the unsolvability of the word problem for groups. a gentle introduction to coset enumeration is given in rotman's text on group theory. more detailed information on correctness, efficiency, and practical implementation can be found in the books by sims and holt et al. = = references = =


in the days of text mode computing, western characters were normally laid out in a grid on the screen, often 80 columns by 24 or 25 lines. each character was displayed as a small dot matrix, often about 8 pixels wide, and a sbcs ( single - byte character set ) was generally used to encode characters of western languages. for aesthetic reasons and readability, it is preferable for chinese characters to be approximately square - shaped, therefore twice as wide as these fixed - width sbcs characters. as these were typically encoded in a dbcs ( double - byte character set ), this also meant that their width on screen in a duospaced font was proportional to their byte length.


their work, known at the time as the ibm 801, eventually led to the risc ( reduced instruction set computing ) concept. microcode was removed, and only the most basic versions of any given instruction were put into the cpu. any more complex code was left to the compiler. the removal of so much circuitry, about 1⁄3 of the transistors in the motorola 68000 for instance, allowed the cpu to include more registers, which had a direct impact on performance. by the mid - 1980s, further developed versions of these basic concepts were delivering performance as much as 10 times that of the fastest cisc designs, in spite of using less - developed fabrication.


in software, an xml pipeline is formed when xml ( extensible markup language ) processes, especially xml transformations and xml validations, are connected. for instance, given two transformations t1 and t2, the two can be connected so that an input xml document is transformed by t1 and then the output of t1 is fed as input document to t2. simple pipelines like the one described above are called linear ; a single input document always goes through the same sequence of transformations to produce a single output document.


in mathematics, the hutchinson metric otherwise known as kantorovich metric is a function which measures " the discrepancy between two images for use in fractal image processing " and " can also be applied to describe the similarity between dna sequences expressed as real or complex genomic signals ".


in the gsm cellular mobile phone standard, timing advance ( ta ) value corresponds to the length of time a signal takes to reach the base station from a mobile phone. gsm uses tdma technology in the radio interface to share a single frequency between several users, assigning sequential timeslots to the individual users sharing a frequency. each user transmits periodically for less than one - eighth of the time within one of the eight timeslots. since the users are at various distances from the base station and radio waves travel at the finite speed of light, the precise arrival - time within the slot can be used by the base station to determine the distance to the mobile phone.


in the united states, a common newspaper column measurement is about 11 picas wide — about 1. 83 inches ( 46 mm ) — though this measure varies from paper to paper and in other countries. the examples in this article follow this assumption for illustrative purposes only.


in the context of this article, all graphs will be simple and undirected, unless stated otherwise. this means that the edges of the graph form a set ( and not a multiset ) and each edge is a pair of distinct vertices. graphs are assumed to have an implicit representation in which each vertex has a unique identifier or label and in which it is possible to test the adjacency of any two vertices, but for which adjacency testing is the only allowed primitive operation. informally, a graph property is a property of a graph that is independent of labeling.


in set theory, the kernel of a function f { \ displaystyle f } ( or equivalence kernel ) may be taken to be either the equivalence relation on the function's domain that roughly expresses the idea of " equivalent as far as the function f { \ displaystyle f } can tell ", or the corresponding partition of the domain. an unrelated notion is that of the kernel of a non - empty family of sets b, { \ displaystyle { \ mathcal { b } }, } which by definition is the intersection of all its elements : this definition is used in the theory of filters to classify them as being free or principal.


for example : the roots of numbers such as 10, 15, 20 which are not squares, the sides of numbers which are not cubes etc. " in contrast to euclid's concept of magnitudes as lines, al - mahani considered integers and fractions as rational magnitudes, and square roots and cube roots as irrational magnitudes. he also introduced an arithmetical approach to the concept of irrationality, as he attributes the following to irrational magnitudes : " their sums or differences, or results of their addition to a rational magnitude, or results of subtracting a magnitude of this kind from an irrational one, or of a rational magnitude from it. " the egyptian mathematician abu kamil shuja ibn aslam ( c.


in programming language theory, the associativity of an operator is a property that determines how operators of the same precedence are grouped in the absence of parentheses. if an operand is both preceded and followed by operators ( for example, ^ 3 ^ ), and those operators have equal precedence, then the operand may be used as input to two different operations ( i. e. the two operations indicated by the two operators ). the choice of which operations to apply the operand to, is determined by the associativity of the operators. operators may be associative ( meaning the operations can be grouped arbitrarily ), left - associative ( meaning the operations are grouped from the left ), right - associative ( meaning the operations are grouped from the right ) or non - associative ( meaning operations cannot be chained, often because the output type is incompatible with the input types ).


while the continuity assumption is usually met, the compactness assumption about the parameter space is often not, as the bounds of the true parameter values might be unknown. in that case, concavity of the likelihood function plays a key role. more specifically, if the likelihood function is twice continuously differentiable on the k - dimensional parameter space θ { \ displaystyle \ theta } assumed to be an open connected subset of r k, { \ displaystyle \ mathbb { r } ^ { k } \,, } there exists a unique maximum θ ^ ∈ θ { \ displaystyle { \ hat { \ theta } } \ in \ theta } if the matrix of second partials is negative definite for every θ ∈ θ { \ displaystyle \, \ theta \ in \ theta \, } at which the gradient ∇ l ≡ i = 1 n i { \ displaystyle \ ; \ nabla l \ equiv \ left _ { i = 1 } ^ { n _ { \ mathrm { i } } } \ ; } vanishes, and if the likelihood function approaches a constant on the boundary of the parameter space, ∂ θ, { \ displaystyle \ ; \ partial \ theta \ ;, } i. e., which may include the points at infinity if θ { \ displaystyle \, \ theta \, } is unbounded.


in the bandwidth - limited regime ( ρ > 2 b / 2 d { \ displaystyle \ rho > 2 ~ b / 2d }, i. e. the domain of non - binary signaling ), the effective coding gain γ e f f ( a ) { \ displaystyle \ gamma _ { \ mathrm { eff } } ( a ) } of a signal set a { \ displaystyle a } at a given target error rate p s ( e ) { \ displaystyle p _ { s } ( e ) } is defined as the difference in db between the s n r n o r m { \ displaystyle snr _ { \ mathrm { norm } } } required to achieve the target p s ( e ) { \ displaystyle p _ { s } ( e ) } with a { \ displaystyle a } and the s n r n o r m { \ displaystyle snr _ { \ mathrm { norm } } } required to achieve the target p s ( e ) { \ displaystyle p _ { s } ( e ) } with m - pam or ( m×m ) - qam ( i. e. no coding ). the nominal coding gain γ c ( a ) { \ displaystyle \ gamma _ { c } ( a ) } is defined as γ c ( a ) = ( 2 ρ − 1 ) d min 2 ( a ) 6 e s. { \ displaystyle \ gamma _ { c } ( a ) = { ( 2 ^ { \ rho } - 1 ) d _ { \ min } ^ { 2 } ( a ) \ over 6e _ { s } }. } this definition is normalized so that γ c ( a ) = 1 { \ displaystyle \ gamma _ { c } ( a ) = 1 } for m - pam or ( m×m ) - qam. the ube becomes p s ( e ) ≈ k s ( a ) q 3 γ c ( a ) s n r n o r m, { \ displaystyle p _ { s } ( e ) \ approx k _ { s } ( a ) q { \ sqrt { 3 \ gamma _ { c } ( a ) snr _ { \ mathrm { norm } } } }, } where k s ( a ) { \ displaystyle k _ { s } ( a ) } is the average number of nearest neighbors per two dimensions.


it follows from zfc alone that π 1 1 { \ displaystyle { \ boldsymbol { \ pi } } _ { 1 } ^ { 1 } } and σ 2 1 { \ displaystyle { \ boldsymbol { \ sigma } } _ { 2 } ^ { 1 } } have the uniformization property. it follows from the existence of sufficient large cardinals that π 2 n + 1 1 { \ displaystyle { \ boldsymbol { \ pi } } _ { 2n + 1 } ^ { 1 } } and σ 2 n + 2 1 { \ displaystyle { \ boldsymbol { \ sigma } } _ { 2n + 2 } ^ { 1 } } have the uniformization property for every natural number n { \ displaystyle n }. therefore, the collection of projective sets has the uniformization property.


in multiple criteria decision aiding ( mcda ), multicriteria classification ( or sorting ) involves problems where a finite set of alternative actions should be assigned into a predefined set of preferentially ordered categories ( classes ). for example, credit analysts classify loan applications into risk categories ( e. g., acceptable / unacceptable applicants ), customers rate products and classify them into attractiveness groups, candidates for a job position are evaluated and their applications are approved or rejected, technical systems are prioritized for inspection on the basis of their failure risk, clinicians classify patients according to the extent to which they have a complex disease or not, etc.


in some n - ary groups there exists an element e ( called an n - ary identity or neutral element ) such that any string of n - elements consisting of all e's, apart from one place, is mapped to the element at that place. e. g., in a quaternary group with identity e, eeae = a for every a. an n - ary group containing a neutral element is reducible. thus, an n - ary group that is not reducible does not contain such elements.


in telephony, ringdown is a method of signaling an operator in which telephone ringing current is sent over the line to operate a lamp or cause the operation of a self - locking relay known as a drop. ringdown is used in manual operation, and is distinguished from automatic signaling by dialing a number. the signal consists of a continuous or pulsed alternating current ( ac ) signal transmitted over the line.


the process also involves taking geographic coordinates of the ground resolution cell with gps technology and comparing those with the coordinates of the " pixel " being studied provided by the remote sensing software to understand and analyze the location errors and how it may affect a particular study. ground truth is important in the initial supervised classification of an image. when the identity and location of land cover types are known through a combination of field work, maps, and personal experience these areas are known as training sites.


in superscalar designs, the number of execution units is invisible to the instruction set. each instruction encodes one operation only. for most superscalar designs, the instruction width is 32 bits or fewer. in contrast, one vliw instruction encodes multiple operations, at least one operation for each execution unit of a device.


in mathematics, a multiplicative character ( or linear character, or simply character ) on a group g is a group homomorphism from g to the multiplicative group of a field ( artin 1966 ), usually the field of complex numbers. if g is any group, then the set ch ( g ) of these morphisms forms an abelian group under pointwise multiplication. this group is referred to as the character group of g. sometimes only unitary characters are considered ( characters whose image is in the unit circle ) ; other such homomorphisms are then called quasi - characters.


in mathematics, dimension theory is the study in terms of commutative algebra of the notion dimension of an algebraic variety ( and by extension that of a scheme ). the need of a theory for such an apparently simple notion results from the existence of many definitions of dimension that are equivalent only in the most regular cases ( see dimension of an algebraic variety ). a large part of dimension theory consists in studying the conditions under which several dimensions are equal, and many important classes of commutative rings may be defined as the rings such that two dimensions are equal ; for example, a regular ring is a commutative ring such that the homological dimension is equal to the krull dimension. the theory is simpler for commutative rings that are finitely generated algebras over a field, which are also quotient rings of polynomial rings in a finite number of indeterminates over a field.


in probability theory, conditional probability is a measure of the probability of an event occurring, given that another event ( by assumption, presumption, assertion or evidence ) has already occurred. this particular method relies on event b occurring with some sort of relationship with another event a. in this event, the event b can be analyzed by a conditional probability with respect to a. if the event of interest is a and the event b is known or assumed to have occurred, " the conditional probability of a given b ", or " the probability of a under the condition b ", is usually written as p ( a | b ) or occasionally pb ( a ). this can also be understood as the fraction of probability b that intersects with a, or the ratio of the probabilities of both events happening to the " given " one happening ( how many times a occurs rather than not assuming b has occurred ) : p ( a b ) = p ( a ∩ b ) p ( b ) { \ displaystyle p ( a \ mid b ) = { \ frac { p ( a \ cap b ) } { p ( b ) } } }. for example, the probability that any given person has a cough on any given day may be only 5 %. but if we know or assume that the person is sick, then they are much more likely to be coughing.


in programming languages and type theory, a product of types is another, compounded, type in a structure. the " operands " of the product are types, and the structure of a product type is determined by the fixed order of the operands in the product. an instance of a product type retains the fixed order, but otherwise may contain all possible instances of its primitive data types. the expression of an instance of a product type will be a tuple, and is called a " tuple type " of expression.


in mathematics, a function between topological spaces is called proper if inverse images of compact subsets are compact. in algebraic geometry, the analogous concept is called a proper morphism.


in the context of the release 8 of 3gpp standards, vcc was replaced by a wider concept that covers all services provided by ims. this work resulted in the specification of ims service continuity and ims centralized services ( ics ), which are meant to be used in particular to provide the continuity of voice calls between lte and legacy 2g / 3g networks.


in signal processing, signal subspace methods are empirical linear methods for dimensionality reduction and noise reduction. these approaches have attracted significant interest and investigation recently in the context of speech enhancement, speech modeling, and speech classification research. the signal subspace is also used in radio direction finding using the music ( algorithm ). essentially the methods represent the application of a principal components analysis ( pca ) approach to ensembles of observed time - series obtained by sampling, for example sampling an audio signal. such samples can be viewed as vectors in a high - dimensional vector space over the real numbers.


multiplication is modulo irreducible polynomial x 8 + x 4 + x 3 + x + 1 { \ displaystyle x ^ { 8 } + x ^ { 4 } + x ^ { 3 } + x + 1 }. if processed bit by bit, then, after shifting, a conditional xor with 1b16 should be performed if the shifted value is larger than ff16 ( overflow must be corrected by subtraction of generating polynomial ). these are special cases of the usual multiplication in gf ( 2 8 ) { \ displaystyle \ operatorname { gf } ( 2 ^ { 8 } ) }.


the baire space is defined to be the cartesian product of countably infinitely many copies of the set of natural numbers, and is given the product topology ( where each copy of the set of natural numbers is given the discrete topology ). the baire space is often represented using the tree of finite sequences of natural numbers. the baire space can be contrasted with cantor space, the set of infinite sequences of binary digits.


the buffer pointer is a proxy for the memory address 0xb8000000. functional programming languages based on lambda - calculus reify the concept of a procedure abstraction and procedure application in the form of the lambda expression. the scheme programming language reifies continuations ( approximately, the call stack ).


on the song's third week on the chart it reached its peak position of 16, where it remained for three weeks. it has since been certified gold by the australian recording industry association ( aria ) for sales of 35, 000 units. in new zealand the single entered at number 38 on the new zealand singles chart. the following week, it rose to position 21 and then proceeded to fall off the charts.


one purpose of xml metadata interchange ( xmi ) is to enable easy interchange of metadata between uml - based modeling tools and mof - based metadata repositories in distributed heterogeneous environments. xmi is also commonly used as the medium by which models are passed from modeling tools to software generation tools as part of model - driven engineering. examples of xmi, and lists of the xml tags that make up xmi - formatted files, are available in the version 2. 5. 1 specification document.


a stronger notion is that of strongly exposed point of c { \ displaystyle c } which is an exposed point x ∈ c { \ displaystyle x \ in c } such that some exposing functional f { \ displaystyle f } of x { \ displaystyle x } attains its strong maximum over c { \ displaystyle c } at x { \ displaystyle x }, i. e. for each sequence ( x n ) ⊂ c { \ displaystyle ( x _ { n } ) \ subset c } we have the following implication : f ( x n ) → max f ( c ) ‖ x n − x ‖ → 0 { \ displaystyle f ( x _ { n } ) \ to \ max f ( c ) \ longrightarrow \ | x _ { n } - x \ | \ to 0 }. the set of all strongly exposed points of c { \ displaystyle c } is usually denoted str exp ( c ) { \ displaystyle \ operatorname { str } \ exp ( c ) }. there are two weaker notions, that of extreme point and that of support point of c { \ displaystyle c }.


in social network theory, social relationships are viewed in terms of nodes and ties. nodes are the individual actors within the networks, and ties are the relationships between the actors. there can be many kinds of ties between the nodes. in its simplest form, a social network is a map of all of the relevant ties between the nodes being studied.


in the japanese kantenji braille, the standard 8 - dot braille patterns 37, 137, 347, and 1347 are the patterns related to braille pattern dots - 23, since the two additional dots of kantenji patterns 023, 237, and 0237 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


during batch processing, several different programs were loaded in the computer memory, and the first one began to run. when the first program reached an instruction waiting for a peripheral, the context of this program was stored away, and the second program in memory was given a chance to run. the process continued until all programs finished running. the use of multiprogramming was enhanced by the arrival of virtual memory and virtual machine technology, which enabled individual programs to make use of memory and operating system resources as if other concurrently running programs were, for all practical purposes, nonexistent. multiprogramming gives no guarantee that a program will run in a timely manner.


in the internet protocol suite, the application layer contains the communications protocols and interface methods used in process - to - process communications across an internet protocol ( ip ) computer network. the application layer only standardizes communication and depends upon the underlying transport layer protocols to establish host - to - host data transfer channels and manage the data exchange in a client – server or peer - to - peer networking model. though the tcp / ip application layer does not describe specific rules or data formats that applications must consider when communicating, the original specification ( in rfc 1123 ) does rely on and recommend the robustness principle for application design.


in statistics and data mining, affinity propagation ( ap ) is a clustering algorithm based on the concept of " message passing " between data points. unlike clustering algorithms such as k - means or k - medoids, affinity propagation does not require the number of clusters to be determined or estimated before running the algorithm. similar to k - medoids, affinity propagation finds " exemplars, " members of the input set that are representative of clusters.


the c programming language uses an integer type, where relational expressions like i > j and logical expressions connected by & & and | | are defined to have value 1 if true and 0 if false, whereas the test parts of if, while, for, etc., treat any non - zero value as true. indeed, a boolean variable may be regarded ( and implemented ) as a numerical variable with one binary digit ( bit ), or as a bit string of length one, which can store only two values. the implementation of booleans in computers are most likely represented as a full word, rather than a bit ; this is usually due to the ways computers transfer blocks of information.


more generally, | z : n z | = n { \ displaystyle | \ mathbb { z } : n \ mathbb { z } | = n } for any positive integer n. when g is finite, the formula may be written as | g : h | = | g | / | h | { \ displaystyle | g : h | = | g | / | h | }, and it implies lagrange's theorem that | h | { \ displaystyle | h | } divides | g | { \ displaystyle | g | }. when g is infinite, | g : h | { \ displaystyle | g : h | } is a nonzero cardinal number that may be finite or infinite. for example, | z : 2 z | = 2 { \ displaystyle | \ mathbb { z } : 2 \ mathbb { z } | = 2 }, but | r : z | { \ displaystyle | \ mathbb { r } : \ mathbb { z } | } is infinite. if n is a normal subgroup of g, then | g : n | { \ displaystyle | g : n | } is equal to the order of the quotient group g / n { \ displaystyle g / n }, since the underlying set of g / n { \ displaystyle g / n } is the set of cosets of n in g.


intermediate angles give intermediate correlations in a way that, on careful analysis, proves inconsistent with the idea that each particle has a definite, independent probability of producing the observed measurements ( the correlations violate bell's inequality ). this subtle dependence of one measurement on the other holds even when measurements are made simultaneously and a great distance apart, which gives the appearance of a superluminal communication taking place between the two electrons. put simply, how can bob's electron " know " what alice measured on hers, so that it can adjust its own behavior accordingly?


comprehensive test procedures which outline the steps, and their expected results clearly identify what is to be seen as a result of performing the step. after the step or set of steps is completed the last step's expected result will call out what has been seen and then identify what requirement or requirements have been verified ( identified by number ). the requirement number, title and verbiage are tied together in another location in the test document.


in some cases, the problem may also be simplified by subtracting a point from both sides of the equation and taking the norm of the result. for example, to solvefor ξ 3 { \ textstyle \ xi _ { 3 } }, where ξ 1 { \ textstyle \ xi _ { 1 } } and ξ 2 { \ textstyle \ xi _ { 2 } } intersect at the point q { \ textstyle q }, both sides of the equation may be applied to a point p { \ textstyle p } that is not on the axis of ξ 3 { \ textstyle \ xi _ { 3 } }. subtracting q { \ textstyle q } and taking the norm of both sides yields this may be solved using subproblem 3.


therefore, in the case of drawing a red card or a king, drawing any of a red king, a red non - king, or a black king is considered a success. in a standard 52 - card deck, there are twenty - six red cards and four kings, two of which are red, so the probability of drawing a red or a king is 26 / 52 + 4 / 52 – 2 / 52 = 28 / 52. events are collectively exhaustive if all the possibilities for outcomes are exhausted by those possible events, so at least one of those outcomes must occur.


in mathematical logic, goodstein's theorem is a statement about the natural numbers, proved by reuben goodstein in 1944, which states that every goodstein sequence eventually terminates at 0. laurence kirby and jeff paris showed that it is unprovable in peano arithmetic ( but it can be proven in stronger systems, such as second - order arithmetic ). this was the third example of a true statement that is unprovable in peano arithmetic, after the examples provided by godel's incompleteness theorem and gerhard gentzen's 1943 direct proof of the unprovability of ε0 - induction in peano arithmetic. the paris – harrington theorem gave another example.


for example, the torus is different from the sphere : the torus has a " hole " ; the sphere doesn't. however, since continuity ( the basic notion of topology ) only deals with the local structure, it can be difficult to formally define the obvious global difference. the homotopy groups, however, carry information about the global structure.


in the example program only normal calls are used, so all the information will be on a single stack. for asynchronous calls, a separate stack is initiated for each asynchronous process so that the processes share data but run asynchronously.


in order for virtual memory compression to provide measurable performance improvements, the throughput of the virtual memory system must be improved when compared to the uncompressed equivalent. thus, the additional amount of processing introduced by the compression must not increase the overall latency. however, in i / o - bound systems or applications with highly compressible data sets, the gains can be substantial.


in plumbing fittings, the " m " or " f " usually comes at the beginning rather than the end of the abbreviated designation. for example : mipt denotes male iron pipe thread ; fipt denotes female iron pipe thread. a short length of pipe having an mip thread at both ends is sometimes called a nipple. a short pipe fitting having an fip thread at both ends is sometimes called a coupling.


in mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. if the primal is a minimization problem then the dual is a maximization problem ( and vice versa ). any feasible solution to the primal ( minimization ) problem is at least as large as any feasible solution to the dual ( maximization ) problem. therefore, the solution to the primal is an upper bound to the solution of the dual, and the solution of the dual is a lower bound to the solution of the primal.


in the following code, neither f nor g functions is reentrant. in the above, f ( ) depends on a non - constant global variable v ; thus, if f ( ) is interrupted during execution by an isr which modifies v, then reentry into f ( ) will return the wrong value of v. the value of v and, therefore, the return value of f, cannot be predicted with confidence : they will vary depending on whether an interrupt modified v during f's execution. hence, f is not reentrant. neither is g, because it calls f, which is not reentrant.


in linear algebra, the n × n { \ displaystyle n \ times n } identity matrix i { \ displaystyle \ mathbf { i } } has entries equal to the kronecker delta : where i { \ displaystyle i } and j { \ displaystyle j } take the values 1, 2,, n { \ displaystyle 1, 2, \ cdots, n }, and the inner product of vectors can be written as here the euclidean vectors are defined as n - tuples : a = ( a 1, a 2, …, a n ) { \ displaystyle \ mathbf { a } = ( a _ { 1 }, a _ { 2 }, \ dots, a _ { n } ) } and b = ( b 1, b 2,..., b n ) { \ displaystyle \ mathbf { b } = ( b _ { 1 }, b _ { 2 },..., b _ { n } ) } and the last step is obtained by using the values of the kronecker delta to reduce the summation over j { \ displaystyle j }. it is common for i and j to be restricted to a set of the form { 1, 2,..., n } or { 0, 1,..., n − 1 }, but the kronecker delta can be defined on an arbitrary set.


in many less - developed countries, such as spain, mexico, brazil, and egypt, calls were placed at a central office the caller went to, filled out a paper slip, sometimes paid in advance for the call, and then waited for it to be connected. in spain these were known as locutorios, literally " a place to talk ". in towns too small to support a phone office, placing long - distance calls was a sideline for some businesses with telephones, such as pharmacies.


internally, the cpu of the computer is built up from a number of separate parts dedicated to a single task, for instance, adding a number, or fetching from memory. normally, as the instruction flows through the machine, only one part is active at any given time. this means that each sequential step of the entire process must complete before a result can be saved.


a bijective function is also called a bijection. that is, combining the definitions of injective and surjective, y ∈ y,! x ∈ x such that y = f ( x ), { \ displaystyle \ forall y \ in y, \ exists! x \ in x { \ text { such that } } y = f ( x ), } where!


in mathematics, particularly abstract algebra, a binary operation • on a set is flexible if it satisfies the flexible identity : a ( b a ) = ( a b ) a { \ displaystyle a \ bullet \ left ( b \ bullet a \ right ) = \ left ( a \ bullet b \ right ) \ bullet a } for any two elements a and b of the set. a magma ( that is, a set equipped with a binary operation ) is flexible if the binary operation with which it is equipped is flexible. similarly, a nonassociative algebra is flexible if its multiplication operator is flexible. every commutative or associative operation is flexible, so flexibility becomes important for binary operations that are neither commutative nor associative, e. g. for the multiplication of sedenions, which are not even alternative. in 1954, richard d. schafer examined the algebras generated by the cayley – dickson process over a field and showed that they satisfy the flexible identity.


in statistics, the monotone likelihood ratio property is a property of the ratio of two probability density functions ( pdfs ). formally, distributions ƒ ( x ) and g ( x ) bear the property if for every x 1 > x 0, f ( x 1 ) g ( x 1 ) ≥ f ( x 0 ) g ( x 0 ) { \ displaystyle { \ text { for every } } x _ { 1 } > x _ { 0 }, \ quad { \ frac { f ( x _ { 1 } ) } { g ( x _ { 1 } ) } } \ geq { \ frac { f ( x _ { 0 } ) } { g ( x _ { 0 } ) } } } that is, if the ratio is nondecreasing in the argument x { \ displaystyle x }. if the functions are first - differentiable, the property may sometimes be stated ∂ ∂ x ( f ( x ) g ( x ) ) ≥ 0 { \ displaystyle { \ frac { \ partial } { \ partial x } } \ left ( { \ frac { f ( x ) } { g ( x ) } } \ right ) \ geq 0 } for two distributions that satisfy the definition with respect to some argument x, we say they " have the mlrp in x. " for a family of distributions that all satisfy the definition with respect to some statistic t ( x ), we say they " have the mlr in t ( x ). "


in mathematics, the chinese remainder theorem states that if one knows the remainders of the euclidean division of an integer n by several integers, then one can determine uniquely the remainder of the division of n by the product of these integers, under the condition that the divisors are pairwise coprime ( no two divisors share a common factor other than 1 ). for example, if we know that the remainder of n divided by 3 is 2, the remainder of n divided by 5 is 3, and the remainder of n divided by 7 is 2, then without knowing the value of n, we can determine that the remainder of n divided by 105 ( the product of 3, 5, and 7 ) is 23. importantly, this tells us that if n is a natural number less than 105, then 23 is the only possible value of n. the earliest known statement of the theorem is by the chinese mathematician sunzi in the sunzi suanjing in the 3rd century ce.


job j { \ displaystyle j } on machine i { \ displaystyle i } takes time p j / s i { \ displaystyle p _ { j } / s _ { i } }. r : unrelated - machines scheduling. there are m { \ displaystyle m } parallel machines, and they are unrelated – job j { \ displaystyle j } on machine i { \ displaystyle i } takes time p i j { \ displaystyle p _ { ij } }. these letters might be followed by the number of machines, which is then fixed.


their specific use as metadata is left to the developer and can cover a wide range of types of information about any given application, classes and members that is not instance - specific. the decision to expose any given attribute as a property is also left to the developer as is the decision to use them as part of a larger application framework. attributes are implemented as classes that are derived from system. attribute.


unlike peano arithmetic, skolem arithmetic is a decidable theory. this means it is possible to effectively determine, for any sentence in the language of skolem arithmetic, whether that sentence is provable from the axioms of skolem arithmetic. the asymptotic running - time computational complexity of this decision problem is triply exponential.


the process responds at the next time step by randomly moving into a new state s ′ { \ displaystyle s'}, and giving the decision maker a corresponding reward r a ( s, s ′ ) { \ displaystyle r _ { a } ( s, s') }. the probability that the process moves into its new state s ′ { \ displaystyle s'} is influenced by the chosen action. specifically, it is given by the state transition function p a ( s, s ′ ) { \ displaystyle p _ { a } ( s, s') }.


in the squoze encoding, identifiers in the symbol table were represented in a 50 - character alphabet, allowing a 36 - bit machine word to represent six alphanumeric characters plus two flag bits, thus saving two bits per six characters, because the six bits normally allocated for each character could store up to 64 states rather than only the 50 states needed to represent the 50 letters of the alphabet, and 506 < 234. using base 50 already saves a single bit every three characters, so it was used in two three - character chunks. the manual has a formula for encoding six characters abcdef : ( a ∗ 50 2 + b ∗ 50 + c ) ∗ 2 17 + ( d ∗ 50 2 + e ∗ 50 + f ) { \ displaystyle ( a * 50 ^ { 2 } + b * 50 + c ) * 2 ^ { 17 } + ( d * 50 ^ { 2 } + e * 50 + f ) } for example " squoze ", normally 36 bits : 35 33 37 31 44 17 ( base 8 ) would be encoded in two 17 - bit pieces to fit in the 34 bits as ( 0o220231 < < 17 ) | 0o175473 = = 0o110114575473. a simpler example of the same logic would be how a three - digit bcd number would take up 12 bits, such as 987 : 9 8 7 ( base 16 ) 1001 1000 0111 ( base 2 ), but any such value could be stored in 10 bits directly, saving two bits, such as 987 : 3db ( base 16 ) 11 1101 1011 ( base 2 ).


in order to state the hypergraph regularity and counting lemmas formally, we need to define several rather technical terms to formalize appropriate notions of pseudo - randomness ( random - likeness ) and boundedness, as well as to describe the random - like blocks and partitions. notation k j ( k ) { \ displaystyle k _ { j } ^ { ( k ) } } denotes a k { \ displaystyle k } - uniform clique on j { \ displaystyle j } vertices. g ( j ) { \ displaystyle { \ mathcal { g } } ^ { ( j ) } } is an l { \ displaystyle l } - partite j { \ displaystyle j } - graph on vertex partition g ( 1 ) = v 1 … v l { \ displaystyle { \ mathcal { g } } ^ { ( 1 ) } = v _ { 1 } \ sqcup \ ldots \ sqcup v _ { l } }. k j ( g ( i ) ) { \ displaystyle { \ mathcal { k } } _ { j } ( { \ mathcal { g } } ^ { ( i ) } ) } is the family of all j { \ displaystyle j } - element vertex sets that span the clique k j ( i ) { \ displaystyle k _ { j } ^ { ( i ) } } in g ( i ) { \ displaystyle { \ mathcal { g } } ^ { ( i ) } }.


in most cases, we want to find out the relationships between social data and another event or we want to get interesting results from social data analyses to predict some events. there are some outstanding articles in this field, including twitter mood predicts the stock market, predicting the present with google trends etc. in order to accomplish these goals, we need the appropriate methods to do the analyses. usually, we use statistic methods, methods of machine learning or methods of data mining to do the analyses. universities all over the world are opening graduate program in social data analysis.


the client decides which commands to execute at which points. to execute a command, it passes the command object to the invoker object.


, y 1 ). { \ displaystyle p ( y _ { i } | x _ { i }, x _ { i - 1 }, x _ { i - 2 },..., x _ { 1 }, y _ { i - 1 }, y _ { i - 2 },..., y _ { 1 } ). }.


for small samples the chi - squared approximation is overly sensitive, often rejecting the null hypothesis when it is true. furthermore, the distribution of p - values departs from a uniform distribution and becomes a right - skewed unimodal distribution, especially for small p - values. this leads to a large type i error rate.


in set theory, the notation y x { \ displaystyle y ^ { x } } is used to denote the set of functions from the set x { \ displaystyle x } to the set y { \ displaystyle y }. currying is the natural bijection between the set a b × c { \ displaystyle a ^ { b \ times c } } of functions from b × c { \ displaystyle b \ times c } to a { \ displaystyle a }, and the set ( a c ) b { \ displaystyle ( a ^ { c } ) ^ { b } } of functions from b { \ displaystyle b } to the set of functions from c { \ displaystyle c } to a { \ displaystyle a }. in symbols : a b × c ( a c ) b { \ displaystyle a ^ { b \ times c } \ cong ( a ^ { c } ) ^ { b } } indeed, it is this natural bijection that justifies the exponential notation for the set of functions. as is the case in all instances of currying, the formula above describes an adjoint pair of functors : for every fixed set c { \ displaystyle c }, the functor b ↦ b × c { \ displaystyle b \ mapsto b \ times c } is left adjoint to the functor a ↦ a c { \ displaystyle a \ mapsto a ^ { c } }. in the category of sets, the object y x { \ displaystyle y ^ { x } } is called the exponential object.


the various problems, algorithms, and tools of cost distance analysis operate over an unconstrained two - dimensional space, meaning that a path could be of any shape. similar cost optimization problems can also arise in a constrained space, especially a one - dimensional linear network such as a road or telecommunications network. although they are similar in principle, the problems in network space require very different ( usually simpler ) algorithms to solve, largely adopted from graph theory. the collection of gis tools for solving these problems are called network analysis.


in modulus 12, one can assert that : 38 ≡ 14 ( mod 12 ) { \ displaystyle 38 \ equiv 14 { \ pmod { 12 } } } because 38 − 14 = 24, which is a multiple of 12. another way to express this is to say that both 38 and 14 have the same remainder 2, when divided by 12. the definition of congruence also applies to negative values. for example : 2 ≡ − 3 ( mod 5 ) − 8 ≡ 7 ( mod 5 ) − 3 ≡ − 8 ( mod 5 ). { \ displaystyle { \ begin { aligned } 2 & \ equiv - 3 { \ pmod { 5 } } \ \ - 8 & \ equiv 7 { \ pmod { 5 } } \ \ - 3 & \ equiv - 8 { \ pmod { 5 } }. \ end { aligned } } }


in mathematics, the birch and swinnerton - dyer conjecture ( often called the birch – swinnerton - dyer conjecture ) describes the set of rational solutions to equations defining an elliptic curve. it is an open problem in the field of number theory and is widely recognized as one of the most challenging mathematical problems. it is named after mathematicians bryan john birch and peter swinnerton - dyer, who developed the conjecture during the first half of the 1960s with the help of machine computation. as of 2023, only special cases of the conjecture have been proven.


gxf5 14. nxf7 kxf7 15. bd2 nd7 16.


renaming truth as a product of the will cannot help it solve the problems of the intellect, according to bittle. bittle cited what he saw as contradictions in pragmatism, such as using objective facts to prove that truth does not emerge from objective fact ; this reveals that pragmatists do recognize truth as objective fact, and not, as they claim, what is useful. bittle argued there are also some statements that cannot be judged on human welfare at all.


in the japanese kantenji braille, the standard 8 - dot braille patterns 2, 12, 24, and 124 are the 8 - dot braille patterns related to braille pattern dots - 1, since the two additional dots of kantenji patterns 01, 17, and 017 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in mathematics, quantales are certain partially ordered algebraic structures that generalize locales ( point free topologies ) as well as various multiplicative lattices of ideals from ring theory and functional analysis ( c * - algebras, von neumann algebras ). quantales are sometimes referred to as complete residuated semigroups.


this can be significantly faster, as setjmp and longjmp must conservatively store all registers which may be in use according to the abi, whereas the clobber method allows the compiler to store ( by spilling to the stack ) only what it knows is actually in use. due to the lack of direct language support, many authors have written their own libraries for coroutines which hide the above details.


for example, 29 / 30 could be written as 1 2 4 2 3 5 { \ displaystyle { \ tfrac { 1 \, \, 2 \, \, 4 } { 2 \, \, 3 \, \, 5 } } }, representing the value 4 5 + 2 3 × 5 + 1 2 × 3 × 5 { \ displaystyle { \ tfrac { 4 } { 5 } } + { \ tfrac { 2 } { 3 \ times 5 } } + { \ tfrac { 1 } { 2 \ times 3 \ times 5 } } }. this can be viewed as a form of mixed radix notation, and was very convenient for dealing with traditional systems of weights, measures, and currency. for instance, for units of length, a foot is 1 / 3 of a yard, and an inch is 1 / 12 of a foot, so a quantity of 5 yards, 2 feet, and 7 3 4 { \ displaystyle 7 { \ tfrac { 3 } { 4 } } } inches could be represented as a composite fraction : 3 7 2 4 12 3 5 { \ displaystyle { \ tfrac { 3 \ \, 7 \, \, 2 } { 4 \, \, 12 \, \, 3 } } \, 5 } yards.


in statistics, factor analysis of mixed data or factorial analysis of mixed data ( famd, in the french original : afdm or analyse factorielle de donnees mixtes ), is the factorial method devoted to data tables in which a group of individuals is described both by quantitative and qualitative variables. it belongs to the exploratory methods developed by the french school called analyse des donnees ( data analysis ) founded by jean - paul benzecri. the term mixed refers to the use of both quantitative and qualitative variables. roughly, we can say that famd works as a principal components analysis ( pca ) for quantitative variables and as a multiple correspondence analysis ( mca ) for qualitative variables.


with stack machines, in contrast, results can be stored in one of two ways. firstly, results can be stored using a temporary variable in memory. storing and subsequent retrievals cost additional instructions and additional data cache cycles.


around 2007, lstm trained by connectionist temporal classification ( ctc ) started to outperform traditional speech recognition in certain applications. in 2015, google's speech recognition reportedly experienced a dramatic performance jump of 49 % through ctc - trained lstm, which is now available through google voice to all smartphone users. transformers, a type of neural network based on solely on attention, have been widely adopted in computer vision and language modeling, sparking the interest of adapting such models to new domains, including speech recognition.


in programming languages that have non - hygienic macro systems, it is possible for existing variable bindings to be hidden from a macro by variable bindings that are created during its expansion. in c, this problem can be illustrated by the following fragment : running the above through the c preprocessor produces : the variable a declared in the top scope is shadowed by the a variable in the macro, which introduces a new scope. as a result, a is never altered by the execution of the program, as the output of the compiled program shows : a is now 4, b is now 9


in parallel france and germany signed a joint development agreement in 1984 and were joined by italy and the uk in 1986. in 1986, the mts and european commission proposed reserving the 900 mhz spectrum band for gsm. it was long believed that the former finnish prime minister harri holkeri made the world's first gsm call on 1 july 1991, mts calling kaarina suonio ( deputy mayor of the city of tampere ) using a network built by nokia and siemens and operated by radiolinja. in 2021 a former nokia engineer pekka lonka revealed to helsingin sanomat making a test call just a couple of hours earlier.


in mutual authentication schemes that require a user's input password as part of the verification process, there is a higher vulnerability to hackers because the password is human - made rather than a computer - generated certificate. while applications could simply require users to use a computer - generated password, it is inconvenient for people to remember. user - made passwords and the ability to change one's password are important for making an application user - friendly, so many schemes work to accommodate the characteristic.


in neuropsychology, linguistics, and philosophy of language, a natural language or ordinary language is any language that occurs naturally in a human community by a process of use, repetition, and change without conscious planning or premeditation. it can take different forms, namely either a spoken language or a sign language. natural languages are distinguished from constructed and formal languages such as those used to program computers or to study logic.


second, synchronization in many concurrent programs in a finite state, and therefore can be adequately described by regular expressions. for precisely the same reasons, path expressions are useful for controlling the behavior of complicated asynchronous circuits. in fact, the finite state assumption may be even more reasonable at the hardware level than at the monitor level. path expressions provide a high level of descriptive synchronization that aids in the prevention and detection of design errors in complex systems and overcomes some of the dangers, such as certain forms of coding errors.


in paging the memory address space or segment is divided into equal - sized blocks called pages. using virtual memory hardware, each page can reside in any location at a suitable boundary of the computer's physical memory, or be flagged as being protected. virtual memory makes it possible to have a linear virtual memory address space and to use it to access blocks fragmented over physical memory address space. most computer architectures which support paging also use pages as the basis for memory protection.


in the above example, the rli mark ( right - to - left isolate ) forces the following text to be interpreted in the reverse order : the triple - quote is first ( ending the string ), followed by a semicolon ( starting a new line ), and finally with the premature return ( returning none and ignoring any code below it ). the new line terminates the rli mark, preventing it from flowing into the below code. because of the bidi character, some source code editors and ides rearrange the code for display without any visual indication that the code has been rearranged, so a human code reviewer would not normally detect them.


if we remove the vertex v, we can four - color the remaining vertices. we can set the colors as ( in clockwise order ) red, yellow, blue, and green. in this situation, there can be a kempe chain joining the red and blue neighbors or a kempe chain joining the green and yellow neighbors, but not both, since these two paths would necessarily intersect, and the vertex where they intersect cannot be colored.


in mathematics, a regular semigroup is a semigroup s in which every element is regular, i. e., for each element a in s there exists an element x in s such that axa = a. regular semigroups are one of the most - studied classes of semigroups, and their structure is particularly amenable to study via green's relations.


infinity can also be used to describe infinite series, as follows : i = 0 ∞ f ( i ) = a { \ displaystyle \ sum _ { i = 0 } ^ { \ infty } f ( i ) = a } means that the sum of the infinite series converges to some real value a. { \ displaystyle a. }


although languages that are described as having imperfective and perfective aspects agree in most cases in their use of these aspects, they may not agree in every situation. for example : some languages have additional grammatical aspects. spanish and ancient greek, for example, have a perfect ( not the same as the perfective ), which refers to a state resulting from a previous action ( also described as a previous action with relevance to a particular time, or a previous action viewed from the perspective of a later time ).


in order to get 128 bits of security for hash based signatures to sign 1 million messages using the fractal merkle tree method of naor shenhav and wool the public and private key sizes are roughly 36, 000 bits in length.


y - axis ( ↑ { \ displaystyle \ uparrow } ) : terms that can bind types, corresponding to polymorphism. z - axis ( { \ displaystyle \ nearrow } ) : types that can bind types, corresponding to ( binding ) type operators. the different ways to combine these three dimensions yield the 8 vertices of the cube, each corresponding to a different kind of typed system. the λ - cube can be generalized into the concept of a pure type system.


( this bound is tight, as a sequence of m − 1 { \ displaystyle m - 1 } zeroes and m − 1 { \ displaystyle m - 1 } ones cannot have any subset of size m { \ displaystyle m } summing to zero. ) there are known proofs of this result using the cauchy - davenport theorem, fermat's little theorem, or the chevalley – warning theorem. generalizing this result, one can define for any abelian group g the minimum quantity e g z ( g ) { \ displaystyle egz ( g ) } of elements of g such that there must be a subsequence of o ( g ) { \ displaystyle o ( g ) } elements ( where o ( g ) { \ displaystyle o ( g ) } is the order of the group ) which adds to zero. it is known that e g z ( g ) ≤ 2 o ( g ) − 1 { \ displaystyle egz ( g ) \ leq 2o ( g ) - 1 }, and that this bound is strict if and only if g = z m { \ displaystyle g = \ mathbb { z } _ { m } }.


in mathematics, the regula falsi, method of false position, or false position method is a very old method for solving an equation with one unknown ; this method, in modified form, is still in use. in simple terms, the method is the trial and error technique of using test ( " false " ) values for the variable and then adjusting the test value according to the outcome. this is sometimes also referred to as " guess and check ". versions of the method predate the advent of algebra and the use of equations.


in the united states, common telephone lines are designed to transmit frequencies between 300 and 3400 hz. since electric power in the united states is distributed at 60 hz, it normally does not interfere with telephone communications because its frequency is too low.


unsatisfiable statements, both through negation and affirmation, are known formally as contradictions. a formula that is neither a tautology nor a contradiction is said to be logically contingent.


in marketing, contact center telephony is the communication and collaboration system used by businesses to either manage high volumes of inbound queries or outbound telephone calls keeping their workforce or agents productive and in control to serve or acquire customers. this business communication system is an extension of computer telephony integration ( cti ).


{ \ displaystyle f \ circ g _ { 1 } = f \ circ g _ { 2 } \ implies g _ { 1 } = g _ { 2 }. } monomorphisms are a categorical generalization of injective functions ( also called " one - to - one functions " ) ; in some categories the notions coincide, but monomorphisms are more general, as in the examples below. in the setting of posets intersections are idempotent : the intersection of anything with itself is itself.


in mistrustful cryptography the participating parties do not trust each other. for example, alice and bob collaborate to perform some computation where both parties enter some private inputs. but alice does not trust bob and bob does not trust alice. thus, a secure implementation of a cryptographic task requires that after completing the computation, alice can be guaranteed that bob has not cheated and bob can be guaranteed that alice has not cheated either.


derived from the causal order is the differential structure and the conformal metric of a manifold. a probability is assigned to a causal set becoming embedded in a manifold ; thus there can be a transition from a discrete planck scale fundamental unit of volume to a classical large scale continuous space. random graphs by antonsen spacetime is described by dynamical graphs with points ( associated with vertices ) and links ( of unit length ) that are created or annihilated according to probability calculations. the parameterization of graphs in a metaspace gives rise to time. bootstrap universe by cahill and klinger an iterative map composed of monads and the relations between them becomes a tree - graph of nodes and links.


the same cannot be done with the other two deductions systems : as context is changed in some of their rules of inferences, they cannot be formalized so that hypothetical judgments could be avoided — not even if we want to use them just for proving derivability of tautologies. this basic diversity among the various calculi allows such difference, that the same basic thought ( e. g. deduction theorem ) must be proven as a metatheorem in hilbert - style deduction system, while it can be declared explicitly as a rule of inference in natural deduction. in type theory, some analogous notions are used as in mathematical logic ( giving rise to connections between the two fields, e. g. curry – howard correspondence ). the abstraction in the notion of judgment in mathematical logic can be exploited also in foundation of type theory as well.


in the 1970s, analysis of high - level languages indicated compilers produced some complex corresponding machine language. it was determined that new instructions could improve performance. some instructions were added that were never intended to be used in assembly language but fit well with compiled high - level languages.


in mathematics, a sporadic group is one of the 26 exceptional groups found in the classification of finite simple groups. a simple group is a group g that does not have any normal subgroups except for the trivial group and g itself. the classification theorem states that the list of finite simple groups consists of 18 countably infinite families plus 26 exceptions that do not follow such a systematic pattern.


in neutral prosody, turkish verb phrases are primarily head - final, as the verb comes after its complement. variation in object - verb ordering is not strictly rigid. however, constructions where the verb precedes the object are less common. ]