in order to achieve the required amount of'testing volume'needed to validate real - world testing, three points must be considered : system accuracy federal and / or state health and safety guidelines and / or standards economic viability based on the first two points. once a particular portable emissions system has been identified and pronounced as accurate, the next step is to ensure that the worker ( s ) are properly protected from work hazards associated with the task ( s ) being performed in the use of the testing equipment. for example, typical functions for a worker may be to transport the equipment to the jobsite ( i. e. car, truck, train, or plane ), carry the equipment to the jobsite, and lift the equipment into position.


in some literature articles, the terms " mechanism of action " and " mode of action " are used interchangeably, typically referring to the way in which the drug interacts and produces a medical effect. however, in actuality, a mode of action describes functional or anatomical changes, at the cellular level, resulting from the exposure of a living organism to a substance. this differs from a mechanism of action since it is a more specific term that focuses on the interaction between the drug itself and an enzyme or receptor and its particular form of interaction, whether through inhibition, activation, agonism, or antagonism. furthermore, the term " mechanism of action " is the main term that is primarily used in pharmacology, whereas " mode of action " will more often appear in the field of microbiology or certain aspects of biology.


in most computer programming languages, a while loop is a control flow statement that allows code to be executed repeatedly based on a given boolean condition. the while loop can be thought of as a repeating if statement.


in statistics, combinatorial data analysis ( cda ) is the study of data sets where the order in which objects are arranged is important. cda can be used either to determine how well a given combinatorial construct reflects the observed data, or to search for a suitable combinatorial construct that does fit the data.


in some situations, the set of edges that are required is different from the edges in the graph. this is modeled by the rural postman problem ( rpp ), where the required edges are a subset of the system of edges.


in mathematics, a bipartite matroid is a matroid all of whose circuits have even size.


in the 1950, waldo tobler published a paper titled " automation and cartography " that established the first use case for computers as aids in cartography. in this paper, tobler established what he referred to as a " map in – map out " ( mimo ) system, which facilitated digitization of traditional maps, changing them, and reproducing them. the mimo system, while simple, established the use of computers for map making in the literature and set the stage for more advanced geographic information systems in later years by geographers such as roger tomlinson.


this is typically done with polynomial or rational ( ratio of polynomials ) approximations. the objective is to make the approximation as close as possible to the actual function, typically with an accuracy close to that of the underlying computer's floating point arithmetic. this is accomplished by using a polynomial of high degree, and / or narrowing the domain over which the polynomial has to approximate the function. narrowing the domain can often be done through the use of various addition or scaling formulas for the function being approximated. modern mathematical libraries often reduce the domain into many tiny segments and use a low - degree polynomial for each segment.


a learning process that involves a method of reward and punishment must be in place that will select desirable patterns in the mind. this whole process, turing mentions, to a large extent is similar to that of evolution by natural selection where the similarities are : structure of the child machine = hereditary material changes of the child machine = mutations natural selection = judgment of the experimenterfollowing this discussion turing addresses certain specific aspects of the learning machine : nature of inherent complexity : the child machine could either be one that is as simple as possible, merely maintaining consistency with general principles, or the machine could be one with a complete system of logical inference programmed into it.


hence the result by cole and vishkin raised the question of whether there is a constant - time distributed algorithm for 3 - coloring an n - cycle. linial ( 1992 ) showed that this is not possible : any deterministic distributed algorithm requires ω ( log * n ) communication steps to reduce an n - coloring to a 3 - coloring in an n - cycle. the technique by cole and vishkin can be applied in arbitrary bounded - degree graphs as well ; the running time is poly ( δ ) + o ( log * n ).


in mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable. it may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value ( e. g., may be a mean or an assumed mean of the data ), in which case it may be known as mean square deviation. when the reference value is the assumed true value, the result is known as mean squared error. a typical estimate for the sample variance from a set of sample values x i { \ displaystyle x _ { i } } uses a divisor of the number of values minus one, n - 1, rather than n as in a simple quadratic mean, and this is still called the " mean square " ( e. g. in analysis of variance ) : s 2 = 1 n − 1 ( x i − x ) 2 { \ displaystyle s ^ { 2 } = \ textstyle { \ frac { 1 } { n - 1 } } \ sum ( x _ { i } - { \ bar { x } } ) ^ { 2 } } the second moment of a random variable, e ( x 2 ) { \ displaystyle e ( x ^ { 2 } ) } is also called the mean square. the square root of a mean square is known as the root mean square ( rms or rms ), and can be used as an estimate of the standard deviation of a random variable. = = references = =


the besicovitch inequality asserts that the inequality can be generalized in the following way. given an n - dimensional riemannian manifold m with connected boundary and a smooth map f : m → n { \ displaystyle f : m \ rightarrow ^ { n } }, such that the restriction of f to the boundary of m is a degree 1 map onto ∂ n { \ displaystyle \ partial ^ { n } }, define then i d i ≥ v o l ( m ) { \ displaystyle \ prod _ { i } d _ { i } \ geq vol ( m ) }. the besicovitch inequality was used to prove systolic inequalities on surfaces.


in order theory a better - quasi - ordering or bqo is a quasi - ordering that does not admit a certain type of bad array. every better - quasi - ordering is a well - quasi - ordering.


the chromatic polynomial, a polynomial whose values at integer arguments give the number of colorings of the graph with that many colors. the dichromatic polynomial, a 2 - variable generalization of the chromatic polynomial the flow polynomial, a polynomial whose values at integer arguments give the number of nowhere - zero flows with integer flow amounts modulo the argument. the ( inverse of the ) ihara zeta function, defined as a product of binomial terms corresponding to certain closed walks in a graph. the martin polynomial, used by pierre martin to study euler tours the matching polynomials, several different polynomials defined as the generating function of the matchings of a graph. the reliability polynomial, a polynomial that describes the probability of remaining connected after independent edge failures the tutte polynomial, a polynomial in two variables that can be defined ( after a small change of variables ) as the generating function of the numbers of connected components of induced subgraphs of the given graph, parameterized by the number of vertices in the subgraph.


in mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain. polynomial factorization is one of the fundamental components of computer algebra systems. the first polynomial factorization algorithm was published by theodor von schubert in 1793. leopold kronecker rediscovered schubert's algorithm in 1882 and extended it to multivariate polynomials and coefficients in an algebraic extension.


individual u. s. states set their own policies for state and local government employees ( i. e. public sector employees ).


in molecular biology, a batch effect occurs when non - biological factors in an experiment cause changes in the data produced by the experiment. such effects can lead to inaccurate conclusions when their causes are correlated with one or more outcomes of interest in an experiment. they are common in many types of high - throughput sequencing experiments, including those using microarrays, mass spectrometers, and single - cell rna - sequencing data. they are most commonly discussed in the context of genomics and high - throughput sequencing research, but they exist in other fields of science as well.


in number theory, bertrand's postulate is a theorem stating that for any integer n > 3 { \ displaystyle n > 3 }, there always exists at least one prime number p { \ displaystyle p } with n < p < 2 n − 2. { \ displaystyle n 1 { \ displaystyle n > 1 }, there is always at least one prime p { \ displaystyle p } such that n < p < 2 n. { \ displaystyle n


laws issue out a command to their constituents which can be realized as an action. when forming a legal contract, speech acts can be made when people are making or accepting an offer. considering the theory of freedom of speech, some speech acts may not be legally protected. for example, a death threat is a type of speech act and is considered to exist outside of the protection of freedom of speech as it is treated as a criminal act.


in mathematics, especially linear algebra, an m - matrix is a z - matrix with eigenvalues whose real parts are nonnegative. the set of non - singular m - matrices are a subset of the class of p - matrices, and also of the class of inverse - positive matrices ( i. e. matrices with inverses belonging to the class of positive matrices ). the name m - matrix was seemingly originally chosen by alexander ostrowski in reference to hermann minkowski, who proved that if a z - matrix has all of its row sums positive, then the determinant of that matrix is positive.


since functional programming languages, by definition, support function literals, which can also be stored in records, records types with subtyping provide some of the features of object - oriented programming. typically, functional programming languages also provide some, usually restricted, form of parametric polymorphism. in a theoretical setting, it is desirable to study the interaction of the two features ; a common theoretical setting is system f < :.


as well as log2, an alternative notation for the binary logarithm is lb ( the notation preferred by iso 31 - 11 and iso 80000 - 2 ). historically, the first application of binary logarithms was in music theory, by leonhard euler : the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. binary logarithms can be used to calculate the length of the representation of a number in the binary numeral system, or the number of bits needed to encode a message in information theory.


in recent years commercial adns have begun to include application firewall functionality to further secure applications during the delivery process. this is a hotly debated subject with many security professionals arguing that the functionality included in an application firewall are unnecessary and should be handled by the application while others consider employing as much security as possible, regardless of position in the delivery network, to be the best practice. many commercial adn companies have acquired and integrated these functions and present such features as part of a defense in depth strategy often cited by security professionals.


ranked set sampling uses a two - phase sampling design that identifies sets of field locations, utilizes inexpensive measurements to rank locations within each set, and then selects one location from each set for sampling. in ranked set sampling, m sets ( each of size r ) of field locations are identified using simple random sampling. the locations are ranked independently within each set using professional judgment or inexpensive, fast, or surrogate measurements.


in statistics, the conditional probability table ( cpt ) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others ( i. e., the probability of each possible value of one variable if we know the values taken on by the other variables ). for example, assume there are three random variables x 1, x 2, x 3 { \ displaystyle x _ { 1 }, x _ { 2 }, x _ { 3 } } where each has k { \ displaystyle k } states. then, the conditional probability table of x 1 { \ displaystyle x _ { 1 } } provides the conditional probability values p ( x 1 = a k x 2, x 3 ) { \ displaystyle p ( x _ { 1 } = a _ { k } \ mid x _ { 2 }, x _ { 3 } ) } – where the vertical bar | { \ displaystyle | } means “ given the values of ” – for each of the k possible values a k { \ displaystyle a _ { k } } of the variable x 1 { \ displaystyle x _ { 1 } } and for each possible combination of values of x 2, x 3. { \ displaystyle x _ { 2 }, \, x _ { 3 }. }


in order to get a grasp on the motivations which inspired the development of the idea of coordinative definitions, it is important to understand the doctrine of formalism as it is conceived in the philosophy of mathematics. for the formalists, mathematics, and particularly geometry, is divided into two parts : the pure and the applied. the first part consists in an uninterpreted axiomatic system, or syntactic calculus, in which terms such as point, straight line and between ( the so - called primitive terms ) have their meanings assigned to them implicitly by the axioms in which they appear. on the basis of deductive rules eternally specified in advance, pure geometry provides a set of theorems derived in a purely logical manner from the axioms.


in order to design a form or document, the writer should understand and evaluate the different constraints in the rhetorical situation ; this is called functional analysis. one of the biggest components in analyzing a form or document is to determine the communicative purpose of the form or document. leo lentz and henk pander maat, at the university of utrecht, break down communicative purpose into four elements : intended communicative effect : the intended effect should fall into one of three categories ; " a cognitive change in the mental state of the reader, who learns something or forms a particular attitude, a change in the reader's behavior, such as handling a machine or buying a product, or a change in the social reality as a result of the collective behavior of readers, such as the sale of a product ". topic : this is based on the reader's needs, since the reader is the one expected to act on the information. target group : this should be a specific group described either by demographic variables or communicative predispositions. organizational goal : this is the change that should occur in every individual reader. after analyzing the communicative purpose, the technical communicator can design a form or document that will match the requirements and meet expectations for it.


when programming in machine code, assembly language, and certain other programming languages, programmers work with the low - level digital structure of the data registers. these registers operate on voltages, where zero volts represents boolean 0, and a reference voltage ( often + 5 v, + 3. 3 v, + 1. 8 v ) represents boolean 1. such languages support both numeric operations and logical operations.


in natural resources management and environmental policy more generally, demand management refers to policies to control consumer demand for environmentally sensitive or harmful goods such as water and energy. within manufacturing firms the term is used to describe the activities of demand forecasting, planning, and order fulfillment. in the environmental context demand management is increasingly taken seriously to reduce the economy's throughput of scarce resources for which market pricing does not reflect true costs. examples include metering of municipal water, and carbon taxes on gasoline.


in mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic ( usually dividing the order of the group ). the study of modular invariants was originated in about 1914 by dickson ( 2004 ).


testing and the overall quality process remain problematic for several key reasons. traditional testing processes are too slow.


however, there are other number systems that are not accurately described by these axioms ; in particular, the theory defined in the same way for integers instead of real numbers is undecidable, even for existential sentences ( diophantine equations ) by matiyasevich's theorem. the existential theory of the reals is the fragment of the first - order theory consisting of sentences in which all the quantifiers are existential and they appear before any of the other symbols. that is, it is the set of all true sentences of the form where f ( x 1, … x n ) { \ displaystyle f ( x _ { 1 }, \ dots x _ { n } ) } is a quantifier - free formula involving equalities and inequalities of real polynomials. the decision problem for the existential theory of the reals is the algorithmic problem of testing whether a given sentence belongs to this theory ; equivalently, for strings that pass the basic syntactical checks ( they use the correct symbols with the correct syntax, and have no unquantified variables ) it is the problem of testing whether the sentence is a true statement about the real numbers.


in the standard model of particle physics, the cabibbo – kobayashi – maskawa matrix, ckm matrix, quark mixing matrix, or km matrix is a unitary matrix which contains information on the strength of the flavour - changing weak interaction. technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. it is important in the understanding of cp violation. this matrix was introduced for three generations of quarks by makoto kobayashi and toshihide maskawa, adding one generation to the matrix previously introduced by nicola cabibbo. this matrix is also an extension of the gim mechanism, which only includes two of the three current families of quarks.


in mathematics, the coclass of a finite p - group of order pn is n − c, where c is the class.


in the context of sensor net, public - key based access control ( pkc ) may be a good solution in the future to cover some issues in wireless access control. for sensor net, the danger from attackers includes ; impersonation which grants access to malicious users, replay attack where the adversary captures sensitive information by replaying it, interleaving which selectively combines messages from previous sessions, reflection where an adversary sends an identical message to the originator similar to impersonation, forced delay which blocks communication message to be sent at a later time, and chosen - text attack where the attacker tries to extract the keys to access the sensor. the solution to this may be public key - based cryptography as a study done by haodong wang shows that pkc - based protocol presented is better than the traditional symmetric key in regards to memory usage, message complexity, and security resilience.


in mathematics, a matrix norm is a vector norm in a vector space whose elements ( vectors ) are matrices ( of given dimensions ).


in the context of centralized linear - quadratic control, with additive uncertainty in the equation of evolution but no uncertainty about coefficient values in that equation, the optimal solution for the control variables taking into account the uncertainty is the same as the solution ignoring uncertainty. this property, which gives a zero expected value of including uncertainty, is called certainty equivalence.


] _ { f } } or ] o ∈ ] f { \ displaystyle \! ] _ { o } \ in \! ] _ { f } }.


category has the value noun phrase whereas the value of agreement is indicated by another feature structure with the features number and person being singular and third. this particular notation is called attribute value matrix ( avm ). the matrix has two columns, one for the feature names and the other for the values.


the carp can be solved with combinatorial optimization including convex hulls. the large - scale capacitated arc routing problem ( lscarp ) is a variant of the capacitated arc routing problem that applies to hundreds of edges and nodes to realistically simulate and model large complex environments. = = references = =


in order to reduce the reliance on legal professionals and the amount of time needed, efforts have been made to create a system to automatically classify legal text and queries. adequate translation of both would allow accurate information retrieval without the high cost of human classification. these automatic systems generally employ natural language processing ( nlp ) techniques that are adapted to the legal domain, and also require the creation of a legal ontology.


in mathematics, specifically in abstract algebra, power associativity is a property of a binary operation that is a weak form of associativity.


the user can direct dial from their handset if the network they are roaming in supports camel ( customized applications for mobile networks enhanced logic ). this allows real time billing by the home operator without having to dial the customer back. the advantage is that it is more natural and works seamlessly. the disadvantage is that not all networks support camel so the list of countries where a prepaid customer can use their phone abroad is smaller than for postpaid mobile phones.


in operating systems architecture a reference monitor concept defines a set of design requirements on a reference validation mechanism, which enforces an access control policy over subjects'( e. g., processes and users ) ability to perform operations ( e. g., read and write ) on objects ( e. g., files and sockets ) on a system. the properties of a reference monitor are captured by the acronym neat, which means : the reference validation mechanism must be non - bypassable, so that an attacker cannot bypass the mechanism and violate the security policy. the reference validation mechanism must be evaluable, i. e., amenable to analysis and tests, the completeness of which can be assured ( verifiable ). without this property, the mechanism might be flawed in such a way that the security policy is not enforced.


in software engineering, a test case is a specification of the inputs, execution conditions, testing procedure, and expected results that define a single test to be executed to achieve a particular software testing objective, such as to exercise a particular program path or to verify compliance with a specific requirement. test cases underlie testing that is methodical rather than haphazard. a battery of test cases can be built to produce the desired coverage of the software being tested. formally defined test cases allow the same tests to be run repeatedly against successive versions of the software, allowing for effective and consistent regression testing.


therefore, r = 1 2 { \ displaystyle r = { \ frac { 1 } { 2 } } }, so b = b 1 / 2 { \ displaystyle { \ sqrt { b } } = b ^ { 1 / 2 } }. the definition of exponentiation can be extended to allow any real or complex exponent. exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices. exponentiation is used extensively in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public - key cryptography.


in the first pass, the forward – backward algorithm computes a set of forward probabilities which provide, for all t ∈ { 1, …, t } { \ displaystyle t \ in \ { 1, \ dots, t \ } }, the probability of ending up in any particular state given the first t { \ displaystyle t } observations in the sequence, i. e. p ( x t | o 1 : t ) { \ displaystyle p ( x _ { t } \ | \ o _ { 1 : t } ) }. in the second pass, the algorithm computes a set of backward probabilities which provide the probability of observing the remaining observations given any starting point t { \ displaystyle t }, i. e. p ( o t + 1 : t | x t ) { \ displaystyle p ( o _ { t + 1 : t } \ | \ x _ { t } ) }. these two sets of probability distributions can then be combined to obtain the distribution over states at any specific point in time given the entire observation sequence : p ( x t | o 1 : t ) = p ( x t | o 1 : t, o t + 1 : t ) p ( o t + 1 : t | x t ) p ( x t | o 1 : t ) { \ displaystyle p ( x _ { t } \ | \ o _ { 1 : t } ) = p ( x _ { t } \ | \ o _ { 1 : t }, o _ { t + 1 : t } ) \ propto p ( o _ { t + 1 : t } \ | \ x _ { t } ) p ( x _ { t } | o _ { 1 : t } ) } the last step follows from an application of the bayes'rule and the conditional independence of o t + 1 : t { \ displaystyle o _ { t + 1 : t } } and o 1 : t { \ displaystyle o _ { 1 : t } } given x t { \ displaystyle x _ { t } }. as outlined above, the algorithm involves three steps : computing forward probabilities computing backward probabilities computing smoothed values. the forward and backward steps may also be called " forward message pass " and " backward message pass " - these terms are due to the message - passing used in general belief propagation approaches.


{ \ displaystyle \ omega. } define u ( h, k ) = f ( a + h, b + k ) − f ( a + h, b ), v ( h, k ) = f ( a + h, b + k ) − f ( a, b + k ), w ( h, k ) = f ( a + h, b + k ) − f ( a + h, b ) − f ( a, b + k ) + f ( a, b ). { \ displaystyle { \ begin { aligned } u \ left ( h, \, k \ right ) & = f \ left ( a + h, \, b + k \ right ) - f \ left ( a + h, \, b \ right ), \ \ v \ left ( h, \, k \ right ) & = f \ left ( a + h, \, b + k \ right ) - f \ left ( a, \, b + k \ right ), \ \ w \ left ( h, \, k \ right ) & = f \ left ( a + h, \, b + k \ right ) - f \ left ( a + h, \, b \ right ) - f \ left ( a, \, b + k \ right ) + f \ left ( a, \, b \ right ). \ end { aligned } } } these functions are defined for | h |, | k | < ε { \ displaystyle \ left | h \ right |, \, \ left | k \ right | < \ varepsilon }, where ε > 0 { \ displaystyle \ varepsilon > 0 } and × { \ displaystyle \ left \ times \ left } is contained in ω.


in systems engineering, the system usability scale ( sus ) is a simple, ten - item attitude likert scale giving a global view of subjective assessments of usability. it was developed by john brooke at digital equipment corporation in the uk in 1986 as a tool to be used in usability engineering of electronic office systems. the usability of a system, as defined by the iso standard iso 9241 part 11, can be measured only by taking into account the context of use of the system — i. e., who is using the system, what they are using it for, and the environment in which they are using it. furthermore, measurements of usability have several different aspects : effectiveness ( can users successfully achieve their objectives ) efficiency ( how much effort and resource is expended in achieving those objectives ) satisfaction ( was the experience satisfactory ) measures of effectiveness and efficiency are also context specific.


different websites and systems have different algorithms, but one approach, used by amazon ( company ) for its online store, is to indicate to a user : " customers who bought x also bought y " ( affinity analysis, collaborative filtering ). this example is oriented around online purchasing behaviour, but an algorithm could also be programmed to provide suggestions based on other factors ( e. g., searching, viewing, etc. ). discoverability is typically referred to in connection with search engines. a highly " discoverable " piece of content would appear at the top, or near the top of a user's search results.


the latter are referred to as vector magnetographs. these measurements are made by exploiting the zeeman effect or, less frequently, the hanle effect. the first magnetograph was constructed by george ellery hale in 1908. = = references = =


this is called the harvard architecture after the harvard mark i computer. modern von neumann computers display some traits of the harvard architecture in their designs, such as in cpu caches.


in mathematics, for positive integers k and s, a vectorial addition chain is a sequence v of k - dimensional vectors of nonnegative integers vi for −k + 1 ≤ i ≤ s together with a sequence w, such that v−k + 1 = v−k + 2 = v0 = vi = vj + vr for all 1≤i≤s with - k + 1≤j, r≤i - 1 vs = w = ( w1,... ws ), wi = ( j, r ). for example, a vectorial addition chain for is v = (,,,,,,,,,,, ) w = ( ( - 2, - 1 ), ( 1, 1 ), ( 2, 2 ), ( - 2, 3 ), ( 4, 4 ), ( 1, 5 ), ( 0, 6 ), ( 7, 7 ), ( 0, 8 ) ) vectorial addition chains are well suited to perform multi - exponentiation : input : elements x0,..., xk - 1 of an abelian group g and a vectorial addition chain of dimension k computing output : the element x0n0... xk - 1nr - 1for i = - k + 1 to 0 do yi → xi + k - 1 for i = 1 to s do yi →yj×yr return ys


in science and in engineering, the celsius scale and the kelvin scale are often used in combination in close contexts, e. g. " a measured value was 0. 01023 °c with an uncertainty of 70 μk ". this practice is permissible because the magnitude of the degree celsius is equal to that of the kelvin. notwithstanding the official endorsement provided by decision no. 3 of resolution 3 of the 13th cgpm, which stated " a temperature interval may also be expressed in degrees celsius ", the practice of simultaneously using both °c and k remains widespread throughout the scientific world as the use of si - prefixed forms of the degree celsius ( such as " μ°c " or " microdegrees celsius " ) to express a temperature interval has not been well adopted.


in number theory, primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression. an example is the sequence of primes ( 3, 7, 11 ), which is given by a n = 3 + 4 n { \ displaystyle a _ { n } = 3 + 4n } for 0 ≤ n ≤ 2 { \ displaystyle 0 \ leq n \ leq 2 }. according to the green – tao theorem, there exist arbitrarily long sequences of primes in arithmetic progression. sometimes the phrase may also be used about primes which belong to an arithmetic progression which also contains composite numbers.


a ccs ( centacall - second ) is often used to describe 100 call - seconds, so 3600 call - seconds = 36 ccs = 1 call - hour. in a communication network, a trunk ( link ) can carry numerous concurrent calls by means of multiplexing. hence a particular number of call - seconds can be carried in infinitely many ways as calls are established and cleared over time.


in mathematical logic, a formal theory is a set of sentences within a formal language. a sentence is a well - formed formula with no free variables. a sentence that is a member of a theory is one of its theorems, and the theory is the set of its theorems. usually a theory is understood to be closed under the relation of logical consequence.


in statistics, the t - statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. it is used in hypothesis testing via student's t - test. the t - statistic is used in a t - test to determine whether to support or reject the null hypothesis.


in proof theory, the dialectica interpretation is a proof interpretation of intuitionistic logic ( heyting arithmetic ) into a finite type extension of primitive recursive arithmetic, the so - called system t. it was developed by kurt godel to provide a consistency proof of arithmetic. the name of the interpretation comes from the journal dialectica, where godel's paper was published in a 1958 special issue dedicated to paul bernays on his 70th birthday.


the two measures are complementary in sense that if one knows the mid - range and the range, one can find the sample maximum and minimum values. the mid - range is rarely used in practical statistical analysis, as it lacks efficiency as an estimator for most distributions of interest, because it ignores all intermediate points, and lacks robustness, as outliers change it significantly. indeed, for many distributions it is one of the least efficient and least robust statistics. however, it finds some use in special cases : it is the maximally efficient estimator for the center of a uniform distribution, trimmed mid - ranges address robustness, and as an l - estimator, it is simple to understand and compute.


in sociology, a social system is the patterned network of relationships constituting a coherent whole that exist between individuals, groups, and institutions. it is the formal structure of role and status that can form in a small, stable group. an individual may belong to multiple social systems at once ; examples of social systems include nuclear family units, communities, cities, nations, college campuses, religions, corporations, and industries. the organization and definition of groups within a social system depend on various shared properties such as location, socioeconomic status, race, religion, societal function, or other distinguishable features.


in mathematics, a product of rings or direct product of rings is a ring that is formed by the cartesian product of the underlying sets of several rings ( possibly an infinity ), equipped with componentwise operations. it is a direct product in the category of rings. since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings. for example, the chinese remainder theorem may be stated as : if m and n are coprime integers, the quotient ring z / m n z { \ displaystyle \ mathbb { z } / mn \ mathbb { z } } is the product of z / m z { \ displaystyle \ mathbb { z } / m \ mathbb { z } } and z / n z. { \ displaystyle \ mathbb { z } / n \ mathbb { z }. }


in numerical analysis, finite - difference methods ( fdm ) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. both the spatial domain and time interval ( if applicable ) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points. finite difference methods convert ordinary differential equations ( ode ) or partial differential equations ( pde ), which may be nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. modern computers can perform these linear algebra computations efficiently which, along with their relative ease of implementation, has led to the widespread use of fdm in modern numerical analysis. today, fdm are one of the most common approaches to the numerical solution of pde, along with finite element methods.


in that work : " a viewpoint can be thought of as a combination of the idea of an “ actor ”, “ knowledge source ”, “ role ” or “ agent ” in the development process and the idea of a “ view ” or “ perspective ” which an actor maintains. " an important idea in this paper was to distinguish " a representation style, the scheme and notation by which the viewpoint expresses what it can see " and " a specification, the statements expressed in the viewpoint's style describing particular domains ". subsequent work, such as ieee 1471, preserved this distinction by utilizing two separate terms : viewpoint and view, respectively.


337 ). we have r + = r if, and only if, r itself is transitive. conversely, transitive reduction adduces a minimal relation s from a given relation r such that they have the same closure, that is, s + = r + ; however, many different s with this property may exist. both transitive closure and transitive reduction are also used in the closely related area of graph theory.


in some cases, particularly with noun and adjective phrases, it is not always clear which dependents are to be classed as complements, and which as adjuncts. although in principle the head - directionality parameter concerns the order of heads and complements only, considerations of head - initiality and head - finality sometimes take account of the position of the head in the phrase as a whole, including adjuncts. the structure of the various types of phrase is analyzed below in relation to specific languages, with a focus on the ordering of head and complement. in some cases ( such as english and japanese ) this ordering is found to be the same in practically all types of phrase, whereas in others ( such as german and gbe ) the pattern is less consistent.


in mathematics, the category of topological spaces, often denoted top, is the category whose objects are topological spaces and whose morphisms are continuous maps. this is a category because the composition of two continuous maps is again continuous, and the identity function is continuous. the study of top and of properties of topological spaces using the techniques of category theory is known as categorical topology. n. b. some authors use the name top for the categories with topological manifolds, with compactly generated spaces as objects and continuous maps as morphisms or with the category of compactly generated weak hausdorff spaces.


examples of this are the iapx 432 ( a project originally named the intel 8800 ), the intel 960, intel 860 and the intel / hewlett - packard itanium architecture. however, the continuous refinement of x86 microarchitectures, circuitry and semiconductor manufacturing would make it hard to replace x86 in many segments. amd's 64 - bit extension of x86 ( which intel eventually responded to with a compatible design ) and the scalability of x86 chips in the form of modern multi - core cpus, is underlining x86 as an example of how continuous refinement of established industry standards can resist the competition from completely new architectures.


the information integration of heterogeneous data sources in traditional database is intricate, which requires the redesign of the database table such as changing the structure and / or addition of new data. in the case of semantic query, sparql query reflects the relationships between entities in a way that aligned with human's understanding of the domain, so the semantic intention of the query can be seen on the query itself. unlike sparql, sql query, which reflects the specific structure of the database and derived from matching the relevant primary and foreign keys of tables, loses the semantics of the query by missing the relationships between entities.


in speech, common combinations of conjugation and auxiliary verbs are contracted in a fairly regular manner. there are occasional others, such as - aranai → - annai as in wakaranai ( 分 からない, don't understand ) → wakannai ( 分 かんない ) and tsumaranai ( つまらない, boring ) → tsumannai ( つまんない ) – these are considered quite casual and are more common among the younger generation. contractions differ by dialect, but behave similarly to the standard ones given above. for example, in the kansai dialect, - te shimau ( 〜 てしまう ) → - temau ( 〜 てまう ).


all direct neighbors of s are visited in the first step, which form the next frontier. after each layer - traversal, the " next frontier " is switched to the frontier and new vertices will be stored in the new next frontier. the following pseudo - code outlines the idea of it, in which the data structures for the frontier and next frontier are called fs and ns respectively. 1 define bfs _ sequential ( graph ( v, e ), source s ) : 2 for all v in v do 3 d = - 1 ; 4 d = 0 ; level = 1 ; fs = { } ; ns = { } ; 5 push ( s, fs ) ; 6 while fs! empty do 7 for u in fs do 8 for each neighbour v of u do 9 if d = - 1 then 10 push ( v, ns ) ; 11 d = level ; 12 fs = ns, ns = { }, level = level + 1 ;


in statistics and signal processing, the method of empirical orthogonal function ( eof ) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. the term is also interchangeable with the geographically weighted principal components analysis in geophysics. the i th basis function is chosen to be orthogonal to the basis functions from the first through i − 1, and to minimize the residual variance. that is, the basis functions are chosen to be different from each other, and to account for as much variance as possible. the method of eof analysis is similar in spirit to harmonic analysis, but harmonic analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed frequencies.


a strategic minority could overpower an honest majority. this problem can be minimized through education or ballot design to encourage uninformed voters to give more - extreme rankings. a different path to minimize this problem is to use median scores instead of total scores, as median scores are less amenable to exaggeration, as in majority judgment.


{ \ displaystyle v ^ { - }. } we denote with δ ( v + ) { \ displaystyle \ delta ( v ^ { + } ) } the set of edges that connect the two sets. we can then rewrite the hamiltonian as h = − i j ∈ e ( v + ) j i j − i j ∈ e ( v − ) j i j + i j ∈ δ ( v + ) j i j = − i j ∈ e ( g ) j i j + 2 i j ∈ δ ( v + ) j i j = c + 2 i j ∈ δ ( v + ) j i j { \ displaystyle { \ begin { aligned } h & = - \ sum _ { ij \ in e ( v ^ { + } ) } j _ { ij } - \ sum _ { ij \ in e ( v ^ { - } ) } j _ { ij } + \ sum _ { ij \ in \ delta ( v ^ { + } ) } j _ { ij } \ \ & = - \ sum _ { ij \ in e ( g ) } j _ { ij } + 2 \ sum _ { ij \ in \ delta ( v ^ { + } ) } j _ { ij } \ \ & = c + 2 \ sum _ { ij \ in \ delta ( v ^ { + } ) } j _ { ij } \ end { aligned } } } minimizing this energy is equivalent to the min - cut problem or by setting the graph weights as w i j = − j i j, { \ displaystyle w _ { ij } = - j _ { ij }, } the max - cut problem.


change - label : it works exactly the same as change - edge. as a summary, we conclude that having n 1 { \ displaystyle n _ { 1 } } calls to create _ node and n 2 { \ displaystyle n _ { 2 } } calls to change _ edge will result in the creation of 2 ⋅ n 1 + n 2 { \ displaystyle 2 \ cdot n _ { 1 } + n _ { 2 } } tables. since each table has size o ( d ) { \ displaystyle o ( d ) } without taking into account the recursive calls, then filling in a table requires o ( d 2 ) { \ displaystyle o ( d ^ { 2 } ) } where the additional d factor comes from updating the inedges at other nodes. therefore the amount of work required to complete a sequence of operations is bounded by the number of tables created multiplied by o ( d 2 ) { \ displaystyle o ( d ^ { 2 } ) }. each access operation can be done in o ( l o g ( d ) ) { \ displaystyle o ( log ( d ) ) } and there are m { \ displaystyle m } edge and label operations, thus it requires m ⋅ o ( l o g ( d ) ) { \ displaystyle m \ cdot o ( log ( d ) ) }. we conclude that there exists a data structure that can complete any n { \ displaystyle n } sequence of create - node, change - edge and change - label in o ( n ⋅ d 2 ) + m ⋅ o ( l o g ( d ) ) { \ displaystyle o ( n \ cdot d ^ { 2 } ) + m \ cdot o ( log ( d ) ) }.


in mathematics, an algebraic matroid is a matroid, a combinatorial structure, that expresses an abstraction of the relation of algebraic independence.


in order of net exports in 2011, 2009 and 2006 in thousand bbl / d and thousand m3 / d : source : us energy information administration 1 peak production already passed in this state 2 canadian statistics are complicated by the fact it is both an importer and exporter of crude oil, and refines large amounts of oil for the u. s. market. it is the leading source of u. s. imports of oil and products, averaging 2, 500, 000 bbl / d ( 400, 000 m3 / d ) in august 2007. total world production / consumption ( as of 2005 ) is approximately 84 million barrels per day ( 13, 400, 000 m3 / d ).


the probability that at least one of the events will occur is equal to one. for example, there are theoretically only two possibilities for flipping a coin. flipping a head and flipping a tail are collectively exhaustive events, and there is a probability of one of flipping either a head or a tail.


in modern poetry, formalist poets may be considered as the opposite of writers of free verse. these are only labels, and rarely sum up matters satisfactorily.'formalism'in poetry represents an attachment to poetry that recognises and uses schemes of rhyme and rhythm to create poetic effects and to innovate. to distinguish it from archaic poetry the term'neo - formalist'is sometimes used. see for example : the formalist, a literary magazine ( now defunct ) for formalist poetry new formalism, a movement within the poetry of the united states.


in mathematics, the muller – schupp theorem states that a finitely generated group g has context - free word problem if and only if g is virtually free. the theorem was proved by david muller and paul schupp in 1983.


in most dynamically - typed languages, the list of methods on an object can be altered at runtime. this requires late binding.


formally, a relation r over a set x can be seen as a set of ordered pairs ( x, y ) of members of x. the relation r holds between x and y if ( x, y ) is a member of r. for example, the relation " is less than " on the natural numbers is an infinite set rless of pairs of natural numbers that contains both ( 1, 3 ) and ( 3, 4 ), but neither ( 3, 1 ) nor ( 4, 4 ). the relation " is a nontrivial divisor of " on the set of one - digit natural numbers is sufficiently small to be shown here : rdiv = { ( 2, 4 ), ( 2, 6 ), ( 2, 8 ), ( 3, 6 ), ( 3, 9 ), ( 4, 8 ) } ; for example 2 is a nontrivial divisor of 8, but not vice versa, hence ( 2, 8 ) ∈ rdiv, but ( 8, 2 ) ∈ rdiv. if r is a relation that holds for x and y one often writes xry.


in the abstract setting of oriented matroids, bland's rule cycles on some examples. a restricted class of oriented matroids on which bland's rule avoids cycling has been termed " bland oriented matroids " by jack edmonds. another pivoting rule, the criss - cross algorithm, avoids cycles on all oriented - matroid linear - programs.


in mathematical logic, godel's β function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. the β function is used, in particular, in showing that the class of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions. the β function was introduced without the name in the proof of the first of godel's incompleteness theorems ( godel 1931 ). the β function lemma given below is an essential step of that proof. godel gave the β function its name in ( godel 1934 ).


such implausible equilibria might arise also in games with complete information, but they may be eliminated by applying subgame perfect nash equilibrium. however, bayesian games often contain non - singleton information sets and since subgames must contain complete information sets, sometimes there is only one subgame — the entire game — and so every nash equilibrium is trivially subgame perfect. even if a game does have more than one subgame, the inability of subgame perfection to cut through information sets can result in implausible equilibria not being eliminated. to summarize : in this variant of the gift game, there are two spes : either the sender always gives and the receiver always accepts, or the sender always does not give and the receiver always rejects. from these, only the first one is a pbe ; the other is not a pbe since it cannot be supported by any belief - system.


in effect, work stealing distributes the scheduling work over idle processors, and as long as all processors have work to do, no scheduling overhead occurs. work stealing contrasts with work sharing, another popular scheduling approach for dynamic multithreading, where each work item is scheduled onto a processor when it is spawned. compared to this approach, work stealing reduces the amount of process migration between processors, because no such migration occurs when all processors have work to do. the idea of work stealing goes back to the implementation of the multilisp programming language and work on parallel functional programming languages in the 1980s. it is employed in the scheduler for the cilk programming language, the java fork / join framework, the. net task parallel library, and the rust tokio runtime.


in morphometrics, landmark point or shortly landmark is a point in a shape object in which correspondences between and within the populations of the object are preserved. in other disciplines, landmarks may be known as vertices, anchor points, control points, sites, profile points,'sampling'points, nodes, markers, fiducial markers, etc. landmarks can be defined either manually by experts or automatically by a computer program. there are three basic types of landmarks : anatomical landmarks, mathematical landmarks or pseudo - landmarks.


in mathematics, an analytic proof is a proof of a theorem in analysis that only makes use of methods from analysis, and which does not predominantly make use of algebraic or geometrical methods. the term was first used by bernard bolzano, who first provided a non - analytic proof of his intermediate value theorem and then, several years later provided a proof of the theorem that was free from intuitions concerning lines crossing each other at a point, and so he felt happy calling it analytic ( bolzano 1817 ). bolzano's philosophical work encouraged a more abstract reading of when a demonstration could be regarded as analytic, where a proof is analytic if it does not go beyond its subject matter ( sebastik 2007 ). in proof theory, an analytic proof has come to mean a proof whose structure is simple in a special way, due to conditions on the kind of inferences that ensure none of them go beyond what is contained in the assumptions and what is demonstrated.


in the field of relational database design, normalization is a systematic way of ensuring that a database structure is suitable for general - purpose querying and free of certain undesirable characteristics — insertion, update, and deletion anomalies that could lead to loss of data integrity. a standard piece of database design guidance is that the designer should create a fully normalized design ; selective denormalization can subsequently be performed, but only for performance reasons. the trade - off is storage space vs performance.


borrow 1 from the thousands place for a ten in the hundreds place, minus 7 from the row below, the difference 3 is added to the 2 on top to form 5. the 7 on the bottom is subtracted, shown by the space. borrow 1 from the hundreds place, which leaves 4.


in mathematics, the relaxation of a ( mixed ) integer linear program is the problem that arises by removing the integrality constraint of each variable. for example, in a 0 – 1 integer program, all constraints are of the form x i ∈ { 0, 1 } { \ displaystyle x _ { i } \ in \ { 0, 1 \ } }. the relaxation of the original integer program instead uses a collection of linear constraints 0 ≤ x i ≤ 1. { \ displaystyle 0 \ leq x _ { i } \ leq 1. } the resulting relaxation is a linear program, hence the name. this relaxation technique transforms an np - hard optimization problem ( integer programming ) into a related problem that is solvable in polynomial time ( linear programming ) ; the solution to the relaxed linear program can be used to gain information about the solution to the original integer program.


in object - oriented programming, behavioral subtyping is the principle that subclasses should satisfy the expectations of clients accessing subclass objects through references of superclass type, not just as regards syntactic safety ( such as the absence of " method - not - found " errors ) but also as regards behavioral correctness. specifically, properties that clients can prove using the specification of an object's presumed type should hold even though the object is actually a member of a subtype of that type. for example, consider a type stack and a type queue, which both have a put method to add an element and a get method to remove one.


in project management, resource leveling is defined by a guide to the project management body of knowledge ( pmbok guide ) as " a technique in which start and finish dates are adjusted based on resource limitation with the goal of balancing demand for resources with the available supply. " resource leveling problem could be formulated as an optimization problem. the problem could be solved by different optimization algorithms such as exact algorithms or meta - heuristic methods. when performing project planning activities, the manager will attempt to schedule certain tasks simultaneously. when more resources such as machines or people are needed than are available, or perhaps a specific person is needed in both tasks, the tasks will have to be rescheduled concurrently or even sequentially to manage the constraint.


in order to determine how judges weigh the different factors, 103 written judgements of commonplace cases were used to establish a database comprising 94 relevant factors for percentage split determination. : 273 the factors relevant for a percentage split determination are : past contributions of a husband relative to those of a wife the husband's future needs relative to those of the wife the wealth of the marriagethe factors relevant for a determination of past contributions are the relative direct and indirect contributions of both parties the length of the marriage the relative contributions of both parties to the homemaking rolethe hierarchy provides a structure that is used to decompose the task of predicting an outcome into 35 subtasks. outputs of tasks further down the hierarchy are used as inputs into sub - tasks higher up the hierarchy. each sub - task is treated as a separate and smaller data mining exercise.


in mathematics, a matrix ( plural matrices ) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. for example, is a matrix with two rows and three columns. this is often referred to as a " two by three matrix ", a " 2 × 3 { \ displaystyle 2 \ times 3 } matrix ", or a matrix of dimension 2 × 3 { \ displaystyle 2 \ times 3 }. without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.


in rank selection, the selection probability does not depend directly on the fitness, but on the fitness rank of an individual within the population. this puts large fitness differences into perspective ; moreover, the exact fitness values themselves do not have to be available, but only a sorting of the individuals according to quality. linear ranking, which goes back to baker, is often used.


in the japanese kantenji braille, the standard 8 - dot braille patterns 2357, 12357, 23457, and 123457 are the patterns related to braille pattern dots - 1234, since the two additional dots of kantenji patterns 01234, 12347, and 012347 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


however, a separation oracle can be implemented using n - 1 applications of the minimum cut procedure. the maximum independent set problem. it can be approximated by an lp with a constraint for every odd - length cycle.


in number theory, a congruum ( plural congrua ) is the difference between successive square numbers in an arithmetic progression of three squares. that is, if x 2 { \ displaystyle x ^ { 2 } }, y 2 { \ displaystyle y ^ { 2 } }, and z 2 { \ displaystyle z ^ { 2 } } ( for integers x { \ displaystyle x }, y { \ displaystyle y }, and z { \ displaystyle z } ) are three square numbers that are equally spaced apart from each other, then the spacing between them, z 2 − y 2 = y 2 − x 2 { \ displaystyle z ^ { 2 } - y ^ { 2 } = y ^ { 2 } - x ^ { 2 } }, is called a congruum. the congruum problem is the problem of finding squares in arithmetic progression and their associated congrua. it can be formalized as a diophantine equation : find integers x { \ displaystyle x }, y { \ displaystyle y }, and z { \ displaystyle z } such that when this equation is satisfied, both sides of the equation equal the congruum.


in mathematical optimization, the rosenbrock function is a non - convex function, introduced by howard h. rosenbrock in 1960, which is used as a performance test problem for optimization algorithms. it is also known as rosenbrock's valley or rosenbrock's banana function. the global minimum is inside a long, narrow, parabolic shaped flat valley. to find the valley is trivial.


in mathematical optimization, the ackley function is a non - convex function used as a performance test problem for optimization algorithms. it was proposed by david ackley in his 1987 phd dissertation. on a 2 - dimensional domain it is defined by : f ( x, y ) = − 20 exp − exp + e + 20 { \ displaystyle { \ begin { aligned } f ( x, y ) = - 20 & { } \ exp \ left \ \ & { } - \ exp \ left + e + 20 \ end { aligned } } } its global optimum point is f ( 0, 0 ) = 0. { \ displaystyle f ( 0, 0 ) = 0. }


in number theory, the ankeny – artin – chowla congruence is a result published in 1953 by n. c. ankeny, emil artin and s. chowla. it concerns the class number h of a real quadratic field of discriminant d > 0. if the fundamental unit of the field is ε = t + u d 2 { \ displaystyle \ varepsilon = { \ frac { t + u { \ sqrt { d } } } { 2 } } } with integers t and u, it expresses in another form h t u ( mod p ) { \ displaystyle { \ frac { ht } { u } } { \ pmod { p } } \ ; } for any prime number p > 2 that divides d. in case p > 3 it states that − 2 m h t u ≡ 0 < k < d χ ( k ) k k / p ( mod p ) { \ displaystyle - 2 { mht \ over u } \ equiv \ sum _ { 0


in the following example, we use the keys janeausten and aeroplanes to encrypt the following plaintext : " transposition ciphers scramble letters like puzzle pieces to create an indecipherable arrangement. " the colors show how the letters are scrambled in each transposition step. while a single step only causes a minor rearrangement, the second step leads to a significant scrambling effect if the last row of the grid is incomplete.


the overlapping sequences are then aligned into contigs and merged. usually, several samples are pooled in one run, and each sample is characterized by a short dna fragment, the tag. in a demultiplexing step, sequences are sorted using these tags to reassemble the separate samples.


the problem of packet size distribution is fairly well - understood today. existing models of packet sizes have proven to be valid and simple. most packet size models do not consider the problem of order in packet sizes.


the denominator is the number of total such friendships, which is twice the total edges in the network ( one from the u's perspective and the other from the v's ). after this analysis, feld goes on to make some more qualitative assumptions about the statistical correlation between the number of friends that two friends have, based on theories of social networks such as assortative mixing, and he analyzes what these assumptions imply about the number of people whose friends have more friends than they do. based on this analysis, he concludes that in real social networks, most people are likely to have fewer friends than the average of their friends'numbers of friends.


a task as simple as counting backwards can change memory recall ; however an empty delay interval has no effect. this is because the person can continue to rehearse the items in their working memory to be remembered without interference. cohen ( 1989 ) found that there is better recall for an action in the presence of interference if that action is physically performed during the encoding phase. it has also been found that recalling some items can interfere and inhibit the recall of other items. another stream of thought and evidence suggests that the effects of interference on recency and primacy are relative, determined by the ratio rule ( retention interval to inter item presentation distractor rate ) and they exhibit time - scale invariance.


in mathematics, certain kinds of mistaken proof are often exhibited, and sometimes collected, as illustrations of a concept called mathematical fallacy. there is a distinction between a simple mistake and a mathematical fallacy in a proof, in that a mistake in a proof leads to an invalid proof while in the best - known examples of mathematical fallacies there is some element of concealment or deception in the presentation of the proof. for example, the reason why validity fails may be attributed to a division by zero that is hidden by algebraic notation. there is a certain quality of the mathematical fallacy : as typically presented, it leads not only to an absurd result, but does so in a crafty or clever way.


if the conditional distribution of y { \ displaystyle y } given x { \ displaystyle x } is a continuous distribution, then its probability density function is known as the conditional density function. the properties of a conditional distribution, such as the moments, are often referred to by corresponding names such as the conditional mean and conditional variance. more generally, one can refer to the conditional distribution of a subset of a set of more than two variables ; this conditional distribution is contingent on the values of all the remaining variables, and if more than one variable is included in the subset then this conditional distribution is the conditional joint distribution of the included variables.


in the c programming language, duff's device is a way of manually implementing loop unrolling by interleaving two syntactic constructs of c : the do - while loop and a switch statement. its discovery is credited to tom duff in november 1983, when duff was working for lucasfilm and used it to speed up a real - time animation program. loop unrolling attempts to reduce the overhead of conditional branching needed to check whether a loop is done, by executing a batch of loop bodies per iteration. to handle cases where the number of iterations is not divisible by the unrolled - loop increments, a common technique among assembly language programmers is to jump directly into the middle of the unrolled loop body to handle the remainder. duff implemented this technique in c by using c's case label fall - through feature to jump into the unrolled body.


a notable series of analog calculating machines were developed by leonardo torres quevedo since 1895, including one that was able to compute the roots of arbitrary polynomials of order eight, including the complex ones, with a precision down to thousandths. an important advance in analog computing was the development of the first fire - control systems for long range ship gunlaying. when gunnery ranges increased dramatically in the late 19th century it was no longer a simple matter of calculating the proper aim point, given the flight times of the shells.


the hierarchical softmax ( introduced by morin and bengio in 2005 ) uses a binary tree structure where the outcomes ( vocabulary words ) are the leaves and the intermediate nodes are suitably selected " classes " of outcomes, forming latent variables. the desired probability ( softmax value ) of a leaf ( outcome ) can then be calculated as the product of the probabilities of all nodes on the path from the root to that leaf. ideally, when the tree is balanced, this would reduce the computational complexity from o ( k ) { \ displaystyle o ( k ) } to o ( log 2 k ) { \ displaystyle o ( \ log _ { 2 } k ) }.


it gets stuck at a basic feasible solution ( a corner of the feasible polytope ) and changes bases in a cyclic way without decreasing the minimization target. such cycles are avoided by bland's rule for choosing a column to enter and a column to leave the basis. bland's rule was developed by robert g. bland, now an emeritus professor of operations research at cornell university, while he was a research fellow at the center for operations research and econometrics in belgium.


in this way they also form two boxes, this time in consecutive corners, with areas a 2 { \ displaystyle a ^ { 2 } } and b 2 { \ displaystyle b ^ { 2 } } which will again lead to a second square of with the area 2 a b + a 2 + b 2 { \ displaystyle 2ab + a ^ { 2 } + b ^ { 2 } }. english mathematician sir thomas heath gives this proof in his commentary on proposition i. 47 in euclid's elements, and mentions the proposals of german mathematicians carl anton bretschneider and hermann hankel that pythagoras may have known this proof. heath himself favors a different proposal for a pythagorean proof, but acknowledges from the outset of his discussion " that the greek literature which we possess belonging to the first five centuries after pythagoras contains no statement specifying this or any other particular great geometric discovery to him. " recent scholarship has cast increasing doubt on any sort of role for pythagoras as a creator of mathematics, although debate about this continues.


that is, a metric should score highly translations that humans score highly, and give low scores to those humans give low scores. human judgment is the benchmark for assessing automatic metrics, as humans are the end - users of any translation output. the measure of evaluation for metrics is correlation with human judgment.


in science and mathematics, an open problem or an open question is a known problem which can be accurately stated, and which is assumed to have an objective and verifiable solution, but which has not yet been solved ( i. e., no solution for it is known ). in the history of science, some of these supposed open problems were " solved " by means of showing that they were not well - defined. in mathematics, many open problems are concerned with the question of whether a certain definition is or is not consistent.


in the context of machine learning, d kl ( p q ) { \ displaystyle d _ { \ text { kl } } ( p \ parallel q ) } is often called the information gain achieved if p { \ displaystyle p } would be used instead of q { \ displaystyle q } which is currently used. by analogy with information theory, it is called the relative entropy of p { \ displaystyle p } with respect to q { \ displaystyle q }. expressed in the language of bayesian inference, d kl ( p q ) { \ displaystyle d _ { \ text { kl } } ( p \ parallel q ) } is a measure of the information gained by revising one's beliefs from the prior probability distribution q { \ displaystyle q } to the posterior probability distribution p { \ displaystyle p }. in other words, it is the amount of information lost when q { \ displaystyle q } is used to approximate p { \ displaystyle p }.


in the discovery with model method, a model is developed via prediction, clustering or by human reasoning knowledge engineering and then used as a component in another analysis, namely in prediction and relationship mining. in the prediction method use, the created model's predictions are used to predict a new variable. for the use of relationship mining, the created model enables the analysis between new predictions and additional variables in the study.


{ \ displaystyle s ^ { 1 }. } the proof is based on normal surface techniques originated by hellmuth kneser. existence was proven by kneser, but the exact formulation and proof of the uniqueness was done more than 30 years later by john milnor.


this project, known as hilbert's program, was seriously affected by godel's incompleteness theorems, which show that the consistency of formal theories of arithmetic cannot be established using methods formalizable in those theories. gentzen showed that it is possible to produce a proof of the consistency of arithmetic in a finitary system augmented with axioms of transfinite induction, and the techniques he developed to do so were seminal in proof theory. a second thread in the history of foundations of mathematics involves nonclassical logics and constructive mathematics.


in mathematics, a pseudomanifold is a special type of topological space. it looks like a manifold at most of its points, but it may contain singularities. for example, the cone of solutions of z 2 = x 2 + y 2 { \ displaystyle z ^ { 2 } = x ^ { 2 } + y ^ { 2 } } forms a pseudomanifold. a pseudomanifold can be regarded as a combinatorial realisation of the general idea of a manifold with singularities. the concepts of orientability, orientation and degree of a mapping make sense for pseudomanifolds and moreover, within the combinatorial approach, pseudomanifolds form the natural domain of definition for these concepts.


perform cholesky decomposition ( a variant of gaussian elimination for symmetric matrices ), ordering the elimination of the variables by the recursive structure of the partition : each of the two subgraphs formed by removing the separator is eliminated first, and then the separator vertices are eliminated. as a consequence of this algorithm, the fill - in ( the set of nonzero matrix entries created in the cholesky decomposition that are not part of the input matrix structure ) is limited to at most the square of the separator size at each level of the recursive partition. in particular, for planar graphs ( frequently arising in the solution of sparse linear systems derived from two - dimensional finite element method meshes ) the resulting matrix has o ( n log n ) nonzeros, due to the planar separator theorem guaranteeing separators of size o ( √n ). for arbitrary graphs there is a nested dissection that guarantees fill - in within a o ( min { d log 4 n, m 1 / 4 log 3. 5 n } ) { \ displaystyle o ( \ min \ { { \ sqrt { d } } \ log ^ { 4 } n, m ^ { 1 / 4 } \ log ^ { 3. 5 } n \ } ) } factor of optimal, where d is the maximum degree and m is the number of non - zeros.


these conditions are very loose, and allow enormous flexibility in the choice of open sets. for example, every subset can be open ( the discrete topology ), or no subset can be open except the space itself and the empty set ( the indiscrete topology ). in practice, however, open sets are usually chosen to provide a notion of nearness that is similar to that of metric spaces, without having a notion of distance defined. in particular, a topology allows defining properties such as continuity, connectedness, and compactness, which were originally defined by means of a distance. the most common case of a topology without any distance is given by manifolds, which are topological spaces that, near each point, resemble an open set of a euclidean space, but on which no distance is defined in general. less intuitive topologies are used in other branches of mathematics ; for example, the zariski topology, which is fundamental in algebraic geometry and scheme theory.


in separate chaining, the process involves building a linked list with key – value pair for each search array index. the collided items are chained together through a single linked list, which can be traversed to access the item with a unique search key. : 464 collision resolution through chaining with linked list is a common method of implementation of hash tables. let t { \ displaystyle t } and x { \ displaystyle x } be the hash table and the node respectively, the operation involves as follows : : 258 chained - hash - insert ( t, k ) insert x at the head of linked list t chained - hash - search ( t, k ) search for an element with key k in linked list t chained - hash - delete ( t, k ) delete x from the linked list t if the element is comparable either numerically or lexically, and inserted into the list by maintaining the total order, it results in faster termination of the unsuccessful searches. : 520 – 521


in statistics, dispersion ( also called variability, scatter, or spread ) is the extent to which a distribution is stretched or squeezed. common examples of measures of statistical dispersion are the variance, standard deviation, and interquartile range. for instance, when the variance of data in a set is large, the data is widely scattered. on the other hand, when the variance is small, the data in the set is clustered. dispersion is contrasted with location or central tendency, and together they are the most used properties of distributions.


the notion directly extends to the product of an arbitrary finite number of types ( a n - ary product type ), and in this case, it characterizes the expressions which behave as tuples of expressions of the corresponding types. a degenerated form of product type is the unit type : it is the product of no types. in call - by - value programming languages, a product type can be interpreted as a set of pairs whose first component is a value in the first type and whose second component is a value in the second type.


in the data warehouse process, data can be aggregated in data marts at different levels of abstraction. the user may start looking at the total sale units of a product in an entire region. then the user looks at the states in that region. finally, they may examine the individual stores in a certain state. therefore, typically, the analysis starts at a higher level and drills down to lower levels of details.


12n ( π ( n + 1 ) + 1 ) where π ( n ) is the prime - counting function. this was subsequently improved by hans frederick blichfeldt who replaced the 12 with a 6. unpublished work on the finite case was also done by boris weisfeiler. subsequently, michael collins, using the classification of finite simple groups, showed that in the finite case, one can take ƒ ( n ) = ( n + 1 )! when n is at least 71, and gave near complete descriptions of the behavior for smaller n.


some studies suggest that these errors can be anywhere between 5 and 10 degrees. these goniometers come in different forms that some argue increase reliability. the universal standard goniometer is a plastic or metal tool with 1 degree increments.


in scalar languages such as c and pascal, operations apply only to single values, so a + b expresses the addition of two numbers. in such languages, adding one array to another requires indexing and looping, the coding of which is tedious. in array - based languages, for example in fortran, the nested for - loop above can be written in array - format in one line, or alternatively, to emphasize the array nature of the objects, while scalar languages like c do not have native array programming elements as part of the language proper, this does not mean programs written in these languages never take advantage of the underlying techniques of vectorization ( i. e., utilizing a cpu's vector - based instructions if it has them or by using multiple cpu cores ). some c compilers like gcc at some optimization levels detect and vectorize sections of code that its heuristics determine would benefit from it. another approach is given by the openmp api, which allows one to parallelize applicable sections of code by taking advantage of multiple cpu cores.


in the context of government documents, redaction ( also called sanitization ) generally refers more specifically to the process of removing sensitive or classified information from a document prior to its publication, during declassification.


other authors call a set directed if and only if it is directed both upward and downward. directed sets are a generalization of nonempty totally ordered sets. that is, all totally ordered sets are directed sets ( contrast partially ordered sets, which need not be directed ). join - semilattices ( which are partially ordered sets ) are directed sets as well, but not conversely.


in mathematics, a matrix coefficient ( or matrix element ) is a function on a group of a special form, which depends on a linear representation of the group and additional data. precisely, it is a function on a compact topological group g obtained by composing a representation of g on a vector space v with a linear map from the endomorphisms of v into v's underlying field. it is also called a representative function.


it is called the policy cycle as the final stage ( evaluation ) often leads back to the first stage ( problem definition ), thus restarting the cycle. harold lasswell's popular model of the policy cycle divided the process into seven distinct stages, asking questions of both how and why public policies should be made. with the stages ranging from ( 1 ) intelligence, ( 2 ) promotion, ( 3 ) prescription, ( 4 ) invocation, ( 5 ) application, ( 6 ) termination and ( 7 ) appraisal, this process inherently attempts to combine policy implementation to formulated policy goals. one version by james e. anderson, in his public policy - making ( 1974 ) has the following stages : agenda setting ( problem identification ) – the recognition of certain subject as a problem demanding further government attention.


in order to compete with intel's advanced programmable interrupt controller ( apic ), which had enabled the first intel 486 - based multiprocessor systems, in early 1995 amd and cyrix proposed as somewhat similar - in - purpose openpic architecture supporting up to 32 processors. the openpic architecture had at least declarative support from ibm and compaq around 1995. no x86 motherboard was released with openpic however. after the openpic's failure in the x86 market, amd licensed the intel apic architecture for its amd athlon and later processors.


if we assume that a function f : r n → r { \ displaystyle f : \ mathbb { r } ^ { n } \ to \ mathbb { r } } is globally continuous and separately differentiable on each variable ( all partial derivatives exist everywhere ), it is not true that f { \ displaystyle f } will necessarily be differentiable. a counterexample in two dimensions is given by f ( x, y ) = 2 x 2 y + y 3 x 2 + y 2. { \ displaystyle f ( x, y ) = { \ dfrac { 2x ^ { 2 } y + y ^ { 3 } } { x ^ { 2 } + y ^ { 2 } } }. } if in addition we define f ( 0, 0 ) = 0 { \ displaystyle f ( 0, 0 ) = 0 }, this function is everywhere continuous and has well - defined partial derivatives in x { \ displaystyle x } and y { \ displaystyle y } everywhere ( also at the origin ), but is not differentiable at the origin.


in the field of bioinformatics, a sequence database is a type of biological database that is composed of a large collection of computerized ( " digital " ) nucleic acid sequences, protein sequences, or other polymer sequences stored on a computer. the uniprot database is an example of a protein sequence database. as of 2013 it contained over 40 million sequences and is growing at an exponential rate. historically, sequences were published in paper form, but as the number of sequences grew, this storage method became unsustainable.


alternatively the two distributions can both be empirically estimated ones ; this is called the two - sample case. the criterion is named after harald cramer and richard edler von mises who first proposed it in 1928 – 1930. the generalization to two samples is due to anderson. the cramer – von mises test is an alternative to the kolmogorov – smirnov test ( 1933 ).


in typical applications, e. g., when discretizing integral equations, preconditioning the resulting systems of linear equations, or solving elliptic partial differential equations, a rank proportional to log ( 1 / ) γ { \ displaystyle \ log ( 1 / \ epsilon ) ^ { \ gamma } } with a small constant γ { \ displaystyle \ gamma } is sufficient to ensure an accuracy of { \ displaystyle \ epsilon }. compared to many other data - sparse representations of non - sparse matrices, hierarchical matrices offer a major advantage : the results of matrix arithmetic operations like matrix multiplication, factorization or inversion can be approximated in o ( n k α log ( n ) β ) { \ displaystyle o ( nk ^ { \ alpha } \, \ log ( n ) ^ { \ beta } ) } operations, where α, β ∈ { 1, 2, 3 }. { \ displaystyle \ alpha, \ beta \ in \ { 1, 2, 3 \ }. }


in mathematics, the signal magnitude area ( abbreviated sma or sma ) is a statistical measure of the magnitude of a varying quantity.


if all coefficients in r { \ displaystyle r } are negative, then z 0 { \ displaystyle z _ { 0 } } is an optimal solution, since all variables ( including all non - basic variables ) must be at least 0, so the second line implies z ≤ z 0 { \ displaystyle z \ leq z _ { 0 } }. if some coefficients in r { \ displaystyle r } are positive, then it may be possible to increase the maximization target.


in recent years, the speed of the cpu has grown many times in comparison to the access speed of the main memory. care needs to be taken to reduce the number of times main memory is accessed in order to maintain performance. if, for instance, every instruction run in the cpu requires an access to memory, the computer gains nothing for increased cpu speed — a problem referred to as being memory bound. it is possible to make extremely fast memory, but this is only practical for small amounts of memory for cost, power and signal routing reasons.


in mathematical optimization, neighborhood search is a technique that tries to find good or near - optimal solutions to a combinatorial optimisation problem by repeatedly transforming a current solution into a different solution in the neighborhood of the current solution. the neighborhood of a solution is a set of similar solutions obtained by relatively simple modifications to the original solution. for a very large - scale neighborhood search, the neighborhood is large and possibly exponentially sized. the resulting algorithms can outperform algorithms using small neighborhoods because the local improvements are larger.


in statistics, linear regression is a linear approach for modelling the relationship between a scalar response and one or more explanatory variables ( also known as dependent and independent variables ). the case of one explanatory variable is called simple linear regression ; for more than one, the process is called multiple linear regression. this term is distinct from multivariate linear regression, where multiple correlated dependent variables are predicted, rather than a single scalar variable. in linear regression, the relationships are modeled using linear predictor functions whose unknown model parameters are estimated from the data. such models are called linear models.


in some languages such as rexx, the precision of all calculations must be set before doing a calculation. other languages, such as python and ruby, extend the precision automatically to prevent overflow.


fortran did not have an equality operator ( it was only possible to compare an expression to zero, using the arithmetic if statement ) until fortran iv was released in 1962, since when it has used the four characters. eq. to test for equality. the language b introduced the use of = = with this meaning, which has been copied by its descendant c and most later languages where = means assignment. the equal sign is also used in defining attribute – value pairs, in which an attribute is assigned a value.


in mathematical physics and gauge theory, the adhm construction or monad construction is the construction of all instantons using methods of linear algebra by michael atiyah, vladimir drinfeld, nigel hitchin, yuri i. manin in their paper " construction of instantons. "


in mathematics, krener's theorem is a result attributed to arthur j. krener in geometric control theory about the topological properties of attainable sets of finite - dimensional control systems. it states that any attainable set of a bracket - generating system has nonempty interior or, equivalently, that any attainable set has nonempty interior in the topology of the corresponding orbit. heuristically, krener's theorem prohibits attainable sets from being hairy.


in mathematics, whitney's planarity criterion is a matroid - theoretic characterization of planar graphs, named after hassler whitney. it states that a graph g is planar if and only if its graphic matroid is also cographic ( that is, it is the dual matroid of another graphic matroid ). in purely graph - theoretic terms, this criterion can be stated as follows : there must be another ( dual ) graph g'= ( v ', e') and a bijective correspondence between the edges e'and the edges e of the original graph g, such that a subset t of e forms a spanning tree of g if and only if the edges corresponding to the complementary subset e - t form a spanning tree of g '.


z is sometimes called the boltzmann sum over states ( or " zustandssumme " in the original german ). if we index the summation via the energy eigenvalues instead of all possible states, degeneracy must be taken into account. the probability of our system having energy ε i { \ displaystyle \ varepsilon _ { i } } is simply the sum of the probabilities of all corresponding microstates : p ( ε i ) = 1 z g i e − ε i / k t { \ displaystyle p ( \ varepsilon _ { i } ) = { \ frac { 1 } { z } } g _ { i } e ^ { - \ varepsilon _ { i } / kt } } where, with obvious modification, z = j g j e − ε j / k t, { \ displaystyle z = \ sum _ { j } g _ { j } e ^ { - \ varepsilon _ { j } / kt }, } this is the same result as before.


in the case of time - dependent vector fields f : r n × r → r n { \ displaystyle { \ boldsymbol { f } } : \ mathbb { r } ^ { n } \ times \ mathbb { r } \ to \ mathbb { r } ^ { n } }, one denotes φ t, t 0 ( x 0 ) = x ( t + t 0 ), { \ displaystyle \ varphi ^ { t, t _ { 0 } } ( { \ boldsymbol { x } } _ { 0 } ) = { \ boldsymbol { x } } ( t + t _ { 0 } ), } where x : r → r n { \ displaystyle { \ boldsymbol { x } } : \ mathbb { r } \ to \ mathbb { r } ^ { n } } is the solution of x ( t ) = f ( x ( t ), t ), x ( t 0 ) = x 0. { \ displaystyle { \ dot { \ boldsymbol { x } } } ( t ) = { \ boldsymbol { f } } ( { \ boldsymbol { x } } ( t ), t ), \ qquad { \ boldsymbol { x } } ( t _ { 0 } ) = { \ boldsymbol { x } } _ { 0 }. } then φ t, t 0 ( x 0 ) { \ displaystyle \ varphi ^ { t, t _ { 0 } } ( { \ boldsymbol { x } } _ { 0 } ) } is the time - dependent flow of f. it is not a " flow " by the definition above, but it can easily be seen as one by rearranging its arguments.


more generally, addition - chain exponentiation may also refer to exponentiation by non - minimal addition chains constructed by a variety of algorithms ( since a shortest addition chain is very difficult to find ). the shortest addition - chain algorithm requires no more multiplications than binary exponentiation and usually less. the first example of where it does better is for a15, where the binary method needs six multiplications but the shortest addition chain requires only five : a 15 = a × ( a × 2 ) 2 { \ displaystyle a ^ { 15 } = a \ times ( a \ times ^ { 2 } ) ^ { 2 } \! }


in the unidirectional mode of operation, packets are only sent in one direction : from compressor to decompressor. this mode therefore makes rohc usable over links where a return path from decompressor to compressor is unavailable or undesirable. in order to handle potential decompression errors, the compressor sends periodic refreshes of the stream context to the decompressor.


in mathematics, the pointwise product of two functions is another function, obtained by multiplying the images of the two functions at each value in the domain. if f and g are both functions with domain x and codomain y, and elements of y can be multiplied ( for instance, y could be some set of numbers ), then the pointwise product of f and g is another function from x to y which maps x in x to f ( x ) g ( x ) in y.


count t max { \ displaystyle t _ { \ max } } : max. countsince the number of indexed items per descriptor is usually distributed according to a power law, for larger ranges of values, a logarithmic representation makes sense. implementations of tag clouds also include text parsing and filtering out unhelpful tags such as common words, numbers, and punctuation. there are also websites creating artificially or randomly weighted tag clouds, for advertising, or for humorous results.


n ) ( ∇ p 0. n ) − π ( ∇ u 0.


this approach allows the system to gather information about the frequency with which various constructions occur in specific contexts. ( see machine learning. ) approaches which have been used include straightforward pcfgs ( probabilistic context - free grammars ), maximum entropy, and neural nets.


this concept can be extended to the multivariate context by an extension of the simple sum to a number of f { \ displaystyle f } sums that cover all dimensions in the feature space : p w ( θ → ) = k 1,..., k f = − ∞ ∞ p ( θ → + 2 π k 1 e 1 + + 2 π k f e f ) { \ displaystyle p _ { w } ( { \ vec { \ theta } } ) = \ sum _ { k _ { 1 },..., k _ { f } = - \ infty } ^ { \ infty } { p ( { \ vec { \ theta } } + 2 \ pi k _ { 1 } \ mathbf { e } _ { 1 } + \ dots + 2 \ pi k _ { f } \ mathbf { e } _ { f } ) } } where e k = ( 0, …, 0, 1, 0, …, 0 ) t { \ displaystyle \ mathbf { e } _ { k } = ( 0, \ dots, 0, 1, 0, \ dots, 0 ) ^ { \ mathsf { t } } } is the k { \ displaystyle k } th euclidean basis vector.


usually, the price also includes a mark - up for profit over the cost of production. more generalized in the field of economics, cost is a metric that is totaling up as a result of a process or as a differential for the result of a decision.


in some developing countries, many people do not have access to banking facilities, especially in tier ii and tier iii cities. taking the example of india, there are more mobile phone users than there are people with active bank accounts. telecom operators, in such locations, have started offering mobile money wallets which allow adding funds easily through their existing mobile subscription number, by visiting physical recharge points close to their homes and offices and converting their cash into mobile wallet currency. this can be used for online transaction and ecommerce purchases.


in processing electronic audio signals, pre - emphasis refers to a system process designed to increase ( within a frequency band ) the magnitude of some ( usually higher ) frequencies with respect to the magnitude of other ( usually lower ) frequencies in order to improve the overall signal - to - noise ratio by minimizing the adverse effects of such phenomena as attenuation distortion or saturation of recording media in subsequent parts of the system. the mirror operation is called de - emphasis, and the system as a whole is called emphasis. pre - emphasis is achieved with a pre - emphasis network which is essentially a calibrated filter. the frequency response is decided by special time constants.


an important aspect of this stage is verification. this effort verifies that the requirement has been implemented correctly. there are 4 methods of verification : analysis, inspection, testing, and demonstration.


the version without negations is sometimes called weakly injective. the existence of value collisions is a strong notion of non - injectivity. and regarding surjectivity, similar considerations exist for outlier - production in the codomain.


in the middle east, hasan ibn al - haytham, latinized as alhazen ( c. 965 – c. 1040 ce ) derived a formula for the sum of fourth powers. he used the results to carry out what would now be called an integration, where the formulas for the sums of integral squares and fourth powers allowed him to calculate the volume of a paraboloid. roshdi rashed has argued that the 12th century mathematician sharaf al - din al - tusi must have used the derivative of cubic polynomials in his treatise on equations. rashed's conclusion has been contested by other scholars, who argue that he could have obtained his results by other methods which do not require the derivative of the function to be known.


in mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions. equivalently, a solvable group is a group whose derived series terminates in the trivial subgroup.


" if the cause, assigned for any effect, be not sufficient to produce it, we must either reject that cause, or add to it such qualities as will give it a just proportion to the effect. " occam's razor : explanations which require fewer unjustified assumptions are more likely to be correct ; avoid unnecessary or improbable assumptions. popper's falsifiability principle : for a theory to be considered scientific, it must be falsifiable. sagan standard : extraordinary claims require extraordinary evidence.


in the book written by frank rosenblatt, published in 1961, a three - layer multilayer perceptron ( mlp ) model with skip connections was presented ( chapter 15, p313 in ). the model was referred to as a " cross - coupled system ", and the skip connections were forms of cross - coupled connections. in two books published in 1994 and 1996, " skip - layer " connections were presented in feed - forward mlp models : " the general definition allows more than one hidden layer, and it also allows'skip - layer'connections from input to output " ( p261 in, p144 in ), "... which allows the non - linear units to perturb a linear functional form " ( p262 in ). this description suggests that the non - linear mlp performs like a residual function ( perturbation ) added to a linear function.


in phonology, voicing ( or sonorization ) is a sound change where a voiceless consonant becomes voiced due to the influence of its phonological environment ; shift in the opposite direction is referred to as devoicing or desonorization. most commonly, the change is a result of sound assimilation with an adjacent sound of opposite voicing, but it can also occur word - finally or in contact with a specific vowel. for example, the english suffix - s is pronounced when it follows a voiceless phoneme ( cats ), and when it follows a voiced phoneme ( dogs ). this type of assimilation is called progressive, where the second consonant assimilates to the first ; regressive assimilation goes in the opposite direction, as can be seen in have to.


it is impossible for an unprivileged application to access a page that has not been explicitly allocated to it, because every memory address either points to a page allocated to that application, or generates an interrupt called a page fault. unallocated pages, and pages allocated to any other application, do not have any addresses from the application point of view. a page fault may not necessarily indicate an error.


in mathematics and theoretical computer science, a set constraint is an equation or an inequation between sets of terms. similar to systems of ( in ) equations between numbers, methods are studied for solving systems of set constraints. different approaches admit different operators ( like " ∪ ", " ∩ ", " \ ", and function application ) on sets and different ( in ) equation relations ( like " = ", " ⊆ ", and " ⊆ " ) between set expressions. systems of set constraints are useful to describe ( in particular infinite ) sets of ground terms. they arise in program analysis, abstract interpretation, and type inference.


in telecommunications, a long - distance call ( u. s. ) or trunk call ( also known as a toll call in the u. k. ) is a telephone call made to a location outside a defined local calling area.


in telecommunications, remote call forwarding is a service feature that allows incoming calls to be forwarded to a remote call forwarding number, such as a cell phone or another office location and is designated by the call receiver. customers may have a remote - forwarding telephone number in a central switching office without having any other local telephone service in that office. one common purpose for this service is to enable customers to retain their telephone number when they move to a location serviced by a different telephone exchange. the service is useful for business customers with widely advertised numbers which appear on headed paper, vehicles and various marketing literature. when customers ring, their calls are forwarded to the new location.


in order to maintain good programming practice, a number of compiler options and flags designed for safety have been enabled by default to help in spotting potential issues so they can be fixed earlier ( - wall, - werror, - wextra, - wuninitialized ). there have also been code readability updates which help future contributors in verifying program correctness ( knf, white - space, line - wrapping, etc. ). modification or removal of unneeded method wrappers and macros also help with code readability and auditing ( error and i / o abstraction library references ). changes were made to ensure that libressl will be year 2038 compatible along with maintaining portability for other similar platforms. in addition, explicit _ bzero and bn _ clear calls were added to prevent the compiler from optimizing them out and prevent attackers from reading previously allocated memory.


females only lay one test clutch and return shortly after laying it. capable males prove their parental quality by defending the brood and not cannibalizing the eggs. test eggs are energetically expensive to create, so this strategy is typically only used by large females at the beginning of the mating phase.


one special type of operand is the parenthesis group. an expression enclosed in parentheses is typically recursively evaluated to be treated as a single operand on the next evaluation level. each operator is given a position, precedence, and an associativity.


in terms of information theory, entropy is considered to be a measure of the uncertainty in a message. to put it intuitively, suppose p = 0 { \ displaystyle p = 0 }. at this probability, the event is certain never to occur, and so there is no uncertainty at all, leading to an entropy of 0. if p = 1 { \ displaystyle p = 1 }, the result is again certain, so the entropy is 0 here as well.


in mathematics, primitive recursive set functions or primitive recursive ordinal functions are analogs of primitive recursive functions, defined for sets or ordinals rather than natural numbers. they were introduced by jensen & karp ( 1971 ).


iteration length has changed from months to weeks or days with the rising popularity of agile, devops, and continuous delivery. traditional methods of testing, which rely heavily on manual testing and automated gui tests that require frequent updating, cannot keep pace.