therefore, there are o ( v ) saturating pushes on ( u, v ), and the total number of saturating pushes is at most 2 | v | | e |. this results in a time bound of o ( ve ) for the saturating push operations. bounding the number of nonsaturating pushes can be achieved via a potential argument.


in the united states, since 2010 the insurance institute for highway safety uses a scheme it has developed that takes into account a combination of both vehicle footprint ( length times width ) and weight. the united states national highway traffic safety administration ( nhtsa ) separates vehicles into classes by the curb weight of the vehicle with standard equipment including the maximum capacity of fuel, oil, coolant, and air conditioning, if so equipped. the united states federal highway administration has developed a classification scheme used for automatically calculating road use tolls. there are two broad categories depending on whether the vehicle carries passengers or commodities.


suppose further that the researcher wants to estimate a bivariate linear model via least squares : y i = β 0 + β 1 x 1 i + β 2 x 2 i + e i { \ displaystyle y _ { i } = \ beta _ { 0 } + \ beta _ { 1 } x _ { 1i } + \ beta _ { 2 } x _ { 2i } + e _ { i } }. if the researcher only has access to n = 2 { \ displaystyle n = 2 } data points, then they could find infinitely many combinations ( β ^ 0, β ^ 1, β ^ 2 ) { \ displaystyle ( { \ hat { \ beta } } _ { 0 }, { \ hat { \ beta } } _ { 1 }, { \ hat { \ beta } } _ { 2 } ) } that explain the data equally well : any combination can be chosen that satisfies y ^ i = β ^ 0 + β ^ 1 x 1 i + β ^ 2 x 2 i { \ displaystyle { \ hat { y } } _ { i } = { \ hat { \ beta } } _ { 0 } + { \ hat { \ beta } } _ { 1 } x _ { 1i } + { \ hat { \ beta } } _ { 2 } x _ { 2i } }, all of which lead to i e ^ i 2 = i ( y ^ i − ( β ^ 0 + β ^ 1 x 1 i + β ^ 2 x 2 i ) ) 2 = 0 { \ displaystyle \ sum _ { i } { \ hat { e } } _ { i } ^ { 2 } = \ sum _ { i } ( { \ hat { y } } _ { i } - ( { \ hat { \ beta } } _ { 0 } + { \ hat { \ beta } } _ { 1 } x _ { 1i } + { \ hat { \ beta } } _ { 2 } x _ { 2i } ) ) ^ { 2 } = 0 } and are therefore valid solutions that minimize the sum of squared residuals. to understand why there are infinitely many options, note that the system of n = 2 { \ displaystyle n = 2 } equations is to be solved for 3 unknowns, which makes the system underdetermined.


in mathematics, a euclidean plane is a euclidean space of dimension two, denoted e2. it is a geometric space in which two real numbers are required to determine the position of each point. it is an affine space, which includes in particular the concept of parallel lines. it has also metrical properties induced by a distance, which allows to define circles, and angle measurement. a euclidean plane with a chosen cartesian coordinate system is called a cartesian plane. the set r 2 { \ displaystyle \ mathbb { r } ^ { 2 } } of the pairs of real numbers ( the real coordinate plane ), equipped with the dot product, is often called the euclidean plane, since every euclidean plane is isomorphic to it.


some boolean operations, in particular do not have inverses that may be defined as functions. in particular the disjunction " or " has inverses that allow two values. in natural language " or " represents alternate possibilities.


if all elements in each sampled cluster are sampled, then this is referred to as a " one - stage " cluster sampling plan. if a simple random subsample of elements is selected within each of these groups, this is referred to as a " two - stage " cluster sampling plan. a common motivation for cluster sampling is to reduce the total number of interviews and costs given the desired accuracy. for a fixed sample size, the expected random error is smaller when most of the variation in the population is present internally within the groups, and not between the groups.


in stochastic gradient descent, feature scaling can sometimes improve the convergence speed of the algorithm. in support vector machines, it can reduce the time to find support vectors. note that feature scaling changes the svm result.


in software testing, test automation is the use of software separate from the software being tested to control the execution of tests and the comparison of actual outcomes with predicted outcomes. test automation can automate some repetitive but necessary tasks in a formalized testing process already in place, or perform additional testing that would be difficult to do manually. test automation is critical for continuous delivery and continuous testing.


it also debuted atop the us billboard top rock albums chart and was later ranked at number 62 on the chart's year - end version. elsewhere in north america, the album peaked at number 19 on the billboard canadian albums chart. in the asia - pacific region, notes on a conditional form reached the top of the australian albums chart, number four on the new zealand albums chart, number 14 on the billboard japan hot albums chart and number 17 on the japanese albums chart.


in the case of a private voip system, the primary telephony system itself is located within the private infrastructure of the end - user organization. usually, the system will be deployed on - premises at a site within the direct control of the organization. this can provide numerous benefits in terms of qos control ( see below ), cost scalability, and ensuring privacy and security of communications traffic. however, the responsibility for ensuring that the voip system remains performant and resilient is predominantly vested in the end - user organization.


in principle, it should be possible to optimize x86 code to favor code morphing software, or even for compilers to target the native vliw architecture directly. however, writing in 2003, linus torvalds apparently dismissed these approaches as unrealistic : the native crusoe code – even if it was documented and available – is not very conducive to general - purpose os stuff. it has no notion of memory protection, and there's no mmu for code accesses, so things like kernel modules simply wouldn't work. the translations are usually better than statically compiled native code ( because the whole cpu is designed for speculation, and the static compilers don't know how to do that ), and thus going to native mode is not necessarily a performance improvement.


for example, book, choice, or decide. the lowercase letters l, o, s, x and z are rotationally symmetrical, while pairs such as b / q, d / p, m / w, n / u, and in some typefaces h / y and a / e, are rotations of each other. thus, the words " sos ", " pod ", " suns ", " yeah ", " swims ", " dollop ", or " passed " form natural rotational ambigrams.


for high - dimensional problems, the exact computation of the hessian is usually prohibitively expensive, and even its storage can be problematic, requiring o ( n 2 ) { \ displaystyle o ( n ^ { 2 } ) } memory ( but see the limited - memory l - bfgs quasi - newton method ). the conjugate gradient method can also be derived using optimal control theory. in this accelerated optimization theory, the conjugate gradient method falls out as a nonlinear optimal feedback controller, u = k ( x, x ) : = − γ a ∇ x f ( x ) − γ b x { \ displaystyle u = k ( x, { \ dot { x } } ) : = - \ gamma _ { a } \ nabla _ { x } f ( x ) - \ gamma _ { b } { \ dot { x } } } for the double integrator system, x ¨ = u { \ displaystyle { \ ddot { x } } = u } the quantities γ a > 0 { \ displaystyle \ gamma _ { a } > 0 } and γ b > 0 { \ displaystyle \ gamma _ { b } > 0 } are variable feedback gains.


similarly, the trace of the matrix equals the sum of its eigenvalues. from this point of view, we can define the pseudo - determinant for a singular matrix to be the product of its nonzero eigenvalues ( the density of multivariate normal distribution will need this quantity ). in many applications, such as pagerank, one is interested in the dominant eigenvalue, i. e. that which is largest in absolute value. in other applications, the smallest eigenvalue is important, but in general, the whole spectrum provides valuable information about a matrix.


b1 generates a random bit b in a secure laboratory and gives it to a1 at a time t1. b0 and b1 communicate a { \ displaystyle a } and b through a secure and authenticated channel. similarly, a0 and a1 communicate a { \ displaystyle a } and b through a secure and authenticated channel.


in probability theory, a random recursive tree is a rooted tree chosen uniformly at random from the recursive trees with a given number of vertices.


see for more details on complex applications. metaheuristics fall in two categories : trajectory - based metaheuristics and population - based metaheuristics. the main difference of these two kind of methods relies in the number of tentative solutions used in each step of the ( iterative ) algorithm.


in orbital mechanics, a frozen orbit is an orbit for an artificial satellite in which natural drifting due to the central body's shape has been minimized by careful selection of the orbital parameters. typically, this is an orbit in which, over a long period of time, the satellite's altitude remains constant at the same point in each orbit. changes in the inclination, position of the apsis of the orbit, and eccentricity have been minimized by choosing initial values so that their perturbations cancel out., which results in a long - term stable orbit that minimizes the use of station - keeping propellant.


{ \ displaystyle | s |. } obviously | s | = δ ( c o u t ( m 1 ), c o u t ( m 2 ) ) ( 1 − r ) n { \ displaystyle | s | = \ delta ( c _ { out } ( m _ { 1 } ), c _ { out } ( m _ { 2 } ) ) \ geqslant ( 1 - r ) n }. due to the wozencraft ensemble theorem, there are at most ε n { \ displaystyle \ varepsilon n } linear codes having distance less than h q − 1 ( 1 2 − ε ) ⋅ 2 k, { \ displaystyle h _ { q } ^ { - 1 } ( { \ tfrac { 1 } { 2 } } - \ varepsilon ) \ cdot 2k, } so t | s | − ε n ( 1 − r ) n − ε n = ( 1 − r − ε ) n.


in regular grammars, the left hand side is again only a single nonterminal symbol, but now the right - hand side is also restricted. the right side may be the empty string, or a single terminal symbol, or a single terminal symbol followed by a nonterminal symbol, but nothing else. ( sometimes a broader definition is used : one can allow longer strings of terminals or single nonterminals without anything else, making languages easier to denote while still defining the same class of languages. ) the language { a n b n n ≥ 1 } { \ displaystyle \ left \ { a ^ { n } b ^ { n } \ mid n \ geq 1 \ right \ } } defined above is not regular, but the language { a n b m m, n ≥ 1 } { \ displaystyle \ left \ { a ^ { n } b ^ { m } \ mid m, n \ geq 1 \ right \ } } ( at least 1 a { \ displaystyle a } followed by at least 1 b { \ displaystyle b }, where the numbers may be different ) is, as it can be defined by the grammar g 3 { \ displaystyle g _ { 3 } } with n = { s, a, b } { \ displaystyle n = \ left \ { s, a, b \ right \ } }, σ = { a, b } { \ displaystyle \ sigma = \ left \ { a, b \ right \ } }, s { \ displaystyle s } the start symbol, and the following production rules : s → a a { \ displaystyle s \ rightarrow aa } a → a a { \ displaystyle a \ rightarrow aa } a → b b { \ displaystyle a \ rightarrow bb } b → b b { \ displaystyle b \ rightarrow bb } b → { \ displaystyle b \ rightarrow \ epsilon } all languages generated by a regular grammar can be recognized in o ( n ) { \ displaystyle o ( n ) } time by a finite - state machine. although in practice, regular grammars are commonly expressed using regular expressions, some forms of regular expression used in practice do not strictly generate the regular languages and do not show linear recognitional performance due to those deviations.


in mathematics, dickson's lemma states that every set of n { \ displaystyle n } - tuples of natural numbers has finitely many minimal elements. this simple fact from combinatorics has become attributed to the american algebraist l. e. dickson, who used it to prove a result in number theory about perfect numbers. however, the lemma was certainly known earlier, for example to paul gordan in his research on invariant theory.


furthermore, rectangles can exist ( a statement equivalent to the parallel postulate ) only in euclidean geometry. a saccheri quadrilateral is a quadrilateral which has two sides of equal length, both perpendicular to a side called the base. the other two angles of a saccheri quadrilateral are called the summit angles and they have equal measure.


in number theory, tijdeman's theorem states that there are at most a finite number of consecutive powers. stated another way, the set of solutions in integers x, y, n, m of the exponential diophantine equation y m = x n + 1, { \ displaystyle y ^ { m } = x ^ { n } + 1, } for exponents n and m greater than one, is finite.


in probability theory, a pitman – yor process denoted py ( d, θ, g0 ), is a stochastic process whose sample path is a probability distribution. a random sample from this process is an infinite discrete probability distribution, consisting of an infinite set of atoms drawn from g0, with weights drawn from a two - parameter poisson - dirichlet distribution. the process is named after jim pitman and marc yor.


sequential search models are used in the field of finance to examine how investors look for information on stocks and other financial assets. the assumption that consumers know what they are looking for and what the standard of the product or service should be is one of the limitations of sequential search models. this presumption might not always be accurate in practical circumstances. another drawback is that sequential search models don't account for the possibility that customers could find out more about the calibre of a good or service as they search further.


forwarding ( described below ) helps correct such errors by depending on the fact that the output of i1 ( which is 3 ) can be used by subsequent instructions before the value 3 is committed to / stored in register 1. forwarding applied to the example means that there is no wait to commit / store the output of i1 in register 1 ( in this example, the output is 3 ) before making that output available to the subsequent instruction ( in this case, i2 ).


he believed that scientific analysis would lead to the discovery of the " one best way " to do things or carrying out an operation. this, according to him could help save cost and time.


however, veblen's theorem applies also to disconnected graphs, and can be generalized to infinite graphs in which every vertex has finite degree ( sabidussi 1964 ). if a countably infinite graph g has no odd - degree vertices, then it may be written as a union of disjoint ( finite ) simple cycles if and only if every finite subgraph of g can be extended ( by including more edges and vertices from g ) to a finite eulerian graph. in particular, every countably infinite graph with only one end and with no odd vertices can be written as a union of disjoint cycles ( sabidussi 1964 ).


n j = i = 1 n ( q i = j ) { \ displaystyle n _ { j } = \ sum _ { i = 1 } ^ { n } ( q _ { i } = j ) } the total number of permutation of q → { \ displaystyle { \ vec { q } } } can be represented by a multinomial as n! j = 0 k n j! { \ displaystyle { \ frac { n!


ibm however developed their multiprocessor interrupt controller ( mpic ) based on the openpic register specification. in the reference ibm design, the processors share the mpic over a dcr bus, with their access to the bus controlled by a dcr arbiter. mpic supports up to four processors and up to 128 interrupt sources.


in pharmacology and biochemistry, mode of action ( moa ) describes a functional or anatomical change, resulting from the exposure of a living organism to a substance. in comparison, a mechanism of action ( moa ) describes such changes at the molecular level. a mode of action is important in classifying chemicals, as it represents an intermediate level of complexity in between molecular mechanisms and physiological outcomes, especially when the exact molecular target has not yet been elucidated or is subject to debate. a mechanism of action of a chemical could be " binding to dna " while its broader mode of action would be " transcriptional regulation ". however, there is no clear consensus and the term mode of action is also often used, especially in the study of pesticides, to describe molecular mechanisms such as action on specific nuclear receptors or enzymes.


in the academic field of films and cinema, several studies involving research have discovered a positive connection between film critics evaluating films and how well the films perform with audience members. also, studies involving research in the fields of films and cinema have discovered a connection between film critics evaluating films and audience members having interests or no interests in viewing those films. based in the perspective of an audience member, a review serves as more than an object that is useful for making decisions. listening to a review from a critic, watching a critic's review, and reading a critic's review are all ways in which the review is useful to an audience member. the critic's review is able to be referenced in conversations where audience members communicate with other individuals, and audience members can communicate messages about the artistic film that was critically examined or connect the criticism to problems that occur in society.


in real mode, the interrupt table is called ivt ( interrupt vector table ). up to the 80286, the ivt always resided at the same location in memory, ranging from 0x0000 to 0x03ff, and consisted of 256 far pointers. hardware interrupts may be mapped to any of the vectors by way of a programmable interrupt controller. on the 80286 and later, the size and locations of the ivt can be changed in the same way as it is done with the idt ( interrupt descriptor table ) in protected mode ( i. e., via the lidt ( load interrupt descriptor table register ) instruction ) though it does not change the format of it.


deterministic context - free grammars were particularly useful because they could be parsed sequentially by a deterministic pushdown automaton, which was a requirement due to computer memory constraints. in 1965, donald knuth invented the lr ( k ) parser and proved that there exists an lr ( k ) grammar for every deterministic context - free language. this parser still required a lot of memory.


in the japanese kantenji braille, the standard 8 - dot braille patterns 3568, 13568, 34568, and 134568 are the patterns related to braille pattern dots - 2456, since the two additional dots of kantenji patterns 02456, 24567, and 024567 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in the branch of linguistics known as pragmatics, a presupposition ( or psp ) is an implicit assumption about the world or background belief relating to an utterance whose truth is taken for granted in discourse. examples of presuppositions include : jane no longer writes fiction. presupposition : jane once wrote fiction. have you stopped eating meat?


in mathematics, the capacitated arc routing problem ( carp ) is that of finding the shortest tour with a minimum graph / travel distance of a mixed graph with undirected edges and directed arcs given capacity constraints for objects that move along the graph that represent snow - plowers, street sweeping machines, or winter gritters, or other real - world objects with capacity constraints. the constraint can be imposed for the length of time the vehicle is away from the central depot, or a total distance traveled, or a combination of the two with different weighting factors. there are many different variations of the carp described in the book arc routing : problems, methods, and applications by angel corberan and gilbert laporte. solving the carp involves the study of graph theory, arc routing, operations research, and geographical routing algorithms to find the shortest path efficiently. the carp is np - hard arc routing problem.


in the early 1990s, when desktop mapping and presentation graphics became accessible to the average office user, data2map hired software engineers and gis - specialists to develop several vector - map series for easy customization by the end user. the prime objective was to enable office users and professional graphics artists to visualize geo - referenced information on pre - designed country - and world - maps within their favorite standard off - the - shelf software.


these also may include full copies of the system images from which machines have their operating systems initially installed, or available for repair of any system files that may get corrupted during a machine's lifecycle. some software may require quite substantial storage space or might be undergoing rapid ( perhaps internal ) development. in those cases the software may be installed on, and configured to be run directly from, the file servers.


in mathematics, pythagorean addition is a binary operation on the real numbers that computes the length of the hypotenuse of a right triangle, given its two sides. according to the pythagorean theorem, for a triangle with sides a { \ displaystyle a } and b { \ displaystyle b }, this length can be calculated as where ⊕ { \ displaystyle \ oplus } denotes the pythagorean addition operation. this operation can be used in the conversion of cartesian coordinates to polar coordinates. it also provides a simple notation and terminology for some formulas when its summands are complicated ; for example, the energy - momentum relation in physics becomes it is implemented in many programming libraries as the hypot function, in a way designed to avoid errors arising due to limited - precision calculations performed on computers. in its applications to signal processing and propagation of measurement uncertainty, the same operation is also called addition in quadrature.


over time, less key travel was accepted in the market, finally landing on 0. 110 inches ( 2. 79 mm ). coincident with this, key tronic was the first company to introduce a keyboard that was only about one inch thick.


examples of their use are : in quantum teleportation, a classical channel together with a previously prepared entangled quantum state are used to transmit quantum information between two parties. neither the classical channel nor the previously prepared quantum state alone can do this task. in quantum cryptography, a classical channel is used along with a quantum channel in protocols for quantum key exchange. in quantum communication, the information rate of a noisy quantum channel can be increased when used together with a noise - free classical channel. in particular, some very noisy quantum channels cannot transmit quantum information if used alone but can transmit it if used together with a classical channel ( which is not capable of transmitting quantum information by itself ).


in number theory, an arithmetic number is an integer for which the average of its positive divisors is also an integer. for instance, 6 is an arithmetic number because the average of its divisors is 1 + 2 + 3 + 6 4 = 3, { \ displaystyle { \ frac { 1 + 2 + 3 + 6 } { 4 } } = 3, } which is also an integer. however, 2 is not an arithmetic number because its only divisors are 1 and 2, and their average 3 / 2 is not an integer. the first numbers in the sequence of arithmetic numbers are 1, 3, 5, 6, 7, 11, 13, 14, 15, 17, 19, 20, 21, 22, 23, 27, 29, 30, 31, 33, 35, 37, 38, 39, 41, 42, 43, 44, 45, 46, 47, 49,... ( sequence a003601 in the oeis ).


in older distributors, adjusting the ignition timing is usually achieved through both mechanical advance and vacuum advance. mechanical advance adjusts the timing based on the engine speed ( rpm ), using a set of hinged weights attached to the distributor shaft. these weights cause the breaker points mounting plate to slightly rotate, thereby advancing the ignition timing. vacuum advance typically uses manifold vacuum to adjust the ignition timing, for example to improve fuel economy and driveability when minimal power is required from the engine. most distributors used on electronic fuel injection engines use electronics to adjust the ignition timing, instead of vacuum and centrifugal systems. this allows the ignition timing to be optimised based on factors other than engine speed and manifold vacuum.


current views vary on whether all languages have a verb phrase ; some schools of generative grammar ( such as principles and parameters ) hold that all languages have a verb phrase, while others ( such as lexical functional grammar ) take the view that at least some languages lack a verb phrase constituent, including those languages with a very free word order ( the so - called non - configurational languages, such as japanese, hungarian, or australian aboriginal languages ), and some languages with a default vso order ( several celtic and oceanic languages ). phrase structure grammars view both finite and nonfinite verb phrases as constituent phrases and, consequently, do not draw any key distinction between them. dependency grammars ( described below ) are much different in this regard.


in metropolitan areas, foma uses the umts band i around 2100 mhz, which has been originally assigned to imt - 2000 services worldwide, except in the americas. in order to improve coverage in rural and mountainous areas, ntt docomo also offers foma services in the 800 mhz band originally assigned to the 2g pdc mova service, which corresponds to umts band vi and is similar to band v used in the united states. these extended service areas are branded foma plus - area ( fomaフラスエリア ) and require multiband terminals. = = references = =


to emphasize that there are an infinite number of terms, a series may be called an infinite series. such a series is represented ( or denoted ) by an expression like or, using the summation sign, the infinite sequence of additions implied by a series cannot be effectively carried on ( at least in a finite amount of time ). however, if the set to which the terms and their finite sums belong has a notion of limit, it is sometimes possible to assign a value to a series, called the sum of the series.


in kent's coin tossing protocol, alice has two agents a0 and a1, and bob has two agents b0 and b1. ai and bi are at location li, for i ∈ { 0, 1 } { \ displaystyle i \ in \ { 0, 1 \ } }.


network theory has applications in many disciplines, including statistical physics, particle physics, computer science, electrical engineering, biology, archaeology, linguistics, economics, finance, operations research, climatology, ecology, public health, sociology, psychology, and neuroscience. applications of network theory include logistical networks, the world wide web, internet, gene regulatory networks, metabolic networks, social networks, epistemological networks, etc. ; see list of network theory topics for more examples. euler's solution of the seven bridges of konigsberg problem is considered to be the first true proof in the theory of networks.


starting from the basic fact stated above that, for any positive integer n { \ displaystyle n }, b n { \ displaystyle b ^ { n } } is n { \ displaystyle n } occurrences of b { \ displaystyle b } all multiplied by each other, several other properties of exponentiation directly follow. in particular : in other words, when multiplying a base raised to one exponent by the same base raised to another exponent, the exponents add. from this basic rule that exponents add, we can derive that b 0 { \ displaystyle b ^ { 0 } } must be equal to 1 for any b = 0 { \ displaystyle b \ neq 0 }, as follows.


in star topology, every peripheral node ( computer workstation or any other peripheral ) is connected to a central node called a hub or switch. the hub is the server and the peripherals are the clients. the network does not necessarily have to resemble a star to be classified as a star network, but all of the peripheral nodes on the network must be connected to one central hub. all traffic that traverses the network passes through the central hub, which acts as a signal repeater.


under one definition, an undirected hypergraph ( x, e ) { \ displaystyle ( x, e ) } is a directed hypergraph which has a symmetric edge set : if ( d, c ) ∈ e { \ displaystyle ( d, c ) \ in e } then ( c, d ) ∈ e { \ displaystyle ( c, d ) \ in e }. for notational simplicity one can remove the " duplicate " hyperedges since the modifier " undirected " is precisely informing us that they exist : if ( d, c ) ∈ e { \ displaystyle ( d, c ) \ in e } then ( c, d ) ∈ → e { \ displaystyle ( c, d ) { \ vec { \ in } } e } where ∈ → { \ displaystyle { \ vec { \ in } } } means implicitly in. while graph edges connect only 2 nodes, hyperedges connect an arbitrary number of nodes.


in real - time computing, the priority ceiling protocol is a synchronization protocol for shared resources to avoid unbounded priority inversion and mutual deadlock due to wrong nesting of critical sections. in this protocol each resource is assigned a priority ceiling, which is a priority equal to the highest priority of any task which may lock the resource. the protocol works by temporarily raising the priorities of tasks in certain situations, thus it requires a scheduler that supports dynamic priority scheduling.


in multi - agent system research, distributed knowledge is all the knowledge that a community of agents possesses and might apply in solving a problem. distributed knowledge is approximately what " a wise man knows ", or what someone who has complete knowledge of what each member of the community knows knows. distributed knowledge might also be called the aggregate knowledge of a community, as it represents all the knowledge that a community might bring to bear to solve a problem.


in mathematical logic, various sublanguages of set theory are decidable. these include : sets with monotone, additive, and multiplicative functions. sets with restricted quantifiers. = = references = =


in order to define a specific proof of knowledge, one need not only define the language, but also the witnesses the verifier should know. in some cases proving membership in a language may be easy, while computing a specific witness may be hard. this is best explained using an example : let ⟨ g ⟩ { \ displaystyle \ langle g \ rangle } be a cyclic group with generator g { \ displaystyle g } in which solving the discrete logarithm problem is believed to be hard. deciding membership of the language l = { x g w = x } { \ displaystyle l = \ { x \ mid g ^ { w } = x \ } } is trivial, as every x { \ displaystyle x } is in ⟨ g ⟩ { \ displaystyle \ langle g \ rangle }. however, finding the witness w { \ displaystyle w } such that g w = x { \ displaystyle g ^ { w } = x } holds corresponds to solving the discrete logarithm problem.


in mathematics, specifically in order theory and functional analysis, the order dual of an ordered vector space x { \ displaystyle x } is the set pos ( x ∗ ) − pos ( x ∗ ) { \ displaystyle \ operatorname { pos } \ left ( x ^ { * } \ right ) - \ operatorname { pos } \ left ( x ^ { * } \ right ) } where pos ( x ∗ ) { \ displaystyle \ operatorname { pos } \ left ( x ^ { * } \ right ) } denotes the set of all positive linear functionals on x { \ displaystyle x }, where a linear function f { \ displaystyle f } on x { \ displaystyle x } is called positive if for all x ∈ x, { \ displaystyle x \ in x, } x ≥ 0 { \ displaystyle x \ geq 0 } implies f ( x ) ≥ 0. { \ displaystyle f ( x ) \ geq 0. } the order dual of x { \ displaystyle x } is denoted by x + { \ displaystyle x ^ { + } }. along with the related concept of the order bound dual, this space plays an important role in the theory of ordered topological vector spaces.


typically both transactions will be cancelled and rolled back, and then they will be started again in a different order, automatically, so that the deadlock doesn't occur again. or sometimes, just one of the deadlocked transactions will be cancelled, rolled back, and automatically restarted after a short delay. deadlocks can also occur among three or more transactions. the more transactions involved, the more difficult they are to detect, to the point that transaction processing systems find there is a practical limit to the deadlocks they can detect.


in statistics, the nemenyi test is a post - hoc test intended to find the groups of data that differ after a global statistical test ( such as the friedman test ) has rejected the null hypothesis that the performance of the comparisons on the groups of data is similar. the test makes pair - wise tests of performance. the test is named after peter nemenyi. the test is sometimes referred to as the " nemenyi – damico – wolfe test ", when regarding one - sided multiple comparisons of " treatments " versus " control ", but it can also be referred to as the " wilcoxon – nemenyi – mcdonald – thompson test ", when regarding two - sided multiple comparisons of " treatments " versus " treatments ".


to make the perfect and pluperfect tenses, the first consonant of the verb's root is usually repeated with the vowel ε ( e ), for example : γραφω, γεγραφα ( gegrapha ) " i write, i have written ", λυω, λελυκα ( luo, leluka ) " i free, i have freed ", διδασκω, δεδιδαχα ( didasko, dedidakha ) " i teach, i have taught " ( all present, perfect ). this is called " reduplication ". some verbs, however, where reduplication is not convenient, use an augment instead, e. g. εσχον, εσχηκα ( eskhon, eskheka ) " i had, i have had " ( aorist, perfect ), ευρισκω, ηυρηκα ( heurisko, heureka ) " i find, i have found " ( present, perfect ). this reduplication or perfect - tense augment appears in every part of the verb, not in the indicative only.


knuth himself attributes the first study of multisets to the indian mathematician bhaskaracharya, who described permutations of multisets around 1150. other names have been proposed or used for this concept, including list, bunch, bag, heap, sample, weighted set, collection, and suite. : 694


in the picture concepts task, children have presented with a series of pictures on two or three rows and asked which pictures ( one from each row ) belong together based on some common characteristic. this task assesses the child's ability to discover the underlying characteristic ( e. g., rule, concept, trend, class membership ) that governs a set of materials.


the kolmogorov – smirnov statistic quantifies a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two samples. the null distribution of this statistic is calculated under the null hypothesis that the sample is drawn from the reference distribution ( in the one - sample case ) or that the samples are drawn from the same distribution ( in the two - sample case ). in the one - sample case, the distribution considered under the null hypothesis may be continuous ( see section 2 ), purely discrete or mixed ( see section 2. 2 ).


in relational database management systems, a unique key is a candidate key. all the candidate keys of a relation can uniquely identify the records of the relation, but only one of them is used as the primary key of the relation. the remaining candidate keys are called unique keys because they can uniquely identify a record in a relation. unique keys can consist of multiple columns.


} } \ end { cases } } } euler's criterion can be concisely reformulated using the legendre symbol : ( a p ) ≡ a p − 1 2 ( mod p ). { \ displaystyle \ left ( { \ frac { a } { p } } \ right ) \ equiv a ^ { \ tfrac { p - 1 } { 2 } } { \ pmod { p } }. } the criterion first appeared in a 1748 paper by leonhard euler.


in straight line fitting, the model is y i = α + β x i + ε i { \ displaystyle y _ { i } = \ alpha + \ beta x _ { i } + \ varepsilon _ { i } \, } where y i { \ displaystyle y _ { i } } is the response variable, x i { \ displaystyle x _ { i } } is the explanatory variable, εi is the random error, and α { \ displaystyle \ alpha } and β { \ displaystyle \ beta } are parameters. the mean, and predicted, response value for a given explanatory value, xd, is given by y ^ d = α ^ + β ^ x d, { \ displaystyle { \ hat { y } } _ { d } = { \ hat { \ alpha } } + { \ hat { \ beta } } x _ { d }, } while the actual response would be y d = α + β x d + ε d { \ displaystyle y _ { d } = \ alpha + \ beta x _ { d } + \ varepsilon _ { d } \, } expressions for the values and variances of α ^ { \ displaystyle { \ hat { \ alpha } } } and β ^ { \ displaystyle { \ hat { \ beta } } } are given in linear regression.


within distributed morphology ( dm ), this is where morphological structure is constructed, where the hierarchical syntactic structure is transformed into a linearized structure, and syntactic features are replaced with vocabulary items, among other things. according to some theories of prosody, the prosodic representation is derived with direct reference to the hierarchical syntactic structure. for example, selkirk ( 2011, and others ) proposes that prosodic structure is constructed by a process of matching, although imperfectly, prosodic constituents to syntactic constituents. kahnemuyipour ( 2009 ) demonstrates, using evidence from several languages, how information structure can be represented in the transfer from syntax to phonology, arguing that transfer can only be uni - directional, from syntax to phonology.


{ \ displaystyle p _ { w } ( s ) = { \ frac { \ pi s } { 2 } } e ^ { - \ pi s ^ { 2 } / 4 }. } here, s = s d { \ displaystyle s = { \ frac { s } { d } } } where s is a particular spacing and d is the mean distance between neighboring intervals. in a mixed sequence ( spin and parity are different ), the probability density function can be obtained by randomly superimposing simple sequences. the above result is exact for 2 × 2 { \ displaystyle 2 \ times 2 } real symmetric matrices m { \ displaystyle m }, with elements that are independent standard gaussian random variables, with joint distribution proportional to e − 1 2 t r ( m 2 ) = e − 1 2 t r ( a b b c ) 2 = e − 1 2 a 2 − 1 2 c 2 − b 2. { \ displaystyle e ^ { - { \ frac { 1 } { 2 } } { \ rm { tr } } ( m ^ { 2 } ) } = e ^ { - { \ frac { 1 } { 2 } } { \ rm { tr } } \ left ( { \ begin { array } { cc } a & b \ \ b & c \ \ \ end { array } } \ right ) ^ { 2 } } = e ^ { - { \ frac { 1 } { 2 } } a ^ { 2 } - { \ frac { 1 } { 2 } } c ^ { 2 } - b ^ { 2 } }. }


in modified policy iteration ( van nunen 1976 ; puterman & shin 1978 ), step one is performed once, and then step two is repeated several times. then step one is again performed once and so on.


in the years 1994 to 2004 the elder 5 - ton van'vamors'was used to develop the capabilities needed for driving on networks of minor ( also unsealed ) roads and for cross - country driving including avoidance of negative obstacles like ditches. turning off onto crossroads of unknown width and intersection angles required a big effort, but has been achieved with " expectation - based, multi - focal, saccadic vision " ( ems - vision ). this vertebrate - type vision uses animation capabilities based on knowledge about subject classes ( including the autonomous vehicle itself ) and their potential behaviour in certain situations.


in quantitative linguistics, linguistic laws are statistical regularities emerging across different linguistic scales ( i. e. phonemes, syllables, words or sentences ) that can be formulated mathematically and that have been deduced from certain theoretical assumptions. they are also required to have been successfully tested through the use of data, that is, not to have been refuted by empirical evidence. among the main linguistic laws proposed by various authors, the following can be highlighted : zipf's law : the frequency of words is inversely proportional to their rank in frequency lists. similar distribution between rank and frequency of sounds, phonemes, and letters can be observed.


the numbers 3 { \ displaystyle { \ sqrt { 3 } } } and 2 3 { \ displaystyle 2 { \ sqrt { 3 } } } are also commensurable because their ratio, 3 2 3 = 1 2 { \ textstyle { \ frac { \ sqrt { 3 } } { 2 { \ sqrt { 3 } } } } = { \ frac { 1 } { 2 } } }, is a rational number. however, the numbers 3 { \ textstyle { \ sqrt { 3 } } } and 2 are incommensurable because their ratio, 3 2 { \ textstyle { \ frac { \ sqrt { 3 } } { 2 } } }, is an irrational number. more generally, it is immediate from the definition that if a and b are any two non - zero rational numbers, then a and b are commensurable ; it is also immediate that if a is any irrational number and b is any non - zero rational number, then a and b are incommensurable. on the other hand, if both a and b are irrational numbers, then a and b may or may not be commensurable.


information can be transmitted either during the given time interval, or encoded as the presence or absence of a change in the received signal. significant conditions are recognized by an appropriate device called a receiver, demodulator, or decoder. the decoder translates the actual signal received into its intended logical value such as a binary digit ( 0 or 1 ), an alphabetic character, a mark, or a space. each significant instant is determined when the appropriate device assumes a condition or state usable for performing a specific function, such as recording, processing, or gating.


in mathematics, in the branch of combinatorics, a graded poset is a partially - ordered set ( poset ) p equipped with a rank function ρ from p to the set n of all natural numbers. ρ must satisfy the following two properties : the rank function is compatible with the ordering, meaning that for all x and y in the order, if x < y then ρ ( x ) < ρ ( y ), and the rank is consistent with the covering relation of the ordering, meaning that for all x and y, if y covers x then ρ ( y ) = ρ ( x ) + 1. the value of the rank function for an element of the poset is called its rank. sometimes a graded poset is called a ranked poset but that phrase has other meanings ; see ranked poset. a rank or rank level of a graded poset is the subset of all the elements of the poset that have a given rank value. graded posets play an important role in combinatorics and can be visualized by means of a hasse diagram.


most variants of realizability begin with a theorem that any statement that is provable in the formal system being studied is realizable. the realizer, however, usually gives more information about the formula than a formal proof would directly provide. beyond giving insight into intuitionistic provability, realizability can be applied to prove the disjunction and existence properties for intuitionistic theories and to extract programs from proofs, as in proof mining. it is also related to topos theory via realizability topoi.


in mathematics and computing, the method of complements is a technique to encode a symmetric range of positive and negative integers in a way that they can use the same algorithm ( or mechanism ) for addition throughout the whole range. for a given number of places half of the possible representations of numbers encode the positive numbers, the other half represents their respective additive inverses. the pairs of mutually additive inverse numbers are called complements. thus subtraction of any number is implemented by adding its complement.


this means that the justification ensures that the belief is true. for example, richard kirkham argues that the justification required for knowledge must be based on self - evident premises that deductively entail the held belief.


in telecommunication, trellis modulation ( also known as trellis coded modulation, or simply tcm ) is a modulation scheme that transmits information with high efficiency over band - limited channels such as telephone lines. gottfried ungerboeck invented trellis modulation while working for ibm in the 1970s, and first described it in a conference paper in 1976. it went largely unnoticed, however, until he published a new, detailed exposition in 1982 that achieved sudden and widespread recognition. in the late 1980s, modems operating over plain old telephone service ( pots ) typically achieved 9. 6 kbit / s by employing four bits per symbol qam modulation at 2, 400 baud ( symbols / second ). this bit rate ceiling existed despite the best efforts of many researchers, and some engineers predicted that without a major upgrade of the public phone infrastructure, the maximum achievable rate for a pots modem might be 14 kbit / s for two - way communication ( 3, 429 baud × 4 bits / symbol, using qam ). 14 kbit / s is only 40 % of the theoretical maximum bit rate predicted by shannon's theorem for pots lines ( approximately 35 kbit / s ). ungerboeck's theories demonstrated that there was considerable untapped potential in the system, and by applying the concept to new modem standards, speed rapidly increased to 14. 4, 28. 8 and ultimately 33. 6 kbit / s.


indeed, a greedy algorithm finds the k - combination corresponding to n : take ck maximal with ( c k k ) ≤ n { \ displaystyle { \ tbinom { c _ { k } } { k } } \ leq n }, then take ck−1 maximal with ( c k − 1 k − 1 ) ≤ n − ( c k k ) { \ displaystyle { \ tbinom { c _ { k - 1 } } { k - 1 } } \ leq n - { \ tbinom { c _ { k } } { k } } }, and so forth. finding the number n, using the formula above, from the k - combination ( ck,..., c2, c1 ) is also known as " ranking ", and the opposite operation ( given by the greedy algorithm ) as " unranking " ; the operations are known by these names in most computer algebra systems, and in computational mathematics. the originally used term " combinatorial representation of integers " was shortened to " combinatorial number system " by knuth, who also gives a much older reference ; the term " combinadic " is introduced by james mccaffrey ( without reference to previous terminology or work ). unlike the factorial number system, the combinatorial number system of degree k is not a mixed radix system : the part ( c i i ) { \ displaystyle { \ tbinom { c _ { i } } { i } } } of the number n represented by a " digit " ci is not obtained from it by simply multiplying by a place value. the main application of the combinatorial number system is that it allows rapid computation of the k - combination that is at a given position in the lexicographic ordering, without having to explicitly list the k - combinations preceding it ; this allows for instance random generation of k - combinations of a given set. enumeration of k - combinations has many applications, among which are software testing, sampling, quality control, and the analysis of lottery games.


it waits for the child that slept 10 seconds first ; all the others have long since exited, so all of the messages ( except the first ) appear in quick succession. there is no possibility of random ordering here, since it is driven by a loop in a single process. the first parent message actually appeared before any of the children messages - the parent was able to continue into the second loop before any of the child processes were able to start.


in order to route calls to a phone, cell towers listen for a signal sent from the phone and negotiate which tower is best able to communicate with the phone. as the phone changes location, the antenna towers monitor the signal, and the phone is " roamed " to an adjacent tower as appropriate. by comparing the relative signal strength from multiple antenna towers, a general location of a phone can be roughly determined.


here α can be large. the following form of this inequality is often seen in more analytic contexts : with the same assumptions on f, for every p ∈ u there is a possibly smaller open neighborhood w of p and constants θ ∈ ( 0, 1 ) and c > 0 such that | f ( x ) − f ( p ) | θ ≤ c | ∇ f ( x ) |. { \ displaystyle | f ( x ) - f ( p ) | ^ { \ theta } \ leq c | \ nabla f ( x ) |. } a special case of the łojasiewicz inequality, due to polyak, is commonly used to prove linear convergence of gradient descent algorithms.


these ran utx - 32, gould's version of unix based on a bsd 4. 2 kernel developed by purdue university to support multiprocessor systems. the powernode 9080 was a symmetrical dual processor system, with both processors having full access to memory and the i / o bus, and capable of being booted up from either processor. it was the first such commercially available system to run any version of unix. the cpu for these system ballooned to about a dozen boards because of the low - density ecl chip footprint.


in the category of sets, injections, surjections, and bijections correspond precisely to monomorphisms, epimorphisms, and isomorphisms, respectively.


failure modes analysis is used to identify and order the impediments to reuse in a given organization. reusability metrics indicate the likelihood that an artifact is reusable. reuse library metrics are used to manage and track usage of a reuse repository.


in probability theory, the theory of large deviations concerns the asymptotic behaviour of remote tails of sequences of probability distributions. while some basic ideas of the theory can be traced to laplace, the formalization started with insurance mathematics, namely ruin theory with cramer and lundberg. a unified formalization of large deviation theory was developed in 1966, in a paper by varadhan. large deviations theory formalizes the heuristic ideas of concentration of measures and widely generalizes the notion of convergence of probability measures. roughly speaking, large deviations theory concerns itself with the exponential decline of the probability measures of certain kinds of extreme or tail events.


in the united states, the term " standard of review " has several different meanings in different contexts and thus there are several standards of review on appeal used in federal courts depending on the nature of the question being appealed and the body that made the decision.


in the area of mathematics called combinatorial group theory, the schreier coset graph is a graph associated with a group g, a generating set { xi : i in i } of g, and a subgroup h ≤ g. the schreier graph encodes the abstract structure of a group modulo an equivalence relation formed by the coset. the graph is named after otto schreier, who used the term “ nebengruppenbild ”. an equivalent definition was made in an early paper of todd and coxeter.


the maximum number of edges for an undirected graph is ( | v | 2 ) = | v | ( | v | − 1 ) 2 { \ displaystyle { \ binom { | v | } { 2 } } = { \ frac { | v | ( | v | - 1 ) } { 2 } } }, so the maximal density is 1 ( for complete graphs ) and the minimal density is 0 ( coleman & more 1983 ). for families of graphs of increasing size, one often calls them sparse if d → 0 { \ displaystyle d \ rightarrow 0 } as | v | → ∞ { \ displaystyle | v | \ rightarrow \ infty }. sometimes, in computer science, a more restrictive definition of sparse is used like | e | = o ( | v | log | v | ) { \ displaystyle | e | = o ( | v | \ log | v | ) } or even | e | = o ( | v | ) { \ displaystyle | e | = o ( | v | ) }.


( k − 1 )! ( k + ρ )!.


one may also regard the unit type as the type of 0 - tuples, i. e. the product of no types. the unit type is the terminal object in the category of types and typed functions. it should not be confused with the zero or bottom type, which allows no values and is the initial object in this category.


the univac 1004 was a plug - board programmed punched card data processing system, introduced in 1962 by univac. total memory was 961 characters ( 6 bits ) of core memory.


common notions such as injectivity and surjectivity can be expressed in a bounded fashion as well, and thus so is bijectivity. both of these tie in to notions of size. importantly, injection existence between any two sets provides a preorder.


it is a generalization and improvement of the minres method due to paige and saunders in 1975. the minres method requires that the matrix is symmetric, but has the advantage that it only requires handling of three vectors. gmres is a special case of the diis method developed by peter pulay in 1980. diis is applicable to non - linear systems.


{ \ displaystyle \ forall y \ in y, \ exists x \ in x { \ text { such that } } y = f ( x ). } the function is bijective ( one - to - one and onto, one - to - one correspondence, or invertible ) if each element of the codomain is mapped to by exactly one element of the domain. that is, the function is both injective and surjective.


this resulted in the move to use microkernels which used a minimal set of the operating system functions. systems such as mach at carnegie mellon university and chorusos at inria were examples of early microkernels. the separation of the operating system into separate components became necessary as supercomputers developed different types of nodes, e. g., compute nodes versus i / o nodes. thus modern supercomputers usually run different operating systems on different nodes, e. g., using a small and efficient lightweight kernel such as cnk or cnl on compute nodes, but a larger system such as a linux - derivative on server and i / o nodes.


the value of ψ ( n ) { \ displaystyle \ psi ( n ) } for the first few integers n { \ displaystyle n } is : 1, 3, 4, 6, 6, 12, 8, 12, 12, 18, 12, 24,... ( sequence a001615 in the oeis ). the function ψ ( n ) { \ displaystyle \ psi ( n ) } is greater than n { \ displaystyle n } for all n { \ displaystyle n } greater than 1, and is even for all n { \ displaystyle n } greater than 2. if n { \ displaystyle n } is a square - free number then ψ ( n ) = σ ( n ) { \ displaystyle \ psi ( n ) = \ sigma ( n ) }, where σ ( n ) { \ displaystyle \ sigma ( n ) } is the divisor function. the ψ { \ displaystyle \ psi } function can also be defined by setting ψ ( p n ) = ( p + 1 ) p n − 1 { \ displaystyle \ psi ( p ^ { n } ) = ( p + 1 ) p ^ { n - 1 } } for powers of any prime p { \ displaystyle p }, and then extending the definition to all integers by multiplicativity.


in the following two examples, we always assume it is difficult to factorize a large composite number ( see integer factorization ).


researchers have begun to use deep learning techniques for language modeling as well. in the long history of speech recognition, both shallow form and deep form ( e. g. recurrent nets ) of artificial neural networks had been explored for many years during 1980s, 1990s and a few years into the 2000s. but these methods never won over the non - uniform internal - handcrafting gaussian mixture model / hidden markov model ( gmm - hmm ) technology based on generative models of speech trained discriminatively.


eve first captures the photon sent by alice and then generates another photon to send to bob. eve manipulates the phase and timing of the " faked " photon in a way that prevents bob from detecting the presence of an eavesdropper. the only way to eliminate this vulnerability is to eliminate differences in photodetector efficiency, which is difficult to do given finite manufacturing tolerances that cause optical path length differences, wire length differences, and other defects.


in the united states there is a rule that wrong - side failures are to be reported to the federal railroad administration.


double negation elimination occurs in classical logics but not in intuitionistic logic. in the context of a formula in the conjunctive normal form, a literal is pure if the literal's complement does not appear in the formula. in boolean functions, each separate occurrence of a variable, either in inverse or uncomplemented form, is a literal. for example, if a { \ displaystyle a }, b { \ displaystyle b } and c { \ displaystyle c } are variables then the expression a b c { \ displaystyle { \ bar { a } } bc } contains three literals and the expression a c + b c { \ displaystyle { \ bar { a } } c + { \ bar { b } } { \ bar { c } } } contains four literals. however, the expression a c + b c { \ displaystyle { \ bar { a } } c + { \ bar { b } } c } would also be said to contain four literals, because although two of the literals are identical ( c { \ displaystyle c } appears twice ) these qualify as two separate occurrences.


this value indicates the mapping of the two items. zero values indicate that no relationship exists. it must be determined if a relationship must be made.


in more general sense, each column is treated as a polynomial over gf ( 2 8 ) { \ displaystyle \ operatorname { gf } ( 2 ^ { 8 } ) } and is then multiplied modulo 01 16 ⋅ z 4 + 01 16 { \ displaystyle { 01 } _ { 16 } \ cdot z ^ { 4 } + { 01 } _ { 16 } } with a fixed polynomial c ( z ) = 03 16 ⋅ z 3 + 01 16 ⋅ z 2 + 01 16 ⋅ z + 02 16 { \ displaystyle c ( z ) = { 03 } _ { 16 } \ cdot z ^ { 3 } + { 01 } _ { 16 } \ cdot z ^ { 2 } + { 01 } _ { 16 } \ cdot z + { 02 } _ { 16 } }. the coefficients are displayed in their hexadecimal equivalent of the binary representation of bit polynomials from gf ( 2 ) { \ displaystyle \ operatorname { gf } ( 2 ) }. the mixcolumns step can also be viewed as a multiplication by the shown particular mds matrix in the finite field gf ( 2 8 ) { \ displaystyle \ operatorname { gf } ( 2 ^ { 8 } ) }. this process is described further in the article rijndael mixcolumns.


two mappings are homotopic if one can be continuously deformed into the other. these homotopy classes form a group, called the n - th homotopy group, π n ( x ), { \ displaystyle \ pi _ { n } ( x ), } of the given space x with base point. topological spaces with differing homotopy groups are never equivalent ( homeomorphic ), but topological spaces that are not homeomorphic can have the same homotopy groups. the notion of homotopy of paths was introduced by camille jordan.


this is typically subject to constraints such as : a variable must be initialized before its value is used. in strongly typed languages, each variable is assigned a type, and all uses of the variable must respect its type. often, its type must be declared explicitly, before use. w - grammars are based on the idea of providing the nonterminal symbols of context - free grammars with attributes ( or affixes ) that pass information between the nodes of the parse tree, used to constrain the syntax and to specify the semantics.


in statistics a minimum - variance unbiased estimator ( mvue ) or uniformly minimum - variance unbiased estimator ( umvue ) is an unbiased estimator that has lower variance than any other unbiased estimator for all possible values of the parameter. for practical statistics problems, it is important to determine the mvue if one exists, since less - than - optimal procedures would naturally be avoided, other things being equal. this has led to substantial development of statistical theory related to the problem of optimal estimation. while combining the constraint of unbiasedness with the desirability metric of least variance leads to good results in most practical settings — making mvue a natural starting point for a broad range of analyses — a targeted specification may perform better for a given problem ; thus, mvue is not always the best stopping point.


in pure integer programming problems, the feasible set is the set of integers ( or some subset thereof ). in linear programming problems, the feasible set is a convex polytope : a region in multidimensional space whose boundaries are formed by hyperplanes and whose corners are vertices. constraint satisfaction is the process of finding a point in the feasible region.


as of february 2020, the smallest 23 of the 54 listed numbers have been factored. while the rsa challenge officially ended in 2007, people are still attempting to find the factorizations. according to rsa laboratories, " now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric - key and public - key algorithms, these challenges are no longer active. "


however, type inference is undecidable. a logic is represented in the lf logical framework by the judgements - as - types representation mechanism. this is inspired by per martin - lof's development of kant's notion of judgement, in the 1983 siena lectures.


a simple algorithm with logarithmic regret is proposed in : ucb - alp algorithm : the framework of ucb - alp is shown in the right figure. ucb - alp is a simple algorithm that combines the ucb method with an adaptive linear programming ( alp ) algorithm, and can be easily deployed in practical systems. it is the first work that show how to achieve logarithmic regret in constrained contextual bandits. although is devoted to a special case with single budget constraint and fixed cost, the results shed light on the design and analysis of algorithms for more general ccb problems.


in metadata, naming and design rules are the formal rules associated with how data elements are structured within a process of creating exchange documents between organizations. naming and design rules are a set of guidelines and naming conventions that go beyond what a single data exchange standard specification will permit. the most common standard that naming and design rules are created on is xml schema.


. both these two groups and the dihedral group are semidirect products of a cyclic group of order 2n−1 with a cyclic group of order 2. such a non - abelian semidirect product is uniquely determined by an element of order 2 in the group of units of the ring z / 2 n − 1 z { \ displaystyle \ mathbb { z } / 2 ^ { n - 1 } \ mathbb { z } } and there are precisely three such elements, 2 n − 1 − 1 { \ displaystyle 2 ^ { n - 1 } - 1 }, 2 n − 2 − 1 { \ displaystyle 2 ^ { n - 2 } - 1 }, and 2 n − 2 + 1 { \ displaystyle 2 ^ { n - 2 } + 1 }, corresponding to the dihedral group, the quasidihedral, and the modular maximal - cyclic group. the generalized quaternion group, the dihedral group, and the quasidihedral group of order 2n all have nilpotency class n − 1, and are the only isomorphism classes of groups of order 2n with nilpotency class n − 1.


because of this need for the traditional channel, the speed of teleportation can be no faster than the speed of light ( hence the no - communication theorem is not violated ). the main advantage with this is that bell states can be shared using photons from lasers making teleportation achievable through open space having no need to send information through physical cables or optical fibers. quantum states can be encoded in various degrees of freedom of atoms.


in mathematics, the trace field of a linear group is the field generated by the traces of its elements. it is mostly studied for kleinian and fuchsian groups, though related objects are used in the theory of lattices in lie groups, often under the name field of definition.


for instance, voice and video services that are provided using internet protocol technology may be classified as “ information services ” and therefore not subject to traditional voice or video regulation. the distinction in the 1996 act between telecommunications services and information services was an outgrowth of a series of fcc orders and decisions dating back to the 1970s that distinguished between “ basic ” services that were subject to regulation and “ enhanced ” services that the commission chose not to regulate in order to foster their development and deployment. the act places on all telecommunications services providers the duty to interconnect “... directly or indirectly with the facilities and equipment of other telecommunications carriers... ” keeping with this regulatory history, the commission has chosen to forbear from regulating information services, again seeking to foster their development and deployment.


the resulting instance will inherit all the methods and properties that were defined in the class, which acts as a kind of template from which similarly typed objects can be constructed. systems that support ex nihilo object creation allow new objects to be created from scratch without cloning from an existing prototype. such systems provide a special syntax for specifying the properties and behaviors of new objects without referencing existing objects.


in mathematics and social science, a collaboration graph is a graph modeling some social network where the vertices represent participants of that network ( usually individual people ) and where two distinct participants are joined by an edge whenever there is a collaborative relationship between them of a particular kind. collaboration graphs are used to measure the closeness of collaborative relationships between the participants of the network.


in probability theory, the brownian tree, or aldous tree, or continuum random tree ( crt ) is a random real tree that can be defined from a brownian excursion. the brownian tree was defined and studied by david aldous in three articles published in 1991 and 1993. this tree has since then been generalized.


in the computer industry, the inverted text usually displays a selected block of text, the current menu item. many older people have a slight, comfortable astigmatism. at the high resolution of modern computer screens, they better see black letters on white background rather than vice versa. therefore, long reversed texts are rare. the reversing is widely used in the various equipment design ( from television remotes to dump trucks ) : a half - erased button or plate remains readable.


in mathematics, an aliquot sequence is a sequence of positive integers in which each term is the sum of the proper divisors of the previous term. if the sequence reaches the number 1, it ends, since the sum of the proper divisors of 1 is 0.


in this regard, some theorists have argued that the additional component would have to ensure that the belief is true. this approach is reflected in the idea that knowledge implies a form of certainty. but it sets the standards of knowledge very high and may require that a belief has to be infallible to amount to knowledge.


in mathematics, computer science and digital electronics, a dependency graph is a directed graph representing dependencies of several objects towards each other. it is possible to derive an evaluation order or the absence of an evaluation order that respects the given dependencies from the dependency graph.


job j { \ displaystyle j } takes time p j { \ displaystyle p _ { j } } on any machine it is scheduled to. q : uniform - machines scheduling. there are m { \ displaystyle m } parallel machines, and they have different given speeds.


much of our day - to - day lives are significantly influenced by digital data and this would not be possible without shannon - fano coding and the ongoing evolution of its methods. in shannon coding, the symbols are arranged in order from most probable to least probable, and assigned codewords by taking the first l i = − log 2 p i { \ displaystyle l _ { i } = \ left \ lceil - \ log _ { 2 } p _ { i } \ right \ rceil } bits from the binary expansions of the cumulative probabilities k = 1 i − 1 p k. { \ displaystyle \ sum \ limits _ { k = 1 } ^ { i - 1 } p _ { k }. } here x { \ displaystyle \ lceil x \ rceil } denotes the ceiling function ( which rounds x { \ displaystyle x } up to the next integer value ).


in the context of fluorescence microscopy, the probability of measuring a set of number of photons ( or digitalization counts proportional to detected light ) m = { \ displaystyle \ mathbf { m } = } for expected values e = { \ displaystyle \ mathbf { e } = } for a detector with k + 1 { \ displaystyle k + 1 } pixels is given by p ( m | e ) = i k p o i s s o n ( e i ) = i k e i m i e − e i m i! { \ displaystyle p ( \ mathbf { m } \ vert \ mathbf { e } ) = \ prod _ { i } ^ { k } \ mathrm { poisson } ( e _ { i } ) = \ prod _ { i } ^ { k } { \ frac { { e _ { i } } ^ { m _ { i } } e ^ { - e _ { i } } } { m _ { i }! } } } it is convenient to work with ln ( p ) { \ displaystyle \ ln ( p ) } since in the context of maximum likelihood estimation we want to find the position of the maximum of the likelihood function and we are not interested in its absolute value. ln ( p ( m | e ) ) = i k { \ displaystyle \ ln ( p ( m \ vert e ) ) = \ sum _ { i } ^ { k } \ left } again since ln ( m i! )


in mathematics and computer science, a history monoid is a way of representing the histories of concurrently running computer processes as a collection of strings, each string representing the individual history of a process. the history monoid provides a set of synchronization primitives ( such as locks, mutexes or thread joins ) for providing rendezvous points between a set of independently executing processes or threads. history monoids occur in the theory of concurrent computation, and provide a low - level mathematical foundation for process calculi, such as csp the language of communicating sequential processes, or ccs, the calculus of communicating systems.


it may give detailed instructions to each participant about how to test, and how to record bugs found. in some organizations, a bug - bashing session is followed by a party and a prize to the person who finds the worst bug, and / or the person who finds the greatest total of bugs. bug bash is a collaboration event, the step - by - step procedure has been given in the article'bug bash — a collaboration episode '.


superscalar cpus use hardware to decide which operations can run in parallel at runtime, while vliw cpus use software ( the compiler ) to decide which operations can run in parallel in advance. because the complexity of instruction scheduling is moved into the compiler, complexity of hardware can be reduced substantially. a similar problem occurs when the result of a parallelizable instruction is used as input for a branch. most modern cpus guess which branch will be taken even before the calculation is complete, so that they can load the instructions for the branch, or ( in some architectures ) even start to compute them speculatively.


this final form is unique ; in other words, it is independent of the sequence of row operations used. for example, in the following sequence of row operations ( where two elementary operations on different rows are done at the first and third steps ), the third and fourth matrices are the ones in row echelon form, and the final matrix is the unique reduced row echelon form. → → → { \ displaystyle { \ begin { bmatrix } 1 & 3 & 1 & 9 \ \ 1 & 1 & - 1 & 1 \ \ 3 & 11 & 5 & 35 \ end { bmatrix } } \ to { \ begin { bmatrix } 1 & 3 & 1 & 9 \ \ 0 & - 2 & - 2 & - 8 \ \ 0 & 2 & 2 & 8 \ end { bmatrix } } \ to { \ begin { bmatrix } 1 & 3 & 1 & 9 \ \ 0 & - 2 & - 2 & - 8 \ \ 0 & 0 & 0 & 0 \ end { bmatrix } } \ to { \ begin { bmatrix } 1 & 0 & - 2 & - 3 \ \ 0 & 1 & 1 & 4 \ \ 0 & 0 & 0 & 0 \ end { bmatrix } } } using row operations to convert a matrix into reduced row echelon form is sometimes called gauss – jordan elimination. in this case, the term gaussian elimination refers to the process until it has reached its upper triangular, or ( unreduced ) row echelon form. for computational reasons, when solving systems of linear equations, it is sometimes preferable to stop row operations before the matrix is completely reduced.


main memory was also moved to an ecl implementation and the machine was equipped with a whopping - for - the - times 256k - words ( 2 megabytes ) standard. the design spread the memory across 64 banks for fast access at about 8 ns / word, even though the cycle time of any one bank was about 250 ns. a high - speed core memory with a 20 ns access ( overall ) was also designed as a backup to the semiconductor memory.


by reversing the steps or using the extended euclidean algorithm, the gcd can be expressed as a linear combination of the two original numbers, that is the sum of the two numbers, each multiplied by an integer ( for example, 21 = 5 × 105 + ( −2 ) × 252 ). the fact that the gcd can always be expressed in this way is known as bezout's identity. the version of the euclidean algorithm described above ( and by euclid ) can take many subtraction steps to find the gcd when one of the given numbers is much bigger than the other.


they needed to know a network of people so that when the time comes for marriage, they were able to seek the services of the match - makers. finally, when someone came to the match - maker, she must be able to pick out a matching suitors according to her knowledge of the local residents. normally a perfect couple must have similar social status, economic status, and age.


in the 1970s, michael d. plummer and laszlo lovasz conjectured that every bridgeless cubic graph has an exponential number of perfect matchings, strengthening petersen's theorem that at least one perfect matching exists. in a pair of papers with different sets of co - authors, kral was able to show that this conjecture is true.


alice determines which operation to perform accordingly to the pair of bits she wants to transmit. she then sends bob the qubit state evolved through the chosen gate. said qubit thus encodes information about the two bits alice used to select the operation, and this information can be retrieved by bob thanks to pre - shared entanglement between them.


in mathematics, a sequence is an enumerated collection of objects in which repetitions are allowed and order matters. like a set, it contains members ( also called elements, or terms ). the number of elements ( possibly infinite ) is called the length of the sequence. unlike a set, the same elements can appear multiple times at different positions in a sequence, and unlike a set, the order does matter.


in multilinear algebra, a tensor decomposition is any scheme for expressing a " data tensor " ( m - way array ) as a sequence of elementary operations acting on other, often simpler tensors. many tensor decompositions generalize some matrix decompositions. tensors are generalizations of matrices to higher dimensions ( or rather to higher orders, i. e. the higher number of dimensions ) and can consequently be treated as multidimensional fields. the main tensor decompositions are : tensor rank decomposition ; higher - order singular value decomposition ; tucker decomposition ; matrix product states, and operators or tensor trains ; online tensor decompositions hierarchical tucker decomposition ; block term decomposition


the chinese remainder theorem is widely used for computing with large integers, as it allows replacing a computation for which one knows a bound on the size of the result by several similar computations on small integers. the chinese remainder theorem ( expressed in terms of congruences ) is true over every principal ideal domain. it has been generalized to any ring, with a formulation involving two - sided ideals.


in mathematics, a regular polytope is a polytope whose symmetry group acts transitively on its flags, thus giving it the highest degree of symmetry. all its elements or j - faces ( for all 0 ≤ j ≤ n, where n is the dimension of the polytope ) — cells, faces and so on — are also transitive on the symmetries of the polytope, and are regular polytopes of dimension ≤ n. regular polytopes are the generalized analog in any number of dimensions of regular polygons ( for example, the square or the regular pentagon ) and regular polyhedra ( for example, the cube ). the strong symmetry of the regular polytopes gives them an aesthetic quality that interests both non - mathematicians and mathematicians. classically, a regular polytope in n dimensions may be defined as having regular facets ( - faces ) and regular vertex figures.


in the application of the section 3 of the 1952 act to scotland it means any of the following offences : theft, housebreaking with intent to steal, opening lockfast places with intent to steal, reset, plagium, breach of trust and embezzlement, falsehood, fraud and wilful imposition, threats to extort money or with intent to extort money, and malicious mischief any offence under section 28 of the road traffic act 1930 any of the following offences in connection with such an attack as is mentioned in section 1 ( 1 ) ( b ) of the internationally protected persons act 1978 : an offence of wilful fireraising an offence under section 2 of the explosive substances act 1883 of causing an explosion likely to cause serious injury to property an offence under section 2 of the nuclear material ( offences ) act 1983, where the circumstances are that either, in the case of a contravention of subsection ( 2 ), the act falling within paragraph ( a ) or ( b ) of that subsection would, had it been done, have constituted an offence falling within sub - paragraph ( a ) or ( b ) of this paragraph, or, in the case of a contravention of subsection ( 3 ) or ( 4 ), the act threatened would, had it been done, have constituted such an offence any of the following offences in connection with such an attack as is mentioned in section 2 ( 1 ) of the united nations personnel act 1997 an offence of wilful fireraising an offence under section 2 of the explosive substances act 1883 of causing an explosion likely to cause serious injury to property


the unintended consequences of sharing can be complex to analyze and should not necessarily be left to the discretion of users who may have a narrow focus on their own critical need. these documents provide standards guidance on risk management : " recommended security controls for federal information systems & organizations ".


another notation for the sign of a permutation is given by the more general levi - civita symbol ( εσ ), which is defined for all maps from x to x, and has value zero for non - bijective maps. the sign of a permutation can be explicitly expressed as sgn ( σ ) = ( −1 ) n ( σ ) where n ( σ ) is the number of inversions in σ. alternatively, the sign of a permutation σ can be defined from its decomposition into the product of transpositions as sgn ( σ ) = ( −1 ) mwhere m is the number of transpositions in the decomposition. although such a decomposition is not unique, the parity of the number of transpositions in all decompositions is the same, implying that the sign of a permutation is well - defined.


in the " twitter revolution ", the relationship between the new media and social movement has three distinct characteristics : 1 ) the twitter streams represent the interaction mechanism of ecological network 2 ) the twitter streams embedding or be embedded into different types of control process ; 3 ) the twitter streams reflect the change of social movement ecology.


{ \ displaystyle a - ( b \ cap c ) = ( a - b ) \ cup ( a - c ). } applications of the rules include simplification of logical expressions in computer programs and digital circuit designs. de morgan's laws are an example of a more general concept of mathematical duality.


in mathematics, the fekete problem is, given a natural number n and a real s ≥ 0, to find the points x1,..., xn on the 2 - sphere for which the s - energy, defined by 1 ≤ i < j ≤ n ‖ x i − x j ‖ − s { \ displaystyle \ sum _ { 1 \ leq i 0 and by 1 ≤ i < j ≤ n log ‖ x i − x j ‖ − 1 { \ displaystyle \ sum _ { 1 \ leq i 0, such points are called s - fekete points, and for s = 0, logarithmic fekete points ( see saff & kuijlaars ( 1997 ) ). more generally, one can consider the same problem on the d - dimensional sphere, or on a riemannian manifold ( in which case | | xi −xj | | is replaced with the riemannian distance between xi and xj ). the problem originated in the paper by michael fekete ( 1923 ) who considered the one - dimensional, s = 0 case, answering a question of issai schur. an algorithmic version of the fekete problem is number 7 on the list of problems discussed by smale ( 1998 ).


in mathematical analysis, ekeland's variational principle, discovered by ivar ekeland, is a theorem that asserts that there exist nearly optimal solutions to some optimization problems. ekeland's principle can be used when the lower level set of a minimization problems is not compact, so that the bolzano – weierstrass theorem cannot be applied. the principle relies on the completeness of the metric space. the principle has been shown to be equivalent to completeness of metric spaces. in proof theory, it is equivalent to π11ca0 over rca0, i. e. relatively strong. it also leads to a quick proof of the caristi fixed point theorem.


in the japanese kantenji braille, the standard 8 - dot braille patterns 237, 1237, 2347, and 12347 are the patterns related to braille pattern dots - 123, since the two additional dots of kantenji patterns 0123, 1237, and 01237 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in mathematics, logic, and computer science, a type theory is the formal presentation of a specific type system, and in general, type theory is the academic study of type systems. some type theories serve as alternatives to set theory as a foundation of mathematics. two influential type theories that were proposed as foundations are alonzo church's typed λ - calculus and per martin - lof's intuitionistic type theory. most computerized proof - writing systems use a type theory for their foundation, a common one is thierry coquand's calculus of inductive constructions.


once an agreement is reached, the partnership is typically enforceable by civil law, especially if well documented. partners who wish to make their agreement affirmatively explicit and enforceable typically draw up articles of partnership. trust and pragmatism are also essential as it cannot be expected that everything can be written in the initial partnership agreement, therefore quality governance and clear communication are critical success factors in the long run. it is common for information about formally partnered entities to be made public, such as through a press release, a newspaper ad, or public records laws.


in the area of mathematics known as ramsey theory, a ramsey class is one which satisfies a generalization of ramsey's theorem. suppose a { \ displaystyle a }, b { \ displaystyle b } and c { \ displaystyle c } are structures and k { \ displaystyle k } is a positive integer. we denote by ( b a ) { \ displaystyle { \ binom { b } { a } } } the set of all subobjects a ′ { \ displaystyle a'} of b { \ displaystyle b } which are isomorphic to a { \ displaystyle a }. we further denote by c → ( b ) k a { \ displaystyle c \ rightarrow ( b ) _ { k } ^ { a } } the property that for all partitions x 1 ∪ x 2 ∪ ∪ x k { \ displaystyle x _ { 1 } \ cup x _ { 2 } \ cup \ dots \ cup x _ { k } } of ( c a ) { \ displaystyle { \ binom { c } { a } } } there exists a b ′ ∈ ( c b ) { \ displaystyle b'\ in { \ binom { c } { b } } } and an 1 ≤ i ≤ k { \ displaystyle 1 \ leq i \ leq k } such that ( b ′ a ) ⊆ x i { \ displaystyle { \ binom { b'} { a } } \ subseteq x _ { i } }.


the principle of the number field sieve ( both special and general ) can be understood as an improvement to the simpler rational sieve or quadratic sieve. when using such algorithms to factor a large number n, it is necessary to search for smooth numbers ( i. e. numbers with small prime factors ) of order n1 / 2. the size of these values is exponential in the size of n ( see below ).


in network theory, multidimensional networks, a special type of multilayer network, are networks with multiple kinds of relations. increasingly sophisticated attempts to model real - world systems as multidimensional networks have yielded valuable insight in the fields of social network analysis, economics, urban and international transport, ecology, psychology, medicine, biology, commerce, climatology, physics, computational neuroscience, operations management, and finance.


a simple application of functional dependencies is heath's theorem ; it says that a relation r over an attribute set u and satisfying a functional dependency x → y can be safely split in two relations having the lossless - join decomposition property, namely into π x y ( r ) π x z ( r ) = r { \ displaystyle \ pi _ { xy } ( r ) \ bowtie \ pi _ { xz } ( r ) = r } where z = u − xy are the rest of the attributes. ( unions of attribute sets are customarily denoted by there juxtapositions in database theory. ) an important notion in this context is a candidate key, defined as a minimal set of attributes that functionally determine all of the attributes in a relation.


if the set has n elements, the number of k - combinations, denoted by c ( n, k ) { \ displaystyle c ( n, k ) } or c k n { \ displaystyle c _ { k } ^ { n } }, is equal to the binomial coefficient which can be written using factorials as n! k! ( n − k )!


in mathematics, a matrix is a rectangular array of numbers or other data. in physics, a matrix model is a particular kind of physical theory whose mathematical formulation involves the notion of a matrix in an important way. a matrix model describes the behavior of a set of matrices within the framework of quantum mechanics. one important example of a matrix model is the bfss matrix model proposed by tom banks, willy fischler, stephen shenker, and leonard susskind in 1997. this theory describes the behavior of a set of nine large matrices.


however, in a few limited instances, a healthcare worker can share personal information without consent if it is in the public interest. these instances are set out in guidance from the general medical council, which is the regulatory body for doctors. sometimes the healthcare worker has to provide the information – if required by law or in response to a court order. the national aids trust has written a guide for people living with hiv to confidentiality in the nhs.


in processing the recall, a health hazard assessment will be conducted by the fda to determine the recall class ( defined above ). level, notification, instructions, mechanics, impacts on economy, and individual consumer must all be considered in determining recall strategy. level of recall refers to which part of the distribution chain to which the recall is extended ( wholesale, retail, pharmacy, medical user, etc. ). notification is the way consumers are alerted to the recall.


in mathematics, an alternating sign matrix is a square matrix of 0s, 1s, and −1s such that the sum of each row and column is 1 and the nonzero entries in each row and column alternate in sign. these matrices generalize permutation matrices and arise naturally when using dodgson condensation to compute a determinant. they are also closely related to the six - vertex model with domain wall boundary conditions from statistical mechanics. they were first defined by william mills, david robbins, and howard rumsey in the former context.


control surfaces with motorized faders can read and write mix automation. the control surface connects to the host computer via many different interfaces. midi was the first major interface created for this purpose, although many devices now use usb, firewire, or ethernet.


in statistics, naive bayes classifiers are a family of simple " probabilistic classifiers " based on applying bayes'theorem with strong ( naive ) independence assumptions between the features ( see bayes classifier ). they are among the simplest bayesian network models, but coupled with kernel density estimation, they can achieve high accuracy levels. naive bayes classifiers are highly scalable, requiring a number of parameters linear in the number of variables ( features / predictors ) in a learning problem. maximum - likelihood training can be done by evaluating a closed - form expression, : 718 which takes linear time, rather than by expensive iterative approximation as used for many other types of classifiers. in the statistics literature, naive bayes models are known under a variety of names, including simple bayes and independence bayes. all these names reference the use of bayes'theorem in the classifier's decision rule, but naive bayes is not ( necessarily ) a bayesian method.


in the 20th century, many generalizations of sets were invented, e. g., fuzzy sets ( zadeh, 1965 ), or rediscovered, e. g., multisets ( knuth, 1997 ). as a result, these generalizations created a unification problem in the foundation of mathematics. the concept of a named set was created as a solution to this problem. its generalization of mathematical structures allowed for the unification of all known generalizations of sets.


in order to deal with high data - rates, several architectural paradigms are commonly used : pipeline of processors - each stage of the pipeline consisting of a processor performing one of the functions listed above. parallel processing with multiple processors, often including multithreading. specialized microcoded engines to more efficiently accomplish the tasks at hand.


in particular, if two random variables x { \ displaystyle x } and y { \ displaystyle y } ( in l 2 ( ω, p ) { \ displaystyle l ^ { 2 } ( \ omega, p ) } ) are independent, then the centered random variables x − e ( x ) { \ displaystyle x - e ( x ) } and y − e ( y ) { \ displaystyle y - e ( y ) } are orthogonal. ( this means that the two variables have zero covariance : they are uncorrelated. ) in that case, the pythagorean theorem in the kernel of the expectation operator implies that the variances of x { \ displaystyle x } and y { \ displaystyle y } satisfy the identity : sometimes called the pythagorean theorem of statistics, and is of importance in linear regression.


with dataflow path widths of 8 bits to 64 bits and beyond, they nevertheless present a common architecture at the machine language level across the entire line. using microcode to implement an emulator enables the computer to present the architecture of an entirely different computer. the system / 360 line used this to allow porting programs from earlier ibm machines to the new family of computers, e. g. an ibm 1401 / 1440 / 1460 emulator on the ibm s / 360 model 40.


in telecommunication, coded mark inversion ( cmi ) is a non - return - to - zero ( nrz ) line code. it encodes zero bits as a half bit time of zero followed by a half bit time of one, and while one bits are encoded as a full bit time of a constant level. the level used for one bits alternates each time one is coded. this is vaguely reminiscent of, but quite different from, miller encoding, which also uses half - bit and full - bit pulses, but additionally uses the half - one / half - zero combination and arranges them so that the signal always spends at least a full bit time at a particular level before transitioning again. cmi doubles the bitstream frequency, when compared to its simple nrz equivalent, but allows easy and reliable clock recovery.


in the direct scheme, the destination decodes the data using the signal received from the source node on the first phase where the second phase transmission is omitted so that the relay node is not involved in transmission. the decoding signal received from the source node is written as : r d, s = h d, s x s + n d, s { \ displaystyle r _ { d, s } = h _ { d, s } x _ { s } + n _ { d, s } \ quad } while the advantage of the direct scheme is its simplicity in terms of the decoding processing, the received signal power can be severely low if the distance between the source node and the destination node is large. thus, in the following we consider non - cooperative scheme which exploits signal relaying to improve the signal quality.


in the x. 509 trust model, a certificate authority ( ca ) is responsible for signing certificates. these certificates act as an introduction between two parties, which means that a ca acts as a trusted third party. a ca processes requests from people or organizations requesting certificates ( called subscribers ), verifies the information, and potentially signs an end - entity certificate based on that information. to perform this role effectively, a ca needs to have one or more broadly trusted root certificates or intermediate certificates and the corresponding private keys.


in statistical mechanics, one sometimes uses negative temperatures to describe systems with population inversion, which can be considered to have a temperature greater than positive infinity, because the coefficient of energy in the population distribution function is −1 / temperature. in this context, a temperature of −0 is a ( theoretical ) temperature larger than any other negative temperature, corresponding to the ( theoretical ) maximum conceivable extent of population inversion, the opposite extreme to + 0.


in the ( currently used ) gregorian calendar, alongside tuesday, the fourteen types of year ( seven common, seven leap ) repeat in a 400 - year cycle ( 20871 weeks ). forty - four common years per cycle or exactly 11 % start on a thursday. the 28 - year sub - cycle only spans across century years divisible by 400, e. g. 1600, 2000, and 2400. 400 year cycle century 1 : 9, 15, 26, 37, 43, 54, 65, 71, 82, 93, 99 century 2 : 105, 111, 122, 133, 139, 150, 161, 167, 178, 189, 195 century 3 : 201, 207, 218, 229, 235, 246, 257, 263, 274, 285, 291 century 4 : 303, 314, 325, 331, 342, 353, 359, 370, 381, 387, 398


in some cases, often where the changes are the most striking, unicode has encoded variant characters, making it unnecessary to switch between fonts or lang attributes. however, some variants with arguably minimal differences get distinct codepoints, and not every variant with arguably substantial changes gets a unique codepoint. as an example, take a character such as ( u + 5165 ), for which the only way to display the variants is to change font ( or lang attribute ) as described in the previous table. on the other hand, for ( u + 5167 ), the variant of 内 ( u + 5185 ) gets a unique codepoint.


algorithm delete ( r ) : d1. find the host leaf : perform an exact match search to find the leaf node l that contains r. d2. delete r : remove r from node l. d3.


in 1975 ibm started a project to develop a telephone switch that required performance about three times that of their fastest contemporary computers. to reach this goal, the development team began to study the massive amount of performance data ibm had collected over the last decade. this study demonstrated that the complex isa was in fact a significant problem ; because only the most basic instructions were guaranteed to be implemented in hardware, compilers ignored the more complex ones that only ran in hardware on certain machines.


main - this is the normal setting when the engine is running. sometimes this position is labeled " on " or " run ". reserve - in this position, a known but small volume of fuel is available to allow the rider to be able to reach a petrol station.


most used simple caching to provide extremely fast risc machines, with very compact code. another benefit was that the interrupt latencies were very small, smaller than most cisc machines ( a rare trait in risc machines ). the burroughs large systems architecture used this approach.


in mathematics, the mersenne conjectures concern the characterization of a kind of prime numbers called mersenne primes, meaning prime numbers that are a power of two minus one.


because its location in parent ’ s node is the only thing of importance, it is symbolised by ( meaning : the current node n is a nil node and left child ) in the left column of the delete diagrams. as the operation proceeds also proper nodes ( of black height ≥ 1 ) may become current ( see e. g. case d2 ). by counting the black bullets ( and ) in a delete diagram it can be observed that the paths through n have one bullet less than the other paths.


the closer the approximation is to zero or one, the more helpful the approximation is in linear cryptanalysis. however, in practice, the binary variables are not independent, as is assumed in the derivation of the piling - up lemma. this consideration has to be kept in mind when applying the lemma ; it is not an automatic cryptanalysis formula.


the specification includes signal names and functions, timing, and electrical constraints. the last mipi board - adopted version of specification for parallel trace interface is version 2. 0 ( october 2011 ). the mipi high - speed trace interface ( mipi hti ) specifies how to stream trace data over the physical layer of standard interfaces, such as pci express, displayport, hdmi, or usb. the current version of the specification allows for one to six lanes.


in mathematics, more specifically in computational algebra, a straight - line program ( slp ) for a finite group g = ⟨ s ⟩ is a finite sequence l of elements of g such that every element of l either belongs to s, is the inverse of a preceding element, or the product of two preceding elements. an slp l is said to compute a group element g ∈ g if g ∈ l, where g is encoded by a word in s and its inverses. intuitively, an slp computing some g ∈ g is an efficient way of storing g as a group word over s ; observe that if g is constructed in i steps, the word length of g may be exponential in i, but the length of the corresponding slp is linear in i. this has important applications in computational group theory, by using slps to efficiently encode group elements as words over a given generating set. straight - line programs were introduced by babai and szemeredi in 1984 as a tool for studying the computational complexity of certain matrix group properties.


in order to explore more complex relationships, axes must be reordered. by arranging the axes in 3 - dimensional space ( however, still in parallel, like nails in a nail bed ), an axis can have more than two neighbors in a circle around the central attribute, and the arrangement problem gets easier ( for example by using a minimum spanning tree ). a prototype of this visualization is available as extension to the data mining software elki. however, the visualization is harder to interpret and interact with than a linear order.


in mathematics, and in particular functional analysis, the shift operator, also known as the translation operator, is an operator that takes a function x ↦ f ( x ) to its translation x ↦ f ( x + a ). in time series analysis, the shift operator is called the lag operator. shift operators are examples of linear operators, important for their simplicity and natural occurrence.


in mathematics, the kleene – rosser paradox is a paradox that shows that certain systems of formal logic are inconsistent, in particular the version of haskell curry's combinatory logic introduced in 1930, and alonzo church's original lambda calculus, introduced in 1932 – 1933, both originally intended as systems of formal logic. the paradox was exhibited by stephen kleene and j. b. rosser in 1935.


as such, the child object can continue to be modified and amended over time without rearranging the structure of its associated prototype as in class - based systems. it is also important to note that not only data, but also methods can be added or changed. for this reason, some prototype - based languages refer to both data and methods as " slots " or " members ".