in monolithic kernels, device drivers reside in the kernel. thus, when a new peripheral is installed, unknown, untrusted code is inserted in the kernel. one bad line of code in a driver can bring down the system.


in the 2020s, concerns over acs vulnerability to cyberattacks and data theft emerged. in 2018 and 2019 former apple engineers were charged with stealing information related to apple's self - driving car project. in 2021 the united states department of justice ( doj ) accused chinese security officials of coordinating a hacking campaign to steal information from government entities, including research related to autonomous vehicles. china has prepared " the provisions on management of automotive data security ( trial ) to protect its own data ". cellular vehicle - to - everything technologies are based on 5g wireless networks. as of november 2022, the us congress was considering the possibility that imported chinese ac technology could facilitate espionage.


in older architectures, nmis were used for interrupts which were typically never disabled because of the required response time. they were hidden signals. examples include the floppy disk controller on the amstrad pcw, the 8087 coprocessor on the x86 when used in the ibm pc or its compatibles ( even though intel recommended connecting it to a normal interrupt ), and the low battery signal on the hp 95lx. in the original ibm pc, an nmi was triggered if a parity error was detected in system memory, or reported by an external device.


in numerical linear algebra, the alternating - direction implicit ( adi ) method is an iterative method used to solve sylvester matrix equations. it is a popular method for solving the large matrix equations that arise in systems theory and control, and can be formulated to construct solutions in a memory - efficient, factored form. it is also used to numerically solve parabolic and elliptic partial differential equations, and is a classic method used for modeling heat conduction and solving the diffusion equation in two or more dimensions. it is an example of an operator splitting method.


internet protocols are designed for simplicity and modularity and fit into a coarse hierarchy of functional layers defined in the internet protocol suite. the first two cooperating protocols, the transmission control protocol ( tcp ) and the internet protocol ( ip ) resulted from the decomposition of the original transmission control program, a monolithic communication protocol, into this layered communication suite. the osi model was developed internationally based on experience with networks that predated the internet as a reference model for general communication with much stricter rules of protocol interaction and rigorous layering.


in probability and statistics, the inverse - chi - squared distribution ( or inverted - chi - square distribution ) is a continuous probability distribution of a positive - valued random variable. it is closely related to the chi - squared distribution. it arises in bayesian inference, where it can be used as the prior and posterior distribution for an unknown variance of the normal distribution.


in statistical mechanics and mathematics, the bethe lattice ( also called a regular tree ) is an infinite connected cycle - free graph where all vertices have the same number of neighbors. the bethe lattice was introduced into the physics literature by hans bethe in 1935. in such a graph, each node is connected to z neighbors ; the number z is called either the coordination number or the degree, depending on the field. due to its distinctive topological structure, the statistical mechanics of lattice models on this graph are often easier to solve than on other lattices. the solutions are related to the often used bethe ansatz for these systems.


in the netherlands the then state - owned phone company ptt ( now kpn ) operated two platforms : viditel ( launched in 1980 ) and videotex nederland. from the user perspective the main difference between these systems was that viditel used standard dial - in phone numbers where videotex used premium - rate telephone numbers. for viditel you needed a ( paid ) subscription and on top of that you paid for each page you visited. for videotex services you normally didn't need a subscription nor was there the need to authenticate : you paid for the services via the premium rate of the modem - connection based on connection time, regardless of the pages or services you retrieved.


in multivariate statistics, if ε { \ displaystyle \ varepsilon } is a vector of n { \ displaystyle n } random variables, and λ { \ displaystyle \ lambda } is an n { \ displaystyle n } - dimensional symmetric matrix, then the scalar quantity ε t λ ε { \ displaystyle \ varepsilon ^ { t } \ lambda \ varepsilon } is known as a quadratic form in ε { \ displaystyle \ varepsilon }.


semantically textual data can be represented in binary format ( e. g. when compressed or in certain formats that intermix various sorts of formatting codes, as in the doc format used by microsoft word ) ; contrarily, image data is sometimes represented in textual format ( e. g. the x pixmap image format used in the x window system ). 1 and 0 are nothing but just two different voltage levels. you can make the computer understand 1 for higher voltage and 0 for lower voltage.


article 14 bis of the dadvsi law explicitly exempts from this regime the act of downloading a copyrighted work on a peer - to - peer network. this exemption is further extended to the act of making some copyrighted work available to the public without any commercial purpose, when this is an automatic result of the use of a peer - to - peer network for obtaining it ; this clause was added because many peer - to - peer networks automatically make downloaded content available to other users, thus merely exempting downloads from the counterfeiting felony would not have been sufficient.


in the european union, the treatment of voip service providers is a decision for each national telecommunications regulator, which must use competition law to define relevant national markets and then determine whether any service provider on those national markets has " significant market power " ( and so should be subject to certain obligations ). a general distinction is usually made between voip services that function over managed networks ( via broadband connections ) and voip services that function over unmanaged networks ( essentially, the internet ). the relevant eu directive is not clearly drafted concerning obligations that can exist independently of market power ( e. g., the obligation to offer access to emergency calls ), and it is impossible to say definitively whether voip service providers of either type are bound by them.


if the neighboring site is s, then let it become i. repeat as long as there are s sites available. making a list of i sites makes this run quickly. the net rate of infecting one neighbor over the rate of removal is λ = ( 1 - c ) / c. for the synchronous model, all sites are updated simultaneously ( using two copies of the lattice ) as in a cellular automaton.


in the following example, the text " paul schuster was born in dresden " on a website will be annotated, connecting a person with their place of birth. the following html fragment shows how a small graph is being described, in rdfa - syntax using a schema. org vocabulary and a wikidata id : the example defines the following five triples ( shown in turtle syntax ). each triple represents one edge in the resulting graph : the first element of the triple ( the subject ) is the name of the node where the edge starts, the second element ( the predicate ) the type of the edge, and the last and third element ( the object ) either the name of the node where the edge ends or a literal value ( e. g. a text, a number, etc. ).


the first instance of " crypto " lines up with " abcdef " and the second instance lines up with " cdefab ". the two instances will encrypt to different ciphertexts and the kasiski examination will reveal nothing. however, with a 5 - character keyword " abcde " ( 5 divides into 20 ) : abcdeabcdeabcdeabcdeabcdeabcdeabc crypto is short for cryptography. both occurrences of " crypto " line up with " abcdea ". the two instances will encrypt to the same ciphertext and the kasiski examination will be effective.


in mathematics, the classic mobius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. it was introduced into number theory in 1832 by august ferdinand mobius. a large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set, with mobius'classical formula applying to the set of the natural numbers ordered by divisibility : see incidence algebra.


class 2 comprises mechanically propelled vehicles such as motorized wheelchairs and mobility scooters, limited to 4 mph. class 3 consists mostly of mobility scooters. they are limited to 8 mph, with a further limiter set to 4 mph which must be enabled when used on a pavement.


these problems already trivially lie in co - np. this was the first strong evidence that these problems are not np - complete, since if they were, it would imply that np is subset of co - np, a result widely believed to be false ; in fact, this was the first demonstration of a problem in np intersect co - np not known, at the time, to be in p. producing certificates for the complement problem, to establish that a number is composite, is straightforward : it suffices to give a nontrivial divisor. standard probabilistic primality tests such as the baillie – psw primality test, the fermat primality test, and the miller – rabin primality test also produce compositeness certificates in the event where the input is composite, but do not produce certificates for prime inputs.


depending on the author, such mappings may or may not be assumed to be linear, or to be defined on the whole space x. { \ displaystyle x. } in computer science, it is synonymous with higher - order functions, that is, functions that take functions as arguments or return them. this article is mainly concerned with the second concept, which arose in the early 18th century as part of the calculus of variations.


( conversation, in formal or informal settings is an example. ) written language, on the other hand, is the common mode used to convey objective information. both vocal and sign languages are composed of words. in vocal languages, words are made up from a limited set of vowels and consonants, and often tone. in sign languages, words are made up from a limited set of shapes, orientations, locations movements of the hands, and often facial expressions ; in both cases, the building blocks are called phonemes. in both vocal and sign languages, words are grammatically and prosodically linked into phrases, clauses, and larger units of discourse.


interfaces are described in microsoft interface definition language. type libraries can be viewed using various tools, such as the microsoft ole / com object viewer ( oleview. exe, part of the microsoft platform sdk ) or the object browser in visual basic ( up to version 6 ) and visual studio. net. type libraries are used to generate proxy pattern / stub code for interoperating between com and other platforms, such as microsoft. net and java.


a system of equations is a subset e of the cartesian product x∗ × x∗ of the free monoid ( finite strings ) over x with itself. the system e is satisfiable in s if there is a map f from x to s, which extends to a semigroup morphism f from x + to s, such that for all ( u, v ) in e we have f ( u ) = f ( v ) in s. such an f is a solution, or satisfying assignment, for the system e. two systems of equations are equivalent if they have the same set of satisfying assignments. a system of equations if independent if it is not equivalent to a proper subset of itself. a semigroup is compact if every independent system of equations is finite.


to find an answer to this problem, a bipartite graph g'= ( a ∪ b, e ) is created where each flight has a copy in set a and set b. if the same plane can perform flight j after flight i, i∈a is connected to j∈b. a matching in g'induces a schedule for f and obviously maximum bipartite matching in this graph produces an airline schedule with minimum number of crews. as it is mentioned in the application part of this article, the maximum cardinality bipartite matching is an application of maximum flow problem.


silver proved the consistency of chang's conjecture from the consistency of an ω1 - erdos cardinal. hans - dieter donder showed a weak version of the reverse implication : if cc is not only consistent but actually holds, then ω2 is ω1 - erdos in k. more generally, chang's conjecture for two pairs ( α, β ), ( γ, δ ) of cardinals is the claim that every model of type ( α, β ) for a countable language has an elementary submodel of type ( γ, δ ). the consistency of ( ω 3, ω 2 ) ( ω 2, ω 1 ) { \ displaystyle ( \ omega _ { 3 }, \ omega _ { 2 } ) \ twoheadrightarrow ( \ omega _ { 2 }, \ omega _ { 1 } ) } was shown by laver from the consistency of a huge cardinal.


, then adding the transformed vectors. a v → + b v → = ( a + b ) v → { \ displaystyle \ mathbf { a } { \ vec { v } } + \ mathbf { b } { \ vec { v } } = ( \ mathbf { a } + \ mathbf { b } ) { \ vec { v } } \! } however, there are other operations that could also be considered addition for matrices, such as the direct sum and the kronecker sum.


in mathematics, a boolean function is a function whose arguments and result assume values from a two - element set ( usually { true, false }, { 0, 1 } or { - 1, 1 } ). alternative names are switching function, used especially in older computer science literature, and truth function ( or logical function ), used in logic. boolean functions are the subject of boolean algebra and switching theory. a boolean function takes the form f : { 0, 1 } k → { 0, 1 } { \ displaystyle f : \ { 0, 1 \ } ^ { k } \ to \ { 0, 1 \ } }, where { 0, 1 } { \ displaystyle \ { 0, 1 \ } } is known as the boolean domain and k { \ displaystyle k } is a non - negative integer called the arity of the function. in the case where k = 0 { \ displaystyle k = 0 }, the function is a constant element of { 0, 1 } { \ displaystyle \ { 0, 1 \ } }.


this can be solved with a variant of mahler and de weger's lattice based analysis of n - adic numbers when n = 2 { \ displaystyle n = 2 } ; by a variant of the euclidean algorithm when n is prime ; and in general by xu's adaptation of the berlekamp - massey algorithm. if l is the size of the smallest fcsr that outputs the sequence ( called the n - adic complexity of the sequence ), then all these algorithms require a prefix of length about 2 l { \ displaystyle 2l } to be successful and have quadratic time complexity.


in most reactor designs, as a safety measure, control rods are attached to the lifting machinery by electromagnets, rather than direct mechanical linkage. this means that in the event of power failure, or if manually invoked due to failure of the lifting machinery, the control rods fall automatically, under gravity, all the way into the pile to stop the reaction. a notable exception to this fail - safe mode of operation is the bwr, which requires hydraulic insertion in the event of an emergency shut - down, using water from a special tank under high pressure. quickly shutting down a reactor in this way is called scramming.


it does not explicitly require the compiler to understand instruction names, as the compiler is only needed to substitute its register assignments, plus a few mov operations, to handle the input requirements. however, the user is prone to specifying clobbered registers incorrectly. the msvc form of an embedded domain - specific language provides ease of writing, but it requires the compiler itself to know about opcode names and their clobbering properties, demanding extra attention in maintenance and porting.


many sets that arise in mathematics do not allow a bijection to be established with { 1, 2,..., n } for any natural number n ; these are called infinite sets, while those sets for which such a bijection does exist ( for some n ) are called finite sets. infinite sets cannot be counted in the usual sense ; for one thing, the mathematical theorems which underlie this usual sense for finite sets are false for infinite sets. furthermore, different definitions of the concepts in terms of which these theorems are stated, while equivalent for finite sets, are inequivalent in the context of infinite sets.


in probability theory, hoeffding's lemma is an inequality that bounds the moment - generating function of any bounded random variable. it is named after the finnish – american mathematical statistician wassily hoeffding. the proof of hoeffding's lemma uses taylor's theorem and jensen's inequality. hoeffding's lemma is itself used in the proof of mcdiarmid's inequality.


in probability theory and statistics, the dirichlet process ( dp ) is one of the most popular bayesian nonparametric models. it was introduced by thomas ferguson as a prior over probability distributions. a dirichlet process d p ( s, g 0 ) { \ displaystyle \ mathrm { dp } \ left ( s, g _ { 0 } \ right ) } is completely defined by its parameters : g 0 { \ displaystyle g _ { 0 } } ( the base distribution or base measure ) is an arbitrary distribution and s { \ displaystyle s } ( the concentration parameter ) is a positive real number ( it is often denoted as α { \ displaystyle \ alpha } ). according to the bayesian paradigm these parameters should be chosen based on the available prior information on the domain.


in probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. the birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50 %. the birthday paradox is a veridical paradox : it seems wrong at first glance but is, in fact, true. while it may seem surprising that only 23 individuals are required to reach a 50 % probability of a shared birthday, this result is made more intuitive by considering that the birthday comparisons will be made between every possible pair of individuals.


then : x = k x k, { \ displaystyle x = \ sum _ { k } x _ { k }, \, } and y can be written as a sum of short convolutions : y = ( k x k ) ∗ h = k ( x k ∗ h ) = k y k, { \ displaystyle { \ begin { aligned } y = \ left ( \ sum _ { k } x _ { k } \ right ) * h & = \ sum _ { k } \ left ( x _ { k } * h \ right ) \ \ & = \ sum _ { k } y _ { k }, \ end { aligned } } } where the linear convolution y k x k ∗ h { \ displaystyle y _ { k } \ \ triangleq \ x _ { k } * h \, } is zero outside the region. and for any parameter n ≥ l + m − 1, { \ displaystyle n \ geq l + m - 1, \, } it is equivalent to the n - point circular convolution of x k { \ displaystyle x _ { k } \, } with h { \ displaystyle h \, } in the region. the advantage is that the circular convolution can be computed more efficiently than linear convolution, according to the circular convolution theorem : where : dftn and idftn refer to the discrete fourier transform and its inverse, evaluated over n discrete points, and l is customarily chosen such that n = l + m - 1 is an integer power - of - 2, and the transforms are implemented with the fft algorithm, for efficiency.


in mathematics, a relevance vector machine ( rvm ) is a machine learning technique that uses bayesian inference to obtain parsimonious solutions for regression and probabilistic classification. the rvm has an identical functional form to the support vector machine, but provides probabilistic classification. it is actually equivalent to a gaussian process model with covariance function : k ( x, x ′ ) = j = 1 n 1 α j φ ( x, x j ) φ ( x ′, x j ) { \ displaystyle k ( \ mathbf { x }, \ mathbf { x'} ) = \ sum _ { j = 1 } ^ { n } { \ frac { 1 } { \ alpha _ { j } } } \ varphi ( \ mathbf { x }, \ mathbf { x } _ { j } ) \ varphi ( \ mathbf { x } ', \ mathbf { x } _ { j } ) } where φ { \ displaystyle \ varphi } is the kernel function ( usually gaussian ), α j { \ displaystyle \ alpha _ { j } } are the variances of the prior on the weight vector w n ( 0, α − 1 i ) { \ displaystyle w \ sim n ( 0, \ alpha ^ { - 1 } i ) }, and x 1, …, x n { \ displaystyle \ mathbf { x } _ { 1 }, \ ldots, \ mathbf { x } _ { n } } are the input vectors of the training set. compared to that of support vector machines ( svm ), the bayesian formulation of the rvm avoids the set of free parameters of the svm ( that usually require cross - validation - based post - optimizations ). however rvms use an expectation maximization ( em ) - like learning method and are therefore at risk of local minima. this is unlike the standard sequential minimal optimization ( smo ) - based algorithms employed by svms, which are guaranteed to find a global optimum ( of the convex problem ). the relevance vector machine was patented in the united states by microsoft ( patent expired september 4, 2019 ).


" b " routes are less significant routes, either as an alternative to an " a " or " m " route, or linking smaller population centres to larger regional centres, but without being a major through - route in the region. these are the major road links in areas without " a " routes. " c " routes link smaller settlements and towns to the rest of the major road network.


in multi - state models, the recurrent event processes of individuals are described by different states. the different states may describe the recurrence number, or whether the subject is at risk of recurrence. a change of state is called a transition ( or an event ) and is central in this framework, which is fully characterized through estimation of transition probabilities between states and transition intensities that are defined as instantaneous hazards of progression to one state, conditional on occupying another state.


( c ) overproduction of information. ( d ) restricted capacity of the individual's brain which can lead to excessive specialization, with consequent dangers of degeneration. ( e ) a crisis precipitated by the creation of artificial intelligent beings.


in mathematics and computer science, connectivity is one of the basic concepts of graph theory : it asks for the minimum number of elements ( nodes or edges ) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. it is closely related to the theory of network flow problems. the connectivity of a graph is an important measure of its resilience as a network.


a blocking device ( a duplexer ), shut the receiver input when the transmitter pulsed. a braun tube ( a crt ) was used for displaying the range. the equipment was first tested at a nva site at the lubecker bay near pelzerhaken.


while not widely reported, it has been noted that the genre, or domain, of a text has an effect on the correlation obtained when using metrics. coughlin ( 2003 ) reports that comparing the candidate text against a single reference translation does not adversely affect the correlation of metrics when working in a restricted domain text. even if a metric correlates well with human judgment in one study on one corpus, this successful correlation may not carry over to another corpus.


in telecommunications, the base 10 definition of the unit ( one million bits ) is standard. in the semiconductor industry, it is still common practice to designate random - access memory ( ram ), read - only memory ( rom ) in a binary interpretation of the metric prefixes, such as the megabit, so that one megabit represents 220bits = 1048576bits. for example, a single discrete ddr3 chip specified at " 512 mb " contains 229 bits = 536870912bits = 512 mibit ( approximately 536. 87 mbit ) of storage, or 671088648 - bit bytes, variously referred to as either 64 mebibytes or 64 ( binary ) megabytes. during the 16 - bit game console era, the megabit ( mb ) was a commonly used measure of the size ( computer data storage capacity ) of game cartridges.


in mathematics, a natural number a is a unitary divisor ( or hall divisor ) of a number b if a is a divisor of b and if a and b a { \ displaystyle { \ frac { b } { a } } } are coprime, having no common factor other than 1. thus, 5 is a unitary divisor of 60, because 5 and 60 5 = 12 { \ displaystyle { \ frac { 60 } { 5 } } = 12 } have only 1 as a common factor, while 6 is a divisor but not a unitary divisor of 60, as 6 and 60 6 = 10 { \ displaystyle { \ frac { 60 } { 6 } } = 10 } have a common factor other than 1, namely 2. 1 is a unitary divisor of every natural number.


in software engineering, the active record pattern is an architectural pattern. it is found in software that stores in - memory object data in relational databases. it was named by martin fowler in his 2003 book patterns of enterprise application architecture. the interface of an object conforming to this pattern would include functions such as insert, update, and delete, plus properties that correspond more or less directly to the columns in the underlying database table.


in the algorithm as written above, there are two expensive operations during each iteration : the multiplication s × s, and the mod m operation. the mod m operation can be made particularly efficient on standard binary computers by observing that k ≡ ( k mod 2 n ) + k / 2 n ( mod 2 n − 1 ). { \ displaystyle k \ equiv ( k \, { \ bmod { \, } } 2 ^ { n } ) + \ lfloor k / 2 ^ { n } \ rfloor { \ pmod { 2 ^ { n } - 1 } }. }


in the united kingdom, the official charts company has included streaming into the uk albums chart since march 2015. the change was decided after the massive growth of streaming ; the number of tracks streamed in the uk in a year doubled from 7. 5 billion in 2013 to just under 15 billion in 2014. under the new methodology, official charts company takes the 12 most - streamed tracks from an album, with the top two songs being given lesser weight so that the figure will reflect the popularity of the album as a whole rather than of one or two successful singles. the adjusted total is divided by 1000 and added to the album sales figure.


in mathematics, the category of medial magmas, also known as the medial category, and denoted med, is the category whose objects are medial magmas ( that is, sets with a medial binary operation ), and whose morphisms are magma homomorphisms ( which are equivalent to homomorphisms in the sense of universal algebra ). the category med has direct products, so the concept of a medial magma object ( internal binary operation ) makes sense. as a result, med has all its objects as medial objects, and this characterizes it. there is an inclusion functor from set to med as trivial magmas, with operations being the right projections ( x, y ) → y. an injective endomorphism can be extended to an automorphism of a magma extension — the colimit of the constant sequence of the endomorphism.


this allows the typesetter to distinguish sentence endings from abbreviations and to typeset them differently. early versions of troff, which only typeset in fixed - width fonts, would automatically add a second space between sentences, which were detected based on the combination of terminal punctuation and a line feed. in the april 2020 update, microsoft word started highlighting two spaces after a period as an error and offers a correction of one space. multiple spaces are eliminated by default in most world wide web content, whether or not they are associated with sentences. there are options for preserving spacing, such as the css white - space property, and the tag.


in the broader sense of the term, game engines themselves can be described as middleware. in the context of video games, however, the term " middleware " is often used to refer to subsystems of functionality within a game engine. some game middleware does only one thing but does it more convincingly or more efficiently than general purpose middleware. the four most widely used middleware packages that provide subsystems of functionality include rad game tools'bink, firelight fmod, havok, and scaleform gfx.


in the japanese kantenji braille, the standard 8 - dot braille patterns 367, 1367, 3467, and 13467 are the patterns related to braille pattern dots - 235, since the two additional dots of kantenji patterns 0235, 2357, and 02357 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


jaccard is not cited in the paper, and it seems likely that the authors were not aware of it. tanimoto goes on to define a " distance coefficient " based on this ratio, defined for bitmaps with non - zero similarity : t d ( x, y ) = − log 2 ( t s ( x, y ) ) { \ displaystyle t _ { d } ( x, y ) = - \ log _ { 2 } ( t _ { s } ( x, y ) ) } this coefficient is, deliberately, not a distance metric. it is chosen to allow the possibility of two specimens, which are quite different from each other, to both be similar to a third. it is easy to construct an example which disproves the property of triangle inequality.


in the case of reliability weights, the weights are normalized : v 1 = i = 1 n w i = 1. { \ displaystyle v _ { 1 } = \ sum _ { i = 1 } ^ { n } w _ { i } = 1. } ( if they are not, divide the weights by their sum to normalize prior to calculating v 1 { \ displaystyle v _ { 1 } } : w i ′ = w i i = 1 n w i { \ displaystyle w _ { i }'= { \ frac { w _ { i } } { \ sum _ { i = 1 } ^ { n } w _ { i } } } } then the weighted mean vector μ ∗ { \ displaystyle \ mathbf { \ mu ^ { * } } } can be simplified to μ ∗ = i = 1 n w i x i. { \ displaystyle \ mathbf { \ mu ^ { * } } = \ sum _ { i = 1 } ^ { n } w _ { i } \ mathbf { x } _ { i }. }


in television, a similar idea is used to signal to a control room that a transition of some sort is about to occur on the broadcast ( such as a commercial break ). the most common type of television cue dot is the iba style, used only in the united kingdom, which consists of a small square in the top right corner of the screen, with black and white moving stripes. the other is a proprietary system used principally by the bbc ( who do not air commercials ). this version is a static square in the top left corner with a white - black - white pattern.


in mathematics, a symmetric boolean function is a boolean function whose value does not depend on the order of its input bits, i. e., it depends only on the number of ones ( or zeros ) in the input. for this reason they are also known as boolean counting functions. there are 2n + 1 symmetric n - ary boolean functions. instead of the truth table, traditionally used to represent boolean functions, one may use a more compact representation for an n - variable symmetric boolean function : the ( n + 1 ) - vector, whose i - th entry ( i = 0,..., n ) is the value of the function on an input vector with i ones. mathematically, the symmetric boolean functions correspond one - to - one with the functions that map n + 1 elements to two elements, f : { 0, 1,.


a fundamental theorem due to georg cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. it is also possible for a proper subset of an infinite set to have the same cardinality as the original set — something that cannot happen with proper subsets of finite sets. there is a transfinite sequence of cardinal numbers : 0, 1, 2, 3, …, n, … ; 0, 1, 2, …, α, ….


in the case of two explanatory variables, this indicator function was defined as yk when n = 1 and 1 - yk when n = 0. this was convenient, but not necessary. again, the optimum beta coefficients may be found by maximizing the log - likelihood function generally using numerical methods. a possible method of solution is to set the derivatives of the log - likelihood with respect to each beta coefficient equal to zero and solve for the beta coefficients : ∂ ℓ ∂ β n m = 0 = k = 1 k δ ( n, y k ) x m k − k = 1 k p n ( x k ) x m k { \ displaystyle { \ frac { \ partial \ ell } { \ partial \ beta _ { nm } } } = 0 = \ sum _ { k = 1 } ^ { k } \ delta ( n, y _ { k } ) x _ { mk } - \ sum _ { k = 1 } ^ { k } p _ { n } ( { \ boldsymbol { x } } _ { k } ) x _ { mk } } where β n m { \ displaystyle \ beta _ { nm } } is the m - th coefficient of the β n { \ displaystyle { \ boldsymbol { \ beta } } _ { n } } vector and x m k { \ displaystyle x _ { mk } } is the m - th explanatory variable of the k - th measurement. once the beta coefficients have been estimated from the data, we will be able to estimate the probability that any subsequent set of explanatory variables will result in any of the possible outcome categories.


in optical mesh networks, nodes are junctions of fiber spans. some nodes might contain highly sophisticated routing equipment — while others may be just a patch panel. whatever the case, a node is a shared risk node group — because if the node fails, the failure affects all signals through that particular node.


trace data generated and merged to a trace stream within the soc can be streamed, via a dedicated unidirectional trace interface, off - chip to a trace analysis tool. the mipi debug architecture provides specifications for both parallel and serial trace ports. the mipi parallel trace interface ( mipi pti ) specifies how to pass the trace data to multiple data pins and a clock pin ( single - ended ).


in polyalphabetic substitution ciphers where the substitution alphabets are chosen by the use of a keyword, the kasiski examination allows a cryptanalyst to deduce the length of the keyword. once the length of the keyword is discovered, the cryptanalyst lines up the ciphertext in n columns, where n is the length of the keyword. then each column can be treated as the ciphertext of a monoalphabetic substitution cipher. as such, each column can be attacked with frequency analysis.


in non - fuzzy clustering ( also known as hard clustering ), data are divided into distinct clusters, where each data point can only belong to exactly one cluster. in fuzzy clustering, data points can potentially belong to multiple clusters. for example, an apple can be red or green ( hard clustering ), but an apple can also be red and green ( fuzzy clustering ).


since 2010, a new open source instruction set architecture ( isa ), risc - v, has been under development at the university of california, berkeley, for research purposes and as a free alternative to proprietary isas. as of 2014, version 2 of the user space isa is fixed. the isa is designed to be extensible from a barebones core sufficient for a small embedded processor to supercomputer and cloud computing use with standard and chip designer – defined extensions and coprocessors. it has been tested in silicon design with the rocket soc, which is also available as an open - source processor generator in the chisel language.


in mathematics, legendre's formula gives an expression for the exponent of the largest power of a prime p that divides the factorial n!. it is named after adrien - marie legendre. it is also sometimes known as de polignac's formula, after alphonse de polignac.


in parallel to the development of the 1972 edition of iso 646, which revised the standard to introduce the concept of national versions of the code in addition to the us - originated ascii, work was also underway with the purpose of defining extension mechanisms for ascii, applicable to both 7 - bit and 8 - bit environments, which would be published as ecma - 35 and iso 2022. these mechanisms were designed so that any conformant 8 - bit code could be converted to a corresponding 7 - bit code, and vice versa. in a 7 - bit environment, the shift out ( so ) control would change the meaning of the 94 bytes 0x21 through 0x7e ( i. e. the graphical codes, excluding the space ) to invoke characters from an alternative set, and the shift in ( si ) control would change them back. in an 8 - bit environment, instead of using shift codes, the eighth bit was set on a byte referencing the additional graphic character set. this meant that bytes 0xa1 through 0xfe were used for the additional graphic characters.


in mathematics, in the field of group theory, especially in the study of p - groups and pro - p - groups, the concept of powerful p - groups plays an important role. they were introduced in ( lubotzky & mann 1987 ), where a number of applications are given, including results on schur multipliers. powerful p - groups are used in the study of automorphisms of p - groups ( khukhro 1998 ), the solution of the restricted burnside problem ( vaughan - lee 1993 ), the classification of finite p - groups via the coclass conjectures ( leedham - green & mckay 2002 ), and provided an excellent method of understanding analytic pro - p - groups ( dixon et al. 1991 ).


in a " planned state " these work orders have estimates such as 2 electricians for 8 hours. these work orders have other attributes such as report date, priority, asset operational requirements, and safety concerns. these same organizations have a need to create weekly schedules.


in mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example s l 2 ( z ). { \ displaystyle \ mathrm { sl } _ { 2 } ( \ mathbb { z } ). } they arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theory. they also give rise to very interesting examples of riemannian manifolds and hence are objects of interest in differential geometry and topology. finally, these two topics join in the theory of automorphic forms which is fundamental in modern number theory.


in modern computers many processes run at once. active processes are placed in an array called a run queue, or runqueue. the run queue may contain priority values for each process, which will be used by the scheduler to determine which process to run next. to ensure each program has a fair share of resources, each one is run for some time period ( quantum ) before it is paused and placed back into the run queue.


instead, the following heuristics are used. 1d partitioning : every processor gets n / p { \ displaystyle n / p } vertices and the corresponding outgoing edges. this can be understood as a row - wise or column - wise decomposition of the adjacency matrix.


4. creating a model, likeness, analogy, metaphor, prototype or narrative which shows what the concept is about or how it is applied ( isomorphism, simulation or successive approximation ). 5.


as another issue, for some programs, the method of taking the greatest lower bound at converging execution paths and adding corresponding down - coercion operations appears to be inadequate. for example, before the return 1 in the following program, all components x, y, and z of coord are initialized, but strom's and yemini's approach fails to recognize this, since each initialization of a struct component in the loop body has to be down - coerced at loop re - entry to meet the typestate of the very first loop entry, viz.. a related problem is that this example would require overloading of typestate transitions ; for example, parse _ int _ attr ( " x ", & coord - > x ) changes a typestate " no component initialized " to " x component initialized ", but also " y component initialized " to " x and y component initialized ".


instead of simply “ taking in ” new information, one goes back to look at their understandings and pulls together information that was “ triggered ” and forms a new connection. this connection becomes tighter and one's understanding of a certain concept is solidified or “ stable ” ( pangaro, 2003 ).


if r is not a member of itself, then its definition entails that it is a member of itself ; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. the resulting contradiction is russell's paradox.


in the context of quantum information theory, the operators { vi } are called the kraus operators ( after karl kraus ) of φ. notice, given a completely positive φ, its kraus operators need not be unique. for example, any " square root " factorization of the choi matrix cφ = b∗b gives a set of kraus operators. let b ∗ =, { \ displaystyle b ^ { * } =, } where bi *'s are the row vectors of b, then c φ = i = 1 n m b i b i ∗. { \ displaystyle c _ { \ phi } = \ sum _ { i = 1 } ^ { nm } b _ { i } b _ { i } ^ { * }. }


all hardware architectures in common use are optimized for strict languages, so the best compilers for non - strict languages produce slower code than the best compilers for strict languages. space complexity of non - strict programs is difficult to understand and predict. strict programming languages are often associated with eager evaluation, and non - strict languages with lazy evaluation, but other evaluation strategies are possible in each case. the terms " eager programming language " and " lazy programming language " are often used as synonyms for " strict programming language " and " non - strict programming language " respectively. in many strict languages, some advantages of non - strict functions can be obtained through the use of macros or thunks.


in the early 2000s, many of the existing copyright laws were designed around printed books, magazines and newspapers. for example, copyright laws often set limits on how much of a book can be mechanically reproduced or copied. electronic publishing raises new questions in relation to copyright, because if an e - book or e - journal is available online, millions of internet users may be able to view a single electronic copy of the document, without any " copies " being made. emerging evidence suggests that e - publishing may be more collaborative than traditional paper - based publishing ; e - publishing often involves more than one author, and the resulting works are more accessible, since they are published online.


the probability of doing so in two draws depends on whether the first card drawn was replaced before the second drawing since without replacement there is one fewer card after the first card was drawn. the probabilities of the individual events ( red, and club ) are multiplied rather than added. the probability of drawing a red and a club in two drawings without replacement is then 26 / 52 × 13 / 51 × 2 = 676 / 2652, or 13 / 51.


data elements are defined by the metamodel view and they are referred to by functional objects in other views. functional viewpointfunctional dataflow view – an abstract view that describes the functional elements in the system, their interactions, behavior, provided services, constraints and data flows among them. defines which functions the system is capable of performing, regardless of how these functions are actually implemented. functional control view – describes the control flows and interactions among functional elements within the system.


in queueing theory, a discipline within the mathematical theory of probability, a bulk queue ( sometimes batch queue ) is a general queueing model where jobs arrive in and / or are served in groups of random size. : vii batch arrivals have been used to describe large deliveries and batch services to model a hospital out - patient department holding a clinic once a week, a transport link with fixed capacity and an elevator. networks of such queues are known to have a product form stationary distribution under certain conditions. under heavy traffic conditions a bulk queue is known to behave like a reflected brownian motion.


vadim schechtman and alexander varchenko introduced a matrix indexed by the regions. the matrix element for the region r i { \ displaystyle r _ { i } } and r j { \ displaystyle r _ { j } } is given by the product of indeterminate variables a h { \ displaystyle a _ { h } } for every hyperplane h that separates these two regions. if these variables are specialized to be all value q, then this is called the q - matrix ( over the euclidean domain q { \ displaystyle \ mathbb { q } } ) for the arrangement and much information is contained in its smith normal form.


franklin proved that the chromatic number of a graph embedded in the klein bottle can be as large as 6 { \ displaystyle 6 }, but never exceeds 6 { \ displaystyle 6 }. later it was proved in the works of gerhard ringel, j. w. t. youngs, and other contributors that the complete graph with h ( s ) { \ displaystyle h ( s ) } vertices can be embedded in the surface s { \ displaystyle s } unless s { \ displaystyle s } is the klein bottle. this established that heawood's bound could not be improved. for example, the complete graph on 7 { \ displaystyle 7 } vertices can be embedded in the torus as follows : the case of the sphere is the four - color conjecture, which was settled by kenneth appel and wolfgang haken in 1976.


evaluation – assesses the effectiveness of a public policy in terms of its perceived intentions and results. policy actors attempt to determine whether the course of action is a success or failure by examining its impact and outcomes. anderson's version of the stages model is the most common and widely recognised out of the models. however, it could also be seen as flawed.


there is a whole research branch dealing with all possible regularizations. in practice, one usually tries a specific regularization and then figures out the probability density that corresponds to that regularization to justify the choice. it can also be physically motivated by common sense or intuition. in machine learning, the data term corresponds to the training data and the regularization is either the choice of the model or modifications to the algorithm. it is always intended to reduce the generalization error, i. e. the error score with the trained model on the evaluation set and not the training data. one of the earliest uses of regularization is tikhonov regularization, related to the method of least squares.


two binary variables are considered positively associated if most of the data falls along the diagonal cells. in contrast, two binary variables are considered negatively associated if most of the data falls off the diagonal. if we have a 2×2 table for two random variables x and y where n11, n10, n01, n00, are non - negative counts of numbers of observations that sum to n, the total number of observations.


in telecommunications, a system that supports simultaneous voice and data ( svd ) is one that can transceive both voice and primary data concurrently over one pstn modem.


in mathematics, the fibonacci numbers form a sequence defined recursively by : f n = { 0 n = 0 1 n = 1 f n − 1 + f n − 2 n > 1 { \ displaystyle f _ { n } = { \ begin { cases } 0 & n = 0 \ \ 1 & n = 1 \ \ f _ { n - 1 } + f _ { n - 2 } & n > 1 \ end { cases } } } that is, after two starting values, each number is the sum of the two preceding numbers. the fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1, by adding more than two numbers to generate the next number, or by adding objects other than numbers.


in mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests ( especially the limit comparison test ), provides a way of deducing the convergence or divergence of an infinite series or an improper integral. in both cases, the test works by comparing the given series or integral to one whose convergence properties are known.


in the japanese kantenji braille, the standard 8 - dot braille patterns 5678, 15678, 45678, and 145678 are the patterns related to braille pattern dots - 3456, since the two additional dots of kantenji patterns 03456, 34567, and 034567 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


a network or protocol that supports qos may agree on a traffic contract with the application software and reserve capacity in the network nodes, for example during a session establishment phase. during the session it may monitor the achieved level of performance, for example the data rate and delay, and dynamically control scheduling priorities in the network nodes. it may release the reserved capacity during a tear down phase.


the reference validation mechanism must be always invoked. without this property, it is possible for the mechanism to not perform when intended, allowing an attacker to violate the security policy. the reference validation mechanism must be tamper - proof.


in statically typed languages such as go or ml, a variable also has a type, meaning that only certain kinds of values can be stored in it. for example, a variable of type " integer " is prohibited from storing text values. in dynamically typed languages such as python, a variable's type is inferred by its value, and can change according to its value. in common lisp, both situations exist simultaneously : a variable is given a type ( if undeclared, it is assumed to be t, the universal supertype ) which exists at compile time.


in software architecture, a messaging pattern is an architectural pattern which describes how two different parts of an application, or different systems connect and communicate with each other. there are many aspects to the concept of messaging which can be divided in the following categories : hardware device messaging ( telecommunications, computer networking, iot, etc. ) and software data exchange ( the different data exchange formats and software capabilities of such data exchange ). despite the difference in the context, both categories exhibit common traits for data exchange.


in the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics. formal verification can be helpful in proving the correctness of systems such as : cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code. the verification of these systems is done by providing a formal proof on an abstract mathematical model of the system, the correspondence between the mathematical model and the nature of the system being otherwise known by construction. examples of mathematical objects often used to model systems are : finite - state machines, labelled transition systems, petri nets, vector addition systems, timed automata, hybrid automata, process algebra, formal semantics of programming languages such as operational semantics, denotational semantics, axiomatic semantics and hoare logic.


the first eight units were delivered to the office of the then prime minister, pierre elliot trudeau, in february 1974. despite these predecessors, wang's product was a standout, and by 1978 it had sold more of these systems than any other vendor. the phrase " word processor " rapidly came to refer to crt - based machines similar to the aes 90.


when analyzing a population, one of the main sources used to gather the required information is insurance by obtaining individual records that belong to a specific population. these are called mortality tables if they show death rates, and morbidity tables if they show various types of sickness or disability rates. the availability of computers and the proliferation of data gathering about individuals has made possible calculations that are more voluminous and intensive than those used in the past ( i. e. they crunch more numbers ) and it is more common to attempt to provide different tables for different uses, and to factor in a range of non - traditional behaviors ( e. g. gambling, debt load ) into specialized calculations utilized by some institutions for evaluating risk. this is particularly the case in non - life insurance ( e. g. the pricing of motor insurance can allow for a large number of risk factors, which requires a correspondingly complex table of expected claim rates ). however the expression " life table " normally refers to human survival rates and is not relevant to non - life insurance.


with the simple addition of the particle ni " at ", for example, / / hashi - ni " at the bridge " acquires a marked drop in pitch, while / hasini / hashi - ni " at the edge " does not. however, because the downstep occurs after the first mora of the accented syllable, a word with a final long accented syllable would contrast all three patterns even in isolation : an accentless word nihon, for example, would be pronounced, differently from either of the words above. in 2014, a study recording the electrical activity of the brain showed that native japanese speakers mainly use context, rather than pitch accent information, to contrast between words that differ only in pitch. this property of the japanese language allows for a certain type of pun, called dajare (, ), combining two words with the same or very similar sounds but different pitch accents and thus meanings.


another strategy to deal with small sample size is to use a shrinkage estimator of the covariance matrix, which can be expressed mathematically as σ = ( 1 − λ ) σ + λ i { \ displaystyle \ sigma = ( 1 - \ lambda ) \ sigma + \ lambda i \, } where i { \ displaystyle i } is the identity matrix, and λ { \ displaystyle \ lambda } is the shrinkage intensity or regularisation parameter. this leads to the framework of regularized discriminant analysis or shrinkage discriminant analysis. also, in many practical cases linear discriminants are not suitable. lda and fisher's discriminant can be extended for use in non - linear classification via the kernel trick.


in the same system, messages are constructed in four parts, the first and last of which are digital and the middle two are audio. the digital sections of a same message are afsk data bursts, with individual bits lasting 1920 μs ( 1. 92 ms ) each, giving a bit rate of 5205⁄6 bits per second. a mark bit is four complete cycles of a sine wave, translating to a mark frequency of 20831⁄3 hz, and a space bit is three complete sine wave cycles, making the space frequency 1562. 5 hz. the data is sent isochronously and encoded in 8 - bit bytes with the most - significant bit of each ascii byte set to zero. the least - significant bit of each byte is transmitted first, including the preamble. the data stream is bit and byte synchronized on the preamble. since there is no error correction, the digital part of a same message is transmitted three times, so that decoders can pick " best two out of three " for each byte, thereby eliminating most errors which can cause an activation to fail.


in physics, the cluster decomposition property states that experiments carried out far from each other cannot influence each other. usually applied to quantum field theory, it requires that vacuum expectation values of operators localized in bounded regions factorize whenever these regions becomes sufficiently distant from each other. first formulated by eyvind h. wichmann and james h. crichton in 1963 in the context of the s - matrix, it was conjectured by steven weinberg that in the low energy limit the cluster decomposition property, together with lorentz invariance and quantum mechanics, inevitably lead to quantum field theory. string theory satisfies all three of the conditions and so provides a counter - example against this being true at all energy scales.


in the osi model, the definition of the application layer is narrower in scope. the osi model defines the application layer as only the interface responsible for communicating with host - based and user - facing applications. osi then explicitly distinguishes the functionality of two additional layers, the session layer and presentation layer, as separate levels below the application layer and above the transport layer. osi specifies a strict modular separation of functionality at these layers and provides protocol implementations for each. in contrast, the internet protocol suite compiles these functions into a single layer.


this algorithm was popular, but significantly more efficient algorithms exist. algorithms based on the newton – raphson method are able to compute quadrature rules for significantly larger problem sizes. in 2014, ignace bogaert presented explicit asymptotic formulas for the gauss – legendre quadrature weights and nodes, which are accurate to within double - precision machine epsilon for any choice of n ≥ 21. this allows for computation of nodes and weights for values of n exceeding one billion.


some used sign - magnitude arithmetic ( - 1 = 10001 ), or ones'complement ( - 1 = 11110 ), rather than modern two's complement arithmetic ( - 1 = 11111 ). most computers used six - bit character sets because they adequately encoded hollerith punched cards. it was a major revelation to designers of this period to realize that the data word should be a multiple of the character size. they began to design computers with 12 -, 24 - and 36 - bit data words ( e. g., see the tx - 2 ). in this era, grosch's law dominated computer design : computer cost increased as the square of its speed.


in statistical classification, two main approaches are called the generative approach and the discriminative approach. these compute classifiers by different approaches, differing in the degree of statistical modelling. terminology is inconsistent, but three major types can be distinguished, following jebara ( 2004 ) : a generative model is a statistical model of the joint probability distribution p ( x, y ) { \ displaystyle p ( x, y ) } on given observable variable x and target variable y ; a discriminative model is a model of the conditional probability p ( y x = x ) { \ displaystyle p ( y \ mid x = x ) } of the target y, given an observation x ; and classifiers computed without using a probability model are also referred to loosely as " discriminative ". the distinction between these last two classes is not consistently made ; jebara ( 2004 ) refers to these three classes as generative learning, conditional learning, and discriminative learning, but ng & jordan ( 2002 ) only distinguish two classes, calling them generative classifiers ( joint distribution ) and discriminative classifiers ( conditional distribution or no distribution ), not distinguishing between the latter two classes. analogously, a classifier based on a generative model is a generative classifier, while a classifier based on a discriminative model is a discriminative classifier, though this term also refers to classifiers that are not based on a model.


the summation of an explicit sequence is denoted as a succession of additions. for example, summation of is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. because addition is associative and commutative, there is no need of parentheses, and the result is the same irrespective of the order of the summands.


in order to improve the optimisation of the valve timing for differing engine speeds and loads, the system is able to vary the timing and duration of the inlet valve opening. it achieves this by using a complex and finely machined mechanism to drive the inlet camshafts. this mechanism can accelerate and decelerate the rotational speed of the camshaft during different parts of its cycle. e. g. to produce longer opening duration, it slows the rotation during the valve open part of the cycle and speeds it up during the valve closed period.


lingvo ". the search engine has learned to understand queries like “ what is in spanish ” and automatically translate them. it became possible to limit search results by region.


even tiny measurement errors, when integrated, add up to an appreciable error known as " drift ". for instance, the n - 1 navigation system developed for the sm - 64 navaho cruise missile drifted at a rate of 1 nautical mile per hour, meaning that after a two - hour flight the ins would be indicating a position 2 nautical miles ( 3. 7 km ; 2. 3 mi ) away from its actual location. this was outside the desired accuracy of about half a mile.


in the above example of coin - tossing we explicitly assumed that each toss is an independent trial, and the probability of getting head or tail is always the same. let x, x 1, x 2, … { \ displaystyle x, x _ { 1 }, x _ { 2 }, \ ldots } be independent and identically distributed ( i. i. d. ) random variables whose common distribution satisfies a certain growth condition. then the following limit exists : lim n → ∞ 1 n ln p ( m n > x ) = − i ( x ) { \ displaystyle \ lim _ { n \ to \ infty } { \ frac { 1 } { n } } \ ln p ( m _ { n } > x ) = - i ( x ) }. here m n = 1 n i = 1 n x i { \ displaystyle m _ { n } = { \ frac { 1 } { n } } \ sum _ { i = 1 } ^ { n } x _ { i } }, as before.


in materials management, abc analysis is an inventory categorisation technique. abc analysis divides an inventory into three categories — " a items " with very tight control and accurate records, " b items " with less tightly controlled and good records, and " c items " with the simplest controls possible and minimal records. the abc analysis provides a mechanism for identifying items that will have a significant impact on overall inventory cost, while also providing a mechanism for identifying different categories of stock that will require different management and controls. the abc analysis suggests that inventories of an organization are not of equal value.


reification data is often said to be made a first class object. reification, at least partially, has been experienced in many languages to date : in early lisp dialects and in current prolog dialects, programs have been treated as data, although the causal connection has often been left to the responsibility of the programmer. in smalltalk - 80, the compiler from the source text to bytecode has been part of the run - time system since the very first implementations of the language.


adding the constraint forces does not change the total energy, as the net work done by the constraint forces ( taken over the set of particles that the constraints act on ) is zero. note that the sign on λ k { \ displaystyle \ lambda _ { k } } is arbitrary and some references have an opposite sign. from integrating both sides of the equation with respect to the time, the constrained coordinates of particles at the time, t + δ t { \ displaystyle t + \ delta t }, are given, x i ( t + δ t ) = x ^ i ( t + δ t ) + k = 1 n λ k ∂ σ k ( t ) ∂ x i ( δ t ) 2 m i − 1, i = 1 … n { \ displaystyle \ mathbf { x } _ { i } ( t + \ delta t ) = { \ hat { \ mathbf { x } } } _ { i } ( t + \ delta t ) + \ sum _ { k = 1 } ^ { n } \ lambda _ { k } { \ frac { \ partial \ sigma _ { k } ( t ) } { \ partial \ mathbf { x } _ { i } } } \ left ( \ delta t \ right ) ^ { 2 } m _ { i } ^ { - 1 }, \ quad i = 1 \ ldots n } where x ^ i ( t + δ t ) { \ displaystyle { \ hat { \ mathbf { x } } } _ { i } ( t + \ delta t ) } is the unconstrained ( or uncorrected ) position of the ith particle after integrating the unconstrained equations of motion.


in the uk, the data protection act is used to ensure that personal data is accessible to those whom it concerns, and provides redress to individuals if there are inaccuracies. this is particularly important to ensure individuals are treated fairly, for example for credit checking purposes. the data protection act states that only individuals and companies with legitimate and lawful reasons can process personal information and cannot be shared.


in telephony, an automated attendant ( also auto attendant, auto - attendant, autoattendant, automatic phone menus, aa, or virtual receptionist ) allows callers to be automatically transferred to an extension without the intervention of an operator / receptionist. many aas will also offer a simple menu system ( " for sales, press 1, for service, press 2, " etc. ). an auto attendant may also allow a caller to reach a live operator by dialing a number, usually " 0 ". typically the auto attendant is included in a business's phone system such as a pbx, but some services allow businesses to use an aa without such a system. modern aa services ( which now overlap with more complicated interactive voice response or ivr systems ) can route calls to mobile phones, voip virtual phones, other aas / ivrs, or other locations using traditional land - line phones or voice message machines.


with 23 individuals, there are 23 × 22 / 2 = 253 pairs to consider, far more than half the number of days in a year. real - world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as calculating the approximate risk of a hash collision existing within the hashes of a given size of population.


in mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. the same definition extends to any object in n - dimensional euclidean space. in geometry, one often assumes uniform mass density, in which case the barycenter or center of mass coincides with the centroid. informally, it can be understood as the point at which a cutout of the shape ( with uniformly distributed mass ) could be perfectly balanced on the tip of a pin. in physics, if variations in gravity are considered, then a center of gravity can be defined as the weighted mean of all points weighted by their specific weight. in geography, the centroid of a radial projection of a region of the earth's surface to sea level is the region's geographical center.


during the 1980s, approaches to achieve inferential programming mostly involved techniques for logical inference. today the term is sometimes used in connection with evolutionary computation techniques that enable a computer to evolve a solution in response to a problem posed as a fitness or reward function. in july 2022, github copilot was released, which is an example of inferential programming.


they have proved that when perfect noiseless recovery occurs, then matrix completion is stable vis a vis perturbations. the error is proportional to the noise level δ { \ displaystyle \ delta }. therefore, when the noise level is small, the error is small.


if in addition p and q are congruent to 1 modulo 8, let p = c2 + 2d2 and q = c2 + 2d2. then ( p | q ) 8 = ( q | p ) 8 = ( a b − b a | q ) 4 ( c d − d c | q ) 2. { \ displaystyle ( p | q ) _ { 8 } = ( q | p ) _ { 8 } = ( ab - ba | q ) _ { 4 } ( cd - dc | q ) _ { 2 } \. }


in some of the academic literature, multiplication denoted by juxtaposition ( also known as implied multiplication ) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ ( 2n ), not ( 1 ÷ 2 ) n. for example, the manuscript submission instructions for the physical review journals state that multiplication is of higher precedence than division, and this is also the convention observed in prominent physics textbooks such as the course of theoretical physics by landau and lifshitz and the feynman lectures on physics. this ambiguity is often exploited in internet memes such as " 8÷2 ( 2 + 2 ) ", for which there are two conflicting interpretations : 8÷ = 1 and ( 2 + 2 ) = 16. the expression " 6÷2 ( 1 + 2 ) " also gained notoriety in the exact same manner, with the two interpretations resulting in the answers 1 and 9. ambiguity can also be caused by the use of the slash symbol,'/ ', for division. the physical review submission instructions suggest to avoid expressions of the form a / b / c ; ambiguity can be avoided by instead writing ( a / b ) / c or a / ( b / c ).


the prism design was notable for several aspects of its instruction set. notably, prism included epicode ( extended processor instruction code ), which defined a number of " special " instructions intended to offer the operating system a stable abi across multiple implementations. epicode was given its own set of 22 32 - bit registers to use. a set of vector processing instructions were later added as well, supported by an additional sixteen 64 - bit vector registers that could be used in a variety of ways.


at the same time the student is generating a list of the multiples of the small number ( i. e., partial quotients ) that have so far been taken away, which when added up together would then become the whole number quotient itself. for example, to calculate 132 ÷ 8, one might successively subtract 80, 40 and 8 to leave 4 : 132 80 ( 10 × 8 ) - - 52 40 ( 5 × 8 ) - - 12 8 ( 1 × 8 ) - - 4 - - - - - - - - 132 = 16 × 8 + 4 because 10 + 5 + 1 = 16, 132 ÷ 8 is 16 with 4 remaining. in the uk, this approach for elementary division sums has come into widespread classroom use in primary schools since the late 1990s, when the national numeracy strategy in its " numeracy hour " brought in a new emphasis on more free - form oral and mental strategies for calculations, rather than the rote learning of standard methods. compared to the short division and long division methods that are traditionally taught, chunking may seem strange, unsystematic, and arbitrary.


in the english language, a hate crime ( also known as a " bias - motivated crime " ) generally refers to criminal acts which are seen to have been motivated by hate. those who commit hate crimes target victims because of their perceived membership in a certain social group, usually defined by race, gender, religion, sexual orientation, mental disorder, disability, class, ethnicity, nationality, age, gender identity, or political affiliation. incidents may involve physical assault, destruction of property, bullying, harassment, verbal abuse or insults, or offensive graffiti or letters ( hate mail ). hate speech is speech perceived to disparage a person or group of people based on their social or ethnic group, such as race, sex, age, ethnicity, nationality, religion, sexual orientation, gender identity, mental disorder, disability, language ability, ideology, social class, occupation, appearance ( height, weight, skin color, etc. ), mental capacity, and any other distinction that might be considered a liability.


when the action executes, and what its actual inputs are, is determined by the concrete action and the behaviors in which it is used. an action is the specification of an executable statement and is the fundamental unit of processing or behavior in an activity node that represents some transformation in the modeled system. an action forms an abstraction of a computational procedure which is an atomic execution and therefore completes without interruption.


a song sold on itunes gives the artist 9 cents in profit. they also reported that customers were purchasing 2. 5 million songs a week which translates to a projected annual run rate of 130 million songs a year. the 50 millionth song was " the path of thorns " by sarah mclachlan. on april 28, 2004, itunes music store marked its first anniversary with 70 million songs sold, clear dominance in the paid online music market and a slight profit.


it can be proved by a back - and - forth method that is also sometimes attributed to cantor but was actually published later, by felix hausdorff. the same back - and - forth method also proves that countable dense unbounded orders are highly symmetric, and can be applied to other kinds of structures. however, cantor's original proof only used the " going forth " half of this method.


in semantic hashing documents are mapped to memory addresses by means of a neural network in such a way that semantically similar documents are located at nearby addresses. deep neural network essentially builds a graphical model of the word - count vectors obtained from a large set of documents. documents similar to a query document can then be found by simply accessing all the addresses that differ by only a few bits from the address of the query document. this way of extending the efficiency of hash - coding to approximate matching is much faster than locality sensitive hashing, which is the fastest current method.


in more sophisticated systems such as large cities, this concept is further extended : some streets are marked as being one - way, and on those streets all traffic must flow in only one direction. pedestrians on the sidewalks are generally not limited to one - way movement. drivers wishing to reach a destination they have already passed must return via other streets. one - way streets, despite the inconveniences to some individual drivers, can greatly improve traffic flow since they usually allow traffic to move faster and tend to simplify intersections.


as per the standard : " an equal month is presumed to have 30. 41666 days ( i. e. 365 / 12 ) regardless of whether or not it is a leap year. " the result is to be expressed to at least one decimal place.


in the field of textual scholarship and the editing of historic texts, the term " normalization " implies a degree of modernization and standardization – for example in the extension of scribal abbreviations and the transliteration of the archaic glyphs typically found in manuscript and early printed sources. a normalized edition is therefore distinguished from a diplomatic edition ( or semi - diplomatic edition ), in which some attempt is made to preserve these features. the aim is to strike an appropriate balance between, on the one hand, rigorous fidelity to the source text ( including, for example, the preservation of enigmatic and ambiguous elements ) ; and, on the other, producing a new text that will be comprehensible and accessible to the modern reader. the extent of normalization is therefore at the discretion of the editor, and will vary. some editors, for example, choose to modernize archaic spellings and punctuation, but others do not.


genus types with sufficient vertical extent to occupy more than one level do not carry any altitude - related prefixes. they are classified formally as low - or mid - level depending on the altitude at which each initially forms, and are also more informally characterized as multi - level or vertical. most of the ten genera derived by this method of classification can be subdivided into species and further subdivided into varieties.


the even dimensional space of dimension d { \ displaystyle d } can be described using complex coordinates w i ∈ c d / 2 { \ displaystyle w _ { i } \ in \ mathbb { c } ^ { d / 2 } } with a metric g i j = ( 1 + ρ d r d ) 2 / d, { \ displaystyle g _ { i { \ bar { j } } } = { \ bigg ( } 1 + { \ frac { \ rho ^ { d } } { r ^ { d } } } { \ bigg ) } ^ { 2 / d } { \ bigg }, } where ρ { \ displaystyle \ rho } is a scale setting constant and r 2 = | w | c d / 2 2 { \ displaystyle r ^ { 2 } = | w | _ { \ mathbb { c } ^ { d / 2 } } ^ { 2 } }. aside from its inherent importance in pure geometry, the space is important in string theory. certain types of k3 surfaces can be approximated as a combination of several eguchi – hanson metrics since both have the same holonomy group.


in music, a rewrite rule is a recursive generative grammar, which creates a chord progression from another. steedman ( 1984 ) has proposed a set of recursive " rewrite rules " which generate all well - formed transformations of jazz, basic i – iv – i – v – i twelve - bar blues chord sequences, and, slightly modified, non - twelve - bar blues i – iv – v sequences ( " rhythm changes " ). the typical 12 - bar blues progression can be notated 1 2 3 4 5 6 7 8 9 10 11 12 i / i / i / i / / iv / iv / i / i / / v / iv / i / i where the top line numbers each bar, one slash indicates a bar line, two indicate both a bar line and a phrase ending and a roman numeral indicates the chord function. important transformations include replacement or substitution of a chord by its dominant or subdominant : 1 2 3 4 5 6 7 8 9 10 11 12 i / iv / i / i7 / / iv / vii7 / iii7 / vi7 / / ii7 / v7 / i / i / / use of chromatic passing chords :... 7 8 9...... iii7 / ♭iii7 / ii7... and chord alterations such as minor chords, diminished sevenths, etc. sequences by fourth, rather than fifth, include jimi hendrix's version of " hey joe " and deep purple's " hush " : 1 2 3 4 5 6 7 8 9 10 11 12 ♭vi, ♭iii / ♭vii, iv / i / i / / ♭vi, ♭iii / ♭vii, iv / i / i / / ♭vi, ♭iii / ♭vii, iv / i / i / / these often result in aeolian harmony and lack perfect cadences ( v – i ).


oses have grown immensely in their size and complexity resulting in attempts to reduce os overhead and improve performance including microkernel, exokernel, tiny - os, os - kit, palacios and kitten, io _ lite, bare - metal linux, ibm - libra and other lean kernels. in addition to the above approaches, in embedded systems such as smart phones, a small and dedicated portion of an os and a given set of applications are closely integrated with the hardware. there are also a myriad of industrial control and gaming applications that run directly on the hardware.


in mathematics, an euler system is a collection of compatible elements of galois cohomology groups indexed by fields. they were introduced by kolyvagin ( 1990 ) in his work on heegner points on modular elliptic curves, which was motivated by his earlier paper kolyvagin ( 1988 ) and the work of thaine ( 1988 ). euler systems are named after leonhard euler because the factors relating different elements of an euler system resemble the euler factors of an euler product. euler systems can be used to construct annihilators of ideal class groups or selmer groups, thus giving bounds on their orders, which in turn has led to deep theorems such as the finiteness of some tate - shafarevich groups. this led to karl rubin's new proof of the main conjecture of iwasawa theory, considered simpler than the original proof due to barry mazur and andrew wiles.


other regression methods that can be used in place of ordinary least squares include least absolute deviations ( minimizing the sum of absolute values of residuals ) and the theil – sen estimator ( which chooses a line whose slope is the median of the slopes determined by pairs of sample points ). deming regression ( total least squares ) also finds a line that fits a set of two - dimensional sample points, but ( unlike ordinary least squares, least absolute deviations, and median slope regression ) it is not really an instance of simple linear regression, because it does not separate the coordinates into one dependent and one independent variable and could potentially return a vertical line as its fit. the remainder of the article assumes an ordinary least squares regression. in this case, the slope of the fitted line is equal to the correlation between y and x corrected by the ratio of standard deviations of these variables. the intercept of the fitted line is such that the line passes through the center of mass ( x, y ) of the data points.


the case ( x, y, z ) = ( 2, 6, n ) and all its permutations were proven for n ≥ 3 by michael bennett and imin chen in 2011 and by bennett, chen, dahmen and yazdani in 2014. the case ( x, y, z ) = ( 2, 2n, 3 ) and all its permutations were proven for 3 ≤ n ≤ 107 except n = 7 and various modulo congruences when n is prime to have no non - catalan solution by bennett, chen, dahmen and yazdani. the cases ( x, y, z ) = ( 2, 2n, 9 ), ( 2, 2n, 10 ), ( 2, 2n, 15 ) and all their permutations were proven for n ≥ 2 by bennett, chen, dahmen and yazdani in 2014.


z i { \ displaystyle z _ { i } } is the idiosyncratic component, the ‘ strength ’ of entity i, possibly measured by entity i's stock price return. from equation ( 10 ) we see, that the correlation between entities i is modeled indirectly by conditioning the latent variable x i { \ displaystyle x _ { i } } on the common factor m { \ displaystyle m }.


in the java programming language, heap pollution is a situation that arises when a variable of a parameterized type refers to an object that is not of that parameterized type. this situation is normally detected during compilation and indicated with an unchecked warning. later, during runtime heap pollution will often cause a classcastexception. heap pollution in java can occur when type arguments and variables are not reified at run - time.


in mathematics, a square number or perfect square is an integer that is the square of an integer ; in other words, it is the product of some integer with itself. for example, 9 is a square number, since it equals 32 and can be written as 3 × 3. the usual notation for the square of a number n is not the product n × n, but the equivalent exponentiation n2, usually pronounced as " n squared ". the name square number comes from the name of the shape.


almost all even positive numbers can be expressed as the sum of two primes. : 489 almost all primes are isolated. moreover, for every positive integer g, almost all primes have prime gaps of more than g both to their left and to their right ; that is, there is no other prime between p − g and p + g.


in the case of indivisible item assignment, when the utility functions of all agents are gs ( and thus an equilibrium exists ), it is possible to find a competitive equilibrium using an ascending auction. in an ascending auction, the auctioneer publishes a price vector, initially zero, and the buyers declare their favorite bundle under these prices. in case each item is desired by at most a single bidder, the items are divided and the auction is over.


in the unix - world, there is commonly a special filesystem mounted at / proc. this filesystem is implemented within the kernel and publishes information about processes. for each process, there is a directory ( named by the process id ), containing detailed information about the process : status, open files, memory maps, mounts, etc. / proc first appeared in unix 8th edition, and its functionality was greatly expanded in plan 9 from bell labs.


to this end the 56800 series added a complete mcu which created a single - chip " dspcontroller " solution, while the opposite occurred in the 68456, a 68000 with a 56000 on it. a still quite prevalent model of the 56000 is the third generation 56300 family, starting with the 56301, which features several models with special applications hard - and firmware built - in, like pci interface logic, crc processors, or audio companders. core clock frequencies ranged up to 250 mhz.


the receiver un - does these transformations in reverse order : demodulation, trellis decoding, error detection and correction, decompression. some communication systems omit one or more of these steps, or use techniques that combine several of these steps together. for example, a morse code transmitter combines source coding, channel coding, and line coding into one step, typically followed by an amplitude modulation step. barcodes, on the other hand, add a checksum digit during channel coding, then translate each digit into a barcode symbol during line coding, omitting modulation.


the f1 score is the harmonic mean of the precision and recall. it thus symmetrically represents both precision and recall in one metric. the more generic f β { \ displaystyle f _ { \ beta } } score applies additional weights, valuing one of precision or recall more than the other. the highest possible value of an f - score is 1. 0, indicating perfect precision and recall, and the lowest possible value is 0, if either precision or recall are zero.


in mathematics, an algebra such as ( r, +, ⋅ ) { \ displaystyle ( \ mathbb { r }, +, \ cdot ) } has multiplication ⋅ { \ displaystyle \ cdot } whose associativity is well - defined on the nose. this means for any real numbers a, b, c ∈ r { \ displaystyle a, b, c \ in \ mathbb { r } } we have a ⋅ ( b ⋅ c ) − ( a ⋅ b ) ⋅ c = 0 { \ displaystyle a \ cdot ( b \ cdot c ) - ( a \ cdot b ) \ cdot c = 0 }. but, there are algebras r { \ displaystyle r } which are not necessarily associative, meaning if a, b, c ∈ r { \ displaystyle a, b, c \ in r } then a ⋅ ( b ⋅ c ) − ( a ⋅ b ) ⋅ c = 0 { \ displaystyle a \ cdot ( b \ cdot c ) - ( a \ cdot b ) \ cdot c \ neq 0 } in general. there is a notion of algebras, called a ∞ { \ displaystyle a _ { \ infty } } - algebras, which still have a property on the multiplication which still acts like the first relation, meaning associativity holds, but only holds up to a homotopy, which is a way to say after an operation " compressing " the information in the algebra, the multiplication is associative. this means although we get something which looks like the second equation, the one of inequality, we actually get equality after " compressing " the information in the algebra.


in number theory, proth's theorem is a primality test for proth numbers. it states that if p is a proth number, of the form k2n + 1 with k odd and k < 2n, and if there exists an integer a for which a p − 1 2 ≡ − 1 ( mod p ), { \ displaystyle a ^ { \ frac { p - 1 } { 2 } } \ equiv - 1 { \ pmod { p } }, } then p is prime. in this case p is called a proth prime. this is a practical test because if p is prime, any chosen a has about a 50 percent chance of working, furthermore, since the calculation is mod p, only values of a smaller than p have to be taken into consideration.


in parallel to the development of l4ka : : hazelnut, in 1998 the operating systems group tud : os of the tu dresden started to develop their own c + + implementation of the l4 kernel interface, named l4 / fiasco. in contrast to l4ka : : hazelnut, which allows no concurrency in the kernel, and its successor l4ka : : pistachio, which allows interrupts in the kernel only at specific preemption points, l4 / fiasco was fully preemptible ( with the exception of extremely short atomic operations ) to achieve a low interrupt latency. this was considered necessary because l4 / fiasco is used as the basis of drops, a hard real - time computing capable operating system, also developed at the tu dresden. however, the complexities of a fully preemptible design prompted later versions of fiasco to return to the traditional l4 approach of running the kernel with interrupts disabled, except for a limited number of preemption points.


in text - based electronic communication, the sign of the horns is represented with the \.. /, \ m / or | m | emoticon and sometimes with /.. /. the unicode character u + 1f918 sign of the horns was introduced in unicode 8. 0 as an emoji, on june 17, 2015.


in terms of sieve theory the selberg sieve is of combinatorial type : that is, derives from a careful use of the inclusion – exclusion principle. selberg replaced the values of the mobius function which arise in this by a system of weights which are then optimised to fit the given problem. the result gives an upper bound for the size of the sifted set. let a { \ displaystyle a } be a set of positive integers ≤ x { \ displaystyle \ leq x } and let p { \ displaystyle p } be a set of primes.


modern power systems are designed to be resistant to this sort of cascading failure, but it may be unavoidable ( see below ). moreover, since there is no short - term economic benefit to preventing rare large - scale failures, researchers have expressed concern that there is a tendency to erode the resilience of the network over time, which is only corrected after a major failure occurs. in a 2003 publication, carreras and co - authors claimed that reducing the likelihood of small outages only increases the likelihood of larger ones.


in mathematics, alhazen built on the mathematical works of euclid and thabit ibn qurra and worked on " the beginnings of the link between algebra and geometry ". he developed a formula for summing the first 100 natural numbers, using a geometric proof to prove the formula.


suppose the documentation associated with these types specifies that type stack's methods shall behave as expected for stacks ( i. e. they shall exhibit lifo behavior ), and that type queue's methods shall behave as expected for queues ( i. e. they shall exhibit fifo behavior ). suppose, now, that type stack was declared as a subclass of type queue. most programming language compilers ignore documentation and perform only the checks that are necessary to preserve type safety.


in software development, a test suite, less commonly known as a validation suite, is a collection of test cases that are intended to be used to test a software program to show that it has some specified set of behaviors. a test suite often contains detailed instructions or goals for each collection of test cases and information on the system configuration to be used during testing. a group of test cases may also contain prerequisite states or steps, and descriptions of the following tests. collections of test cases are sometimes termed a test plan, a test script, or even a test scenario.


they can also be described as subsets of a set of 24 elements, where addition is defined as taking the symmetric difference of the subsets. in the extended binary golay code, all code words have hamming weights of 0, 8, 12, 16, or 24. code words of weight 8 are called octads and code words of weight 12 are called dodecads.


in probability theory and statistics, the logistic distribution is a continuous probability distribution. its cumulative distribution function is the logistic function, which appears in logistic regression and feedforward neural networks. it resembles the normal distribution in shape but has heavier tails ( higher kurtosis ). the logistic distribution is a special case of the tukey lambda distribution.


in predictive analytics, a table of confusion ( sometimes also called a confusion matrix ) is a table with two rows and two columns that reports the number of true positives, false negatives, false positives, and true negatives. this allows more detailed analysis than simply observing the proportion of correct classifications ( accuracy ). accuracy will yield misleading results if the data set is unbalanced ; that is, when the numbers of observations in different classes vary greatly. for example, if there were 95 cancer samples and only 5 non - cancer samples in the data, a particular classifier might classify all the observations as having cancer.


in structural typing, an element is considered to be compatible with another if, for each feature within the second element's type, a corresponding and identical feature exists in the first element's type. some languages may differ on the details, such as whether the features must match in name. this definition is not symmetric, and includes subtype compatibility. two types are considered to be identical if each is compatible with the other.


again in contrast to linear regression, there may be many local minima of the function to be optimized and even the global minimum may produce a biased estimate. in practice, estimated values of the parameters are used, in conjunction with the optimization algorithm, to attempt to find the global minimum of a sum of squares. for details concerning nonlinear data modeling see least squares and non - linear least squares.


in measure theory, given a measurable space ( x, σ ) { \ displaystyle ( x, \ sigma ) } and a signed measure μ { \ displaystyle \ mu } on it, a set a ∈ σ { \ displaystyle a \ in \ sigma } is called a positive set for μ { \ displaystyle \ mu } if every σ { \ displaystyle \ sigma } - measurable subset of a { \ displaystyle a } has nonnegative measure ; that is, for every e ⊆ a { \ displaystyle e \ subseteq a } that satisfies e ∈ σ, { \ displaystyle e \ in \ sigma, } μ ( e ) ≥ 0 { \ displaystyle \ mu ( e ) \ geq 0 } holds. similarly, a set a ∈ σ { \ displaystyle a \ in \ sigma } is called a negative set for μ { \ displaystyle \ mu } if for every subset e ⊆ a { \ displaystyle e \ subseteq a } satisfying e ∈ σ, { \ displaystyle e \ in \ sigma, } μ ( e ) ≤ 0 { \ displaystyle \ mu ( e ) \ leq 0 } holds. intuitively, a measurable set a { \ displaystyle a } is positive ( resp. negative ) for μ { \ displaystyle \ mu } if μ { \ displaystyle \ mu } is nonnegative ( resp.


in software testing, error guessing is a test method in which test cases used to find bugs in programs are established based on experience in prior testing. the scope of test cases usually rely on the software tester involved, who uses experience and intuition to determine what situations commonly cause software failure, or may cause errors to appear. typical errors include divide by zero, null pointers, or invalid parameters. error guessing has no explicit rules for testing ; test cases can be designed depending on the situation, either drawing from functional documents or when an unexpected / undocumented error is found while testing operations. = = references = =


in optimization, a gradient method is an algorithm to solve problems of the form min x ∈ r n f ( x ) { \ displaystyle \ min _ { x \ in \ mathbb { r } ^ { n } } \ ; f ( x ) } with the search directions defined by the gradient of the function at the current point. examples of gradient methods are the gradient descent and the conjugate gradient.


in robust statistics, repeated median regression, also known as the repeated median estimator, is a robust linear regression algorithm. the estimator has a breakdown point of 50 %. although it is equivariant under scaling, or under linear transformations of either its explanatory variable or its response variable, it is not under affine transformations that combine both variables. it can be calculated in o ( n 2 ) { \ displaystyle o ( n ^ { 2 } ) } time by brute force, in o ( n log 2 n ) { \ displaystyle o ( n \ log ^ { 2 } n ) } time using more sophisticated techniques, or in o ( n log n ) { \ displaystyle o ( n \ log n ) } randomized expected time. it may also be calculated using an on - line algorithm with o ( n ) { \ displaystyle o ( n ) } update time.


a number of false proofs and false counterexamples have appeared since the first statement of the four color theorem in 1852. the four color theorem was ultimately proven in 1976 by kenneth appel and wolfgang haken. it was the first major theorem to be proved using a computer.


in focused calculi, it is possible to define positive connectives by giving only their introduction rules, with the shape of the elimination rules being forced by this choice. ( symmetrically, negative connectives can be defined in focused calculi by giving only the elimination rules, with the introduction rules forced by this choice. ) the second view, which might be termed the computational or brouwer – heyting – kolmogorov interpretation of propositions, takes the view that we fix a computational system up front, and then give a realizability interpretation of propositions to give them constructive content.


the process is then iterated until it converges. this algorithm is a stripped - down version of the jacobi transformation method of matrix diagonalization. the method is named after carl gustav jacob jacobi.


next, kleene proceeds to present " turing's thesis ", where results are shown to be uncomputable, using his simplified derivation of a turing machine based on the work of emil post. both theses are proven equivalent by use of " theorem xxx ". thesis i. every effectively calculable function ( effectively decidable predicate ) is general recursive. theorem xxx : the following classes of partial functions are coextensive, i. e. have the same members : ( a ) the partial recursive functions, ( b ) the computable functions... turing's thesis : turing's thesis that every function which would naturally be regarded as computable is computable under his definition, i. e. by one of his machines, is equivalent to church's thesis by theorem xxx. kleene, finally, uses for the first time the term the " church - turing thesis " in a section in which he helps to give clarifications to concepts in alan turing's paper " the word problem in semi - groups with cancellation ", as demanded in a critique from william boone.


in the 2 - ary case, there can be zero or one identity elements : the empty set is a 2 - ary group, since the empty set is both a semigroup and a quasigroup, and every inhabited 2 - ary group is a group. in n - ary groups for n ≥ 3 there can be zero, one, or many identity elements. an n - ary groupoid ( g, f ) with f = ( x1 x2 xn ), where ( g, ) is a group is called reducible or derived from the group ( g, ). in 1928 dornte published the first main results : an n - ary groupoid which is reducible is an n - ary group, however for all n > 2 there exist inhabited n - ary groups which are not reducible.


in mathematical set theory, cantor's theorem is a fundamental result which states that, for any set a { \ displaystyle a }, the set of all subsets of a, { \ displaystyle a, } the power set of a, { \ displaystyle a, } has a strictly greater cardinality than a { \ displaystyle a } itself. for finite sets, cantor's theorem can be seen to be true by simple enumeration of the number of subsets. counting the empty set as a subset, a set with n { \ displaystyle n } elements has a total of 2 n { \ displaystyle 2 ^ { n } } subsets, and the theorem holds because 2 n > n { \ displaystyle 2 ^ { n } > n } for all non - negative integers. much more significant is cantor's discovery of an argument that is applicable to any set, and shows that the theorem holds for infinite sets also.


it follows that, as with lfsrs and linear complexity, any stream cipher whose n - adic complexity is low should not be used for cryptography. fcsrs and lfsrs are special cases of a very general algebraic construction of sequence generators called algebraic feedback shift registers ( afsrs ) in which the integers are replaced by an arbitrary ring r and n is replaced by an arbitrary non - unit in r. a general reference on the subject of lfsrs, fcsrs, and afsrs is the book. = = references = =


in the united states, the books were most popular as a5 - sized paperback volumes, and were usually between 150 and 200 pages long, divided into just under thirty chapters. the front covers featured images of the narrating animorph undergoing the various stages of one of the morphs from the story, with a few exceptions ( noted in each book's article ). behind the morphing character were images of clouds and skies, which became more colorful and elaborate as the series progressed. all the covers of the regular series books had a small cutout over part of the full morph's anatomy, revealing a computer - generated illustration on the first page, which was printed on glossy paper.


the concept of dimension is not restricted to physical objects. high - dimensional spaces frequently occur in mathematics and the sciences. they may be euclidean spaces or more general parameter spaces or configuration spaces such as in lagrangian or hamiltonian mechanics ; these are abstract spaces, independent of the physical space.


in message queueing a dead letter queue ( dlq ) is a service implementation to store messages that the messaging system cannot or should not deliver. although implementation - specific, messages can be routed to the dlq for the following reasons : the message is sent to a queue that does not exist. the maximum queue length is exceeded. the message exceeds the size limit.