on the other hand, an outcome of | ψ 11 ⟩ { \ displaystyle | \ psi _ { 11 } \ rangle } cannot possibly be observed from a qubit in state | ψ 01 ⟩ { \ displaystyle | \ psi _ { 01 } \ rangle }. thus in the case that bob measures in the hadamard basis and observes state | ψ 11 ⟩ { \ displaystyle | \ psi _ { 11 } \ rangle } ( and only in that case ), bob can deduce which state he was sent and therefore what the secret bit is. from the remaining k { \ displaystyle k } bits where both bob's measurement was conclusive, alice randomly chooses k / 2 { \ displaystyle k / 2 } bits and discloses her choices over the public channel.


nelder ( 1990 ) described continuous counts, continuous ratios, count ratios, and categorical modes of data. see also chrisman ( 1998 ), van den berg ( 1991 ). the issue of whether or not it is appropriate to apply different kinds of statistical methods to data obtained from different kinds of measurement procedures is complicated by issues concerning the transformation of variables and the precise interpretation of research questions. " the relationship between the data and what they describe merely reflects the fact that certain kinds of statistical statements may have truth values which are not invariant under some transformations. whether or not a transformation is sensible to contemplate depends on the question one is trying to answer " ( hand, 2004, p. 82 ).


sprint reviews can be seen as a powerful method to improve external correspondence whilst they help to share data about the features and prerequisite conditions between partners or stakeholders. agile practices also assist in building trust between various teams associated with the process by stimulating consistent communication and conveyance of programming deliverables. as indicated by an investigation made by passivara, durasiewicz and, lassenius, the software quality and correspondence are improved and communication and coordinated effort are more regular comparatively as a result of the scrum approach utilized in the undertaking.


the multiplication axiom for integers defined this way is ( x p, x m ) × ( y p, y m ) = ( x p × y p + x m × y m, x p × y m + x m × y p ). { \ displaystyle ( x _ { p }, \, x _ { m } ) \ times ( y _ { p }, \, y _ { m } ) = ( x _ { p } \ times y _ { p } + x _ { m } \ times y _ { m }, \ ; x _ { p } \ times y _ { m } + x _ { m } \ times y _ { p } ). } the rule that −1 × −1 = 1 can then be deduced from ( 0, 1 ) × ( 0, 1 ) = ( 0 × 0 + 1 × 1, 0 × 1 + 1 × 0 ) = ( 1, 0 ). { \ displaystyle ( 0, 1 ) \ times ( 0, 1 ) = ( 0 \ times 0 + 1 \ times 1, \, 0 \ times 1 + 1 \ times 0 ) = ( 1, 0 ). } multiplication is extended in a similar way to rational numbers and then to real numbers.


a hash table to keep track of already defined pairs. this table is updated each time a new pair is created or removed. since the hash table and the priority queue refer to the same elements ( pairs ), they can be implemented by a common data structure called pair with pointers for the hash table ( h _ next ) and the priority queue ( p _ next and p _ prev ). furthermore, each pair points to the beginning of the first ( f _ pos ) and the last ( b _ pos ) occurrences of the string represented by the pair in the sequence. the following picture shows an overview of this data structure. the following two pictures show an example of how these data structures look after the initialization and after applying one step of the pairing process ( pointers to null are not displayed ) :


in mathematics, an embedding ( or imbedding ) is one instance of some mathematical structure contained within another instance, such as a group that is a subgroup. when some object x { \ displaystyle x } is said to be embedded in another object y { \ displaystyle y }, the embedding is given by some injective and structure - preserving map f : x → y { \ displaystyle f : x \ rightarrow y }. the precise meaning of " structure - preserving " depends on the kind of mathematical structure of which x { \ displaystyle x } and y { \ displaystyle y } are instances. in the terminology of category theory, a structure - preserving map is called a morphism.


timestamps and vector clocks are often used to detect concurrency between updates. some people use " first writer wins " in situations where " last writer wins " is unacceptable. reconciliation of concurrent writes must occur sometime before the next read, and can be scheduled at different instants : read repair : the correction is done when a read finds an inconsistency. this slows down the read operation. write repair : the correction takes place during a write operation, slowing down the write operation. asynchronous repair : the correction is not part of a read or write operation.


in most philosophical languages, words are constructed from a limited set of morphemes that are treated as " elemental " or " fundamental ". " philosophical language " is sometimes used synonymously with " taxonomic language ". vocabularies of oligosynthetic languages are made of compound words, which are coined from a small ( theoretically minimal ) set of morphemes. languages like toki pona similarly use a limited set of root words but produce phrases which remain series of distinct words.


in mathematics, the super - logarithm is one of the two inverse functions of tetration. just as exponentiation has two inverse functions, roots and logarithms, tetration has two inverse functions, super - roots and super - logarithms. there are several ways of interpreting super - logarithms : as the abel function of exponential functions, as the inverse function of tetration with respect to the height, as a generalization of robert munafo's large number class system, for positive integer values, the super - logarithm with base - e is equivalent to the number of times a logarithm must be iterated to get to 1 ( the iterated logarithm ).


it can respond to people touching it. it's very satisfying, although we obviously have a long way to go yet. " in his opinion, it may be possible to build an android that is indistinguishable from a human, at least during a brief encounter.


{ \ displaystyle f ( x ) \ cdot g ( x ) = \ sum _ { k = 0 } ^ { \ infty } \ left ( \ sum _ { i = 0 } ^ { k } a _ { i } b _ { k - i } \ right ) x ^ { k }. } in particular, we write f 2 = f ( x ) ⋅ f ( x ) { \ displaystyle f ^ { 2 } = f ( x ) \ cdot f ( x ) }, f 3 = f ( x ) ⋅ f ( x ) ⋅ f ( x ) { \ displaystyle f ^ { 3 } = f ( x ) \ cdot f ( x ) \ cdot f ( x ) }, and so on. in analogy to algebraic numbers, a power series f ( x ) { \ displaystyle f ( x ) } is called algebraic over q ( x ) { \ displaystyle \ mathbb { q } ( x ) }, if there exists a finite set of polynomials p 0 ( x ), p 1 ( x ), p 2 ( x ), …, p n ( x ) { \ displaystyle p _ { 0 } ( x ), p _ { 1 } ( x ), p _ { 2 } ( x ), \ ldots, p _ { n } ( x ) } each with rational coefficients such that p 0 ( x ) + p 1 ( x ) ⋅ f + p 2 ( x ) ⋅ f 2 + + p n ( x ) ⋅ f n = 0.


they help to describe frequency ratios of musical intervals, appear in formulas counting prime numbers or approximating factorials, inform some models in psychophysics, and can aid in forensic accounting. the concept of logarithm as the inverse of exponentiation extends to other mathematical structures as well. however, in general settings, the logarithm tends to be a multi - valued function. for example, the complex logarithm is the multi - valued inverse of the complex exponential function. similarly, the discrete logarithm is the multi - valued inverse of the exponential function in finite groups ; it has uses in public - key cryptography.


in mathematics, a directed set ( or a directed preorder or a filtered set ) is a nonempty set a { \ displaystyle a } together with a reflexive and transitive binary relation ≤ { \ displaystyle \, \ leq \, } ( that is, a preorder ), with the additional property that every pair of elements has an upper bound. in other words, for any a { \ displaystyle a } and b { \ displaystyle b } in a { \ displaystyle a } there must exist c { \ displaystyle c } in a { \ displaystyle a } with a ≤ c { \ displaystyle a \ leq c } and b ≤ c. { \ displaystyle b \ leq c. } a directed set's preorder is called a direction.


in mathematics, and more specifically in order theory, several different types of ordered set have been studied. they include : cyclic orders, orderings in which triples of elements are either clockwise or counterclockwise lattices, partial orders in which each pair of elements has a greatest lower bound and a least upper bound. many different types of lattice have been studied ; see map of lattices for a list. partially ordered sets ( or posets ), orderings in which some pairs are comparable and others might not be preorders, a generalization of partial orders allowing ties ( represented as equivalences and distinct from incomparabilities ) semiorders, partial orders determined by comparison of numerical values, in which values that are too close to each other are incomparable ; a subfamily of partial orders with certain restrictions total orders, orderings that specify, for every two distinct elements, which one is less than the other weak orders, generalizations of total orders allowing ties ( represented either as equivalences or, in strict weak orders, as transitive incomparabilities ) well - orders, total orders in which every non - empty subset has a least element well - quasi - orderings, a class of preorders generalizing the well - orders


in particular, given a graph g { \ displaystyle g } and a specific community partition σ : v ( g ) → { 1,..., b } { \ displaystyle \ sigma : v ( g ) \ rightarrow \ { 1,..., b \ } } ( an assignment of a community - index σ ( v ) { \ displaystyle \ sigma ( v ) } ( here taken as an integer from 1 { \ displaystyle 1 } to b { \ displaystyle b } ) to each vertex v ∈ v ( g ) { \ displaystyle v \ in v ( g ) } in the graph ), the modularity measures the difference between the number of links from / to each pair of communities, from that expected in a graph that is completely random in all respects other than the set of degrees of each of the vertices ( the degree sequence ). in other words, the modularity contrasts the exhibited community structure in g { \ displaystyle g } with that of a null model, which in this case is the configuration model ( the maximally random graph subject to a constraint on the degree of each vertex ).


in telecommunication, bipolar encoding is a type of return - to - zero ( rz ) line code, where two nonzero values are used, so that the three values are +, −, and zero. such a signal is called a duobinary signal. standard bipolar encodings are designed to be dc - balanced, spending equal amounts of time in the + and − states. the reason why bipolar encoding is classified as a return to zero ( rz ) is that when a bipolar encoded channel is idle the line is held at a constant " zero " level, and when it is transmitting bits the line is either in a + v or - v state corresponding to the binary bit being transmitted. thus, the line always returns to the " zero " level to denote optionally a separation of bits or to denote idleness of the line.


{ \ displaystyle f _ { x, y } ( x, y ) = f _ { x } ( x ) f _ { y } ( y ). } that is, the joint distribution is equal to the product of the marginal distributions. unless it is not clear in context, in practice the modifier " mutual " is usually dropped so that independence means mutual independence. a statement such as " x, y, z are independent random variables " means that x, y, z are mutually independent.


other types of grammatical features, by contrast, may be relevant to semantics ( morphosemantic features ), such as tense, aspect and mood, or may only be relevant to morphology ( morphological features ). inflectional class ( a word's membership of a particular verb class or noun class ) is a purely morphological feature, because it is only relevant to the morphological realisation of the word. in formal models of grammar, features can be represented as attribute - value pairs. for example, in lexical functional grammar, syntactic features are represented alongside grammatical functions at the level of functional structure ( f - structure ), which takes the form of an attribute - value matrix.


in symbolic logic, the universal quantifier symbol { \ displaystyle \ forall } ( a turned " a " in a sans - serif font, unicode u + 2200 ) is used to indicate universal quantification. it was first used in this way by gerhard gentzen in 1935, by analogy with giuseppe peano's { \ displaystyle \ exists } ( turned e ) notation for existential quantification and the later use of peano's notation by bertrand russell. for example, if p ( n ) is the predicate " 2 · n > 2 + n " and n is the set of natural numbers, then n ∈ n p ( n ) { \ displaystyle \ forall n \! \ in \! \ mathbb { n } \ ; p ( n ) } is the ( false ) statement " for all natural numbers n, one has 2 · n > 2 + n ". similarly, if q ( n ) is the predicate " n is composite ", then n ∈ n ( q ( n ) → p ( n ) ) { \ displaystyle \ forall n \! \ in \! \ mathbb { n } \ ; { \ bigl ( } q ( n ) \ rightarrow p ( n ) { \ bigr ) } } is the ( true ) statement " for all natural numbers n, if n is composite, then 2 · n > 2 + n ". several variations in the notation for quantification ( which apply to all forms ) can be found in the quantifier article.


for example : an isometry is an isomorphism of metric spaces. a homeomorphism is an isomorphism of topological spaces. a diffeomorphism is an isomorphism of spaces equipped with a differential structure, typically differentiable manifolds.


a variety of these ways have been triedfor storing objects in a database. some products have approached the problem from the application programming end, by making the objects manipulated by the program persistent. this typically requires the addition of some kind of query language, since conventional programming languages do not have the ability to find objects based on their information content.


in sparse direct solvers, pivoting may be needed, where ultimately the resulting matrix has 2x2 blocks on the diagonal, rather than a working towards a completely pure llh cholesky decomposition for positive definite symmetric or hermitian systems. pivoting may result in unpredictable memory usage increases. for iterative solvers, only gmres based solvers work, rather than slightly " cheaper " minres based solvers.


in the context of the ttf a testing tactic is a means to partition any test class of any operation. however, some of the testing tactics used in practice actually do not always generate a partition of some test classes. some testing tactics originally proposed for the ttf are the following : disjunctive normal form ( dnf ). by applying this tactic the operation is written in disjunctive normal form and the test class is divided in as many test classes as terms are in the resulting operation's predicate.


in the formal language of first - order logic, set a { \ displaystyle a } has the property of being inhabited if z. ( z ∈ a ). { \ displaystyle \ exists z. ( z \ in a ). }


in some countries, text messages can be used to contact emergency services. in the uk, text messages can be used to call emergency services only after registering with the emergency sms service. this service is primarily aimed at people who, because of disability, are unable to make a voice call. it has recently been promoted as a means for walkers and climbers to call emergency services from areas where a voice call is not possible due to low signal strength.


( indeed, the lower bound is easy to see : the multiset containing n − 1 copies of 0 and n − 1 copies of 1 contains no n - subset summing to a multiple of n. ) this result is known as the erdos – ginzburg – ziv theorem after its discoverers. it may also be deduced from the cauchy – davenport theorem. more general results than this theorem exist, such as olson's theorem, kemnitz's conjecture ( proved by christian reiher in 2003 ), and the weighted egz theorem ( proved by david j. grynkiewicz in 2005 ).


if the bottom type is inhabited, its terms typically correspond to error conditions such as undefined behavior, infinite recursion, or unrecoverable errors. in bounded quantification with bottom, pierce says that " bot " has many uses : in a language with exceptions, a natural type for the raise construct is raise ∈ exception - > bot, and similarly for other control structures.


the transition at np = 1 from giant component to small component has analogs for these graphs, but for lattices the transition point is difficult to determine. physicists often refer to study of the complete graph as a mean field theory. thus the erdos – renyi process is the mean - field case of percolation.


bloomfield's " sign base " morpheme hypothesis : as morphemes, they are dualistic signs, since they have both ( phonological ) form and meaning. bloomfield's " lexical morpheme " hypothesis : morphemes, affixes and roots alike are stored in the lexicon. morpheme - based morphology comes in two flavours, one bloomfieldian and one hockettian. for bloomfield, the morpheme was the minimal form with meaning, but did not have meaning itself.


in mathematics, zero - sum ramsey theory or zero - sum theory is a branch of combinatorics. it deals with problems of the following kind : given a combinatorial structure whose elements are assigned different weights ( usually elements from an abelian group a { \ displaystyle a } ), one seeks for conditions that guarantee the existence of certain substructure whose weights of its elements sum up to zero ( in a { \ displaystyle a } ). it combines tools from number theory, algebra, linear algebra, graph theory, discrete analysis, and other branches of mathematics. the classic result in this area is the 1961 theorem of paul erdos, abraham ginzburg, and abraham ziv : for any 2 m − 1 { \ displaystyle 2m - 1 } elements of z m { \ displaystyle \ mathbb { z } _ { m } }, there is a subset of size m { \ displaystyle m } that sums to zero.


in mathematics, a mersenne prime is a prime number that is one less than a power of two. that is, it is a prime number of the form mn = 2n − 1 for some integer n. they are named after marin mersenne, a french minim friar, who studied them in the early 17th century. if n is a composite number then so is 2n − 1. therefore, an equivalent definition of the mersenne primes is that they are the prime numbers of the form mp = 2p − 1 for some prime p. the exponents n which give mersenne primes are 2, 3, 5, 7, 13, 17, 19, 31,... ( sequence a000043 in the oeis ) and the resulting mersenne primes are 3, 7, 31, 127, 8191, 131071, 524287, 2147483647,... ( sequence a000668 in the oeis ).


in mathematics the function field sieve is one of the most efficient algorithms to solve the discrete logarithm problem ( dlp ) in a finite field. it has heuristic subexponential complexity. leonard adleman developed it in 1994 and then elaborated it together with m. d. huang in 1999.


in some cases, theory shows that collaboration emerges spontaneously in smaller groups rather than in large ones ( see e. g. dunbar's number ). this explains why labor unions or charities often have a federated structure.


example : seq x : = x + 1 y : = x * x par begins a list of expressions that may be evaluated concurrently. example : par p ( ) q ( ) alt specifies a list of guarded commands. the guards are a combination of a boolean condition and an input expression, both optional.


in the context of efficient representations of graphs, j. h. muller defined a local structure or adjacency labeling scheme for a graph g in a given family f of graphs to be an assignment of an o ( log n ) - bit identifier to each vertex of g, together with an algorithm ( that may depend on f but is independent of the individual graph g ) that takes as input two vertex identifiers and determines whether or not they are the endpoints of an edge in g. that is, this type of implicit representation is analogous to an adjacency matrix : it is straightforward to check whether two vertices are adjacent but finding the neighbors of any vertex may involve looping through all vertices and testing which ones are neighbors. graph families with adjacency labeling schemes include : bounded degree graphs if every vertex in g has at most d neighbors, one may number the vertices of g from 1 to n and let the identifier for a vertex be the ( d + 1 ) - tuple of its own number and the numbers of its neighbors. two vertices are adjacent when the first numbers in their identifiers appear later in the other vertex's identifier. more generally, the same approach can be used to provide an implicit representation for graphs with bounded arboricity or bounded degeneracy, including the planar graphs and the graphs in any minor - closed graph family. intersection graphs an interval graph is the intersection graph of a set of line segments in the real line.


in psychology, semantic memory is memory for meaning – in other words, the aspect of memory that preserves only the gist, the general significance, of remembered experience – while episodic memory is memory for the ephemeral details – the individual features, or the unique particulars of experience. the term " episodic memory " was introduced by tulving and schacter in the context of " declarative memory ", which involved simple association of factual or objective information concerning its object. word meaning is measured by the company they keep, i. e. the relationships among words themselves in a semantic network.


if −1 < x < 0 or 1 < x, then x3 > x. if x < −1 or 0 < x < 1, then x3 < x. all aforementioned properties pertain also to any higher odd power ( x5, x7,... ) of real numbers. equalities and inequalities are also true in any ordered ring.


in the field of data management, data classification as a part of the information lifecycle management ( ilm ) process can be defined as a tool for categorization of data to enable / help organizations to effectively answer the following questions : what data types are available? where are certain data located? what access levels are implemented?


in mathematics, a conjecture is a conclusion or a proposition that is proffered on a tentative basis without proof. some conjectures, such as the riemann hypothesis ( still a conjecture ) or fermat's last theorem ( a conjecture until proven in 1995 by andrew wiles ), have shaped much of mathematical history as new areas of mathematics are developed in order to prove them.


in mathematics, the artin – hasse exponential, introduced by artin and hasse ( 1928 ), is the power series given by e p ( x ) = exp ( x + x p p + x p 2 p 2 + x p 3 p 3 + ). { \ displaystyle e _ { p } ( x ) = \ exp \ left ( x + { \ frac { x ^ { p } } { p } } + { \ frac { x ^ { p ^ { 2 } } } { p ^ { 2 } } } + { \ frac { x ^ { p ^ { 3 } } } { p ^ { 3 } } } + \ cdots \ right ). }


in some real networks, the same methods as for generated networks can also be used. in many cases, however, it may not make sense to consider multiple edges between two vertices, or such information is not available. the high degree vertices ( hubs ) may also be an important part of the network that cannot be removed without changing other fundamental properties. to determine whether the assortativity or disassortativity of a network is of structural origin, the network can be compared with a degree - preserving randomized version of itself ( without multiple edges ).


in the 1920s, leon chwistek and frank p. ramsey noticed that, if one is willing to give up the vicious circle principle, the hierarchy of levels of types in the " ramified theory of types " can be collapsed. the resulting restricted logic is called the theory of simple types or, perhaps more commonly, simple type theory. detailed formulations of simple type theory were published in the late 1920s and early 1930s by r. carnap, f. ramsey, w. v. o. quine, and a. tarski.


in the 1960s, noam chomsky formulated the generative theory of language. according to this theory, the most basic form of language is a set of syntactic rules that is universal for all humans and which underlies the grammars of all human languages. this set of rules is called universal grammar ; for chomsky, describing it is the primary objective of the discipline of linguistics. thus, he considered that the grammars of individual languages are only of importance to linguistics insofar as they allow us to deduce the universal underlying rules from which the observable linguistic variability is generated. in opposition to the formal theories of the generative school, functional theories of language propose that since language is fundamentally a tool, its structures are best analyzed and understood by reference to their functions.


in other words, it cannot be a fully conserved ( i. e., invariable ) site nor can it be a ( singleton ) site with a difference in only one sequence ( as seen, for example, in single - nucleotide polymorphisms and single - nucleotide variants ). in both cases, the number of character - state changes is the same regardless of the topology of the tree, equal to 0 and 1 respectively. = = references = =


estimation theory is concerned with the properties of estimators ; that is, with defining properties that can be used to compare different estimators ( different rules for creating estimates ) for the same quantity, based on the same data. such properties can be used to determine the best rules to use under given circumstances. however, in robust statistics, statistical theory goes on to consider the balance between having good properties, if tightly defined assumptions hold, and having less good properties that hold under wider conditions.


in quicksort, there is a subprocedure called partition that can, in linear time, group a list ( ranging from indices left to right ) into two parts : those less than a certain element, and those greater than or equal to the element. here is pseudocode that performs a partition about the element list : function partition ( list, left, right, pivotindex ) is pivotvalue : = list swap list and list / / move pivot to end storeindex : = left for i from left to right − 1 do if list < pivotvalue then swap list and list increment storeindex swap list and list / / move pivot to its final place return storeindex this is known as the lomuto partition scheme, which is simpler but less efficient than hoare's original partition scheme. in quicksort, we recursively sort both branches, leading to best - case o ( n log n ) { \ displaystyle o ( n \ log n ) } time. however, when doing selection, we already know which partition our desired element lies in, since the pivot is in its final sorted position, with all those preceding it in an unsorted order and all those following it in an unsorted order.


x is the number of faces of each dice. for example, if a game calls for a roll of d4 or 1d4, it means " roll one 4 - sided die. " if the final number is omitted, it is typically assumed to be a six, but in some contexts, other defaults are used. 3d6 would mean " roll three six - sided dice. "


in software design, model - driven integration is a subset of model - driven architecture ( mda ) which focuses purely on solving application integration problems using executable unified modeling language ( uml ).


in technology, living documents can be implemented using a wiki. other common living document tools include google docs and nextcloud collabora. living documentation is a key concept in specification by example.


in order to be able to use the available standard indexes to locations where index data is not available we have to incorporate a new term called the location factor ( lf ) to the standard index value. it is a dimensionless value for a particular location relative to either of the above - mentioned basis. cost in a = cost in usgc x lf ( a ) where a is the location for which cost is being evaluated and lf ( a ) is the location factor for the location a relative to usgc location factors are greatly influenced by currency exchange rates due to their significant effect on index value and hence vary drastically with time. over the past couple of decades the location factors for various locations are trending close to the value 1.


note that the concerning interior flow is horizontal, so w = 0 { \ displaystyle w = 0 } at all depths, even in the boundary layers. in this case, the navier - stokes momentum equations, governing geophysical motion can now be reduced to : − f v = − 1 ρ 0 ∂ p ∂ x + ν e ∂ 2 u ∂ z 2, f u = − 1 ρ 0 ∂ p ∂ y + ν e ∂ 2 v ∂ z 2, 0 = − 1 ρ 0 ∂ p ∂ z, { \ displaystyle { \ begin { aligned } - fv & = - { \ frac { 1 } { \ rho _ { 0 } } } { \ frac { \ partial p } { \ partial x } } + \ nu _ { e } { \ frac { \ partial ^ { 2 } u } { \ partial z ^ { 2 } } }, \ \ fu & = - { \ frac { 1 } { \ rho _ { 0 } } } { \ frac { \ partial p } { \ partial y } } + \ nu _ { e } { \ frac { \ partial ^ { 2 } v } { \ partial z ^ { 2 } } }, \ \ 0 & = - { \ frac { 1 } { \ rho _ { 0 } } } { \ frac { \ partial p } { \ partial z } }, \ end { aligned } } } where f { \ displaystyle f } is the coriolis parameter, ρ 0 { \ displaystyle \ rho _ { 0 } } the fluid density and ν e { \ displaystyle \ nu _ { e } } the eddy viscosity, which are all taken as a constant here for simplicity. these parameters have a small variance on the scale of an ekman spiral, thus this approximation will hold.


in this example, all uris, both for edges and nodes ( e. g. http : / / schema. org / person, http : / / schema. org / birthplace, http : / / www. wikidata. org / entity / q1731 ) can be dereferenced and will result in further rdf graphs, describing the uri, e. g. that dresden is a city in germany, or that a person, in the sense of that uri, can be fictional. the second graph shows the previous example, but now enriched with a few of the triples from the documents that result from dereferencing https : / / schema. org / person ( green edge ) and https : / / www. wikidata. org / entity / q1731 ( blue edges ). additionally to the edges given in the involved documents explicitly, edges can be automatically inferred : the triple from the original rdfa fragment and the triple from the document at https : / / schema. org / person ( green edge in the figure ) allow to infer the following triple, given owl semantics ( red dashed line in the second figure ) :


in order to connect this to tango trees, we will find an upper bound on the work done by the tango tree for a given access sequence. our upper bound will be ( k + 1 ) o ( log log n ) { \ displaystyle ( k + 1 ) o ( \ log \ log n ) }, where k is the number of interleaves. the total cost is divided into two parts, searching for the element, and updating the structure of the tango tree to maintain the proper invariants ( switching preferred children and re - arranging preferred paths ).


software has always been electronically transferred, and encryption has always been part of computing. the introduction of unified commercial software distribution catalog with a true application storefront to collectively manage and provide encryption for apps and media was a seminal invention. this is because by protecting the digital rights of artists online, the app store provided the first viable economic and instant distribution mechanism which ultimately exploded the pace of software adoption and created an economic boom.


in the area of constraint satisfaction problems, flexible variants exist that deal with soft constraints in a similar way to preferences in preference - based planning. = = references = =


for example, one call - hour could be one call for an hour or two ( possibly concurrent ) calls for half an hour each. call - seconds give a measure of the average number of concurrent calls. offered load is defined as the traffic density per unit time, measured in erlangs. an erlang is defined as one call - hour per hour, or 3, 600 call - seconds per hour. hence, if one ccs is measured over a one - hour period, the offered load is 1 / 36 erlangs.


in mathematics, the newton polytope is an integral polytope associated with a multivariate polynomial. it can be used to analyze the polynomial's behavior when specific variables are considered negligible relative to the others. specifically, given a vector x = ( x 1, …, x n ) { \ displaystyle \ mathbf { x } = ( x _ { 1 }, \ ldots, x _ { n } ) } of variables and a finite family ( a k ) k { \ displaystyle ( \ mathbf { a } _ { k } ) _ { k } } of pairwise distinct vectors from n n { \ displaystyle \ mathbb { n } ^ { n } } each encoding the exponents within a monomial, consider the multivariate polynomial f ( x ) = k c k x a k { \ displaystyle f ( \ mathbf { x } ) = \ sum _ { k } c _ { k } \ mathbf { x } ^ { \ mathbf { a } _ { k } } } where we use the shorthand notation ( x 1, …, x n ) ( y 1, …, y n ) { \ displaystyle ( x _ { 1 }, \ ldots, x _ { n } ) ^ { ( y _ { 1 }, \ ldots, y _ { n } ) } } for the monomial x 1 y 1 x 2 y 2 x n y n { \ displaystyle x _ { 1 } ^ { y _ { 1 } } x _ { 2 } ^ { y _ { 2 } } \ cdots x _ { n } ^ { y _ { n } } }. then the newton polytope associated to f { \ displaystyle f } is the convex hull of the vectors a k { \ displaystyle \ mathbf { a } _ { k } } ; that is newt ( f ) = { k α k a k : k α k = 1 & j α j ≥ 0 }.


{ \ displaystyle p _ { 0 } ( x ) + p _ { 1 } ( x ) \ cdot f + p _ { 2 } ( x ) \ cdot f ^ { 2 } + \ cdots + p _ { n } ( x ) \ cdot f ^ { n } = 0. } a context - free grammar is said to be unambiguous if every string generated by the grammar admits a unique parse tree or, equivalently, only one leftmost derivation.


in mathematics, the category of topological vector spaces is the category whose objects are topological vector spaces and whose morphisms are continuous linear maps between them. this is a category because the composition of two continuous linear maps is again a continuous linear map. the category is often denoted tvect or tvs. fixing a topological field k, one can also consider the subcategory tvectk of topological vector spaces over k with continuous k - linear maps as the morphisms.


the order - dependent composition 1 + 3 is the same partition as 3 + 1, and the two distinct compositions 1 + 2 + 1 and 1 + 1 + 2 represent the same partition as 2 + 1 + 1. an individual summand in a partition is called a part. the number of partitions of n is given by the partition function p ( n ).


it is sometimes referred to as a sub - channel, but this is a misnomer because no additional channels are created. all users with different ctcss tones on the same channel are still transmitting on the identical radio frequency, and their transmissions interfere with each other ; however ; the interference is masked under most conditions. the ctcss feature also does not offer any security. a receiver with just a carrier or noise squelch does not suppress any sufficiently strong signal ; in ctcss mode it unmutes only when the signal also carries the correct sub - audible audio tone. the tones are not actually below the range of human hearing, but are poorly reproduced by most communications - grade speakers and in any event are usually filtered out before being sent to the speaker or headphone.


in the cuboctahedron - first parallel projection of the rectified tesseract into 3 - dimensional space, the image has the following layout : the projection envelope is a cube. a cuboctahedron is inscribed in this cube, with its vertices lying at the midpoint of the cube's edges. the cuboctahedron is the image of two of the cuboctahedral cells. the remaining 6 cuboctahedral cells are projected to the square faces of the cube. the 8 tetrahedral volumes lying at the triangular faces of the central cuboctahedron are the images of the 16 tetrahedral cells, two cells to each image.


in quantum mechanics, bra – ket notation is used ubiquitously to denote quantum states. the notation uses angle brackets, ⟨ { \ displaystyle \ langle } and ⟩ { \ displaystyle \ rangle }, and a vertical bar | { \ displaystyle | }, to construct " bras " and " kets ". a ket is of the form | v ⟩ { \ displaystyle | v \ rangle }. mathematically it denotes a vector, v { \ displaystyle { \ boldsymbol { v } } }, in an abstract ( complex ) vector space v { \ displaystyle v }, and physically it represents a state of some quantum system.


in mathematics, neville's algorithm is an algorithm used for polynomial interpolation that was derived by the mathematician eric harold neville in 1934. given n + 1 points, there is a unique polynomial of degree ≤ n which goes through the given points. neville's algorithm evaluates this polynomial. neville's algorithm is based on the newton form of the interpolating polynomial and the recursion relation for the divided differences. it is similar to aitken's algorithm ( named after alexander aitken ), which is nowadays not used.


for example, a matrix is often used to represent the coefficients in a system of linear equations, and determinants can be used to solve these equations ( cramer's rule ), although other methods of solution are computationally much more efficient. determinants are used for defining the characteristic polynomial of a matrix, whose roots are the eigenvalues. in geometry, the signed n - dimensional volume of a n - dimensional parallelepiped is expressed by a determinant, and the determinant of ( the matrix of ) a linear transformation determines how the orientation and the n - dimensional volume are transformed. this is used in calculus with exterior differential forms and the jacobian determinant, in particular for changes of variables in multiple integrals.


in mathematics, the sieve of pritchard is an algorithm for finding all prime numbers up to a specified bound. like the ancient sieve of eratosthenes, it has a simple conceptual basis in number theory. it is especially suited to quick hand computation for small bounds.


in the united states, sec. 204. 2 ( d ) ( 1 ) of regulation d ( frb ) previously limited withdrawals from savings accounts to six transfers or withdrawals per month, a limitation which was removed in april 2020, though some banks continue to impose a limit voluntarily as of 2021. there is no limit to the number of deposits into the account. violations of the regulation may result in a service charge or may result in the account being changed to a checking account. regulation d sets smaller reserve requirements for savings account balances. in addition, customers can plan withdrawals to avoid fees and earn interest, which contributes to more stable savings account balances on which banks can lend. a savings account linked to a checking account at the same financial institution can help avoid fees due to overdrafts and reduce banking costs.


bob communicates over a public channel with alice to determine which b i { \ displaystyle b _ { i } } and b i ′ { \ displaystyle b'_ { i } } are not equal. both alice and bob now discard the bits in a { \ displaystyle a } and a ′ { \ displaystyle a'} where b { \ displaystyle b } and b ′ { \ displaystyle b'} do not match. from the remaining k { \ displaystyle k } bits where both alice and bob measured in the same basis, alice randomly chooses k / 2 { \ displaystyle k / 2 } bits and discloses her choices over the public channel.


in mathematics and mathematical optimization, the convex conjugate of a function is a generalization of the legendre transformation which applies to non - convex functions. it is also known as legendre – fenchel transformation, fenchel transformation, or fenchel conjugate ( after adrien - marie legendre and werner fenchel ). it allows in particular for a far reaching generalization of lagrangian duality.


the runtime of the algorithm is t ( n, p ) = t c o l l ( n / n, p ) + n ∗ t s e q ( n / n ) + 2 ( n − 1 ) ( t s t a r t + t b y t e ( n / n ) 2 ) { \ displaystyle t { \ mathcal { ( n, p ) } } = t _ { coll } ( n / n, p ) + n * t _ { seq } ( n / n ) + 2 ( n - 1 ) ( t _ { start } + t _ { byte } ( n / n ) ^ { 2 } ) }, where t c o l l { \ displaystyle t _ { coll } } is the time of the initial distribution of the matrices in the first step, t s e q { \ displaystyle t _ { seq } } is the calculation of the intermediate results and t s t a r t { \ displaystyle t _ { start } } and t b y t e { \ displaystyle t _ { byte } } stands for the time it takes to establish a connection and transmission of byte respectively. a disadvantage of the algorithm is that there are many connection setups, with small message sizes. it would be better to be able to transmit more data in each message.


in mathematics, the hausdorff distance, or hausdorff metric, also called pompeiu – hausdorff distance, measures how far two subsets of a metric space are from each other. it turns the set of non - empty compact subsets of a metric space into a metric space in its own right. it is named after felix hausdorff and dimitrie pompeiu. informally, two sets are close in the hausdorff distance if every point of either set is close to some point of the other set.


we can't prevent aging, but we can understand its causes, take steps to limit its effects, temporarily reverse some of the damage it has caused, and prepare for the day when the software is no longer viable. " from both an academic and industrial point of view, the software aging phenomenon has increased. recent research has focussed on clarifying its causes and effects. memory bloating and leaking, along with data corruption and unreleased file - locks are particular causes of software aging.


without this property, an attacker can undermine the mechanism itself and hence violate the security policy. for example, windows 3. x and 9x operating systems were not built with a reference monitor, whereas the windows nt line, which also includes windows 2000 and windows xp, was designed to contain a reference monitor, although it is not clear that its properties ( tamperproof, etc. ) have ever been independently verified, or what level of computer security it was intended to provide. the claim is that a reference validation mechanism that satisfies the reference monitor concept will correctly enforce a system's access control policy, as it must be invoked to mediate all security - sensitive operations, must not be tampered with, and has undergone complete analysis and testing to verify correctness. the abstract model of a reference monitor has been widely applied to any type of system that needs to enforce access control and is considered to express the necessary and sufficient properties for any system making this security claim. according to ross anderson, the reference monitor concept was introduced by james anderson in an influential 1972 paper. peter denning in a 2013 oral history stated that james anderson credited the concept to a paper he and scott graham presented at a 1972 conference. systems evaluated at b3 and above by the trusted computer system evaluation criteria ( tcsec ) must enforce the reference monitor concept.


the original metadata schema contributed to oasis is listed in its entirety in section 7 of the liberty metadata version 1. 0 specification. similarly, the specification for liberty metadata version 1. 1 includes a listing of the version 1. 1 schema. both the version 1. 0 schema and the version 1. 1 schema are linked here courtesy of the internet archive's wayback machine.


in mathematics ( specifically linear algebra ), the woodbury matrix identity, named after max a. woodbury, says that the inverse of a rank - k correction of some matrix can be computed by doing a rank - k correction to the inverse of the original matrix. alternative names for this formula are the matrix inversion lemma, sherman – morrison – woodbury formula or just woodbury formula. however, the identity appeared in several papers before the woodbury report. the woodbury matrix identity is ( a + u c v ) − 1 = a − 1 − a − 1 u ( c − 1 + v a − 1 u ) − 1 v a − 1, { \ displaystyle \ left ( a + ucv \ right ) ^ { - 1 } = a ^ { - 1 } - a ^ { - 1 } u \ left ( c ^ { - 1 } + va ^ { - 1 } u \ right ) ^ { - 1 } va ^ { - 1 }, } where a, u, c and v are conformable matrices : a is n×n, c is k×k, u is n×k, and v is k×n. this can be derived using blockwise matrix inversion.


moreover, it facilitates the construction of complex multi - step instructions, while simultaneously reducing the complexity of computer circuits. the act of writing microcode is often referred to as microprogramming, and the microcode in a specific processor implementation is sometimes termed a microprogram. through extensive microprograming, microarchitectures of smaller scale and simplicity can emulate more robust architectures with wider word lengths, additional execution units, and so forth.


in planned economies, production is typically limited only to necessity, which would eliminate externalities created by overproduction. the central planner can decide to create and allocate jobs in industries that work to mitigate externalities, rather than waiting for the market to create a demand for these jobs.


for our purpose it is fine to use either ω or j. however, they have a different meaning : j is contravariant and ω is covariant. the matrix ω corresponds to the lagrange brackets of classical mechanics and j corresponds to the poisson brackets. note the important relation ω = j − 1.


tableseer : in scholarly articles tables are used to present, list, summarize, and structure important data. tableseer automatically identifies tables in digital documents, extracts the table metadata as well as the cells content, and stores them in such a way that allows users to either query the table content or search for tables in a large set of documents. dataset search : chemxseer provides tools to incorporate datasets from different experiments sources. the system is able to manipulate results from multiple formats such as xml, microsoft excel, gaussian, and charmm, create databases, to allow direct queries over the data, create metadata, using an annotation tool, which will allow users to search over the datasets, as well as a way to create links among datasets and / or between datasets and documents. in addition to these tools, chemxseer will integrate the advances made by its sister project citeseerx to provide : full text search author, affiliation, title and venue search citation and acknowledgement search citation linking and statistics


in mathematics, a bilinear program is a nonlinear optimization problem whose objective or constraint functions are bilinear. an example is the pooling problem.


in the field of internet vigilantism, information entropy is an act intended to disrupt online services.


in mathematics, for a natural number n ≥ 2 { \ displaystyle n \ geq 2 }, the nth fibonacci group, denoted f ( 2, n ) { \ displaystyle f ( 2, n ) } or sometimes f ( n ) { \ displaystyle f ( n ) }, is defined by n generators a 1, a 2, …, a n { \ displaystyle a _ { 1 }, a _ { 2 }, \ dots, a _ { n } } and n relations : a 1 a 2 = a 3, { \ displaystyle a _ { 1 } a _ { 2 } = a _ { 3 }, } a 2 a 3 = a 4, { \ displaystyle a _ { 2 } a _ { 3 } = a _ { 4 }, } … { \ displaystyle \ dots } a n − 2 a n − 1 = a n, { \ displaystyle a _ { n - 2 } a _ { n - 1 } = a _ { n }, } a n − 1 a n = a 1, { \ displaystyle a _ { n - 1 } a _ { n } = a _ { 1 }, } a n a 1 = a 2 { \ displaystyle a _ { n } a _ { 1 } = a _ { 2 } }. these groups were introduced by john conway in 1965. the group f ( 2, n ) { \ displaystyle f ( 2, n ) } is of finite order for n = 2, 3, 4, 5, 7 { \ displaystyle n = 2, 3, 4, 5, 7 } and infinite order for n = 6 { \ displaystyle n = 6 } and n ≥ 8 { \ displaystyle n \ geq 8 }. the infinitude of f ( 2, 9 ) { \ displaystyle f ( 2, 9 ) } was proved by computer in 1990.


it has been suggested that what interrogators expect as human responses is not necessarily typical of humans. as a result, some individuals can be categorised as machines. this can therefore work in favour of a competing machine. the humans are instructed to " act themselves ", but sometimes their answers are more like what the interrogator expects a machine to say. this raises the question of how to ensure that the humans are motivated to " act human ".


the resulting phylogeny can approximate the transmission history, and a variety of methods have been developed to adjust for confounding factors. due to the associated stigma and the criminalization of transmission for specific infectious diseases, molecular source attribution at the level of individuals can be a controversial use of data that was originally collected in a healthcare setting, with potentially severe legal consequences for individuals who become identified as putative sources. in these contexts, the development and application of molecular source attribution techniques may involve trade - offs between public health responsibilities and individual rights to data privacy.


for example, a student is a person. therefore, the set of students is a subset of the set of persons.


in the hits algorithm, the first step is to retrieve the most relevant pages to the search query. this set is called the root set and can be obtained by taking the top pages returned by a text - based search algorithm. a base set is generated by augmenting the root set with all the web pages that are linked from it and some of the pages that link to it. the web pages in the base set and all hyperlinks among those pages form a focused subgraph.


in term logic, a " proposition " is simply a form of language : a particular kind of sentence, in which the subject and predicate are combined, so as to assert something true or false. it is not a thought, or an abstract entity. the word " propositio " is from the latin, meaning the first premise of a syllogism.


in the multics operating system all files, including executables, are segments. a call to a routine not part of the current segment will cause the system to find the referenced segment, in memory or on disk, and add it to the address space of the running process. dynamic linking is the normal method of operation, and static linking ( using the binder ) is the exception.


for example, ( 2 + 3 ) × 4 = 20 forces addition to precede multiplication, while ( 3 + 5 ) 2 = 64 forces addition to precede exponentiation. if multiple pairs of parentheses are required in a mathematical expression ( such as in the case of nested parentheses ), the parentheses may be replaced by brackets or braces to avoid confusion, as in − 5 = 9.


in philosophy, a process ontology refers to a universal model of the structure of the world as an ordered wholeness. such ontologies are fundamental ontologies, in contrast to the so - called applied ontologies. fundamental ontologies do not claim to be accessible to any empirical proof in itself but to be a structural design pattern, out of which empirical phenomena can be explained and put together consistently. throughout western history, the dominating fundamental ontology is the so - called substance theory.


in peer - to - peer networking, a supernode is any node that also serves as one of that network's relayers and proxy servers, handling data flow and connections for other users. this semi - distributed architecture allows data to be decentralized without requiring excessive overhead at every node. however, the increased workload of supernodes generally requires additional network bandwidth and central processing unit ( cpu ) time. = = references = =


in the clustering of biological information such as data from microarray experiments, the cophenetic similarity or cophenetic distance of two objects is a measure of how similar those two objects have to be in order to be grouped into the same cluster. the cophenetic distance between two objects is the height of the dendrogram where the two branches that include the two objects merge into a single branch. outside the context of a dendrogram, it is the distance between the largest two clusters that contain the two objects individually when they are merged into a single cluster that contains both.


when applied component - wise to vectors, the discrete distance from zero behaves like a non - homogeneous " norm ", which counts the number of non - zero components in its vector argument ; again, this non - homogeneous " norm " is discontinuous. in signal processing and statistics, david donoho referred to the zero " norm " with quotation marks. following donoho's notation, the zero " norm " of x { \ displaystyle x } is simply the number of non - zero coordinates of x, { \ displaystyle x, } or the hamming distance of the vector from zero.


in statistics, latent variables ( from latin : present participle of lateo, “ lie hidden ” ) are variables that can only be inferred indirectly through a mathematical model from other observable variables that can be directly observed or measured. such latent variable models are used in many disciplines, including political science, demography, engineering, medicine, ecology, physics, machine learning / artificial intelligence, bioinformatics, chemometrics, natural language processing, management, psychology and the social sciences. latent variables may correspond to aspects of physical reality.


. should be restricted to those officials with a need for such information. these minimization requirements complement and supplement traditional standards under the fourth amendment to the united states constitution.


different operating systems offer distinct methods for applications to identify their security requirements : sudo centralizes all privilege authorization information in a single configuration file, / etc / sudoers, which contains a list of users and the privileged applications and actions that those users are permitted to use. the grammar of the sudoers file is intended to be flexible enough to cover many different scenarios, such as placing restrictions on command - line parameters.


in the context of osha's psm, mechanical integrity requirements apply to the following equipment : pressure vessels and storage tanks. piping systems ( including piping components such as valves ). relief and vent systems and devices. emergency shutdown systems. controls ( including monitoring devices and sensors, alarms, and interlocks ). pumps. in order to minimize the risk of unwanted releases of hazardous materials, companies must establish and implement adequate maintenance strategies. psm schemes other than osha's usually extend this element to cover the integrity assurance of safety - critical systems in general, not just those directly responsible for fluid containment, according to a wider asset integrity management strategy that includes systems such as active and passive fire protection, fire and gas detection, sources of emergency power, etc.


in the united states, many of the regulatory efforts put forth in response to predatory advertising practices, especially those involving the usage of personal data, have been spearheaded by the federal trade commission. congress too, has brought forth numerous legislative measures to address the informational asymmetry and privacy concerns of modern data - collection and advertising. proponents of regulatory action have explained that data regulation can be exceptionally hard to craft for a number of reasons. though many have called for greater transparency in data - collection efforts, critics claims that transparency alone falls short, as data is often repackaged and sold through many brokerage firms, leading to many uses that may not have been clearly outlined as the original purpose or intent.


other well - known examples are a sphere equipped with the angular distance and the hyperbolic plane. a metric may correspond to a metaphorical, rather than physical, notion of distance : for example, the set of 100 - character unicode strings can be equipped with the hamming distance, which measures the number of characters that need to be changed to get from one string to another.


in practice, data elements ( fields, columns, attributes, etc. ) are sometimes " overloaded ", meaning a given data element will have multiple potential meanings. while a known bad practice, overloading is nevertheless a very real factor or barrier to understanding what a system is doing.


in salt - fingering staircases, vertical temperature and salinity fluxes are downgradient, while the vertical density flux is upgradient. this is explained by the fact that the potential energy released in transporting salt downward must exceed that expended in transporting heat upward, resulting in a net downward transport of mass. this negative diffusion sharpens the fluctuations and therefore suggests a means for generating and maintaining staircases.


for example, ocaml uses structural typing on methods for compatibility of object types. go uses structural typing on methods to determine compatibility of a type with an interface. c + + template functions exhibit structural typing on type arguments.


this technology allows analysts to search through large volumes of recorded conversations and isolate mentions of keywords. recordings can be indexed and analysts can run queries over the database to find conversations of interest. some government research programs focused on intelligence applications of speech recognition, e. g. darpa's ears's program and iarpa's babel program.


it was reported to be " the first very deep feedforward network with hundreds of layers ". it is like an lstm with forget gates unfolded in time, while the later residual nets have no equivalent of forget gates and are like the unfolded original lstm. if the skip connections in highway networks are " without gates ", or if their gates are kept open ( activation 1. 0 ) through strong positive bias weights, they become the identity skip connections in residual networks.


in statistics, the logistic model ( or logit model ) is a statistical model that models the probability of an event taking place by having the log - odds for the event be a linear combination of one or more independent variables. in regression analysis, logistic regression ( or logit regression ) is estimating the parameters of a logistic model ( the coefficients in the linear combination ). formally, in binary logistic regression there is a single binary dependent variable, coded by an indicator variable, where the two values are labeled " 0 " and " 1 ", while the independent variables can each be a binary variable ( two classes, coded by an indicator variable ) or a continuous variable ( any real value ). the corresponding probability of the value labeled " 1 " can vary between 0 ( certainly the value " 0 " ) and 1 ( certainly the value " 1 " ), hence the labeling ; the function that converts log - odds to probability is the logistic function, hence the name.


in number theory, euler's criterion is a formula for determining whether an integer is a quadratic residue modulo a prime. precisely, let p be an odd prime and a be an integer coprime to p. then a p − 1 2 ≡ { 1 ( mod p ) if there is an integer x such that x 2 ≡ a ( mod p ), − 1 ( mod p ) if there is no such integer. { \ displaystyle a ^ { \ tfrac { p - 1 } { 2 } } \ equiv { \ begin { cases } \ ; \ ; \, 1 { \ pmod { p } } & { \ text { if there is an integer } } x { \ text { such that } } x ^ { 2 } \ equiv a { \ pmod { p } }, \ \ - 1 { \ pmod { p } } & { \ text { if there is no such integer.


in the standard encoding the least significant bit follows a repetitive pattern of 2 on, 2 off ( … 11001100 … ) ; the next digit a pattern of 4 on, 4 off ; the ith least significant bit a pattern of 2i on 2i off. the most significant digit is an exception to this ; for an n - bit gray code, the most significant digit follows 2n - 1 on 2n - 1 off, the same as for the second - most significant digit, but starting at a different point in the sequence. the four - bit version of this is shown below : for decimal 15 the code rolls over to decimal 0 with only one switch change.


formally, a sequence can be defined as a function from natural numbers ( the positions of elements in the sequence ) to the elements at each position. the notion of a sequence can be generalized to an indexed family, defined as a function from an arbitrary index set. for example, ( m, a, r, y ) is a sequence of letters with the letter'm'first and'y'last.


in a vliw, the compiler uses heuristics or profile information to guess the direction of a branch. this allows it to move and preschedule operations speculatively before the branch is taken, favoring the most likely path it expects through the branch. if the branch takes an unexpected way, the compiler has already generated compensating code to discard speculative results to preserve program semantics. vector processor cores ( designed for large one - dimensional arrays of data called vectors ) can be combined with the vliw architecture such as in the fujitsu fr - v microprocessor, further increasing throughput and speed.


this can be proven by showing that for a schema s = ( d, r, h ), a given set k of constants in the query expression, a tuple variable v and a header h we can construct a safe formula for every pair v. a with a in h that states that its value is in the active domain. for example, assume that k = { 1, 2 }, r = { " r " } and h = { ( " r ", { " a, " b " } ) } then the corresponding safe formula for v. b is : v. b = 1 ∨ v. b = 2 ∨ w ( r ( w ) ∧ ( v. b = w. a ∨ v. b = w. b ) ) this formula, then, can be used to rewrite any unsafe query expression to an equivalent safe query expression by adding such a formula for every variable v and column name a in its type where it is used in the expression. effectively this means that we let all variables range over the active domain, which, as was already explained, does not change the semantics if the expressed query is domain independent.


in psychometrics and psychophysics, the term accuracy is interchangeably used with validity and constant error. precision is a synonym for reliability and variable error. the validity of a measurement instrument or psychological test is established through experiment or correlation with behavior. reliability is established with a variety of statistical techniques, classically through an internal consistency test like cronbach's alpha to ensure sets of related questions have related responses, and then comparison of those related question between reference and target population.


in words : a demonstration that a number is somehow apart from zero is also a demonstration that this number is non - zero. but constructively it does not follow that the doubly negative statement ¬ ( x 0 ) { \ displaystyle \ neg ( x \ cong 0 ) } would imply x # 0 { \ displaystyle x \ # 0 }. consequently, many classically equivalent statements bifurcate into distinct statement.


operations defined on feature structures, e. g. unification, are used extensively in phrase structure grammars. in most theories ( e. g. hpsg ), operations are strictly speaking defined over equations describing feature structures and not over feature structures themselves, though feature structures are usually used in informal exposition. often, feature structures are written like this : ] { \ displaystyle { \ begin { bmatrix } { \ mbox { category } } & noun \ phrase \ \ { \ mbox { agreement } } & { \ begin { bmatrix } { \ mbox { number } } & singular \ \ { \ mbox { person } } & third \ end { bmatrix } } \ end { bmatrix } } } here there are the two features category and agreement.


a deep result in the classification of finite semigroups is krohn – rhodes theory, analogous to the jordan – holder decomposition for finite groups. some other techniques for studying semigroups, like green's relations, do not resemble anything in group theory. the theory of finite semigroups has been of particular importance in theoretical computer science since the 1950s because of the natural link between finite semigroups and finite automata via the syntactic monoid.


in the nirukta, written in the 6th or 5th century bce, the sanskrit grammarian yaska defined four main categories of words : नाम nama – noun ( including adjective ) आखयात akhyata – verb उपसरग upasarga – pre - verb or prefix निपात nipata – particle, invariant word ( perhaps preposition ) these four were grouped into two larger classes : inflectable ( nouns and verbs ) and uninflectable ( pre - verbs and particles ). the ancient work on the grammar of the tamil language, tolkappiyam, argued to have been written around 2nd century ce, classifies tamil words as peyar ( ; noun ), vinai ( வினை ; verb ), idai ( part of speech which modifies the relationships between verbs and nouns ), and uri ( word that further qualifies a noun or verb ).


the term " inheritance " is loosely used for both class - based and prototype - based programming, but in narrow use the term is reserved for class - based programming ( one class inherits from another ), with the corresponding technique in prototype - based programming being instead called delegation ( one object delegates to another ). class - modifying inheritance patterns can be pre - defined according to simple network interface parameters such that inter - language compatibility is preserved. inheritance should not be confused with subtyping. in some languages inheritance and subtyping agree, whereas in others they differ ; in general, subtyping establishes an is - a relationship, whereas inheritance only reuses implementation and establishes a syntactic relationship, not necessarily a semantic relationship ( inheritance does not ensure behavioral subtyping ).


the idea is that a triggering condition in the home or a desire of the user can trigger the execution of a complex process. the process is defined in the moment that it needs to be executed. it automatically composes services available on home devices and appliances.


in mathematics, elliptic curve primality testing techniques, or elliptic curve primality proving ( ecpp ), are among the quickest and most widely used methods in primality proving. it is an idea put forward by shafi goldwasser and joe kilian in 1986 and turned into an algorithm by a. o. l. atkin the same year. the algorithm was altered and improved by several collaborators subsequently, and notably by atkin and francois morain, in 1993. the concept of using elliptic curves in factorization had been developed by h. w. lenstra in 1985, and the implications for its use in primality testing ( and proving ) followed quickly.


in mathematics, a solinas prime, or generalized mersenne prime, is a prime number that has the form f ( 2 m ) { \ displaystyle f ( 2 ^ { m } ) }, where f ( x ) { \ displaystyle f ( x ) } is a low - degree polynomial with small integer coefficients. these primes allow fast modular reduction algorithms and are widely used in cryptography. they are named after jerome solinas. this class of numbers encompasses a few other categories of prime numbers : mersenne primes, which have the form 2 k − 1 { \ displaystyle 2 ^ { k } - 1 }, crandall or pseudo - mersenne primes, which have the form 2 k − c { \ displaystyle 2 ^ { k } - c } for small odd c { \ displaystyle c }.


it is defined by the equations : | a & b | = | a | + | b | = ( { 1 } × | a | ) ∪ ( { 2 } × | b | ) { \ displaystyle | { \ mathcal { a } } \ \ & \ { \ mathcal { b } } | = | { \ mathcal { a } } | + | { \ mathcal { b } } | = ( \ { 1 \ } \ times | { \ mathcal { a } } | ) \ cup ( \ { 2 \ } \ times | { \ mathcal { b } } | ) } ( i. e. the set of tokens of a & b { \ displaystyle { \ mathcal { a } } \ \ & \ { \ mathcal { b } } } is the coproduct ( or disjoint union ) of the token sets of a { \ displaystyle { \ mathcal { a } } } and b { \ displaystyle { \ mathcal { b } } }. tokens from differents sets are always coherent and tokens from the same set are coherent exactly when they are coherent in that set. ( 1, α ) a & b ( 1, α ′ ) α a α ′ { \ displaystyle ( 1, \ alpha ) \ sim _ { { \ mathcal { a } } \ \ & \ { \ mathcal { b } } } ( 1, \ alpha') \ iff \ alpha \ sim _ { \ mathcal { a } } \ alpha'} ( 2, β ) a & b ( 2, β ′ ) β b β ′ { \ displaystyle ( 2, \ beta ) \ sim _ { { \ mathcal { a } } \ \ & \ { \ mathcal { b } } } ( 2, \ beta') \ iff \ beta \ sim _ { \ mathcal { b } } \ beta'} ( 1, α ) a & b ( 2, β ), α ∈ | a |, β ∈ | b | { \ displaystyle ( 1, \ alpha ) \ sim _ { { \ mathcal { a } } \ \ & \ { \ mathcal { b } } } ( 2, \ beta ), \ forall \ alpha \ in | { \ mathcal { a } } |, \ beta \ in | { \ mathcal { b } } |


in mathematics, a unary operation is an operation with only one operand, i. e. a single input. this is in contrast to binary operations, which use two operands. an example is any function f : a → a, where a is a set.


additionally, some programming languages allow for some types to be automatically converted to other types ; for example, an int can be used where the program expects a float. dynamic typing, also called latent typing, determines the type - safety of operations at run time ; in other words, types are associated with run - time values rather than textual expressions. as with type - inferred languages, dynamically - typed languages do not require the programmer to write explicit type annotations on expressions.


, c n ) { \ displaystyle { \ dot { c _ { i } } } = { \ operatorname { d } \! c _ { i } \ over \ operatorname { d } \! t } = f ( c _ { 1 }, c _ { 2 },..., c _ { n } ) } which shows how the number of people in compartment c i { \ displaystyle c _ { i } } changes over time. for example, in a sir model, c 1 = s { \ displaystyle c _ { 1 } = s }, c 2 = i { \ displaystyle c _ { 2 } = i }, and c 3 = r { \ displaystyle c _ { 3 } = r }. compartmental models have a disease - free equilibrium ( dfe ) meaning that it is possible to find an equilibrium while setting the number of infected people to zero, i = 0 { \ displaystyle i = 0 }.


( and this principle is valid in a theory like c z f { \ displaystyle { \ mathsf { czf } } }. also compare with the replacement axiom. ) that is, the mapping information exists as set and it has a pair for each element in the domain.


s { \ displaystyle \ lambda : s. s ^ { \ prime } \ to s ^ { \ prime }. s } such that ( s ′, λ ) { \ displaystyle \ left ( s ^ { \ prime }, \ lambda \ right ) } is a lax map of monads s → s { \ displaystyle s \ to s } and ( s, λ ) { \ displaystyle ( s, \ lambda ) } is a colax map of monads s ′ → s ′. { \ displaystyle s ^ { \ prime } \ to s ^ { \ prime }. } this is exactly the data needed to define a monad structure on s ′.


in informal logic this is called a counter argument. the form of an argument can be shown by the use of symbols. for each argument form, there is a corresponding statement form, called a corresponding conditional, and an argument form is valid if and only if its corresponding conditional is a logical truth.


in statistics, classification is the problem of identifying which of a set of categories ( sub - populations ) an observation ( or observations ) belongs to. examples are assigning a given email to the " spam " or " non - spam " class, and assigning a diagnosis to a given patient based on observed characteristics of the patient ( sex, blood pressure, presence or absence of certain symptoms, etc. ). often, the individual observations are analyzed into a set of quantifiable properties, known variously as explanatory variables or features. these properties may variously be categorical ( e. g. " a ", " b ", " ab " or " o ", for blood type ), ordinal ( e. g. " large ", " medium " or " small " ), integer - valued ( e. g. the number of occurrences of a particular word in an email ) or real - valued ( e. g. a measurement of blood pressure ).


in statistics, apophenia is an example of a type i error – the false identification of patterns in data. it may be compared to a so - called false positive in other test situations.


in mathematics, arithmetic combinatorics is a field in the intersection of number theory, combinatorics, ergodic theory and harmonic analysis.


in practice the classical relational algebra described above is extended with various operations such as outer joins, aggregate functions and even transitive closure.


in the semantic web approach, data from multiple websites or databases is searched via metadata. metadata is machine - readable code, which defines the contents of the page for the program so that the comparisons between the data and the search terms are more accurate. this serves to decrease the number of results that are irrelevant or unhelpful. some meta - data exists as definitions called ontologies, which can be tagged by either users or programs ; these serve to facilitate searches by using key terms or phrases to find and return the data.


n. r. campbell and the ferguson committee were thus proven wrong.


this could be the set of all subsets of the array of bits that are skeletonized 4 - connected ( width of the font is 1 ). let e x ( c, d ) { \ displaystyle ex ( c, d ) } be a procedure that draws an example, x { \ displaystyle x }, using a probability distribution d { \ displaystyle d } and gives the correct label c ( x ) { \ displaystyle c ( x ) }, that is 1 if x ∈ c { \ displaystyle x \ in c } and 0 otherwise. now, given 0 <, δ < 1 { \ displaystyle 0 < \ epsilon, \ delta < 1 }, assume there is an algorithm a { \ displaystyle a } and a polynomial p { \ displaystyle p } in 1 /, 1 / δ { \ displaystyle 1 / \ epsilon, 1 / \ delta } ( and other relevant parameters of the class c { \ displaystyle c } ) such that, given a sample of size p { \ displaystyle p } drawn according to e x ( c, d ) { \ displaystyle ex ( c, d ) }, then, with probability of at least 1 − δ { \ displaystyle 1 - \ delta }, a { \ displaystyle a } outputs a hypothesis h ∈ c { \ displaystyle h \ in c } that has an average error less than or equal to { \ displaystyle \ epsilon } on x { \ displaystyle x } with the same distribution d { \ displaystyle d }. further if the above statement for algorithm a { \ displaystyle a } is true for every concept c ∈ c { \ displaystyle c \ in c } and for every distribution d { \ displaystyle d } over x { \ displaystyle x }, and for all 0 <, δ < 1 { \ displaystyle 0 < \ epsilon, \ delta < 1 } then c { \ displaystyle c } is ( efficiently ) pac learnable ( or distribution - free pac learnable ). we can also say that a { \ displaystyle a } is a pac learning algorithm for c { \ displaystyle c }.


in mathematics, the lower convex envelope f { \ displaystyle { \ breve { f } } } of a function f { \ displaystyle f } defined on an interval { \ displaystyle } is defined at each point of the interval as the supremum of all convex functions that lie under that function, i. e. f ( x ) = sup { g ( x ) g is convex and g ≤ f over }. { \ displaystyle { \ breve { f } } ( x ) = \ sup \ { g ( x ) \ mid g { \ text { is convex and } } g \ leq f { \ text { over } } \ }. }


in most dialects of lisp including common lisp, by convention the value nil evaluates to the value false in a boolean expression. in scheme, since the ieee standard in 1991, all values except # f, including nil's equivalent in scheme which is written as'( ), evaluate to the value true in a boolean expression. ( r5rs sec. 6. 3. 1 ) where the constant representing the boolean value of true is t in most lisps, in scheme it is # t.


a related result, sometimes called the second borel – cantelli lemma, is a partial converse of the first borel – cantelli lemma. the lemma states that, under certain conditions, an event will have probability of either zero or one. accordingly, it is the best - known of a class of similar theorems, known as zero - one laws. other examples include kolmogorov's zero – one law and the hewitt – savage zero – one law.


in semiconductor testing, the device under test is a die on a wafer or the resulting packaged part. a connection system is used, connecting the part to automatic or manual test equipment. the test equipment then applies power to the part, supplies stimulus signals, then measures and evaluates the resulting outputs from the device.


this is meant to indicate that the application is temporarily unresponsive, a state from which it should recover. it may also indicate that all or part of the application has entered an unrecoverable state or an infinite loop.


in some applications, the input data may contain features that are irrelevant for comparison purposes. for example, when looking up a personal name, it may be desirable to ignore the distinction between upper and lower case letters. for such data, one must use a hash function that is compatible with the data equivalence criterion being used : that is, any two inputs that are considered equivalent must yield the same hash value. this can be accomplished by normalizing the input before hashing it, as by upper - casing all letters.


in power supply networks, the power generation and the electrical load ( demand ) must be very close to equal every second to avoid overloading of network components, which can severely damage them. protective relays and fuses are used to automatically detect overloads and to disconnect circuits at risk of damage. under certain conditions, a network component shutting down can cause current fluctuations in neighboring segments of the network leading to a cascading failure of a larger section of the network. this may range from a building, to a block, to an entire city, to an entire electrical grid.


in mathematics, a ratio ( ) shows how many times one number contains another. for example, if there are eight oranges and six lemons in a bowl of fruit, then the ratio of oranges to lemons is eight to six ( that is, 8 : 6, which is equivalent to the ratio 4 : 3 ). similarly, the ratio of lemons to oranges is 6 : 8 ( or 3 : 4 ) and the ratio of oranges to the total amount of fruit is 8 : 14 ( or 4 : 7 ). the numbers in a ratio may be quantities of any kind, such as counts of people or objects, or such as measurements of lengths, weights, time, etc. in most contexts, both numbers are restricted to be positive.


in his phd thesis, berardi defined a cube of constructive logics akin to the lambda cube ( these specifications are non - dependent ). a modification of this cube was later called the l - cube by geuvers, who in his phd thesis extended the curry – howard correspondence to this setting. based on these ideas, barthe and others defined classical pure type systems ( cpts ) by adding a double negation operator.


in number theory, the ruler function of an integer n { \ displaystyle n } can be either of two closely related functions. one of these functions counts the number of times n { \ displaystyle n } can be evenly divided by two, which for the numbers 1, 2, 3,... is alternatively, the ruler function can be defined as the same numbers plus one, which for the numbers 1, 2, 3,... produces the sequence as well as being related by adding one, these two sequences are related in a different way : the second one can be formed from the first one by removing all the zeros, and the first one can be formed from the second one by adding zeros at the start and between every pair of numbers. for either definition of the ruler function, the rising and falling patterns of the values of this function resemble the lengths of marks on rulers with traditional units such as inches. these functions should be distinguished from thomae's function, a function on real numbers which behaves similarly to the ruler function when restricted to the dyadic rational numbers.


similarly, a " 300 gb " hard drive can be expected to offer only slightly more than 300×109 = 300000000000, bytes, not 300 × 230 ( which would be about 322×109 bytes or " 322 gb " ). the first terabyte ( si prefix, 1000000000000 bytes ) hard disk drive was introduced in 2007. decimal prefixes were generally used by information processing publications when comparing hard disk capacities. users must be aware that some programs and operating systems, such as earlier versions of microsoft windows and macos, may use " mb " and " gb " to denote binary prefixes even when displaying disk drive capacities. thus, for example, the capacity of a " 10 mb " ( decimal " m " ) disk drive could be reported as " 9. 56 mb ", and that of a " 300 gb " drive as " 279. 4 gb ". good software and documentation should specify clearly whether " k ", " m ", " g " mean binary or decimal multipliers.


in telecommunication, transmit - after - receive time delay is the time interval from removal of rf energy at the local receiver input until the local transmitter is automatically keyed on and the transmitted rf signal amplitude has increased to 90 % of its steady - state value. an exception : high - frequency ( hf ) transceiver equipment is normally not designed with an interlock between receiver squelch and transmitter on - off key. the transmitter can be keyed on at any time, independent of whether or not a signal is being received at the receiver input.


in the following descriptions, α, β, and γ represent any string of terminals / nonterminals ( including the empty string ), x and y represent single nonterminals, and a represents a terminal symbol. earley's algorithm is a top - down dynamic programming algorithm. in the following, we use earley's dot notation : given a production x → αβ, the notation x → α • β represents a condition in which α has already been parsed and β is expected.


the player with the most accurate predictions wins the top prize, or a share of it if more than one player has these predictions. in addition, there is a special £3, 000, 000 prize or share of it for correctly predicting the nine score draws ( draws of 1 - 1 or higher ) when these are the only score draws on the coupon. players can win large cash prizes in a variety of other ways, under a points - based scoring system.


the above procedure is repeated until the solution of constraint equations, σ k ( t + δ t ) { \ displaystyle \ sigma _ { k } ( t + \ delta t ) }, converges to a prescribed tolerance of a numerical error. although there are a number of algorithms to compute the lagrange multipliers, these difference is rely only on the methods to solve the system of equations. for this methods, quasi - newton methods are commonly used.


in object - oriented programming, sequential coupling ( also known as temporal coupling ) is a form of coupling where a class requires its methods to be called in a particular sequence. this may be an anti - pattern, depending on context. methods whose name starts with init, begin, start, etc. may indicate the existence of sequential coupling.


it provides a user interface, and reads and writes to the post office files directly in order to send, access, and manage email messages. this arrangement is called a " shared - file mail system " ( which was also implemented later in competing products such as microsoft mail ). this is in contrast to a " client / server mail system " which involves a mail client application interacting with a mail server application ( the latter then being the focal point of message handling ).


in the four color theorem, kempe was able to prove that all graphs necessarily have a vertex of five or less, or containing a vertex that touches five other vertices, called its neighbors. as such, to prove the four color theorem, it is sufficient to prove that vertices of five or less were all four - colorable. kempe was able to prove the case of degree four and give a partial proof of degree five using kempe chains. in this case, kempe chains are used to prove the idea that no vertex has to be touching four colors different from itself, i. e., having a degree of 4. first, one can create a graph with a vertex v and four vertices as neighbors.


in mathematics, the splitting principle is a technique used to reduce questions about vector bundles to the case of line bundles. in the theory of vector bundles, one often wishes to simplify computations, say of chern classes. often computations are well understood for line bundles and for direct sums of line bundles. in this case the splitting principle can be quite useful.


a positive impact of coalescing on inference graph colorability is, for example, when a node interferes with both nodes being coalesced, the degree of the node is reduced by one which leads to improving the overall colorability of the interference graph. there are several coalescing heuristics available : aggressive coalescing it was first introduced by chaitin original register allocator. this heuristic aims at coalescing any non - interfering, copy - related nodes.


in mathematics, particularly in the area of arithmetic, a modular multiplicative inverse of an integer a is an integer x such that the product ax is congruent to 1 with respect to the modulus m. in the standard notation of modular arithmetic this congruence is written as a x ≡ 1 ( mod m ), { \ displaystyle ax \ equiv 1 { \ pmod { m } }, } which is the shorthand way of writing the statement that m divides ( evenly ) the quantity ax − 1, or, put another way, the remainder after dividing ax by the integer m is 1. if a does have an inverse modulo m, then there are an infinite number of solutions of this congruence, which form a congruence class with respect to this modulus. furthermore, any integer that is congruent to a ( i. e., in a's congruence class ) has any element of x's congruence class as a modular multiplicative inverse. using the notation of w { \ displaystyle { \ overline { w } } } to indicate the congruence class containing w, this can be expressed by saying that the modulo multiplicative inverse of the congruence class a { \ displaystyle { \ overline { a } } } is the congruence class x { \ displaystyle { \ overline { x } } } such that : a ⋅ m x = 1, { \ displaystyle { \ overline { a } } \ cdot _ { m } { \ overline { x } } = { \ overline { 1 } }, } where the symbol ⋅ m { \ displaystyle \ cdot _ { m } } denotes the multiplication of equivalence classes modulo m. written in this way, the analogy with the usual concept of a multiplicative inverse in the set of rational or real numbers is clearly represented, replacing the numbers by congruence classes and altering the binary operation appropriately.


in social choice theory, tournaments naturally arise as majority relations of preference profiles. let a { \ displaystyle a } be a finite set of alternatives, and consider a list p = ( 1, …, n ) { \ displaystyle p = ( \ succ _ { 1 }, \ dots, \ succ _ { n } ) } of linear orders over a { \ displaystyle a }. we interpret each order i { \ displaystyle \ succ _ { i } } as the preference ranking of a voter i { \ displaystyle i }. the ( strict ) majority relation maj { \ displaystyle \ succ _ { \ text { maj } } } of p { \ displaystyle p } over a { \ displaystyle a } is then defined so that a maj b { \ displaystyle a \ succ _ { \ text { maj } } b } if and only if a majority of the voters prefer a { \ displaystyle a } to b { \ displaystyle b }, that is | { i ∈ : a i b } | > | { i ∈ : b i a } | { \ displaystyle | \ { i \ in : a \ succ _ { i } b \ } | > | \ { i \ in : b \ succ _ { i } a \ } | }.


in probability theory and statistics, a cross - covariance matrix is a matrix whose element in the i, j position is the covariance between the i - th element of a random vector and j - th element of another random vector. a random vector is a random variable with multiple dimensions. each element of the vector is a scalar random variable. each element has either a finite number of observed empirical values or a finite or infinite number of potential values.


δ i k p k m ( l ) ⟩ ⟩ = ( 2 l + 2 k + 1 )!! ⟨ ⟨ m ( l − 2 k ) ⟩ ⟩ { \ displaystyle { \ hat { t } } r _ { 1 }... { \ hat { t } } r _ { k } \ left \ langle \ left \ langle \ delta _ { i _ { 1 } p _ { 1 } }... \ delta _ { i _ { k } p _ { k } } \ mathbf { m } _ { } ^ { ( l ) } \ right \ rangle \ right \ rangle = ( 2l + 2k + 1 )!! \ left \ langle \ left \ langle \ mathbf { m } _ { } ^ { ( l - 2k ) } \ right \ rangle \ right \ rangle }.


the resulting function behaves like a while or a for loop in an imperative language. used in this way, the y combinator implements simple recursion. in the lambda calculus, it is not possible to refer to the definition of a function inside its own body by name.


to distinguish this type of vector from those described above, it is common and useful in physics to denote an element { \ displaystyle \ phi } of an abstract complex vector space as a ket | ⟩ { \ displaystyle | \ phi \ rangle }, to refer to it as a " ket " rather than as a vector, and to pronounce it " ket - { \ displaystyle \ phi } " or " ket - a " for | a ⟩. symbols, letters, numbers, or even words — whatever serves as a convenient label — can be used as the label inside a ket, with the | ⟩ { \ displaystyle | \ \ rangle } making clear that the label indicates a vector in vector space.


the most familiar example of a paired difference test occurs when subjects are measured before and after a treatment. such a " repeated measures " test compares these measurements within subjects, rather than across subjects, and will generally have greater power than an unpaired test. another example comes from matching cases of a disease with comparable controls.


in pattern recognition, information retrieval, object detection and classification ( machine learning ), precision and recall are performance metrics that apply to data retrieved from a collection, corpus or sample space. precision ( also called positive predictive value ) is the fraction of relevant instances among the retrieved instances. written as a formula : r e l e v a n t _ r e t r i e v e d _ i n s t a n c e s a l l _ r e t r i e v e d _ i n s t a n c e s { \ displaystyle { \ frac { relevant \ _ retrieved \ _ instances } { all \ _ { \ mathbf { retrieved } } \ _ instances } } }. recall ( also known as sensitivity ) is the fraction of relevant instances that were retrieved.


in mathematics, loop - erased random walk is a model for a random simple path with important applications in combinatorics, physics and quantum field theory. it is intimately connected to the uniform spanning tree, a model for a random tree. see also random walk for more general treatment of this topic.


in most models of communication protocol participants communicate through authenticated channels. this means that messages are not anonymous, and receivers know the source of every message they receive. some models assume a stronger, transferable form of authentication, where each message is signed by the sender, so that a receiver knows not just the immediate source of every message, but the participant that initially created the message. this stronger type of authentication is achieved by digital signatures, and when this stronger form of authentication is available, protocols can tolerate a larger number of faults. the two different authentication models are often called oral communication and written communication models. in an oral communication model, the immediate source of information is known, whereas in stronger, written communication models, every step along the receiver learns not just the immediate source of the message, but the communication history of the message.


they are weakly structured in common use, and become strongly structured in individual - site use. they may be abstract or concrete. they have different meanings in different social worlds but their structure is common enough to more than one world to make them recognizable, a means of translation.


note that in the probability inequalities above, the outcome of the protocol is understood to depend only on the random string ; both strings x and y remain fixed. in other words, if r ( x, y ) yields g ( x, y, r ) when using random string r, then g ( x, y, r ) = f ( x, y ) for at least 2 / 3 of all choices for the string r. the randomized complexity is simply defined as the number of bits exchanged in such a protocol. note that it is also possible to define a randomized protocol with one - sided error, and the complexity is defined similarly.


common phonological features that define the natural classes of vowels involved in vowel harmony include vowel backness, vowel height, nasalization, roundedness, and advanced and retracted tongue root. vowel harmony is found in many agglutinative languages. the given domain of vowel harmony taking effect often spans across morpheme boundaries, and suffixes and prefixes will usually follow vowel harmony rules.


in mathematical logic, the diagonal lemma ( also known as diagonalization lemma, self - reference lemma or fixed point theorem ) establishes the existence of self - referential sentences in certain formal theories of the natural numbers — specifically those theories that are strong enough to represent all computable functions. the sentences whose existence is secured by the diagonal lemma can then, in turn, be used to prove fundamental limitative results such as godel's incompleteness theorems and tarski's undefinability theorem.


it is still generally called the " liar paradox " although abstraction is made precisely from the liar making the statement. trying to assign to this statement, the strengthened liar, a classical binary truth value leads to a contradiction. if " this sentence is false " is true, then it is false, but the sentence states that it is false, and if it is false, then it must be true, and so on.


by 1963 – 1964 godel would disavow herbrand – godel recursion and the λ - calculus in favor of the turing machine as the definition of " algorithm " or " mechanical procedure " or " formal system ". a hypothesis leading to a natural law? : in late 1936 alan turing's paper ( also proving that the entscheidungsproblem is unsolvable ) was delivered orally, but had not yet appeared in print. on the other hand, emil post's 1936 paper had appeared and was certified independent of turing's work.


it was implemented in ecl running at 25 mhz. major functional modules were implemented using amcc ecl asics. the project grew beyond its original definition to include a front - end general purpose processor ensemble based on the multiple 68020 processors running unix system v. the numeric processor ran a small kernel that would allow it to receive job submissions from the unix system.


in the classification of programming languages, an applicative programming language is built out of functions applied to arguments. applicative languages are functional, and applicative is often used as a synonym for functional. however, concatenative languages can be functional, while not being applicative. the semantics of applicative languages are based on beta reduction of terms, and side effects such as mutation of state are not permitted. lisp and ml are applicative programming languages.


in practice, there exist several methods to construct knowledge spaces. the most frequently used method is querying experts. there exist several querying algorithms that allow one or several experts to construct a knowledge space by answering a sequence of simple questions. another method is to construct the knowledge space by explorative data analysis ( for example by item tree analysis ) from data. a third method is to derive the knowledge space from an analysis of the problem solving processes in the corresponding domain. = = references = =


in telecommunications networks, ranap ( radio access network application part ) is a protocol specified by 3gpp in ts 25. 413 and used in umts for signaling between the core network, which can be a msc or sgsn, and the utran. ranap is carried over iu - interface. ranap signalling protocol resides in the control plane of radio network layer of iu interface in the umts ( universal mobile telecommunication system ) protocol stack. iu interface is the interface between rnc ( radio network controller ) and cn ( core network ).


in probability theory and statistics, the negative hypergeometric distribution describes probabilities for when sampling from a finite population without replacement in which each sample can be classified into two mutually exclusive categories like pass / fail or employed / unemployed. as random selections are made from the population, each subsequent draw decreases the population causing the probability of success to change with each draw. unlike the standard hypergeometric distribution, which describes the number of successes in a fixed sample size, in the negative hypergeometric distribution, samples are drawn until r { \ displaystyle r } failures have been found, and the distribution describes the probability of finding k { \ displaystyle k } successes in such a sample. in other words, the negative hypergeometric distribution describes the likelihood of k { \ displaystyle k } successes in a sample with exactly r { \ displaystyle r } failures.


in mathematics, the nth - term test for divergence is a simple test for the divergence of an infinite series : if lim n → ∞ a n = 0 { \ displaystyle \ lim _ { n \ to \ infty } a _ { n } \ neq 0 } or if the limit does not exist, then n = 1 ∞ a n { \ displaystyle \ sum _ { n = 1 } ^ { \ infty } a _ { n } } diverges. many authors do not name this test or give it a shorter name. when testing if a series converges or diverges, this test is often checked first due to its ease of use. in the case of p - adic analysis the term test is a necessary and sufficient condition for convergence due to the non - archimedean triangle inequality.


in telecommunication, a two - wire circuit is characterized by supporting transmission in two directions simultaneously, as opposed to four - wire circuits, which have separate pairs for transmit and receive. the subscriber local loop from the telco central office are almost all two wire for analog baseband voice calls ( and some digital services like isdn ), and converted to four - wire at the line card back when telephone switching was performed on baseband audio. today the audio is digitized and processed completely in the digital domain upstream from the local loop. the reason for using two wires rather than four is simple economics — half the materials cost half as much to purchase and install.


in mathematics, the tent map with parameter μ is the real - valued function fμ defined by f μ ( x ) : = μ min { x, 1 − x }, { \ displaystyle f _ { \ mu } ( x ) : = \ mu \ min \ { x, \, 1 - x \ }, } the name being due to the tent - like shape of the graph of fμ. for the values of the parameter μ within 0 and 2, fμ maps the unit interval into itself, thus defining a discrete - time dynamical system on it ( equivalently, a recurrence relation ). in particular, iterating a point x0 in gives rise to a sequence x n { \ displaystyle x _ { n } } : x n + 1 = f μ ( x n ) = { μ x n f o r x n < 1 2 μ ( 1 − x n ) f o r 1 2 ≤ x n { \ displaystyle x _ { n + 1 } = f _ { \ mu } ( x _ { n } ) = { \ begin { cases } \ mu x _ { n } & \ mathrm { for } ~ ~ x _ { n } < { \ frac { 1 } { 2 } } \ \ \ mu ( 1 - x _ { n } ) & \ mathrm { for } ~ ~ { \ frac { 1 } { 2 } } \ leq x _ { n } \ end { cases } } } where μ is a positive real constant.


in order to gain access to gsm services, a user needs three things : a billing relationship with a mobile phone operator. this is usually either where services are paid for in advance of them being consumed ( prepaid ), or where bills are issued and settled after the service has been consumed ( postpaid ). a mobile phone that is gsm compliant and operates at the same frequency as the operator.