even if they are not words, morphemes can prime for complete words that include them. an example of this would be that the morpheme'psych'can prime for the word'psychology '. in support with further detail, when an individual processes a word sometimes that word can be affected when the prior word is linked semantically.


in pseudocode, the general algorithm for building decision trees is : check for the above base cases. for each attribute a, find the normalized information gain ratio from splitting on a. let a _ best be the attribute with the highest normalized information gain. create a decision node that splits on a _ best. recurse on the sublists obtained by splitting on a _ best, and add those nodes as children of node.


the edges forming the silhouette are extruded away from the light to construct the faces of the shadow volume. this volume must extend over the range of the entire visible scene ; often the dimensions of the shadow volume are extended to infinity to accomplish this ( see optimization below. ) to form a closed volume, the front and back end of this extrusion must be covered.


that is, given the neighbors n i { \ displaystyle n _ { i } } of x i, x i { \ displaystyle x _ { i }, x _ { i } } is independent of all other x j { \ displaystyle x _ { j } } ( markov property ). the main difference with a hidden markov model is that neighborhood is not defined in 1 dimension but within a network, i. e. x i { \ displaystyle x _ { i } } is allowed to have more than the two neighbors that it would have in a markov chain.


in mathematics, especially order theory, a prefix ordered set generalizes the intuitive concept of a tree by introducing the possibility of continuous progress and continuous branching. natural prefix orders often occur when considering dynamical systems as a set of functions from time ( a totally - ordered set ) to some phase space. in this case, the elements of the set are usually referred to as executions of the system. the name prefix order stems from the prefix order on words, which is a special kind of substring relation and, because of its discrete character, a tree.


a transition takes place to the next state as a result of a binary input 1 or 0 and the encoder's present output state. the encoding procedure is as follows. in general, the encoder outputs + level for a binary 1 input and a − level for a binary 0 input.


in network science, a biased random walk on a graph is a time path process in which an evolving variable jumps from its current state to one of various potential new states ; unlike in a pure random walk, the probabilities of the potential new states are unequal. biased random walks on a graph provide an approach for the structural analysis of undirected graphs in order to extract their symmetries when the network is too complex or when it is not large enough to be analyzed by statistical methods. the concept of biased random walks on a graph has attracted the attention of many researchers and data companies over the past decade especially in the transportation and social networks.


in marketing, discriminant analysis was once often used to determine the factors which distinguish different types of customers and / or products on the basis of surveys or other forms of collected data. logistic regression or other methods are now more commonly used. the use of discriminant analysis in marketing can be described by the following steps : formulate the problem and gather data — identify the salient attributes consumers use to evaluate products in this category — use quantitative marketing research techniques ( such as surveys ) to collect data from a sample of potential customers concerning their ratings of all the product attributes. the data collection stage is usually done by marketing research professionals.


in the oxford advanced learner's dictionary, the word alphabet is defined as " a set of letters or symbols in a fixed order used for writing a language ". the yes " alphabet " is a list of chinese character strokes in the order of " ". this stroke alphabet is built on the basis of unicode cjk strokes and the standard of chinese character bending strokes of the gb13000. 1 character set. there are totally 30 strokes, sorted by the standard basic strokes order of “ heng (,, 一 ), ti (, ), shu (,, ), pie (, ), dian (,, ), na (, ) ” and the bending points order of “ zhe ( ), wan (, ) and gou (, ) ”.


in this context, " numeric " means that the computer treats sequences of bits as binary numbers ( base two numbers ) and executes arithmetic operations like add, subtract, multiply, or divide. " logical " refers to the boolean logical operations of disjunction, conjunction, and negation between two sequences of bits, in which each bit in one sequence is simply compared to its counterpart in the other sequence. programmers therefore have the option of working in and applying the rules of either numeric algebra or boolean algebra as needed. a core differentiating feature between these families of operations is the existence of the carry operation in the first but not the second.


phonetically palatalized consonants may vary in their exact realization. some languages add semivowels before or after the palatalized consonant ( onglides or offglides ). in such cases, the vowel ( especially a non - front vowel ) following a palatalized consonant typically has a palatal onglide.


in natural language processing a w - shingling is a set of unique shingles ( therefore n - grams ) each of which is composed of contiguous subsequences of tokens within a document, which can then be used to ascertain the similarity between documents. the symbol w denotes the quantity of tokens in each shingle selected, or solved for. the document, " a rose is a rose is a rose " can therefore be maximally tokenized as follows : ( a, rose, is, a, rose, is, a, rose ) the set of all contiguous sequences of 4 tokens ( thus 4 = n, thus 4 - grams ) is { ( a, rose, is, a ), ( rose, is, a, rose ), ( is, a, rose, is ), ( a, rose, is, a ), ( rose, is, a, rose ) } which can then be reduced, or maximally shingled in this particular instance to { ( a, rose, is, a ), ( rose, is, a, rose ), ( is, a, rose, is ) }.


in number theory, octic reciprocity is a reciprocity law relating the residues of 8th powers modulo primes, analogous to the law of quadratic reciprocity, cubic reciprocity, and quartic reciprocity. there is a rational reciprocity law for 8th powers, due to williams. define the symbol ( x p ) k { \ displaystyle \ left ( { \ frac { x } { p } } \ right ) _ { k } } to be + 1 if x is a k - th power modulo the prime p and - 1 otherwise. let p and q be distinct primes congruent to 1 modulo 8, such that ( p q ) 4 = ( q p ) 4 = + 1.


in mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. equivalently, a set is countable if there exists an injective function from it into the natural numbers ; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements. in more technical terms, assuming the axiom of countable choice, a set is countable if its cardinality ( the number of elements of the set ) is not greater than that of the natural numbers. a countable set that is not finite is said to be countably infinite. the concept is attributed to georg cantor, who proved the existence of uncountable sets, that is, sets that are not countable ; for example the set of the real numbers.


for each cell c { \ displaystyle c }, we let w ( c ) { \ displaystyle w ( c ) } be the sum of all w ( k ) { \ displaystyle w ( k ) }, where the sum is taken over all sampled k { \ displaystyle k } in the cell c { \ displaystyle c }. for each cell c { \ displaystyle c }, we let t ( c ) { \ displaystyle t ( c ) } be the auxiliary value for cell c { \ displaystyle c }, which is commonly called the " benchmark target " for cell c { \ displaystyle c }. next, we compute a benchmark factor f ( c ) = t ( c ) / w ( c ) { \ displaystyle f ( c ) = t ( c ) / w ( c ) }.


one of the most widely used transmission system technologies in the internet and the public switched telephone network ( pstn ) is synchronous optical networking ( sonet ). also, transmission system is the medium through which data is transmitted from one point to another. examples of common transmission systems people use everyday are : the internet, mobile networks, cordless cables, etc.


in mathematics, a set b of vectors in a vector space v is called a basis ( pl : bases ) if every element of v may be written in a unique way as a finite linear combination of elements of b. the coefficients of this linear combination are referred to as components or coordinates of the vector with respect to b. the elements of a basis are called basis vectors. equivalently, a set b is a basis if its elements are linearly independent and every element of v is a linear combination of elements of b. in other words, a basis is a linearly independent spanning set. a vector space can have several bases ; however all the bases have the same number of elements, called the dimension of the vector space. this article deals mainly with finite - dimensional vector spaces. however, many of the principles are also valid for infinite - dimensional vector spaces.


in statistics, family - wise error rate ( fwer ) is the probability of making one or more false discoveries, or type i errors when performing multiple hypotheses tests.


these two conditions are sufficient to ensure that all faces are alike and all vertices are alike. note, however, that this definition does not work for abstract polytopes. a regular polytope can be represented by a schlafli symbol of the form { a, b, c,..., y, z }, with regular facets as { a, b, c,..., y }, and regular vertex figures as { b, c,..., y, z }.


in practice, loop variants are often taken to be non - negative integers, or even required to be so, but the requirement that every loop have an integer variant removes the expressive power of unbounded iteration from a programming language. unless such a ( formally verified ) language allows a transfinite proof of termination for some other equally powerful construct such as a recursive function call, it is no longer capable of full μ - recursion, but only primitive recursion. ackermann's function is the canonical example of a recursive function that cannot be computed in a loop with an integer variant. in terms of their computational complexity, however, functions that are not primitive recursive lie far beyond the realm of what is usually considered tractable.


in statistics, binomial regression is a regression analysis technique in which the response ( often referred to as y ) has a binomial distribution : it is the number of successes in a series of n { \ displaystyle n } independent bernoulli trials, where each trial has probability of success p { \ displaystyle p }. in binomial regression, the probability of a success is related to explanatory variables : the corresponding concept in ordinary regression is to relate the mean value of the unobserved response to explanatory variables. binomial regression is closely related to binary regression : a binary regression can be considered a binomial regression with n = 1 { \ displaystyle n = 1 }, or a regression on ungrouped binary data, while a binomial regression can be considered a regression on grouped binary data ( see comparison ). binomial regression models are essentially the same as binary choice models, one type of discrete choice model : the primary difference is in the theoretical motivation ( see comparison ). in machine learning, binomial regression is considered a special case of probabilistic classification, and thus a generalization of binary classification.


linnaeus made the same distinction between plantains and bananas when first naming two " species " of musa. members of the " plantain subgroup " of banana cultivars, most important as food in west africa and latin america, correspond to the chiquita description, having long pointed fruit. they are described by ploetz et al. as " true " plantains, distinct from other cooking bananas.


in recent years the long - standing use of term " disorder " to discuss entropy has met with some criticism. critics of the terminology state that entropy is not a measure of'disorder'or'chaos ', but rather a measure of energy's diffusion or dispersal to more microstates. shannon's use of the term'entropy'in information theory refers to the most compressed, or least dispersed, amount of code needed to encompass the content of a signal.


the induced action of g { \ displaystyle g } on the symplectic manifold ( t ∗ n, d τ ) { \ displaystyle ( t ^ { * } n, \ mathrm { d } \ tau ) }, given by g ⋅ η : = ( t π ( η ) g − 1 ) ∗ η { \ displaystyle g \ cdot \ eta : = ( t _ { \ pi ( \ eta ) } g ^ { - 1 } ) ^ { * } \ eta } for g ∈ g, η ∈ t ∗ n { \ displaystyle g \ in g, \ eta \ in t ^ { * } n } is hamiltonian with momentum map − ι ρ ( ξ ) τ { \ displaystyle - \ iota _ { \ rho ( \ xi ) } \ tau } for all ξ ∈ g { \ displaystyle \ xi \ in { \ mathfrak { g } } }. here ι ρ ( ξ ) τ { \ displaystyle \ iota _ { \ rho ( \ xi ) } \ tau } denotes the contraction of the vector field ρ ( ξ ) { \ displaystyle \ rho ( \ xi ) }, the infinitesimal action of ξ { \ displaystyle \ xi }, with the 1 - form τ { \ displaystyle \ tau }. the facts mentioned below may be used to generate more examples of momentum maps.


in mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross - multiply to simplify the equation or determine the value of a variable. the method is also occasionally known as the " cross your heart " method because lines resembling a heart outline can be drawn to remember which things to multiply together. given an equation like a b = c d, { \ displaystyle { \ frac { a } { b } } = { \ frac { c } { d } }, } where b and d are not zero, one can cross - multiply to get a d = b c or a = b c d. { \ displaystyle ad = bc \ quad { \ text { or } } \ quad a = { \ frac { bc } { d } }. } in euclidean geometry the same calculation can be achieved by considering the ratios as those of similar triangles.


.., n 2 { \ displaystyle 1, 2,..., n ^ { 2 } }, the magic square is said to be'normal '.


the size of a graph is | e | { \ displaystyle | e | }, its number of edges. the degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. the degree of a graph is the maximum of the degrees of its vertices.


in some scenarios, an argument by example may be valid if it leads from a singular premise to an existential conclusion ( i. e. proving that a claim is true for at least one case, instead of for all cases ). for example : socrates is wise. therefore, someone is wise.


successful runs might also write a result on magnetic tape or generate some data cards to be used in a later computation. the turnaround time for a single job often spanned entire days.


in semiotics, the commutation test is used to analyze a signifying system. the test identifies signifiers as well as their signifieds, value and significance.


in set theory a serial relation is a homogeneous relation expressing the connection of an element of a sequence to the following element. the successor function used by peano to define natural numbers is the prototype for a serial relation. bertrand russell used serial relations in the principles of mathematics ( 1903 ) as he explored the foundations of order theory and its applications.


the algorithm takes time bounded by a polynomial in n { \ displaystyle n }, the dimension of k { \ displaystyle k } and 1 / ε { \ displaystyle 1 / \ varepsilon }. the algorithm combines two ideas : by using a markov chain monte carlo ( mcmc ) method, it is possible to generate points that are nearly uniformly randomly distributed within a given convex body. the basic scheme of the algorithm is a nearly uniform sampling from within k { \ displaystyle k } by placing a grid consisting of n { \ displaystyle n } - dimensional cubes and doing a random walk over these cubes.


however, this set of nodes is optimal for interpolation over c m n { \ displaystyle c _ { m } ^ { n } } the set of n times differentiable functions whose n - th derivatives are bounded in absolute values by a constant m as shown by n. s. hoang. using a computer, one can approximate the values of the minimal lebesgue constants, here for the canonical interval : there are uncountable infinitely many sets of nodes in that minimize, for fixed n > 1, the lebesgue constant. though if we assume that we always take −1 and 1 as nodes for interpolation ( which is called a canonical node configuration ), then such a set is unique and zero - symmetric.


900 mhz ( 902 – 928 mhz, allocated in 1993 ) 1. 9 ghz ( 1920 – 1930 mhz, developed in 1993 and allocated in october 2005, especially with dect 6. 0 ) 2. 4 ghz ( 2400 – 2500 mhz, allocated in 1998 ) 5. 8 ghz ( 5725 – 5875 mhz, allocated in 2003 due to crowding on the 2. 4 ghz band ) over - crowding of earlier frequency allocations led users to discontinue using telephone equipment that operated on those frequencies, leaving those bands relatively clear. radio hobbyists monitor usage of the older equipment with telephone activity in the us am broadcast band, some 27 mhz frequencies and most older 43 - 50 mhz frequencies. 1. 7 mhz cordless phones were the earliest models available at retailers, and are generally identifiable by their large metal telescoping antennas.


in the multiset { a, a, a, b, b, b }, a and b both have multiplicity 3. these objects are all different when viewed as multisets, although they are the same set, since they all consist of the same elements. as with sets, and in contrast to tuples, the order in which elements are listed does not matter in discriminating multisets, so { a, a, b } and { a, b, a } denote the same multiset. to distinguish between sets and multisets, a notation that incorporates square brackets is sometimes used : the multiset { a, a, b } can be denoted by. the cardinality of a multiset is the sum of the multiplicities of all its elements.


in mathematical analysis, idempotent analysis is the study of idempotent semirings, such as the tropical semiring. the lack of an additive inverse in the semiring is compensated somewhat by the idempotent rule a ⊕ a = a { \ displaystyle a \ oplus a = a }. = = references = =


in quantum information theory, the conditional entropy is generalized to the conditional quantum entropy. the latter can take negative values, unlike its classical counterpart.


about the year 1900 i found this out ". sheila ostrander and lynn schroeder, authors of the paranormal, visited czechoslovakia in 1968, where they happened upon a cardboard pyramid manufactured commercially by drbal. they met drbal, and dedicated a chapter of their popular 1970 book psychic discoveries behind the iron curtain to pyramid power. this book introduced both the concept of pyramid power and the story about antoine bovis to the english - speaking world.


in the united states, the federal communications commission requires all interconnected voip service providers to comply with requirements comparable to those for traditional telecommunications service providers. voip operators in the us are required to support local number portability ; make service accessible to people with disabilities ; pay regulatory fees, universal service contributions, and other mandated payments ; and enable law enforcement authorities to conduct surveillance pursuant to the communications assistance for law enforcement act ( calea ). operators of interconnected voip ( fully connected to the pstn ) are mandated to provide enhanced 911 service without special request, provide for customer location updates, clearly disclose any limitations on their e - 911 functionality to their consumers, obtain affirmative acknowledgements of these disclosures from all consumers, and may not allow their customers to opt - out of 911 service. voip operators also receive the benefit of certain us telecommunications regulations, including an entitlement to interconnection and exchange of traffic with incumbent local exchange carriers via wholesale carriers.


in telephone systems where calls from distant automated exchanges arrive for manual subscribers or non - dialable points, there often would be a ringdown operator ( reachable from the distant operator console by dialling npa + 181 ) who would manually ring the desired subscriber on a party line or toll station. on some systems, this function was carried out by the inward operator ( npa + 121 ). in both cases, this is a telephone operator at the destination who provides assistance solely to other operators on inbound toll calls ; the ringdown operator nominally cannot be dialed directly by the subscriber.


in mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by hugo steinhaus for the analysis of comparison sort algorithms. these numbers give the worst - case number of comparisons used by both binary insertion sort and merge sort. however, there are other algorithms that use fewer comparisons.


in modern field of computational intelligence, the social learning theory is adopted to develop a new computer optimization algorithm, the social learning algorithm. emulating the observational learning and reinforcement behaviors, a virtual society deployed in the algorithm seeks the strongest behavioral patterns with the best outcome. this corresponds to searching for the best solution in solving optimization problems. compared with other bio - inspired global optimization algorithms that mimic natural evolution or animal behaviors, the social learning algorithm has its prominent advantages.


when the feature works properly, it is nearly transparent to the user, appearing as a single long text message. previously, due to incompatibilities between providers and lack of support in some phone models, there was not widespread use of this feature. in the late 2000s to early 2010s, this feature was adopted more widely. not only do many handsets support this feature, but support for the feature also exists amongst sms gateway providers. the way concatenation works in gsm and umts networks is specified in sms point to point specification, 3gpp ts 23. 040. on networks which do not support concatenated sms ( neither the standard scheme nor the simplified one ), the message is delivered as individual sms text messages rather than one concatenated message.


{ \ displaystyle 1, 1, 2, 4, 10, 32, 122, 544, 2770, 15872, 101042. } ( sequence a001250 in the oeis ). the number of antichains in a fence is a fibonacci number ; the distributive lattice with this many elements, generated from a fence via birkhoff's representation theorem, has as its graph the fibonacci cube. a partially ordered set is series - parallel if and only if it does not have four elements forming a fence. several authors have also investigated the number of order - preserving maps from fences to themselves, or to fences of other sizes. an up - down poset q ( a, b ) is a generalization of a zigzag poset in which there are a downward orientations for every upward one and b total elements.


in mathematics, zero dynamics is known as the concept of evaluating the effect of zero on systems.


both of these tie in to notions of size. importantly, injection existence between any two sets provides a preorder. a power class does not inject into its underlying set and the latter does not map onto the former.


in the following code sample, two optimizations can be applied. although the calculation x = y + z and x * x is loop - invariant, precautions must be taken before moving the code outside the loop. it is possible that the loop condition is false ( for example, if n holds a negative value ), and in such case, the loop body should not be executed at all. one way of guaranteeing correct behaviour is using a conditional branch outside of the loop.


in queueing theory, a discipline within the mathematical theory of probability, a bcmp network is a class of queueing network for which a product - form equilibrium distribution exists. it is named after the authors of the paper where the network was first described : baskett, chandy, muntz, and palacios. the theorem is a significant extension to a jackson network allowing virtually arbitrary customer routing and service time distributions, subject to particular service disciplines. the paper is well known, and the theorem was described in 1990 as " one of the seminal achievements in queueing theory in the last 20 years " by j. michael harrison and ruth j. williams.


{ \ displaystyle t \ geqslant | s | - \ varepsilon n \ geqslant ( 1 - r ) n - \ varepsilon n = ( 1 - r - \ varepsilon ) n. } finally, we have δ ( c ∗ ( m 1 ), c ∗ ( m 2 ) ) h q − 1 ( 1 2 − ε ) ⋅ 2 k ⋅ t h q − 1 ( 1 2 − ε ) ⋅ 2 k ⋅ ( 1 − r − ε ) ⋅ n. { \ displaystyle \ delta ( c ^ { * } ( m _ { 1 } ), c ^ { * } ( m _ { 2 } ) ) \ geqslant h _ { q } ^ { - 1 } \ left ( { \ tfrac { 1 } { 2 } } - \ varepsilon \ right ) \ cdot 2k \ cdot t \ geqslant h _ { q } ^ { - 1 } \ left ( { \ tfrac { 1 } { 2 } } - \ varepsilon \ right ) \ cdot 2k \ cdot ( 1 - r - \ varepsilon ) \ cdot n. } this is true for any arbitrary m 1 = m 2 { \ displaystyle m _ { 1 } \ neq m _ { 2 } }. so c ∗ { \ displaystyle c ^ { * } } has the relative distance at least ( 1 − r − ε ) h q − 1 ( 1 2 − ε ), { \ displaystyle ( 1 - r - \ varepsilon ) h _ { q } ^ { - 1 } \ left ( { \ tfrac { 1 } { 2 } } - \ varepsilon \ right ), } which completes the proof.


in the following, n { \ displaystyle n } denotes the number of people in the initial circle, and k { \ displaystyle k } denotes the count for each step, that is, k − 1 { \ displaystyle k - 1 } people are skipped and the k { \ displaystyle k } - th is executed. the people in the circle are numbered from 1 { \ displaystyle 1 } to n { \ displaystyle n }, the starting position being 1 { \ displaystyle 1 } and the counting being inclusive.


however it is not the smallest such graph : it is known that there is a universal graph for n - vertex trees, with only n vertices and o ( n log n ) edges, and that this is optimal. a construction based on the planar separator theorem can be used to show that n - vertex planar graphs have universal graphs with o ( n3 / 2 ) edges, and that bounded - degree planar graphs have universal graphs with o ( n log n ) edges.


inversion of control has been widely used by application development frameworks since the rise of gui environments and continues to be used both in gui environments and in web server application frameworks. inversion of control makes the framework extensible by the methods defined by the application programmer. event - driven programming is often implemented using ioc so that the custom code need only be concerned with the handling of events, while the event loop and dispatch of events / messages is handled by the framework or the runtime environment. in web server application frameworks, dispatch is usually called routing, and handlers may be called endpoints. the phrase " inversion of control " has separately also come to be used in the community of java programmers to refer specifically to the patterns of injecting objects'dependencies that occur with " ioc containers " in java frameworks such as the spring framework. in this different sense, " inversion of control " refers to granting the framework control over the implementations of dependencies that are used by application objects rather than to the original meaning of granting the framework control flow ( control over the time of execution of application code e. g. callbacks ).


to illustrate this, consider the following statements : p { \ displaystyle p } : sam ate an orange for lunch q { \ displaystyle q } : sam ate a fruit for lunchthen, to say, " sam ate an orange for lunch " implies " sam ate a fruit for lunch " ( p → q { \ displaystyle p \ to q } ). logically, if sam did not eat a fruit for lunch, then sam also cannot have eaten an orange for lunch ( by contraposition ). however, merely saying that sam did not eat an orange for lunch provides no information on whether or not sam ate a fruit ( of any kind ) for lunch.


in the context of spoken languages, a phone is an unanalyzed sound of a language. a phone is a speech segment that possesses distinct physical or perceptual properties and serves as the basic unit of phonetic speech analysis. phones are generally either vowels or consonants. a phonetic transcription ( based on phones ) is enclosed within square brackets ( ), rather than the slashes ( / / ) of a phonemic transcription, ( based on phonemes ).


in some cases, the importance of the raters ( experts ) might not be the same as each other. in this case, the weighted kendall's w should be used. suppose that object i { \ displaystyle i } is given the rank r i j { \ displaystyle r _ { ij } } by judge number j { \ displaystyle j }, where there are in total n { \ displaystyle n } objects and m { \ displaystyle m } judges. also, the weight of judge j { \ displaystyle j } is shown by j { \ displaystyle \ vartheta _ { j } } ( in real - world situation, the importance of each rater can be different ).


an outstanding rationale for email authentication is the ability to automate email filtering at receiving servers. that way, spoofed messages can be rejected before they arrive to a user's inbox. while protocols strive to devise ways to reliably block distrusted mail, security indicators can tag unauthenticated messages that still reach the inbox. a 2018 study shows that security indicators can lower the click - through ratio by more than ten points, 48. 9 % to 37. 2 % of the users who open spoofed messages.


in set theory, an infinite set is a set that is not a finite set. infinite sets may be countable or uncountable.


in second - order intuitionistic logic, the second - order polymorphic lambda calculus ( f2 ) was discovered by girard ( 1972 ) and independently by reynolds ( 1974 ). girard proved the representation theorem : that in second - order intuitionistic predicate logic ( p2 ), functions from the natural numbers to the natural numbers that can be proved total, form a projection from p2 into f2. reynolds proved the abstraction theorem : that every term in f2 satisfies a logical relation, which can be embedded into the logical relations p2. reynolds proved that a girard projection followed by a reynolds embedding form the identity, i. e., the girard - reynolds isomorphism.


in telecommunication, a convolutional code is a type of error - correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. the sliding application represents the'convolution'of the encoder over the data, which gives rise to the term'convolutional coding '. the sliding nature of the convolutional codes facilitates trellis decoding using a time - invariant trellis. time invariant trellis decoding allows convolutional codes to be maximum - likelihood soft - decision decoded with reasonable complexity.


{ \ textstyle \ bigcup _ { n \ in \ mathbb { n } } a _ { n } \ in n. } briefly, a sigma - ideal must contain the empty set and contain subsets and countable unions of its elements.


the algorithms then adjust the weights, instead of adjusting the values associated with the individual state - action pairs. methods based on ideas from nonparametric statistics ( which can be seen to construct their own features ) have been explored. value iteration can also be used as a starting point, giving rise to the q - learning algorithm and its many variants. including deep q - learning methods when a neural network is used to represent q, with various applications in stochastic search problems. the problem with using action - values is that they may need highly precise estimates of the competing action values that can be hard to obtain when the returns are noisy, though this problem is mitigated to some extent by temporal difference methods. using the so - called compatible function approximation method compromises generality and efficiency.


this can be visualized as a checkerboard pattern in a matrix. therefore, each processing unit can only have outgoing edges to pes in the same row and column. this bounds the amount of communication partners for each pe to p r + p c − 1 { \ displaystyle p _ { r } + p _ { c } - 1 } out of p = p r × p c { \ displaystyle p = p _ { r } \ times p _ { c } } possible ones.


in most unix and unix - like operating systems, the ps program ( short for " process status " ) displays the currently - running processes. a related unix utility named top provides a real - time view of the running processes.


examples include 1ess switch. a machine with three replications of each element is termed triple modular redundant ( tmr ). the voting circuit can determine which replication is in error when a two - to - one vote is observed.


in the above procedure, the algorithm checks whether the middle element ( m { \ displaystyle m } ) is equal to the target ( t { \ displaystyle t } ) in every iteration. some implementations leave out this check during each iteration. the algorithm would perform this check only when one element is left ( when l = r { \ displaystyle l = r } ).


beaumont created a list of over 150 personally significant books and collected replicas from bookstores. the books were treated, burned, displayed, and arranged in over thirty feet of floor to ceiling shelving. through the metaphor of fire and the social horror of book burning, the project grieves the irretrievable loss of species ( dna ) contained in the rainforest, as irretrievable as the loss of the ancient body of knowledge contained at the library of alexandria — both sources of encyclopedic information.


the information asymmetry problem occurs in a scenario where one of the two people has more or less information than the other. in the context of public administration, bureaucrats have an information advantage over the government and ministers as the former work at the ground level and have more knowledge about the dynamic and changing situation. due to this government may frame policies that are not based on complete information and therefore problems in the implementation of public policies may occur.


in mathematics, physics, and engineering, a euclidean vector or simply a vector ( sometimes called a geometric vector or spatial vector ) is a geometric object that has magnitude ( or length ) and direction. vectors can be added to other vectors according to vector algebra. a euclidean vector is frequently represented by a directed line segment, or graphically as an arrow connecting an initial point a with a terminal point b, and denoted by a b → { \ displaystyle { \ overrightarrow { ab } } }. a vector is what is needed to " carry " the point a to the point b ; the latin word vector means " carrier ".


these are implemented in part because of the difficulty in ensuring that different terminals transmit at exactly the times required. handsets that are moving will need to constantly adjust their timings to ensure their transmission is received at precisely the right time, because as they move further from the base station, their signal will take longer to arrive. this also means that the major tdma systems have hard limits on cell sizes in terms of range, though in practice the power levels required to receive and transmit over distances greater than the supported range would be mostly impractical anyway.


in order to provide access to relevant data to users chemxseer provides new features that are not available in traditional search engines or digital libraries. chemical entity search : a tool capable of identifying chemical formulae and chemical names, and extracting and disambiguating them from general terms within documents. those disambiguated terms are used for performing searches.


this is determined to a great degree by the stage of the call setup procedure at which a call is counted as connected. in modern communications systems, such as cellular ( mobile ) networks, the call setup procedure maybe very complex and the point at which a call is considered successfully connected may be defined in a number of ways, thus influencing the way the call setup success rate is calculated. if a call is connected successfully but the dialled number is busy, the call is counted as successful.


though multiple systems have been postulated, few have reported results. one system, “ smile, ” which attempted to automatically extract classifications from case texts, resulted in an f - measure ( which is a calculation of both recall rate and precision ) of under 0. 3 ( compared to perfect f - measure of 1. 0 ). this is probably much lower than an acceptable rate for general usage. despite the limited results, many theorists predict that the evolution of such systems will eventually replace manual classification systems.


in india, an idea was mooted in 2003 to create a national do not call registry, and finally got implemented in 2014. since then the government is taking various measures to curb the menace that includes termination of the violators telecom resources. as of now there is no regulation for telecallers to classify an abandoned call or allowed percentage as yet, but it will come sooner or later.


in the following compilation, m is the length of the longest pattern, m their total length, n the length of the searchable text, o the number of occurrences.


in mycology, the terms teleomorph, anamorph, and holomorph apply to portions of the life cycles of fungi in the phyla ascomycota and basidiomycota : teleomorph : the sexual reproductive stage ( morph ), typically a fruiting body. anamorph : an asexual reproductive stage ( morph ), often mold - like. when a single fungus produces multiple morphologically distinct anamorphs, these are called synanamorphs. holomorph : the whole fungus, including anamorphs and teleomorph.


in order to recommend the most appropriate users to provide answers in a social network, we need to find approaches to detect users'authority in a social network. in the field of information retrieval, there has been a trend of research investigating ways to detect users'authority effectively and accurately in a social network. cha et al. investigate possible metrics for determining authority users on popular social network twitter. they propose the following three simple network - based metrics and discuss their usefulness in determining a user's influence.


given iterates x 1, x 2,..


with virtual memory, a contiguous range of virtual addresses can be mapped to several non - contiguous blocks of physical memory ; this non - contiguous allocation is one of the benefits of paging. however, paged mapping causes another problem, internal fragmentation. this occurs when a program requests a block of memory that does not cleanly map into a page, for instance, if a program requests a 1 kb buffer to perform file work. in this case, the request results in an entire page being set aside even though only 1 kb of the page will ever be used ; if pages are larger than 1 kb, the remainder of the page is wasted. if many small allocations of this sort are made, memory can be used up even though much of it remains empty. in some early microprocessor designs, memory management was performed by a separate integrated circuit such as the vlsi technology vi475 ( 1986 ), the motorola 68851 ( 1984 ) used with the motorola 68020 cpu in the macintosh ii, or the z8010 and z8015 ( 1985 ) used with the zilog z8000 family of processors. later microprocessors ( such as the motorola 68030 and the zilog z280 ) placed the mmu together with the cpu on the same integrated circuit, as did the intel 80286 and later x86 microprocessors.


in probability theory, kolmogorov equations, including kolmogorov forward equations and kolmogorov backward equations, characterize continuous - time markov processes. in particular, they describe how the probability that a continuous - time markov process is in a certain state changes over time.


these are normally used with vowels, but may occur with consonants. for example, in the athabaskan language hupa, voiceless velar fricatives distinguish three degrees of labialization, transcribed either / x /, / x /, / xʷ / or / x /, / xʷ /, / xʷ /. the extensions to the ipa has two additional symbols for degrees of rounding : spread and open - rounded ( as in english ).


at the software level, portability of measurement description is the key attribute that distinguishes a synthetic instrument from the more commonly found instrumentation software — software that is limited to hardware scripting and data flow processing. not all measurement related software systems inherently provide for the abstract, portable synthesis of measurements. even if they do have such provisions, they may not typically be applied that way by users, especially if the system encourages non - abstracted access to hardware.


in recent years, there has been a surge in large data sets available on human movements. these data sets are usually obtained from cell phone or gps data, with varying degrees of accuracy. for example, cell phone data is usually recorded whenever a call or a text message has been made or received by the user, and contains the location of the tower that the phone has connected to as well as the time stamp. in urban areas, user and the telecommunication tower might be only a few hundred meters away from each other, while in rural areas this distance might well be in region of a few kilometers.


for polynomials, the standard basis thus consists of the monomials and is commonly called monomial basis. for matrices m m × n { \ displaystyle { \ mathcal { m } } _ { m \ times n } }, the standard basis consists of the m×n - matrices with exactly one non - zero entry, which is 1. for example, the standard basis for 2×2 matrices is formed by the 4 matrices e 11 = ( 1 0 0 0 ), e 12 = ( 0 1 0 0 ), e 21 = ( 0 0 1 0 ), e 22 = ( 0 0 0 1 ). { \ displaystyle \ mathbf { e } _ { 11 } = { \ begin { pmatrix } 1 & 0 \ \ 0 & 0 \ end { pmatrix } }, \ quad \ mathbf { e } _ { 12 } = { \ begin { pmatrix } 0 & 1 \ \ 0 & 0 \ end { pmatrix } }, \ quad \ mathbf { e } _ { 21 } = { \ begin { pmatrix } 0 & 0 \ \ 1 & 0 \ end { pmatrix } }, \ quad \ mathbf { e } _ { 22 } = { \ begin { pmatrix } 0 & 0 \ \ 0 & 1 \ end { pmatrix } }. }


in 1964, ibm introduced its system / 360 series which used microcode to allow a single expansive instruction set architecture ( isa ) to run across a wide variety of machines by implementing more or less instructions in hardware depending on the need. this allowed the isa to be expansive, and this became the paragon of computer design in the 1960s and 70s, the so - called orthogonal design. this style of memory access with wide variety of modes led to instruction sets with hundreds of different instructions, a style known today as cisc ( complex instruction set computing ).


in the uk " abandoned " calls must not be called back within 72 hours unless there is a dedicated agent available. gdpr ( general data protection regulation ) also requires that the purpose of any call be related to the reason for collecting data in the first place. in the united states, if someone answers but no agent is available within 2 seconds of the person's greeting, federal communications commission ( fcc ) regulations consider the call " abandoned " and require the dialer to play a recorded message. the fcc requires that predictive dialers abandon less than 3 % of answered calls. in 1991 the telephone consumer protection act prohibited the use of an “ automatic telephone dialing system ” to contact “ any telephone number assigned to a mobile telephone service ” without “ express prior consent ” from the party being called.


in modular representation theory, while maschke's theorem does not hold when the characteristic divides the group order, the group algebra may be decomposed as the direct sum of a maximal collection of two - sided ideals known as blocks. when the field f has characteristic 0, or characteristic coprime to the group order, there is still such a decomposition of the group algebra f as a sum of blocks ( one for each isomorphism type of simple module ), but the situation is relatively transparent when f is sufficiently large : each block is a full matrix algebra over f, the endomorphism ring of the vector space underlying the associated simple module. to obtain the blocks, the identity element of the group g is decomposed as a sum of primitive idempotents in z ( r ), the center of the group algebra over the maximal order r of f. the block corresponding to the primitive idempotent e is the two - sided ideal e r. for each indecomposable r - module, there is only one such primitive idempotent that does not annihilate it, and the module is said to belong to ( or to be in ) the corresponding block ( in which case, all its composition factors also belong to that block ). in particular, each simple module belongs to a unique block. each ordinary irreducible character may also be assigned to a unique block according to its decomposition as a sum of irreducible brauer characters. the block containing the trivial module is known as the principal block.


for example, to the stem of bog ( to move ) is added - a giving as its subjunctive in the first person boga me : first conjugation : second conjugation : e. g. " go mbeannai dia thu " – may god bless you. there is also some irregularity in certain verbs in the subjunctive. the verb bi ( to be ) is the most irregular verb in irish ( as in most indo - european languages ) : the irish phrase for " thank you " – go raibh maith agat – uses the subjunctive of " bi " and literally means " may there be good at - you ".


technology companies have risen to meet the demand to help manage these complex systems. cloud - based scm technologies are at the forefront of next - generation supply chains due to their impact on optimization of time, resources, and inventory visibility. cloud technologies facilitate work being processed offline from a mobile app which solves the common issue of inventory residing in areas with no online coverage or connectivity.


in number theory, a wall – sun – sun prime or fibonacci – wieferich prime is a certain kind of prime number which is conjectured to exist, although none are known.


in the c + + programming language, static _ cast is an operator that performs an explicit type conversion.


hartman, newman & ziv ( 1991 ) and de fraysseix, ossona de mendez & pach ( 1991 ) proved that every bipartite planar graph can be represented as an intersection graph of horizontal and vertical line segments ; for this result see also czyzowicz, kranakis & urrutia ( 1998 ). de castro et al. ( 2002 ) proved that every triangle - free planar graph can be represented as an intersection graph of line segments having only three directions ; this result implies grotzsch's theorem ( grotzsch 1959 ) that triangle - free planar graphs can be colored with three colors. de fraysseix & ossona de mendez ( 2005 ) proved that if a planar graph g can be 4 - colored in such a way that no separating cycle uses all four colors, then g has a representation as an intersection graph of segments.


some early soviet computer designers implemented systems based on ternary logic ; that is, a bit could have three states : + 1, 0, or - 1, corresponding to positive, zero, or negative voltage. an early project for the u. s. air force, binac attempted to make a lightweight, simple computer by using binary arithmetic.


other approaches are loosely based on the idea of distributional semantics applied to sentences. skip - thought trains an encoder - decoder structure for the task of neighboring sentences predictions. though this has been shown to achieve worse performance than approaches such as infersent or sbert.


in protected mode, there are four privilege levels or rings, numbered from 0 to 3, with ring 0 being the most privileged and 3 being the least. the use of rings allows for system software to restrict tasks from accessing data, call gates or executing privileged instructions. in most environments, the operating system and some device drivers run in ring 0 and applications run in ring 3.


in the case of a continuously differentiable function f, a coordinate descent algorithm can be sketched as : the step size can be chosen in various ways, e. g., by solving for the exact minimizer of f ( xi ) = f ( x ) ( i. e., f with all variables but xi fixed ), or by traditional line search criteria.


in several scientific fields, " complexity " has a precise meaning : in computational complexity theory, the amounts of resources required for the execution of algorithms is studied. the most popular types of computational complexity are the time complexity of a problem equal to the number of steps that it takes to solve an instance of the problem as a function of the size of the input ( usually measured in bits ), using the most efficient algorithm, and the space complexity of a problem equal to the volume of the memory used by the algorithm ( e. g., cells of the tape ) that it takes to solve an instance of the problem as a function of the size of the input ( usually measured in bits ), using the most efficient algorithm. this allows classification of computational problems by complexity class ( such as p, np, etc. ). an axiomatic approach to computational complexity was developed by manuel blum.


in some processor architectures, like that of the intel 4004 4 - bit processor, memory was divided into ( 256 byte ) pages and special precautions had to be taken when the control flow crossed page boundaries, as some machine instructions exhibited different behaviour if located in the last few instructions of a page, so that only few instructions were recommended to jump between pages.


in mathematics, the geometric mean is a mean or average which indicates a central tendency of a finite set of real numbers by using the product of their values ( as opposed to the arithmetic mean which uses their sum ). the geometric mean is defined as the nth root of the product of n numbers, i. e., for a set of numbers a1, a2,..., an, the geometric mean is defined as ( i = 1 n a i ) 1 n = a 1 a 2 a n n { \ displaystyle \ left ( \ prod _ { i = 1 } ^ { n } a _ { i } \ right ) ^ { \ frac { 1 } { n } } = { \ sqrt { a _ { 1 } a _ { 2 } \ cdots a _ { n } } } } or, equivalently, as the arithmetic mean in logscale : exp ( 1 n i = 1 n ln a i ) { \ displaystyle \ exp { \ left ( { { \ frac { 1 } { n } } \ sum \ limits _ { i = 1 } ^ { n } \ ln a _ { i } } \ right ) } } most commonly the numbers are restricted to being non - negative, to avoid complications related to negative numbers not having real roots, and frequently they are restricted to being positive, to enable the use of logarithms. for instance, the geometric mean of two numbers, say 2 and 8, is just the square root of their product, that is, 2 ⋅ 8 = 4 { \ displaystyle { \ sqrt { 2 \ cdot 8 } } = 4 }. as another example, the geometric mean of the three numbers 4, 1, and 1 / 32 is the cube root of their product ( 1 / 8 ), which is 1 / 2, that is, 4 ⋅ 1 ⋅ 1 / 32 3 = 1 / 2 { \ displaystyle { \ sqrt { 4 \ cdot 1 \ cdot 1 / 32 } } = 1 / 2 }.


some points of clarification : first, the definitions above involve quantification over properties and hence higher - order logic. second, in ( 1 ), expressions of the form ( x ( x x ↔ x y ) ) { \ displaystyle ( \ forall x ( xx \ leftrightarrow xy ) ) } capture the concept of sharing all properties, or being indiscernible with respect to a set of properties. thus, ( 1 ) can be understood more intuitively as the claim that all objects that are indiscernible with respect to a base set of properties are indiscernible with respect to a supervenient set of properties, or, as it is also sometimes said, that b - twins are a - twins.


formally, it is the sequence ( z i ), i = 0, 1, 2, … { \ displaystyle ( z _ { i } ), i = 0, 1, 2, \ ldots } given by z i : = { x i / 2 if i is even, y ( i − 1 ) / 2 if i is odd. { \ displaystyle z _ { i } : = { \ begin { cases } x _ { i / 2 } & { \ text { if } } i { \ text { is even, } } \ \ y _ { ( i - 1 ) / 2 } & { \ text { if } } i { \ text { is odd. } } \ end { cases } } }


codes defined via a hamming space necessarily have the same length for every codeword, so they are called block codes when it is necessary to distinguish them from variable - length codes that are defined by unique factorization on a monoid. the hamming distance endows a hamming space with a metric, which is essential in defining basic notions of coding theory such as error detecting and error correcting codes. hamming spaces over non - field alphabets have also been considered, especially over finite rings ( most notably over z4 ) giving rise to modules instead of vector spaces and ring - linear codes ( identified with submodules ) instead of linear codes.


all arbitrary ( i. e. zero - symmetric or zero - asymmetric ) optimal sets of nodes in when n = 2 have been determined by f. schurer, and in an alternative fashion by h. - j. rack and r. vajda ( 2014 ). if we assume that we take −1 and 1 as nodes for interpolation, then as shown by h. - j.


in set theory, this multiplication principle is often taken to be the definition of the product of cardinal numbers. we have | s 1 | ⋅ | s 2 | | s n | = | s 1 × s 2 × × s n | { \ displaystyle | s _ { 1 } | \ cdot | s _ { 2 } | \ cdots | s _ { n } | = | s _ { 1 } \ times s _ { 2 } \ times \ cdots \ times s _ { n } | } where × { \ displaystyle \ times } is the cartesian product operator. these sets need not be finite, nor is it necessary to have only finitely many factors in the product ; see cardinal number. an extension of the rule of product considers there are n different types of objects, say sweets, to be associated with k objects, say people. how many different ways can the people receive their sweets? each person may receive any of the n sweets available, and there are k people, so there are n ⋅ n k = n k { \ displaystyle \ overbrace { n \ cdots \ cdot n } ^ { k } = n ^ { k } } ways to do this.


in mathematics, the generalized minimal residual method ( gmres ) is an iterative method for the numerical solution of an indefinite nonsymmetric system of linear equations. the method approximates the solution by the vector in a krylov subspace with minimal residual. the arnoldi iteration is used to find this vector. the gmres method was developed by yousef saad and martin h. schultz in 1986.


due to the nature of virtualization, the mapping of logical to physical requires some processing power and lookup tables. therefore, every implementation will add some small amount of latency. in addition to response time concerns, throughput has to be considered.


the polytope described by the linear program upper bounding the sum of edges taken per vertex is integral in the case of bipartite graphs, that is, it exactly describes the matching polytope, while for general graphs it is non - integral. hence, for bipartite graphs, it suffices to solve the corresponding linear program to obtain a valid matching. for general graphs, however, there are two other characterizations of the matching polytope one of which makes use of the blossom inequality for odd subsets of vertices and hence allows to relax the integer program to a linear program while still obtaining valid matchings. these characterizations are of further interest in edmonds'famous blossom algorithm used for finding such matchings in general graphs.


in mathematics, especially homological algebra and other applications of abelian category theory, the short five lemma is a special case of the five lemma. it states that for the following commutative diagram ( in any abelian category, or in the category of groups ), if the rows are short exact sequences, and if g and h are isomorphisms, then f is an isomorphism as well. it follows immediately from the five lemma. the essence of the lemma can be summarized as follows : if you have a homomorphism f from an object b to an object b ′, and this homomorphism induces an isomorphism from a subobject a of b to a subobject a ′ of b ′ and also an isomorphism from the factor object b / a to b ′ / a ′, then f itself is an isomorphism. note however that the existence of f ( such that the diagram commutes ) has to be assumed from the start ; two objects b and b ′ that simply have isomorphic sub - and factor objects need not themselves be isomorphic ( for example, in the category of abelian groups, b could be the cyclic group of order four and b ′ the klein four - group ).


in the case of a shared - secret pepper, a single compromised password ( via password reuse or other attack ) along with a user's salt can lead to an attack to discover the pepper, rendering it ineffective. if an attacker knows a plaintext password and a user's salt, as well as the algorithm used to hash the password, then discovering the pepper can be a matter of brute forcing the values of the pepper. this is why nist recommends the secret value be at least 112 bits, so that discovering it by exhaustive search is intractable. the pepper must be generated anew for every application it is deployed in, otherwise a breach of one application would result in lowered security of another application.


in pseudocode, the algorithm works as follows :


in the context of linear programming and related problems in mathematical optimization, convex polytopes are often described by a system of linear inequalities that their points must obey. when a polytope is integral, linear programming can be used to solve integer programming problems for the given system of inequalities, a problem that can otherwise be more difficult. some polyhedra arising from combinatorial optimization problems are automatically integral.


regularisation is particularly important feature for non - linear models and also often used in linear adaptive filters to reduce statistical uncertainties. however because nonlinear filters typically have a much higher potential structural complexity ( or higher dimensional feature space ) compared to the subspace actually required, regularisation of some kind must deal with the under - determined model. though some specific forms of parameter regularisation such as prescribed by vapink's srm & svm address the dimensionality problem statistically to some extent, there remain further statistical and practical issues for truly adaptive non - linear filters.


pal et al. designed features to measure a user's authority on a certain topic. for example, retweet impact refers to how many times a certain user has been retweeted on a certain topic. the impact is dampened by a factor measuring how many times the user had been retweeted by a unique author to avoid the cases when a user has fans who retweet regardless of the content. they first used a clustering approach to find the target cluster which has the highest average score across all features, and used a ranking algorithm to find the most authoritative users within the cluster. with these authority detection methods, social q & a could be more effective in providing accurate answers to askers.


in most mathematics, the operations of addition and multiplication are associative. the associative law for addition, for example, states that ( a + b ) + c = a + ( b + c ) { \ displaystyle ( a + b ) + c = a + ( b + c ) }. this means that once the associative law is stated, the parentheses are unnecessary and are usually omitted. more generally, any sum, of any number of terms, can be written without parentheses and any product, of any number of factors, can be written without parentheses.


in order to construct a shadow volume, project a ray from the light source through each vertex in the shadow casting object to some point ( generally at infinity ). these projections will together form a volume ; any point inside that volume is in shadow, everything outside is lit by the light. for a polygonal model, the volume is usually formed by classifying each face in the model as either facing toward the light source or facing away from the light source. the set of all edges that connect a toward - face to an away - face form the silhouette with respect to the light source.


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 l e v a n t _ i n s t a n c e s { \ displaystyle { \ frac { relevant \ _ retrieved \ _ instances } { all \ _ { \ mathbf { relevant } } \ _ instances } } }. both precision and recall are therefore based on relevance.


in the context of group theory, a sequence g 0 → f 1 g 1 → f 2 g 2 → f 3 → f n g n { \ displaystyle g _ { 0 } \ ; { \ xrightarrow { f _ { 1 } } } \ ; g _ { 1 } \ ; { \ xrightarrow { f _ { 2 } } } \ ; g _ { 2 } \ ; { \ xrightarrow { f _ { 3 } } } \ ; \ cdots \ ; { \ xrightarrow { f _ { n } } } \ ; g _ { n } } of groups and group homomorphisms is called exact, if the image ( or range ) of each homomorphism is equal to the kernel of the next : i m ( f k ) = k e r ( f k + 1 ) { \ displaystyle \ mathrm { im } ( f _ { k } ) = \ mathrm { ker } ( f _ { k + 1 } ) } the sequence of groups and homomorphisms may be either finite or infinite. a similar definition can be made for certain other algebraic structures. for example, one could have an exact sequence of vector spaces and linear maps, or of modules and module homomorphisms.


the sinclair zx80 and zx81 characters sets used x0c ( ascii : form feed ). the zx spectrum and the bbc micro used x60 ( ascii : `, grave ).


first compute m p ≡ c d p mod p { \ displaystyle m _ { p } \ equiv c ^ { d _ { p } } { \ bmod { p } } } and m q ≡ c d q mod q { \ displaystyle m _ { q } \ equiv c ^ { d _ { q } } { \ bmod { q } } }. 2. use the chinese remainder theorem to compute the unique value of m ∈ z n { \ displaystyle m \ in \ mathbb { z _ { n } } } which satisfies m ≡ m p mod p { \ displaystyle m \ equiv m _ { p } { \ bmod { p } } } and m ≡ m q mod q { \ displaystyle m \ equiv m _ { q } { \ bmod { q } } }. the result of m { \ displaystyle m } satisfies m ≡ c d mod n { \ displaystyle m \ equiv c ^ { d } { \ bmod { n } } } as needed. the point is that wiener ’ s attack does not apply here because the value of d mod λ ( n ) { \ displaystyle d { \ bmod { \ lambda } } ( n ) } can be large.


in order to generate a single constraint from a pair of constraints applied to the same ( pair of ) variable, we formalize the notion of intersection of constraints and of order over constraints. similarly, in order to define a new constraints from existing constraints, a notion of sum of constraint must also be defined.


when euclidean space is represented by a cartesian coordinate system in analytic geometry, euclidean distance satisfies the pythagorean relation : the squared distance between two points equals the sum of squares of the difference in each coordinate between the points. the theorem can be generalized in various ways : to higher - dimensional spaces, to spaces that are not euclidean, to objects that are not right triangles, and to objects that are not triangles at all but n - dimensional solids. the pythagorean theorem has attracted interest outside mathematics as a symbol of mathematical abstruseness, mystique, or intellectual power ; popular references in literature, plays, musicals, songs, stamps, and cartoons abound.


in recent years a number of neural and deep - learning techniques have been proposed, some of which generalize traditional matrix factorization algorithms via a non - linear neural architecture. while deep learning has been applied to many different scenarios : context - aware, sequence - aware, social tagging etc. its real effectiveness when used in a simple collaborative filtering scenario has been put into question. systematic analysis of publications applying deep learning or neural methods to the top - k recommendation problem, published in top conferences ( sigir, kdd, www, recsys, ijcai ), has shown that on average less than 40 % of articles are reproducible, with as little as 14 % in some conferences.


newer digital spread spectrum ( dss ) variants spread their signal over a range of frequencies, providing more resistance to signal fade. this technology enabled the digital information to spread in pieces among several frequencies between the receiver and the base, thereby making it almost impossible to eavesdrop on the cordless conversation. the fcc only allows dss model phones to transmit at the full power of 1 watt, which allows increased range over older analog and digital models. virtually all new cordless phones sold in the us use dect 6. 0 on the 1. 9 ghz band, though legacy phones can remain in use on the older 900 mhz, 2. 4 ghz and 5. 8 ghz bands.


in modern landscape design olive trees are frequently used as ornamental features for their distinctively gnarled trunks and " evergreen " silvery gray foliage.


the feasible set of the problem is separate from the objective function, which states the criterion to be optimized and which in the above example is x 2 + y 4. { \ displaystyle x ^ { 2 } + y ^ { 4 }. } in many problems, the feasible set reflects a constraint that one or more variables must be non - negative.


in the 1710s, leibniz described grandi's series in his correspondence with several other mathematicians. the letter with the most lasting impact was his first reply to wolff, which he published in the acta eruditorum. in this letter, leibniz attacked the problem from several angles. in general, leibniz believed that the algorithms of calculus were a form of " blind reasoning " that ultimately had to be founded upon geometrical interpretations.


in ordinary language, an average is a single number taken as representative of a list of numbers, usually the sum of the numbers divided by how many numbers are in the list ( the arithmetic mean ). for example, the average of the numbers 2, 3, 4, 7, and 9 ( summing to 25 ) is 5. depending on the context, an average might be another statistic such as the median, or mode. for example, the average personal income is often given as the median — the number below which are 50 % of personal incomes and above which are 50 % of personal incomes — because the mean would be higher by including personal incomes from a few billionaires. for this reason, it is recommended to avoid using the word " average " when discussing measures of central tendency.


in number theory, szpiro's conjecture relates to the conductor and the discriminant of an elliptic curve. in a slightly modified form, it is equivalent to the well - known abc conjecture. it is named for lucien szpiro, who formulated it in the 1980s. szpiro's conjecture and its equivalent forms have been described as " the most important unsolved problem in diophantine analysis " by dorian goldfeld, in part to its large number of consequences in number theory including roth's theorem, the mordell conjecture, the fermat – catalan conjecture, and brocard's problem.


the general problem remains unsolved, apart from the best - known lower bound ω ( ( log n ) / n 2 ) { \ displaystyle \ omega ( ( \ log n ) / n ^ { 2 } ) } ( achievable ; hence, heilbronn's conjecture is not correct for general n { \ displaystyle n } ) and upper bound exp ( c log n ) / n 8 / 7 { \ displaystyle \ exp ( c { \ sqrt { \ log n } } ) / n ^ { 8 / 7 } } ( proven by komlos, pintsz and szemeredi in 1982 and 1981, respectively ). using the incompressibility method, the average case was studied. it was proven that if the area is too small ( or large ) it can be compressed below the kolmogorov complexity of a uniformly - random arrangement ( high kolmogorov complexity ). this proves that for the overwhelming majority of the arrangements ( and the expectation ), the area of the smallest triangle formed by three of n { \ displaystyle n } points thrown uniformly at random in the unit square is θ ( 1 / n 3 ) { \ displaystyle \ theta ( 1 / n ^ { 3 } ) }. in this case, the incompressibility method proves the lower and upper bounds of the property involved.


then given a query in natural language, the embedding for the query can be generated. a top k similarity search algorithm is then used between the query embedding and the document chunk embeddings to retrieve the most relevant document chunks as context information for question answering tasks. this approach is also known formally as retrieval augmented generationthough not as predominant as bertscore, sentence embeddings are commonly used for sentence similarity evaluation which sees common use for the task of optimizing a large language model's generation parameters is often performed via comparing candidate sentences against reference sentences. by using the cosine - similarity of the sentence embeddings of candidate and reference sentences as the evaluation function, a grid - search algorithm can be utilized to automate hyperparameter optimization. sentence embedding is used by the deep learning software libraries pytorch and tensorflow.


to properly evaluate the truth ( or falsehood ) of a sentence, one must make reference to an interpretation of the theory. for first - order theories, interpretations are commonly called structures. given a structure or interpretation, a sentence will have a fixed truth value. a theory is satisfiable when it is possible to present an interpretation in which all of its sentences are true. the study of algorithms to automatically discover interpretations of theories that render all sentences as being true is known as the satisfiability modulo theories problem.


in mathematics, the burr – erdos conjecture was a problem concerning the ramsey number of sparse graphs. the conjecture is named after stefan burr and paul erdos, and is one of many conjectures named after erdos ; it states that the ramsey number of graphs in any sparse family of graphs should grow linearly in the number of vertices of the graph. the conjecture was proven by choongbum lee. thus it is now a theorem.


in plane geometry, constructing the diagonal of a square results in a triangle whose three angles are in the ratio 1 : 1 : 2, adding up to 180° or π radians. hence, the angles respectively measure 45° ( π / 4 ), 45° ( π / 4 ), and 90° ( π / 2 ). the sides in this triangle are in the ratio 1 : 1 : √2, which follows immediately from the pythagorean theorem. of all right triangles, the 45° - 45° - 90° degree triangle has the smallest ratio of the hypotenuse to the sum of the legs, namely √2 / 2.


in optimization theory, the duality principle states that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. in general given two dual pairs separated locally convex spaces ( x, x ∗ ) { \ displaystyle \ left ( x, x ^ { * } \ right ) } and ( y, y ∗ ). { \ displaystyle \ left ( y, y ^ { * } \ right ). } then given the function f : x →, { \ displaystyle f : x \ to, } we can define the primal problem as finding x { \ displaystyle x } such that inf x ∈ x f ( x ).


in military terminology, vulnerability is a subset of survivability, the others being susceptibility and recoverability. vulnerability is defined in various ways depending on the nation and service arm concerned, but in general it refers to the near - instantaneous effects of a weapon attack. in aviation it is defined as the inability of an aircraft to withstand the damage caused by the man - made hostile environment. in some definitions, recoverability ( damage control, firefighting, restoration of capability ) is included in vulnerability. some military services develop their own concept of vulnerability.


in pure prolog, normal dcg rules with no extra arguments on the functors, such as the previous example, can only express context - free grammars ; there is only one argument on the left side of the production. however, context - sensitive grammars can also be expressed with dcgs, by providing extra arguments, such as in the following example : this set of dcg rules describes the grammar which generates the language that consists of strings of the form a n b n c n { \ displaystyle a ^ { n } b ^ { n } c ^ { n } }. this set of dcg rules describes the grammar which generates the language that consists of strings of the form a n b n c n { \ displaystyle a ^ { n } b ^ { n } c ^ { n } }, by structurally representing n


in statistics, k - medians clustering is a cluster analysis algorithm. it is a variation of k - means clustering where instead of calculating the mean for each cluster to determine its centroid, one instead calculates the median. this has the effect of minimizing error over all clusters with respect to the 1 - norm distance metric, as opposed to the squared 2 - norm distance metric ( which k - means does. ) this relates directly to the k - median problem with respect to the 1 - norm, which is the problem of finding k centers such that the clusters formed by them are the most compact.


in scientific visualization the asymptotic decider is an algorithm developed by nielson and hamann in 1991 that creates isosurfaces from a given scalar field. it was proposed as an improvement to the marching cubes algorithm, which can produce some " bad " topology, but can also be considered an algorithm in its own right.


definition. the constraint equations ( 6 ) define an n { \ displaystyle \ displaystyle n } - dimensional manifold m { \ displaystyle \ displaystyle m } within the configuration space of the newtonian dynamical system ( 3 ). this manifold m { \ displaystyle \ displaystyle m } is called the configuration space of the constrained system.


in remote areas, an additional stage of clustering is used, in order to reduce travel requirements. although cluster sampling and stratified sampling bear some superficial similarities, they are substantially different. in stratified sampling, a random sample is drawn from all the strata, where in cluster sampling only the selected clusters are studied, either in single - or multi - stage. advantages cost and speed that the survey can be done in convenience of finding the survey sample normally more accurate than cluster sampling for the same size sampledisadvantages not as accurate as simple random sample if the sample is the same size more testing is difficult to do


in order to bound the competitive ratio for tango trees, we must find a lower bound on the performance of the optimal offline tree that we use as a benchmark. once we find an upper bound on the performance of the tango tree, we can divide them to bound the competitive ratio.


additivity and sigma - additivity are particularly important properties of measures. they are abstractions of how intuitive properties of size ( length, area, volume ) of a set sum when considering multiple objects. additivity is a weaker condition than σ - additivity ; that is, σ - additivity implies additivity. the term modular set function is equivalent to additive set function ; see modularity below.


in mathematics, the absolute value or modulus of a real number x { \ displaystyle x }, denoted | x | { \ displaystyle | x | }, is the non - negative value of x { \ displaystyle x } without regard to its sign. namely, | x | = x { \ displaystyle | x | = x } if x { \ displaystyle x } is a positive number, and | x | = − x { \ displaystyle | x | = - x } if x { \ displaystyle x } is negative ( in which case negating x { \ displaystyle x } makes − x { \ displaystyle - x } positive ), and | 0 | = 0 { \ displaystyle | 0 | = 0 }. for example, the absolute value of 3 is 3, and the absolute value of −3 is also 3.


narrowing reduces those worlds by eliminating combinations of different worlds from the same world set. narrowing rules also detect situations where some combinations of worlds are shown to be impossible. no back tracking is required in the use of narrowing. by packaging the possible values in a value set all combinations of values may be considered at the same time. evaluation proceeds as for a functional language, combining combinations of values in value sets, with narrowing rules eliminating impossible values from the sets.


two companies have emerged that specialize in building multi - core processor devices using the mips architecture. raza microelectronics, inc. bought the product line from failing sandcraft and later produced devices that contained eight cores for the telecommunication and networking markets. cavium, originally a security processor vendor also produced devices with eight cpu cores, and later up to 32 cores, for the same markets. both of these firms designed their cores in - house, only licensing the architecture instead of buying cores from mips.


in mathematics, bezout's identity ( also called bezout's lemma ), named after etienne bezout, is the following theorem : here the greatest common divisor of 0 and 0 is taken to be 0. the integers x and y are called bezout coefficients for ( a, b ) ; they are not unique. a pair of bezout coefficients can be computed by the extended euclidean algorithm, and this pair is, in the case of integers one of the two pairs such that | x | ≤ | b / d | { \ displaystyle | x | \ leq | b / d | } and | y | ≤ | a / d | ; { \ displaystyle | y | \ leq | a / d | ; } equality occurs only if one of a and b is a multiple of the other.


in telecommunications there may be different reasons why a handover might be conducted : when the phone is moving away from the area covered by one cell and entering the area covered by another cell the call is transferred to the second cell in order to avoid call termination when the phone gets outside the range of the first cell ; when the capacity for connecting new calls of a given cell is used up and an existing or new call from a phone, which is located in an area overlapped by another cell, is transferred to that cell in order to free - up some capacity in the first cell for other users, who can only be connected to that cell ; in non - cdma networks when the channel used by the phone becomes interfered by another phone using the same channel in a different cell, the call is transferred to a different channel in the same cell or to a different channel in another cell in order to avoid the interference ; again in non - cdma networks when the user behaviour changes, e. g. when a fast - travelling user, connected to a large, umbrella - type of cell, stops then the call may be transferred to a smaller macro cell or even to a micro cell in order to free capacity on the umbrella cell for other fast - traveling users and to reduce the potential interference to other cells or users ( this works in reverse too, when a user is detected to be moving faster than a certain threshold, the call can be transferred to a larger umbrella - type of cell in order to minimize the frequency of the handovers due to this movement ) ; in cdma networks a handover ( see further down ) may be induced in order to reduce the interference to a smaller neighboring cell due to the " near – far " effect even when the phone still has an excellent connection to its current cell. the most basic form of handover is when a phone call in progress is redirected from its current cell ( called source ) to a new cell ( called target ). in terrestrial networks the source and the target cells may be served from two different cell sites or from one and the same cell site ( in the latter case the two cells are usually referred to as two sectors on that cell site ). such a handover, in which the source and the target are different cells ( even if they are on the same cell site ) is called inter - cell handover. the purpose of inter - cell handover is to maintain the call as the subscriber is moving out of the area covered by the source cell and entering the area of the target cell


in pure prolog, naf literals of the form n o t p { \ displaystyle \ mathrm { not } ~ p } can occur in the body of clauses and can be used to derive other naf literals. for example, given only the four clauses p ← q ∧ n o t r { \ displaystyle p \ leftarrow q \ land \ mathrm { not } ~ r } q ← s { \ displaystyle q \ leftarrow s } q ← t { \ displaystyle q \ leftarrow t } t ← { \ displaystyle t \ leftarrow } naf derives n o t s { \ displaystyle \ mathrm { not } ~ s }, n o t r { \ displaystyle \ mathrm { not } ~ r } and p { \ displaystyle ~ p } as well as t { \ displaystyle ~ t } and q { \ displaystyle ~ q }.


a function is most often denoted by letters such as f, g and h, and the value of a function f at an element x of its domain is denoted by f ( x ) ; the numerical value resulting from the function evaluation at a particular input value is denoted by replacing x with this value ; for example, the value of f at x = 4 is denoted by f ( 4 ). when the function is not named and is represented by an expression e, the value of the function at, say, x = 4 may be denoted by e | x = 4. for example, the value at 4 of the function that maps x to ( x + 1 ) 2 { \ displaystyle ( x + 1 ) ^ { 2 } } may be denoted by ( x + 1 ) 2 | x = 4 { \ displaystyle \ left.


in telecommunications, long - term evolution ( lte ) is a standard for wireless broadband communication for mobile devices and data terminals, based on the gsm / edge and umts / hspa standards. it improves on those standards'capacity and speed by using a different radio interface and core network improvements. lte is the upgrade path for carriers with both gsm / umts networks and cdma2000 networks. because lte frequencies and bands differ from country to country, only multi - band phones can use lte in all countries where it is supported.


additionally, dba functions are often automated using restructuring tools that are tightly coupled to an active data dictionary. software frameworks aimed at rapid application development sometimes include high - level data dictionary facilities, which can substantially reduce the amount of programming required to build menus, forms, reports, and other components of a database application, including the database itself. for example, phplens includes a php class library to automate the creation of tables, indexes, and foreign key constraints portably for multiple databases.


in real network problems, people are interested in determining the likelihood of occurring double links ( with opposite directions ) between vertex pairs. this problem is fundamental for several reasons. first, in the networks that transport information or material ( such as email networks, world wide web ( www ), world trade web, or wikipedia ), mutual links facilitate the transportation process. second, when analyzing directed networks, people often treat them as undirected ones for simplicity ; therefore, the information obtained from reciprocity studies helps to estimate the error introduced when a directed network is treated as undirected ( for example, when measuring the clustering coefficient ). finally, detecting nontrivial patterns of reciprocity can reveal possible mechanisms and organizing principles that shape the observed network's topology.


in mathematical morphology, the closing of a set ( binary image ) a by a structuring element b is the erosion of the dilation of that set, a b = ( a ⊕ b ) b, { \ displaystyle a \ bullet b = ( a \ oplus b ) \ ominus b, \, } where ⊕ { \ displaystyle \ oplus } and { \ displaystyle \ ominus } denote the dilation and erosion, respectively. in image processing, closing is, together with opening, the basic workhorse of morphological noise removal. opening removes small objects, while closing removes small holes.


in statistics and research design, an index is a composite statistic – a measure of changes in a representative group of individual data points, or in other words, a compound measure that aggregates multiple indicators. indexes – also known as composite indicators – summarize and rank specific observations. much data in the field of social sciences and sustainability are represented in various indices such as gender gap index, human development index or the dow jones industrial average. the ‘ report by the commission on the measurement of economic performance and social progress ’, written by joseph stiglitz, amartya sen, and jean - paul fitoussi in 2009 suggests that these measures have experienced a dramatic growth in recent years due to three concurring factors : improvements in the level of literacy ( including statistical ) increased complexity of modern societies and economies, and widespread availability of information technology. according to earl babbie, items in indexes are usually weighted equally, unless there are some reasons against it ( for example, if two items reflect essentially the same aspect of a variable, they could have a weight of 0. 5 each ). according to the same author, constructing the items involves four steps. first, items should be selected based on their content validity, unidimensionality, the degree of specificity in which a dimension is to be measured, and their amount of variance.


in statistics, regression validation is the process of deciding whether the numerical results quantifying hypothesized relationships between variables, obtained from regression analysis, are acceptable as descriptions of the data. the validation process can involve analyzing the goodness of fit of the regression, analyzing whether the regression residuals are random, and checking whether the model's predictive performance deteriorates substantially when applied to data that were not used in model estimation.


in the equations below, the lowercase variables represent vectors. matrices w q { \ displaystyle w _ { q } } and u q { \ displaystyle u _ { q } } contain, respectively, the weights of the input and recurrent connections, where the subscript q { \ displaystyle _ { q } } can either be the input gate i { \ displaystyle i }, output gate o { \ displaystyle o }, the forget gate f { \ displaystyle f } or the memory cell c { \ displaystyle c }, depending on the activation being calculated. in this section, we are thus using a " vector notation ". so, for example, c t ∈ r h { \ displaystyle c _ { t } \ in \ mathbb { r } ^ { h } } is not just one unit of one lstm cell, but contains h { \ displaystyle h } lstm cell's units.


if there is a dependence of each state on an overall entity ( e. g. a map or simply an overall state variable ), one typically uses slam ( simultaneous localization and mapping ) techniques, which include the sequential estimator as a special case ( when the overall state variable has just one state ). it will estimate the state sequence and the overall entity. there are also none - causal variants, that have all measurements at the same time, batches of measurements or revert the state evolution to go backwards again.


for each node on the phylogeny, the nodal support is the percentage of pseudoreplicates containing that node. the statistical rigor of the bootstrap test has been empirically evaluated using viral populations with known evolutionary histories, finding that 70 % bootstrap support corresponds to a 95 % probability that the clade exists. however, this was tested under ideal conditions ( e. g. no change in evolutionary rates, symmetric phylogenies ). in practice, values above 70 % are generally supported and left to the researcher or reader to evaluate confidence.


in mathematics, a summability kernel is a family or sequence of periodic integrable functions satisfying a certain set of properties, listed below. certain kernels, such as the fejer kernel, are particularly useful in fourier analysis. summability kernels are related to approximation of the identity ; definitions of an approximation of identity vary, but sometimes the definition of an approximation of the identity is taken to be the same as for a summability kernel.


in sociolinguistics, a variety, also called an isolect or lect, is a specific form of a language or language cluster. this may include languages, dialects, registers, styles, or other forms of language, as well as a standard variety. the use of the word " variety " to refer to the different forms avoids the use of the term language, which many people associate only with the standard language, and the term dialect, which is often associated with non - standard varieties thought of as less prestigious or " correct " than the standard. linguists speak of both standard and non - standard ( vernacular ) varieties. " lect " avoids the problem in ambiguous cases of deciding whether two varieties are distinct languages or dialects of a single language. variation at the level of the lexicon, such as slang and argot, is often considered in relation to particular styles or levels of formality ( also called registers ), but such uses are sometimes discussed as varieties as well.


in order to add first order protection against phase - flips within a single degree of freedom, a higher dimension manifold is required. the 4 - component cat code uses the even - parity submanifold of the superposition of 4 coherent states to encode information. the odd - parity submanifold is also 2 - dimensional and serves as an error space since a single photon loss switches the parity of the state. hence, monitoring the parity is sufficient to detect errors caused by single photon loss.


in statistics and machine learning, ensemble methods use multiple learning algorithms to obtain better predictive performance than could be obtained from any of the constituent learning algorithms alone. unlike a statistical ensemble in statistical mechanics, which is usually infinite, a machine learning ensemble consists of only a concrete finite set of alternative models, but typically allows for much more flexible structure to exist among those alternatives.


a slide is a specially mounted individual transparency intended for projection onto a screen using a slide projector. this allows the photograph to be viewed by a large audience at once. the most common form is the 35 mm slide, with the image framed in a 2×2 inch cardboard or plastic mount. some specialized labs produce photographic slides from digital camera images in formats such as jpeg, from computer - generated presentation graphics, and from a wide variety of physical source material such as fingerprints, microscopic sections, paper documents, astronomical images, etc. reversal film is sometimes used as motion picture film, mostly in the 16 mm, super 8 and 8 mm " cine " formats, to yield a positive image on the camera original. this avoids the expense of using negative film, which requires additional film and processing to create a positive film print for projection.


the three - dimensional angular momentum for a point particle is classically represented as a pseudovector r × p, the cross product of the particle's position vector r ( relative to some origin ) and its momentum vector ; the latter is p = mv in newtonian mechanics. unlike linear momentum, angular momentum depends on where this origin is chosen, since the particle's position is measured from it. angular momentum is an extensive quantity ; that is, the total angular momentum of any composite system is the sum of the angular momenta of its constituent parts.


in the classical untyped lambda calculus, every function has a fixed point. a particular implementation of fix is curry's paradoxical combinator y, represented by y = λ f. ( λ x. f ( x x ) ) ( λ x.


in the dominican republic, number portability in both mobile and local telephony was launched september 30, 2009. in march, 2009, the dominican telecommunications institute ( indotel ) selected informatica el corte ingles to administer the number portability.


in the above uml class diagram, the client class refers ( 1 ) to the aggregate interface for creating an iterator object ( createiterator ( ) ) and ( 2 ) to the iterator interface for traversing an aggregate object ( next ( ), hasnext ( ) ). the iterator1 class implements the iterator interface by accessing the aggregate1 class. the uml sequence diagram shows the run - time interactions : the client object calls createiterator ( ) on an aggregate1 object, which creates an iterator1 object and returns it to the client. the client uses then iterator1 to traverse the elements of the aggregate1 object.


however, the only way the process can use or set'-'values in its vas is to ask the os to map them to bytes from a file. a common way to use vas memory in this way is to map it to the page file. the page file is a single file, but multiple distinct sets of contiguous bytes can be mapped into a vas : 0 4 gib vas | - - - vvv - - - - - - - - vvvvvv - - - vvvv - - - - vv - - - v - - - - vvv - - | mapping | | | | | | | | | | | | | | | | | | | file bytes app kernel user system _ page _ file and different parts of the page file can map into the vas of different processes : 0 4 gib vas 1 | - - - vvvv - - - - - - - vvvvvv - - - vvvv - - - - vv - - - v - - - - vvv - - | mapping | | | | | | | | | | | | | | | | | | | | file bytes app1 app2 kernel user system _ page _ file mapping | | | | | | | | | | | | | | | | | vas 2 | - - - - - - - - vvvv - - vvvvvv - - - vvvv - - - - - - - vv - - - v - - - - - - | on microsoft windows 32 - bit, by default, only 2 gib are made available to processes for their own use.


in real - time computing, priority inheritance is a method for eliminating unbounded priority inversion. using this programming method, a process scheduling algorithm increases the priority of a process ( a ) to the maximum priority of any other process waiting for any resource on which a has a resource lock ( if it is higher than the original priority of a ). the basic idea of the priority inheritance protocol is that when a job blocks one or more high - priority jobs, it ignores its original priority assignment and executes its critical section at an elevated priority level. after executing its critical section and releasing its locks, the process returns to its original priority level.


" world's first gsm call was actually made by me. i called marjo jousinen, in salo. ", lonka informed. the following year saw the sending of the first short messaging service ( sms or " text message " ) message, ms and vodafone uk and telecom finland signed the first international roaming agreement.


many digital modulation methods such as cofdm use the electromagnetic spectrum very efficiently, allowing for a very tight spectral mask. this allows placement of broadcast stations or other transmissions on channels right next to each other without interference, allowing for an increase in a band's total capacity. conversely, it is allowing the u. s. to eliminate tv channels 52 to 69, freeing up 108 mhz ( from approximately 700 to 800 mhz ) for emergency services and to be auctioned off to the highest bidder, while still retaining ( although moving ) all existing tv stations.


as a result, students inherit all the attributes common to all persons. additionally, students have unique attributes that other persons don't have. object - oriented languages model subset / superset relationships using inheritance.


the driving force for the cathodic protection current is the difference in electrode potential between the anode and the cathode. during the initial phase of high current, the potential of the steel surface is polarized ( pushed ) more negative protecting the steel which hydroxide ion generation at the steel surface and ionic migration restore the concrete environment. over time the galvanic anode continues to corrode, consuming the anode material until eventually it must be replaced. galvanic or sacrificial anodes are made in various shapes and sizes using alloys of zinc, magnesium, and aluminum.


then [ 0, 1⁄2 ) is open in s but not in r { \ displaystyle \ mathbb { r } }. likewise [ 1⁄2, 1 ) is closed in s but not in r { \ displaystyle \ mathbb { r } }. s is both open and closed as a subset of itself but not as a subset of r { \ displaystyle \ mathbb { r } }.


therefore, there is varying degree of accuracy when it comes to locating a person using cell phone data. these datasets are anonymized by the phone companies so as to hide and protect the identity of actual users. as example of its usage, researchers used the trajectory of 100, 000 cell phone users within a period of six months, while in much larger scale trajectories of three million cell phone users were analyzed.


in optimization theory, semi - infinite programming ( sip ) is an optimization problem with a finite number of variables and an infinite number of constraints, or an infinite number of variables and a finite number of constraints. in the former case the constraints are typically parameterized.


in mathematics, a statistical manifold is a riemannian manifold, each of whose points is a probability distribution. statistical manifolds provide a setting for the field of information geometry. the fisher information metric provides a metric on these manifolds. following this definition, the log - likelihood function is a differentiable map and the score is an inclusion.


in mathematics, the herzog – schonheim conjecture is a combinatorial problem in the area of group theory, posed by marcel herzog and jochanan schonheim in 1974. let g { \ displaystyle g } be a group, and let a = { a 1 g 1, …, a k g k } { \ displaystyle a = \ { a _ { 1 } g _ { 1 }, \ \ ldots, \ a _ { k } g _ { k } \ } } be a finite system of left cosets of subgroups g 1, …, g k { \ displaystyle g _ { 1 }, \ ldots, g _ { k } } of g { \ displaystyle g }. herzog and schonheim conjectured that if a { \ displaystyle a } forms a partition of g { \ displaystyle g } with k > 1 { \ displaystyle k > 1 }, then the ( finite ) indices, …, { \ displaystyle, \ ldots, } cannot be distinct. in contrast, if repeated indices are allowed, then partitioning a group into cosets is easy : if h { \ displaystyle h } is any subgroup of g { \ displaystyle g } with index k = < ∞ { \ displaystyle k = < \ infty } then g { \ displaystyle g } can be partitioned into k { \ displaystyle k } left cosets of h { \ displaystyle h }.


on the other hand, if the running time of the algorithm is much smaller than d communication rounds, then the nodes in the network must produce their output without having the possibility to obtain information about distant parts of the network. in other words, the nodes must make globally consistent decisions based on information that is available in their local d - neighbourhood. many distributed algorithms are known with the running time much smaller than d rounds, and understanding which problems can be solved by such algorithms is one of the central research questions of the field.