at a higher logical level, the mch also sees two channels, each with four ranks. in contrast, banks, while similar from a logical perspective to ranks, are implemented quite differently in physical hardware. banks are sub - units inside a single memory chip, while ranks are sub - units composed of a subset of the chips on a module. similar to chip select, banks are selected by bank select bits, which are part of the memory interface.


in telecommunication, the term bit - count integrity ( bci ) has the following meanings : in message communications, the preservation of the exact number of bits that are in the original message. in connection - oriented services, preservation of the number of bits per unit time. note : bit - count integrity is not the same as bit integrity, which requires that the delivered bits correspond exactly with the original bits. source : from federal standard 1037c and from mil - std - 188


in sequential code it is possible to control the flow of the program using if - then - else statements and various forms of loops. such flow control structures have only recently been added to gpus. conditional writes could be performed using a properly crafted series of arithmetic / bit operations, but looping and conditional branching were not possible. recent gpus allow branching, but usually with a performance penalty. branching should generally be avoided in inner loops, whether in cpu or gpu code, and various methods, such as static branch resolution, pre - computation, predication, loop splitting, and z - cull can be used to achieve branching when hardware support does not exist.


social hierarchies within the 17th century were highly regarded, as architecture was able to epitomize the servants and the upper class. more privacy is offered to the occupant as pratt further claims, " the ordinary servants may never publicly appear in passing to and fro for their occasions there. " this social divide between rich and poor favored the physical integration of the corridor into housing by the 19th century. sociologist witold rybczynski wrote, " the subdivision of the house into day and night uses, and into formal and informal areas, had begun. " rooms were changed from public to private as single entryways forced notions of entering a room with a specific purpose.


since classical algorithms for np - complete problems require exponentially many steps, and grover's algorithm provides at most a quadratic speedup over the classical solution for unstructured search, this suggests that grover's algorithm by itself will not provide polynomial - time solutions for np - complete problems ( as the square root of an exponential function is an exponential, not polynomial, function ). unlike other quantum algorithms, which may provide exponential speedup over their classical counterparts, grover's algorithm provides only a quadratic speedup. however, even quadratic speedup is considerable when n { \ displaystyle n } is large, and grover's algorithm can be applied to speed up broad classes of algorithms. grover's algorithm could brute - force a 128 - bit symmetric cryptographic key in roughly 264 iterations, or a 256 - bit key in roughly 2128 iterations. it may not be the case that grover's algorithm poses a significantly increased risk to encryption over existing classical algorithms, however.


{ \ displaystyle { \ boldsymbol { s } } = j ~ { \ boldsymbol { f } } ^ { - 1 } \ cdot { \ boldsymbol { \ sigma } } \ cdot { \ boldsymbol { f } } ^ { - t } ~. } in index notation with respect to an orthonormal basis, s i l = j f i k − 1 f l m − 1 σ k m = j ∂ x i ∂ x k ∂ x l ∂ x m σ k m { \ displaystyle s _ { il } = j ~ f _ { ik } ^ { - 1 } ~ f _ { lm } ^ { - 1 } ~ \ sigma _ { km } = j ~ { \ cfrac { \ partial x _ { i } } { \ partial x _ { k } } } ~ { \ cfrac { \ partial x _ { l } } { \ partial x _ { m } } } ~ \ sigma _ { km } \! \, \! } this tensor, a one - point tensor, is symmetric. if the material rotates without a change in stress state ( rigid rotation ), the components of the second piola – kirchhoff stress tensor remain constant, irrespective of material orientation. the second piola – kirchhoff stress tensor is energy conjugate to the green – lagrange finite strain tensor.


259 ) but offers no firm resolution. he asserts : " in general a rpt operation could not be an instruction in the finite - state part of the machine... this might exhaust any particular amount of storage allowed in the finite part of the computer. rpt operations require infinite registers of their own. "


in the example on the right, the rows restricted to the first three columns contain the 8 possible ordered triples consisting of 0's and 1's, each appearing once. the same holds for any other choice of three columns. thus this is an orthogonal array of strength 3.


in probability and statistics, the tweedie distributions are a family of probability distributions which include the purely continuous normal, gamma and inverse gaussian distributions, the purely discrete scaled poisson distribution, and the class of compound poisson – gamma distributions which have positive mass at zero, but are otherwise continuous. tweedie distributions are a special case of exponential dispersion models and are often used as distributions for generalized linear models. the tweedie distributions were named by bent jørgensen after maurice tweedie, a statistician and medical physicist at the university of liverpool, uk, who presented the first thorough study of these distributions in 1984.


in the japanese kantenji braille, the standard 8 - dot braille patterns 23678, 123678, 234678, and 1234678 are the patterns related to braille pattern dots - 12356, since the two additional dots of kantenji patterns 012356, 123567, and 0123567 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in mathematics, the spectral radius of a square matrix is the maximum of the absolute values of its eigenvalues. more generally, the spectral radius of a bounded linear operator is the supremum of the absolute values of the elements of its spectrum. the spectral radius is often denoted by ρ ( · ).


this control structure can be known as a post - test loop. this means the do - while loop is an exit - condition loop. however a while loop will test the condition before the code within the block is executed.


in semantics, pragmatics, and philosophy of language, the common ground of a conversation is the set of propositions that the interlocutors have agreed to treat as true. for a proposition to be in the common ground, it must be common knowledge in the conversational context. the set of possible worlds compatible with the common ground is often called the context set. the concept is fundamental to many theories of discourse.


in the following diagram, only one instance ( or " execution " ) of the basic paxos protocol, with an initial leader ( a proposer ), is shown. note that a multi - paxos consists of several instances of the basic paxos protocol. client proposer acceptor learner | | | | | | | - - - first request - - - x - - - - - - - - > | | | | | | request | x - - - - - - - - - > | - > | - > | | | prepare ( n ) | | < - - - - - - - - - x - - x - - x | | promise ( n, i, { va, vb, vc } ) | x - - - - - - - - - > | - > | - > | | | accept! ( n, i, v ) | | < - - - - - - - - - x - - x - - x - - - - - - > | - > | accepted ( n, i, v ) | < - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - x - - x response | | | | | | | where v = last of ( va, vb, vc ).


in a compression oracle attack the use of adaptive data compression on a mixture of chosen plaintext and unknown plaintext can result in content - sensitive changes in the length of the compressed text that can be detected even though the content of the compressed text itself is then encrypted. this can be used in protocol attacks to detect when the injected known plaintext is even partially similar to the unknown content of a secret part of the message, greatly reducing the complexity of a search for a match for the secret text. the crime and breach attacks are examples of protocol attacks using this phenomenon.


in the field of psychometrics, the standards for educational and psychological testing place standards about validity and reliability, along with errors of measurement and issues related to the accommodation of individuals with disabilities. the third and final major topic covers standards related to testing applications, credentialing, plus testing in program evaluation and public policy.


the largest known prime number, 282, 589, 933 − 1, is a mersenne prime. since 1997, all newly found mersenne primes have been discovered by the great internet mersenne prime search, a distributed computing project. in december 2020, a major milestone in the project was passed after all exponents below 100 million were checked at least once.


in most deployments of paxos, each participating process acts in three roles ; proposer, acceptor and learner. this reduces the message complexity significantly, without sacrificing correctness : in paxos, clients send commands to a leader. during normal operation, the leader receives a client's command, assigns it a new command number i { \ displaystyle i }, and then begins the i { \ displaystyle i } th instance of the consensus algorithm by sending messages to a set of acceptor processes. by merging roles, the protocol " collapses " into an efficient client - master - replica style deployment, typical of the database community. the benefit of the paxos protocols ( including implementations with merged roles ) is the guarantee of its safety properties. a typical implementation's message flow is covered in the section multi - paxos.


in mathematics, especially in algebraic topology, an induced homomorphism is a homomorphism derived in a canonical way from another map. for example, a continuous map from a topological space x to a topological space y induces a group homomorphism from the fundamental group of x to the fundamental group of y. more generally, in category theory, any functor by definition provides an induced morphism in the target category for each morphism in the source category. for example, fundamental groups, higher homotopy groups, singular homology, and de rham cohomology are algebraic structures that are functorial, meaning that their definition provides a functor from ( e. g. ) the category of topological spaces to ( e. g. ) the category of groups or rings. this means that each space is associated with an algebraic structure, while each continuous map between spaces is associated with a structure - preserving map between structures, called an induced homomorphism.


in statistics, least - angle regression ( lars ) is an algorithm for fitting linear regression models to high - dimensional data, developed by bradley efron, trevor hastie, iain johnstone and robert tibshirani. suppose we expect a response variable to be determined by a linear combination of a subset of potential covariates. then the lars algorithm provides a means of producing an estimate of which variables to include, as well as their coefficients. instead of giving a vector result, the lars solution consists of a curve denoting the solution for each value of the l1 norm of the parameter vector. the algorithm is similar to forward stepwise regression, but instead of including variables at each step, the estimated parameters are increased in a direction equiangular to each one's correlations with the residual.


in mathematics, the infinity symbol is used more often to represent a potential infinity, rather than an actually infinite quantity as included in the cardinal numbers and the ordinal numbers ( which use other notations, such as 0 { \ displaystyle \, \ aleph _ { 0 } \, } and ω, for infinite values ). for instance, in mathematical expressions with summations and limits such as the infinity sign is conventionally interpreted as meaning that the variable grows arbitrarily large towards infinity, rather than actually taking an infinite value, although other interpretations are possible. the infinity symbol may also be used to represent a point at infinity, especially when there is only one such point under consideration. this usage includes, in particular, the infinite point of a projective line, and the point added to a topological space to form its one - point compactification.


in the area of mathematics known as graph theory, a tree is said to be starlike if it has exactly one vertex of degree greater than 2. this high - degree vertex is the root and a starlike tree is obtained by attaching at least three linear graphs to this central vertex.


computer frameworks may have a few audit trails each gave to a specific sort of action. related to proper apparatuses and systems, audit trails can help with distinguishing security infringement, execution issues and application issues. routine log audits and investigation are valuable for distinguishing security episodes, approach infringement, fake movement, and operational issues soon after they have happened, and for giving information valuable to settling such issues.


capturing two opposing tokens by occupying the single square separating them, also known as interception. declaring an " attack " on an opposing token, and then determining the outcome of the attack, either in a deterministic way by the game rules ( e. g. stratego, illuminati ), or by using a randomising method ( e. g. illuminati : new world order ). surrounding a token or region with one's own tokens in some manner ( e. g. go ), also known as enclosure.


programming languages commonly associated with buffer overflows include c and c + +, which provide no built - in protection against accessing or overwriting data in any part of memory and do not automatically check that data written to an array ( the built - in buffer type ) is within the boundaries of that array. bounds checking can prevent buffer overflows, but requires additional code and processing time. modern operating systems use a variety of techniques to combat malicious buffer overflows, notably by randomizing the layout of memory, or deliberately leaving space between buffers and looking for actions that write into those areas ( " canaries " ).


for each integer n { \ displaystyle n } the smallest fusible number that is greater than n { \ displaystyle n } has the form n + 1 / 2 k { \ displaystyle n + 1 / 2 ^ { k } }. the existence of k { \ displaystyle k } for each n { \ displaystyle n } cannot be proven in peano arithmetic, and k { \ displaystyle k } grows so rapidly as a function of n { \ displaystyle n } that for n = 3 { \ displaystyle n = 3 } it is ( in knuth's up - arrow notation for large numbers ) already larger than 2 ↑ 9 16 { \ displaystyle 2 \ uparrow ^ { 9 } 16 }. the usual proof of urysohn's lemma utilizes the dyadic fractions for constructing the separating function from the lemma. = = references = =


the upper bound on the fraction of agents that can be guaranteed 1 of their best c items ( a property weaker than 1 - out - of - c mms ) is ( 1 − 1 / 2 c ) { \ displaystyle ( 1 - 1 / 2 ^ { c } ) }. for c = 2 { \ displaystyle c = 2 }, the lower bound for 1 - out - of - best - c allocation can be improved from 1 / 2 to 3 / 5 ; it is an open question whether the upper bound of 3 / 4 can always be attained. it is np - hard to decide if a given instance admits an allocation that gives each agent a positive utility.


in metadata, the term data element is an atomic unit of data that has precise meaning or precise semantics. a data element has : an identification such as a data element name a clear data element definition one or more representation terms optional enumerated values code ( metadata ) a list of synonyms to data elements in other metadata registries synonym ringdata elements usage can be discovered by inspection of software applications or application data files through a process of manual or automated application discovery and understanding. once data elements are discovered they can be registered in a metadata registry. in telecommunication, the term data element has the following components : a named unit of data that, in some contexts, is considered indivisible and in other contexts may consist of data items.


: 87 as quine points out :'the basis combination in which general and singular terms find their contrasting roles is that of predication.': 87 predication combines general terms with singular terms, in a sentence that is true or false just as the general term ('f') is true or false of the object to which the singular term ('a') refers. predication is thus logically represented as'fa '.


in the application of integrated circuits, process control monitoring ( pcm ) is the procedure followed to obtain detailed information about the process used. pcm is associated with designing and fabricating special structures that can monitor technology specific parameters such as vth in cmos and vbe in bipolars. these structures are placed across the wafer at specific locations along with the chip produced so that a closer look into the process variation is possible.


in mathematics, the besicovitch inequality is a geometric inequality relating volume of a set and distances between certain subsets of its boundary. the inequality was first formulated by abram besicovitch. consider the n - dimensional cube n { \ displaystyle ^ { n } } with a riemannian metric g { \ displaystyle g }. let denote the distance between opposite faces of the cube.


in the 1980s and early 1990s, when the 8088 and 80286 were still in common use, the term x86 usually represented any 8086 - compatible cpu. today, however, x86 usually implies a binary compatibility also with the 32 - bit instruction set of the 80386. this is due to the fact that this instruction set has become something of a lowest common denominator for many modern operating systems and probably also because the term became common after the introduction of the 80386 in 1985. a few years after the introduction of the 8086 and 8088, intel added some complexity to its naming scheme and terminology as the " iapx " of the ambitious but ill - fated intel iapx 432 processor was tried on the more successful 8086 family of chips, applied as a kind of system - level prefix.


in mathematics, and in particular, algebra, a generalized inverse ( or, g - inverse ) of an element x is an element y that has some properties of an inverse element but not necessarily all of them. the purpose of constructing a generalized inverse of a matrix is to obtain a matrix that can serve as an inverse in some sense for a wider class of matrices than invertible matrices. generalized inverses can be defined in any mathematical structure that involves associative multiplication, that is, in a semigroup. this article describes generalized inverses of a matrix a { \ displaystyle a }.


in the japanese kantenji braille, the standard 8 - dot braille patterns 36, 136, 346, and 1346 are the patterns related to braille pattern dots - 25, since the two additional dots of kantenji patterns 025, 257, and 0257 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by michael artin for use in deformation theory. intuitively, schemes are given by gluing together affine schemes using the zariski topology, while algebraic spaces are given by gluing together affine schemes using the finer etale topology. alternatively one can think of schemes as being locally isomorphic to affine schemes in the zariski topology, while algebraic spaces are locally isomorphic to affine schemes in the etale topology. the resulting category of algebraic spaces extends the category of schemes and allows one to carry out several natural constructions that are used in the construction of moduli spaces but are not always possible in the smaller category of schemes, such as taking the quotient of a free action by a finite group ( cf. the keel – mori theorem ).


in philosophy, counterexamples are usually used to argue that a certain philosophical position is wrong by showing that it does not apply in certain cases. alternatively, the first philosopher can modify their claim so that the counterexample no longer applies ; this is analogous to when a mathematician modifies a conjecture because of a counterexample. for example, in plato's gorgias, callicles, trying to define what it means to say that some people are " better " than others, claims that those who are stronger are better. but socrates replies that, because of their strength of numbers, the class of common rabble is stronger than the propertied class of nobles, even though the masses are prima facie of worse character.


in probability theory and statistics chow – liu tree is an efficient method for constructing a second - order product approximation of a joint probability distribution, first described in a paper by chow & liu ( 1968 ). the goals of such a decomposition, as with such bayesian networks in general, may be either data compression or inference.


this is useful if the user wants to do a prior art search ( e. g. finding an existing approach to complete a specific task, finding a document that discloses a system that exhibits a procedural behavior collaboratively conducted by several components and links between these components ). web search engines which support proximity search via an explicit proximity operator in their query language include walhello, exalead, yandex, yahoo!, altavista, and bing : when using the walhello search - engine, the proximity can be defined by the number of characters between the keywords. the search engine exalead allows the user to specify the required proximity, as the maximum number of words between keywords.


in statistics and, in particular, in the fitting of linear or logistic regression models, the elastic net is a regularized regression method that linearly combines the l1 and l2 penalties of the lasso and ridge methods.


in the 1930s, j. h. c. whitehead claimed a proof but then retracted it. in the process, he discovered some examples of simply - connected ( indeed contractible, i. e. homotopically equivalent to a point ) non - compact 3 - manifolds not homeomorphic to r 3 { \ displaystyle \ mathbb { r } ^ { 3 } }, the prototype of which is now called the whitehead manifold. in the 1950s and 1960s, other mathematicians attempted proofs of the conjecture only to discover that they contained flaws. influential mathematicians such as georges de rham, r. h. bing, wolfgang haken, edwin e. moise, and christos papakyriakopoulos attempted to prove the conjecture.


in order for the minimization problem to have a well - defined solution, we have to place constraints on the set h { \ displaystyle { \ mathcal { h } } } of hypotheses being considered. if h { \ displaystyle { \ mathcal { h } } } is a normed space ( as is the case for svm ), a particularly effective technique is to consider only those hypotheses f { \ displaystyle f } for which ‖ f ‖ h < k { \ displaystyle \ lvert f \ rvert _ { \ mathcal { h } }


all these results are employed in probability and statistics with a particular importance in the theory of point processes and queueing theory as well as the related fields stochastic geometry, continuum percolation theory, and spatial statistics. another result by the name of campbell's theorem is specifically for the poisson point process and gives a method for calculating moments as well as the laplace functional of a poisson point process. the name of both theorems stems from the work by norman r. campbell on thermionic noise, also known as shot noise, in vacuum tubes, which was partly inspired by the work of ernest rutherford and hans geiger on alpha particle detection, where the poisson point process arose as a solution to a family of differential equations by harry bateman. in campbell's work, he presents the moments and generating functions of the random sum of a poisson process on the real line, but remarks that the main mathematical argument was due to g. h. hardy, which has inspired the result to be sometimes called the campbell – hardy theorem.


in statistics, the explained sum of squares ( ess ), alternatively known as the model sum of squares or sum of squares due to regression ( ssr – not to be confused with the residual sum of squares ( rss ) or sum of squares of errors ), is a quantity used in describing how well a model, often a regression model, represents the data being modelled. in particular, the explained sum of squares measures how much variation there is in the modelled values and this is compared to the total sum of squares ( tss ), which measures how much variation there is in the observed data, and to the residual sum of squares, which measures the variation in the error between the observed data and modelled values.


to prevent critical races and inconsistency, only one processor ( cpu ) at a given time is allowed to access a particular data structure ( a memory portion ), while other cpus trying to access at the same time are locked - out, waiting in idle status. three cases can be distinguished when this idle wait is either necessary, convenient, or not convenient. the idle wait is necessary when the access is to a ready list for a low level scheduling operation. the idle wait is not necessary but convenient in the case of a critical section for synchronization / ipc operations, which require less time than a context switch ( executing another process to avoid idle wait ).


godel's incompleteness theorems were other examples that uncovered fundamental limitations in the provability of formal systems. in computational complexity theory, techniques like relativization ( the addition of an oracle ) allow for " weak " proofs of impossibility, in that proofs techniques that are not affected by relativization cannot resolve the p versus np problem. another technique is the proof of completeness for a complexity class, which provides evidence for the difficulty of problems by showing them to be just as hard to solve as any other problem in the class. in particular, a complete problem is intractable if one of the problems in its class is.


in the japanese kantenji braille, the standard 8 - dot braille patterns 278, 1278, 2478, and 12478 are the patterns related to braille pattern dots - 136, since the two additional dots of kantenji patterns 0136, 1367, and 01367 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in the field of transportation, bilevel optimization commonly appears in the toll - setting problem. consider a network of highways that is operated by the government. the government wants to maximize its revenues by choosing the optimal toll setting for the highways. however, the government can maximize its revenues only by taking the highway users'problem into account.


let g denote the subcollection of f consisting of all balls from the cn disjoint families a1,..., acn. the less precise following statement is clearly true : every point x ∈ rn belongs to at most cn different balls from the subcollection g, and g remains a cover for e ( every point y ∈ e belongs to at least one ball from the subcollection g ). this property gives actually an equivalent form for the theorem ( except for the value of the constant ). there exists a constant bn depending only on the dimension n with the following property : given any besicovitch cover f of a bounded set e, there is a subcollection g of f such that g is a cover of the set e and every point x ∈ e belongs to at most bn different balls from the subcover g. in other words, the function sg equal to the sum of the indicator functions of the balls in g is larger than 1e and bounded on rn by the constant bn, 1 e ≤ s g : = b ∈ g 1 b ≤ b n. { \ displaystyle \ mathbf { 1 } _ { e } \ leq s _ { \ mathbf { g } } : = \ sum _ { b \ in \ mathbf { g } } \ mathbf { 1 } _ { b } \ leq b _ { n }. }


proposer acceptor learner | | | | | | | x - - - - - - - - - > | - > | - > | | | prepare ( 1 ) | < - - - - - - - - - x - - x - - x | | promise ( 1, { null, null, null } ) x - - - - - - - - - > | - > | | | | accept! ( 1, v1 ) | | x - - x - - - - - - - - - > | - > | accepted ( 1, v1 )! | | | | | |!!


in statistical mechanics, probability theory, graph theory, etc. the random cluster model is a random graph that generalizes and unifies the ising model, potts model, and percolation model. it is used to study random combinatorial structures, electrical networks, etc. it is also referred to as the rc model or sometimes the fk representation after its founders cees fortuin and piet kasteleyn.


conclusions that assume limiting operations do'commute'are called formal. the analyst tries to delineate conditions under which such conclusions are valid ; in other words mathematical rigour is established by the specification of some set of sufficient conditions for the formal analysis to hold. this approach justifies, for example, the notion of uniform convergence.


by comparison, the sun microsystems sparc architecture provides simultaneous visibility into four sets of eight registers each. three sets of eight registers each are " windowed ". eight registers ( i0 through i7 ) form the input registers to the current procedure level.


in mathematics, a polycyclic group is a solvable group that satisfies the maximal condition on subgroups ( that is, every subgroup is finitely generated ). polycyclic groups are finitely presented, which makes them interesting from a computational point of view.


in telecommunications, a transverse redundancy check ( trc ) or vertical redundancy check is a redundancy check for synchronized parallel bits applied once per bit time, across the bit streams. this requires additional parallel channels for the check bit or bits. the term usually applies to a single parity bit, although it could also be used to refer to a larger hamming code.


this brings one to idea of using approximate factorization lu of a as the iteration matrix m. a version of incomplete lower - upper decomposition method was proposed by stone in 1968. this method is designed for equation system arising from discretisation of partial differential equations and was firstly used for a pentadiagonal system of equations obtained while solving an elliptic partial differential equation in a two - dimensional space by a finite difference method. the lu approximate decomposition was looked in the same pentadiagonal form as the original matrix ( three diagonals for l and three diagonals for u ) as the best match of the seven possible equations for the five unknowns for each row of the matrix.


a chain of responsibility can be used to allow native code to better inter - operate with the jvm. on windows platforms, structured exception handling ( seh ) may be employed to wrap native code in seh try / catch blocks so as to capture machine ( cpu / fpu ) generated software interrupts ( such as null pointer access violations and divide - by - zero operations ), and to handle these situations before the interrupt is propagated back up into the jvm ( i. e. java side code ), in all likelihood resulting in an unhandled exception. the encoding used for the newstringutf, getstringutflength, getstringutfchars, releasestringutfchars and getstringutfregion functions is " modified utf - 8 ", which is not valid utf - 8 for all inputs, but a different encoding really. the null character ( u + 0000 ) and codepoints not on the basic multilingual plane ( greater than or equal to u + 10000, i. e. those represented as surrogate pairs in utf - 16 ) are encoded differently in modified utf - 8. many programs actually use these functions incorrectly and treat the utf - 8 strings returned or passed into the functions as standard utf - 8 strings instead of modified utf - 8 strings. programs should use the newstring, getstringlength, getstringchars, releasestringchars, getstringregion, getstringcritical and releasestringcritical functions, which use utf - 16le encoding on little - endian architectures and utf - 16be on big - endian architectures, and then use a utf - 16 to utf - 8 conversion routine.


diophantine approximations and transcendental number theory are very close areas that share many theorems and methods. diophantine approximations also have important applications in the study of diophantine equations. the 2022 fields medal was awarded to james maynard for his work on diophantine approximation.


there is, however, the information commissioner's office ( ico ), an independent public body set up to promote access to official information and protect personal information. they do this by promoting good practice, ruling on eligible complaints, giving information to individuals and organisations, and taking action when the law is broken. the relevant uk laws include : data protection act 1998 ; freedom of information act 2000 ; environmental information regulations 2004 ; privacy and electronic communications regulations 2003. the ico has also provided a " personal information toolkit " online which explains in more detail the various ways of protecting privacy online.


for every representation ( ρ, v ) { \ displaystyle ( \ rho, v ) } of a group g { \ displaystyle g } we define v g : = { v ∈ v : ρ ( s ) v = v s ∈ g }. { \ displaystyle v ^ { g } : = \ { v \ in v : \ rho ( s ) v = v \, \, \, \, \ forall \, s \ in g \ }. } in general, ρ ( s ) : v → v { \ displaystyle \ rho ( s ) : v \ to v } is not g { \ displaystyle g } - linear.


in telecommunications, asynchronous communication is transmission of data, generally without the use of an external clock signal, where data can be transmitted intermittently rather than in a steady stream. any timing required to recover data from the communication symbols is encoded within the symbols. the most significant aspect of asynchronous communications is that data is not transmitted at regular intervals, thus making possible variable bit rate, and that the transmitter and receiver clock generators do not have to be exactly synchronized all the time. in asynchronous transmission, data is sent one byte at a time and each byte is preceded by start and stop bits.


in the first of their famous series of papers on graph minors, neil robertson and paul seymour ( 1983 ) define a path - decomposition of a graph g to be a sequence of subsets xi of vertices of g, with two properties : for each edge of g, there exists an i such that both endpoints of the edge belong to subset xi, and for every three indices i ≤ j ≤ k, x i ∩ x k ⊆ x j. { \ displaystyle x _ { i } \ cap x _ { k } \ subseteq x _ { j }. } the second of these two properties is equivalent to requiring that the subsets containing any particular vertex form a contiguous subsequence of the whole sequence. in the language of the later papers in robertson and seymour's graph minor series, a path - decomposition is a tree decomposition ( x, t ) in which the underlying tree t of the decomposition is a path graph. the width of a path - decomposition is defined in the same way as for tree - decompositions, as maxi | xi | − 1, and the pathwidth of g is the minimum width of any path - decomposition of g. the subtraction of one from the size of xi in this definition makes little difference in most applications of pathwidth, but is used to make the pathwidth of a path graph be equal to one.


in some cases, one may wish to compute the location of a corner with subpixel accuracy. to achieve an approximate solution, the forstner algorithm solves for the point closest to all the tangent lines of the corner in a given window and is a least - square solution. the algorithm relies on the fact that for an ideal corner, tangent lines cross at a single point. the equation of a tangent line t x ′ ( x ) { \ displaystyle t _ { \ mathbf { x }'} ( \ mathbf { x } ) } at pixel x ′ { \ displaystyle \ mathbf { x }'} is given by : t x ′ ( x ) = ∇ i ( x ′ ) ( x − x ′ ) = 0 { \ displaystyle t _ { \ mathbf { x'} } ( \ mathbf { x } ) = \ nabla i ( \ mathbf { x'} ) ^ { \ top } ( \ mathbf { x } - \ mathbf { x'} ) = 0 } where ∇ i ( x ′ ) = { \ displaystyle \ nabla i ( \ mathbf { x'} ) = { \ begin { bmatrix } i _ { \ mathbf { x } } & i _ { \ mathbf { y } } \ end { bmatrix } } ^ { \ top } } is the gradient vector of the image i { \ displaystyle i } at x ′ { \ displaystyle \ mathbf { x'} }.


in principle, a sufficiently aggressive optimizing compiler could destroy the effectiveness of kahan summation : for example, if the compiler simplified expressions according to the associativity rules of real arithmetic, it might " simplify " the second step in the sequence t = sum + y ; c = ( t - sum ) - y ; to c = ( ( sum + y ) - sum ) - y ; and then to c = 0 ; thus eliminating the error compensation. in practice, many compilers do not use associativity rules ( which are only approximate in floating - point arithmetic ) in simplifications, unless explicitly directed to do so by compiler options enabling " unsafe " optimizations, although the intel c + + compiler is one example that allows associativity - based transformations by default. the original k & r c version of the c programming language allowed the compiler to re - order floating - point expressions according to real - arithmetic associativity rules, but the subsequent ansi c standard prohibited re - ordering in order to make c better suited for numerical applications ( and more similar to fortran, which also prohibits re - ordering ), although in practice compiler options can re - enable re - ordering, as mentioned above. a portable way to inhibit such optimizations locally is to break one of the lines in the original formulation into two statements, and make two of the intermediate products volatile : function kahansum ( input ) var sum = 0. 0 var c = 0. 0 for i = 1 to input. length do var y = input - c volatile var t = sum + y volatile var z = t - sum c = z - y sum = t next i return sum


those object types in turn reference the primitive object types defined in the gml standard. some other markup languages for geography use schema constructs, but gml builds on the existing xml schema model instead of creating a new schema language. application schemas are normally designed using iso 19103 ( geographic information – conceptual schema language ) conformant uml, and then the gml application created by following the rules given in annex e of iso 19136.


to assure that no single particle could trigger the counters he spread them out in a horizontal plane. in this configuration, the frequency of coincidences was greater than that calculated on the basis of the individual rates and the resolving time of the coincidence circuit. rossi concluded that :... once in a while the recording equipment is struck by very extensive showers of particles, which cause coincidences between counters, even placed at large distances from one another.


in single - linkage or nearest - neighbor clustering, the oldest form of agglomerative hierarchical clustering, the dissimilarity between clusters is measured as the minimum distance between any two points from the two clusters. with this dissimilarity, d ( a ∪ b, c ) = min ( d ( a, c ), d ( b, c ) ), { \ displaystyle d ( a \ cup b, c ) = \ min ( d ( a, c ), d ( b, c ) ), } meeting as an equality rather than an inequality the requirement of reducibility. ( single - linkage also obeys a lance – williams formula, but with a negative coefficient from which it is more difficult to prove reducibility. )


one can use this isomorphism to construct a lot of non - commutative endomorphism rings. for example : end ( z × z ) m 2 ( z ) { \ displaystyle \ operatorname { end } ( \ mathbb { z } \ times \ mathbb { z } ) \ cong m _ { 2 } ( \ mathbb { z } ) }, since end ( z ) z { \ displaystyle \ operatorname { end } ( \ mathbb { z } ) \ cong \ mathbb { z } }. also, when r = k { \ displaystyle r = k } is a field, there is a canonical isomorphism end ( k ) k { \ displaystyle \ operatorname { end } ( k ) \ cong k }, so end ( k n ) m n ( k ) { \ displaystyle \ operatorname { end } ( k ^ { n } ) \ cong m _ { n } ( k ) }, that is, the endomorphism ring of a k { \ displaystyle k } - vector space is identified with the ring of n - by - n matrices with entries in k { \ displaystyle k }. more generally, the endomorphism algebra of the free module m = r n { \ displaystyle m = r ^ { n } } is naturally n { \ displaystyle n } - by - n { \ displaystyle n } matrices with entries in the ring r { \ displaystyle r }. as a particular example of the last point, for any ring r with unity, end ( rr ) = r, where the elements of r act on r by left multiplication. in general, endomorphism rings can be defined for the objects of any preadditive category.


in physics, the term clusters denotes small, polyatomic particles. as a rule of thumb, any particle made of between 3×100 and 3×107 atoms is considered a cluster. the term can also refer to the organization of protons and neutrons within an atomic nucleus, e. g. the alpha particle ( also known as " α - cluster " ), consisting of two protons and two neutrons ( as in a helium nucleus ).


in mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator. specifically, given an algebra a over a ring or a field k, a k - derivation is a k - linear map d : a → a that satisfies leibniz's law : d ( a b ) = a d ( b ) + d ( a ) b. { \ displaystyle d ( ab ) = ad ( b ) + d ( a ) b. } more generally, if m is an a - bimodule, a k - linear map d : a → m that satisfies the leibniz law is also called a derivation.


equivalently, a divisor a of b is a unitary divisor if and only if every prime factor of a has the same multiplicity in a as it has in b. the sum - of - unitary - divisors function is denoted by the lowercase greek letter sigma thus : σ * ( n ). the sum of the k - th powers of the unitary divisors is denoted by σ * k ( n ) : σ k ∗ ( n ) = d n gcd ( d, n / d ) = 1 d k. { \ displaystyle \ sigma _ { k } ^ { * } ( n ) = \ sum _ { d \, \ mid \, n \ atop \ gcd ( d, \, n / d ) = 1 } \! \! d ^ { k }. } if the proper unitary divisors of a given number add up to that number, then that number is called a unitary perfect number. the concept of a unitary divisor originates from r. vaidyanathaswamy ( 1931 ) who used the term block divisor.


it was initially optimized for the pentium 4 processor and managed to immediately boost the performance of a supercomputer based on that cpu from 1. 5 tflops to 2 tflops. as of 2005, the library was available at no cost for noncommercial use. a later open source version was released under the terms of the bsd license.


but if there is both a right identity and a left identity, then they must be equal, resulting in a single two - sided identity. to see this, note that if l is a left identity and r is a right identity, then l = l ∗ r = r. in particular, there can never be more than one two - sided identity : if there were two, say e and f, then e ∗ f would have to be equal to both e and f. it is also quite possible for ( s, ∗ ) to have no identity element, such as the case of even integers under the multiplication operation. another common example is the cross product of vectors, where the absence of an identity element is related to the fact that the direction of any nonzero cross product is always orthogonal to any element multiplied. that is, it is not possible to obtain a non - zero vector in the same direction as the original. yet another example of structure without identity element involves the additive semigroup of positive natural numbers.


once all the multiples of each discovered prime have been marked as composites, the remaining unmarked numbers are primes. the earliest known reference to the sieve ( ancient greek : κοσκινον ερατοσθενους, koskinon eratosthenous ) is in nicomachus of gerasa's introduction to arithmetic, an early 2nd cent. ce book which attributes it to eratosthenes of cyrene, a 3rd cent. bce greek mathematician, though describing the sieving by odd numbers instead of by primes. one of a number of prime number sieves, it is one of the most efficient ways to find all of the smaller primes. it may be used to find primes in arithmetic progressions.


in mathematics, computer science and network science, network theory is a part of graph theory. it defines networks as graphs where the nodes or edges possess attributes. network theory analyses these networks over the symmetric relations or asymmetric relations between their ( discrete ) components.


+ error term { \ displaystyle y _ { t } = a + w _ { 0 } x _ { t } + w _ { 1 } x _ { t - 1 } + w _ { 2 } x _ { t - 2 } +... + { \ text { error term } } } or the form y t = a + w 0 x t + w 1 x t − 1 + w 2 x t − 2 +...


for type sum, the identity object is the void type, which stores no information and it is impossible to address an inhabitant. the concept of monoidal category does not presume that values of such aggregate types can be taken apart ; on the contrary, it provides a framework that unifies classical and quantum information theory. in category theory, monoidal categories can be used to define the concept of a monoid object and an associated action on the objects of the category. they are also used in the definition of an enriched category.


in some cases these functions are not defined on the whole of ℝ3. for example, the trilinears of x365 which is the 365th entry in the encyclopedia of triangle centers, are a1 / 2 : b1 / 2 : c1 / 2 so a, b, c cannot be negative. furthermore, in order to represent the sides of a triangle they must satisfy the triangle inequality. so, in practice, every function's domain is restricted to the region of ℝ3 where a ≤ b + c, b ≤ c + a, and c ≤ a + b. this region t is the domain of all triangles, and it is the default domain for all triangle - based functions.


in gis, the rmsd is one measure used to assess the accuracy of spatial analysis and remote sensing. in hydrogeology, rmsd and nrmsd are used to evaluate the calibration of a groundwater model. in imaging science, the rmsd is part of the peak signal - to - noise ratio, a measure used to assess how well a method to reconstruct an image performs relative to the original image.


in planning and problem solving, or more formally one - person games, the search space is seen as a directed graph with states as nodes, and transitions as edges. states can have properties, and such a property p is hereditary if for each state s that has p, each state that can be reached from s also has p. the subset of all states that have p plus the subset of all states that have ~ p form a partition of the set of states called a hereditary partition. this notion can trivially be extended to more discriminating partitions by instead of properties, considering aspects of states and their domains. if states have an aspect a, with di ⊂ d a partition of the domain d of a, then the subsets of states for which a ∈ di form a hereditary partition of the total set of states iff, from any state where a ∈ di only other states where a ∈ di can be reached.


in relational algebra, if r ⊆ x × y { \ displaystyle r \ subseteq x \ times y } and s ⊆ y × z { \ displaystyle s \ subseteq y \ times z } are relations, then the composite relation s r ⊆ x × z { \ displaystyle sr \ subseteq x \ times z } is defined so that x s r z { \ displaystyle x \, sr \, z } if and only if there is a y ∈ y { \ displaystyle y \ in y } such that x r y { \ displaystyle x \, r \, y } and y s z { \ displaystyle y \, s \, z }. this definition is a generalisation of the definition of functional composition. the defining properties of an equivalence relation r { \ displaystyle r } on a set x { \ displaystyle x } can then be reformulated as follows : id ⊆ r { \ displaystyle \ operatorname { id } \ subseteq r }.


additional methods for improving the algorithm's efficiency were developed in the 20th century. the euclidean algorithm has many theoretical and practical applications. it is used for reducing fractions to their simplest form and for performing division in modular arithmetic.


in telephony, a message - waiting indicator ( mwi ) is a telcordia technologies ( formerly bellcore ) term for an fsk - based telephone calling feature that illuminates an led on selected telephones to notify a telephone user of waiting voicemail messages on most north american public telephone networks and pbxs. as described in telcordia generic requirements document gr - 283 - core, a message _ waiting _ indicator ( mwi ) is a mechanism that informs the subscriber about the status of recorded messages. the subscriber may subscribe to a notification feature that makes use of the status of this mwi.


with the keyboard and display modules strapped to the operator's forearms, text could be entered by bringing the wrists together and typing. the same technology was used by ibm researchers to create the half - keyboard " belt computer. also in 1994, mik lamming and mike flynn at xerox europarc demonstrated the forget - me - not, a wearable device that would record interactions with people and devices and store this information in a database for later query.


in mathematical optimization, linear - fractional programming ( lfp ) is a generalization of linear programming ( lp ). whereas the objective function in a linear program is a linear function, the objective function in a linear - fractional program is a ratio of two linear functions. a linear program can be regarded as a special case of a linear - fractional program in which the denominator is the constant function 1. formally, a linear - fractional program is defined as the problem of maximizing ( or minimizing ) a ratio of affine functions over a polyhedron, maximize c t x + α d t x + β subject to a x ≤ b, { \ displaystyle { \ begin { aligned } { \ text { maximize } } \ quad & { \ frac { \ mathbf { c } ^ { t } \ mathbf { x } + \ alpha } { \ mathbf { d } ^ { t } \ mathbf { x } + \ beta } } \ \ { \ text { subject to } } \ quad & a \ mathbf { x } \ leq \ mathbf { b }, \ end { aligned } } } where x ∈ r n { \ displaystyle \ mathbf { x } \ in \ mathbb { r } ^ { n } } represents the vector of variables to be determined, c, d ∈ r n { \ displaystyle \ mathbf { c }, \ mathbf { d } \ in \ mathbb { r } ^ { n } } and b ∈ r m { \ displaystyle \ mathbf { b } \ in \ mathbb { r } ^ { m } } are vectors of ( known ) coefficients, a ∈ r m × n { \ displaystyle a \ in \ mathbb { r } ^ { m \ times n } } is a ( known ) matrix of coefficients and α, β ∈ r { \ displaystyle \ alpha, \ beta \ in \ mathbb { r } } are constants. the constraints have to restrict the feasible region to { x | d t x + β > 0 } { \ displaystyle \ { \ mathbf { x } | \ mathbf { d } ^ { t } \ mathbf { x } + \ beta > 0 \ } }, i. e. the region on which the denominator is positive. alternatively, the denominator of the objective function has to be strictly negative in the entire feasible region.


the utility function has the linear form : u ( x 1, x 2 ) = x 1 + x 2. { \ displaystyle u ( x _ { 1 }, x _ { 2 } ) = x _ { 1 } + x _ { 2 }. } the utility function is only weakly convex, and indeed the demand is not unique : when p 1 = p 2 { \ displaystyle p _ { 1 } = p _ { 2 } }, the consumer may divide his income in arbitrary ratios between product types 1 and 2 and get the same utility.


in programming, several notations denote hexadecimal numbers, usually involving a prefix. the prefix 0x is used in c, which would denote this value as 0x60cb. hexadecimal is used in the transfer encoding base16, in which each byte of the plaintext is broken into two 4 - bit values and represented by two hexadecimal digits.


in the unified modeling language ( uml ), an element is an abstract class with no superclass. it is used as the superclass or base class, as known by object oriented programmers, for all the metaclasses in the uml infrastructure library. all other elements in the uml inherit, directly or indirectly from element. an element has a derived composition association to itself to support the general capability for elements to own other elements. as such, it has no additional attributes as part of its specification.


in mathematics, a sparsely totient number is a certain kind of natural number. a natural number, n, is sparsely totient if for all m > n, φ ( m ) > φ ( n ) { \ displaystyle \ varphi ( m ) > \ varphi ( n ) } where φ { \ displaystyle \ varphi } is euler's totient function. the first few sparsely totient numbers are : 2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630, 660, 690, 840, 870, 1050, 1260, 1320, 1470, 1680, 1890, 2310, 2730, 2940, 3150, 3570, 3990, 4620, 4830, 5460, 5610, 5670, 6090, 6930, 7140, 7350, 8190, 9240, 9660, 9870,... ( sequence a036913 in the oeis ). the concept was introduced by david masser and peter man - kit shiu in 1986. as they showed, every primorial is sparsely totient.


in some cases, the phenomenon under study may have important spatial or temporal structure that must be considered during analysis, such as time series or image - based data. in 2005, tibshirani and colleagues introduced the fused lasso to extend the use of lasso to this type of data. the fused lasso objective function is min β { 1 n i = 1 n ( y i − x i t β ) 2 } subject to j = 1 p | β j | ≤ t 1 and j = 2 p | β j − β j − 1 | ≤ t 2. { \ displaystyle { \ begin { aligned } & \ min _ { \ beta } \ left \ { { \ frac { 1 } { n } } \ sum _ { i = 1 } ^ { n } \ left ( y _ { i } - x _ { i } ^ { t } \ beta \ right ) ^ { 2 } \ right \ } \ \ & { \ text { subject to } } \ sum _ { j = 1 } ^ { p } | \ beta _ { j } | \ leq t _ { 1 } { \ text { and } } \ sum _ { j = 2 } ^ { p } | \ beta _ { j } - \ beta _ { j - 1 } | \ leq t _ { 2 }. \ end { aligned } } } the first constraint is the lasso constraint, while the second directly penalizes large changes with respect to the temporal or spatial structure, which forces the coefficients to vary smoothly to reflect the system's underlying logic.


all these principles limit the set of possible correlations in non - trivial ways. moreover, they are all device - independent : this means that they can be falsified under the assumption that we can decide if two or more events are space - like separated. the drawback of the device - independent approach is that, even when taken together, all the afore - mentioned physical principles do not suffice to single out the set of quantum correlations. in other words : all such reconstructions are partial.


by quadratic reciprocity and the restriction of the vertices to primes congruent to 1 mod 4, this is a symmetric relation, so it defines an undirected graph, which turns out to be isomorphic to the rado graph. another construction of the rado graph shows that it is an infinite circulant graph, with the integers as its vertices and with an edge between each two integers whose distance ( the absolute value of their difference ) belongs to a particular set s { \ displaystyle s }. to construct the rado graph in this way, s { \ displaystyle s } may be chosen randomly, or by choosing the indicator function of s { \ displaystyle s } to be the concatenation of all finite binary sequences. the rado graph can also be constructed as the block intersection graph of an infinite block design in which the number of points and the size of each block are countably infinite. it can also be constructed as the fraisse limit of the class of finite graphs.


z ∈ i ∗ { \ displaystyle z \ in i ^ { * } } if and only if there exists a c ∈ r { \ displaystyle c \ in r }, where c { \ displaystyle c } is not contained in any minimal prime ideal of r { \ displaystyle r }, such that c z p e ∈ i { \ displaystyle cz ^ { p ^ { e } } \ in i ^ { } } for all e 0 { \ displaystyle e \ gg 0 }. if r { \ displaystyle r } is reduced, then one can instead consider all e > 0 { \ displaystyle e > 0 }. here i { \ displaystyle i ^ { } } is used to denote the ideal of r { \ displaystyle r } generated by the p e { \ displaystyle p ^ { e } }'th powers of elements of i { \ displaystyle i }, called the e { \ displaystyle e } th frobenius power of i { \ displaystyle i }. an ideal is called tightly closed if i = i ∗ { \ displaystyle i = i ^ { * } }.


in mathematics, specifically group theory, finite groups of prime power order p n { \ displaystyle p ^ { n } }, for a fixed prime number p { \ displaystyle p } and varying integer exponents n ≥ 0 { \ displaystyle n \ geq 0 }, are briefly called finite p - groups. the p - group generation algorithm by m. f. newman and e. a. o'brien is a recursive process for constructing the descendant tree of an assigned finite p - group which is taken as the root of the tree.


this signal would feed into the sound - card audio - input of the pc, and banpaia would decode the esn / mdn pair from this signal and display it on the screen. the hacker could then copy that data into the oki 900 phone and reboot it, after which the phone network could not distinguish the oki from the original phone whose signal had been received. this gave the cloner, through the oki phone, the ability to use the mobile - phone service of the legitimate subscriber whose phone was cloned – just as if that phone had been physically stolen, except that the subscriber retained his or her phone, unaware that the phone had been cloned — at least until that subscriber received his or her next bill.


for every input position, the parser generates a state set. each state is a tuple ( x → α • β, i ), consisting of the production currently being matched ( x → α β ) the current position in that production ( visually represented by the dot • ) the position i in the input at which the matching of this production began : the origin position ( earley's original algorithm included a look - ahead in the state ; later research showed this to have little practical effect on the parsing efficiency, and it has subsequently been dropped from most implementations. ) a state is finished when its current position is the last position of the right side of the production, that is, when there is no symbol to the right of the dot • in the visual representation of the state.


in operations research, the makespan of a project is the length of time that elapses from the start of work to the end. this type of multi - mode resource constrained project scheduling problem ( mrcpsp ) seeks to create the shortest logical project schedule, by efficiently using project resources, adding the lowest number of additional resources as possible to achieve the minimum makespan. the term commonly appears in the context of scheduling.


{ \ displaystyle ( a - \ mu i ) ^ { - 1 }. } the closer the approximation μ { \ displaystyle \ mu } to the eigenvalue is chosen, the faster the algorithm converges ; however, incorrect choice of μ { \ displaystyle \ mu } can lead to slow convergence or to the convergence to an eigenvector other than the one desired. in practice, the method is used when a good approximation for the eigenvalue is known, and hence one needs only few ( quite often just one ) iterations.


in the data transformation stage, a series of rules or functions are applied to the extracted data in order to prepare it for loading into the end target. an important function of transformation is data cleansing, which aims to pass only " proper " data to the target. the challenge when different systems interact is in the relevant systems'interfacing and communicating.


( see, for example, the fermi – pasta – ulam – tsingou experiment of 1953. ) assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the second kind are impossible. systems that are ergodic are said to have the property of ergodicity ; a broad range of systems in geometry, physics, and probability are ergodic. ergodic systems are studied in ergodic theory.


in the 1980s, a tiny cpu that executed forth was fabricated into a dram chip to improve push and pop. forth is a stack - oriented programming language and this improved its efficiency. the transputer also had large on chip memory given that it was made in the early 1980s making it essentially a processor - in - memory. notable pim projects include the berkeley iram project ( iram ) at the university of california, berkeley project and the university of notre dame pim effort.


for example, rd2xbd6. concise reversible algebraic notation is similar to reversible algebraic notation, but omits the file or rank if it is not needed to disambiguate the move. for example, rd2xb6.


in modular construction, modules are a bundle of redundant project components that are produced en masse prior to installation. building components are often arranged into modules in the industrialization of construction. in industrial design, modularity refers to an engineering technique that builds larger systems by combining smaller subsystems. in manufacturing, modularity typically refers to modular design, either as the use of exchangeable parts or options in the fabrication of an object or the design and manufacture of modular components. in organizational design, richard l. daft and arie y. lewin ( 1993 ) identified a paradigm called " modular organization " that had as its ground the need for flexible learning organizations in constant change and the need to solve their problems through coordinated self - organizing processes. this modular organization is characterized by decentralized decision - making, flatter hierarchies, self - organization of units.


in the microsoft family of operating systems, windows vista and later versions have support for both msi and msi - x. support was added in the longhorn development cycle around 2004. msi is not supported in earlier versions like windows xp or windows server 2003. solaris express 6 / 05 released in 2005 added support for msi an msi - x as part of their new device driver interface ( ddi ) interrupt framework. freebsd 6. 3 and 7. 0 released in 2008 added support for msi and msi - x. openbsd 5. 0 released in 2011 added support for msi. 6. 0 added support for msi - x. linux gained support for msi and msi - x around 2003.


portuguese and spanish also have unique forms for 1st, 2nd and 3rd person reflexive when they follow the preposition com / con ('with'). that holds true for both singular and plural pronouns for portuguese, but only for singular in spanish.


in metadata, annotea is an rdf standard sponsored by the w3c to enhance document - based collaboration via shared document metadata based on tags, bookmarks, and other annotations. in this case document metadata includes : keywords comments notes explanations errors correctionsin general, annotea associates text strings to a web document or selected parts of a web document without actually needing to modify the original document. users that access any web documents can also load the metadata associated with it from a selected annotation server ( or groups of servers ) and see a peer group's comments on the document. similarly shared metadata tags can be attached to web documents to help in future retrieval.


tikhonov ( tychonoff ) fixed - point theorem : let v be a locally convex topological vector space. for any nonempty compact convex set x in v, any continuous function f : x → x has a fixed point. browder fixed - point theorem : let k be a nonempty closed bounded convex set in a uniformly convex banach space.


in set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets.


in non - pae modes of 32 - bit x86 processors, the usable ram may be limited to less than 4 gb. limits on memory and address space vary by platform and operating system. limits on physical memory for 32 - bit platforms also depend on the presence and use of physical address extension ( pae ), which allows 32 - bit systems to use more than 4 gb of physical memory. pae and 64 - bit systems may be able to address up to the full address space of the x86 processor.


in mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations ( called hyperoperations in this context ) that starts with a unary operation ( the successor function with n = 0 ). the sequence continues with the binary operations of addition ( n = 1 ), multiplication ( n = 2 ), and exponentiation ( n = 3 ). after that, the sequence proceeds with further binary operations extending beyond exponentiation, using right - associativity. for the operations beyond exponentiation, the nth member of this sequence is named by reuben goodstein after the greek prefix of n suffixed with - ation ( such as tetration ( n = 4 ), pentation ( n = 5 ), hexation ( n = 6 ), etc. ) and can be written as using n − 2 arrows in knuth's up - arrow notation. each hyperoperation may be understood recursively in terms of the previous one by : a b = a ( a ( a ( ( a ( a a ) ) ) ) ) b copies of a, n ≥ 2 { \ displaystyle ab = \ underbrace { a ( a ( a ( \ cdots ( a ( aa ) ) \ cdots ) ) ) } _ { \ displaystyle b { \ mbox { copies of } } a }, \ quad n \ geq 2 } it may also be defined according to the recursion rule part of the definition, as in knuth's up - arrow version of the ackermann function : a b = a ( a ( b − 1 ) ), n ≥ 1 { \ displaystyle ab = a \ left ( a \ left ( b - 1 \ right ) \ right ), \ quad n \ geq 1 } this can be used to easily show numbers much larger than those which scientific notation can, such as skewes's number and googolplexplex ( e. g. 50 50 { \ displaystyle 5050 } is much larger than skewes's number and googolplexplex ), but there are some numbers which even they cannot easily show, such as graham's number and tree ( 3 ). this recursion rule is common to many variants of hyperoperations.


in network theory, link analysis is a data - analysis technique used to evaluate relationships ( tap link ) between nodes. relationships may be identified among various types of nodes ( 100k ), including organizations, people and transactions. link analysis has been used for investigation of criminal activity ( fraud, counterterrorism, and intelligence ), computer security analysis, search engine optimization, market research, medical research, and art.


the opteron cpu directly supports up to an 8 - way configuration, which can be found in mid - level servers. enterprise - level servers use additional ( and expensive ) routing chips to support more than 8 cpus per box. in a variety of computing benchmarks, the opteron architecture has demonstrated better multi - processor scaling than the intel xeon which didn't have a point to point system until qpi and integrated memory controllers with the nehalem design.


equipped with the λ - calculus and " general " recursion, kleene with help of church and j. barkley rosser produced proofs ( 1933, 1935 ) to show that the two calculi are equivalent. church subsequently modified his methods to include use of herbrand – godel recursion and then proved ( 1936 ) that the entscheidungsproblem is unsolvable : there is no algorithm that can determine whether a well formed formula has a beta normal form. many years later in a letter to davis ( c. 1965 ), godel said that " he was, at the time of these lectures, not at all convinced that his concept of recursion comprised all possible recursions ".


another popular strategy for avoiding linguistic controversy is dependency grammar parsing. most modern parsers are at least partly statistical ; that is, they rely on a corpus of training data which has already been annotated ( parsed by hand ).


some machines that support parity or ecc allow checking to be enabled or disabled in the bios, permitting cheaper non - parity ram to be used. if parity ram is used the chipset will usually use it to implement error correction, rather than halting the machine on a single - bit parity error. however, as discussed in the article on ecc memory, errors, while not everyday events, are not negligibly infrequent. even in the absence of manufacturing defects, naturally occurring radiation causes random errors ; tests on google's many servers found that memory errors were not rare events, and that the incidence of memory errors and the range of error rates across different dimms were much higher than previously reported.


in probability theory and statistics, a sequence of independent bernoulli trials with probability 1 / 2 of success on each trial is metaphorically called a fair coin. one for which the probability is not 1 / 2 is called a biased or unfair coin. in theoretical studies, the assumption that a coin is fair is often made by referring to an ideal coin. john edmund kerrich performed experiments in coin flipping and found that a coin made from a wooden disk about the size of a crown and coated on one side with lead landed heads ( wooden side up ) 679 times out of 1000.


in neural networking or heuristic algorithms ( computer terms generally used to describe'learning'computers or'ai simulations'), a black box is used to describe the constantly changing section of the program environment which cannot easily be tested by the programmers. this is also called a white box in the context that the program code can be seen, but the code is so complex that it is functionally equivalent to a black box. in physics, a black box is a system whose internal structure is unknown, or need not be considered for a particular purpose. in cryptography to capture the notion of knowledge obtained by an algorithm through the execution of a cryptographic protocol such as a zero - knowledge proof protocol. if the output of an algorithm when interacting with the protocol matches that of a simulator given some inputs, it only needs to know the inputs.


in number theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset s of positive integers can be partitioned into two subsets s1 and s2 such that the sum of the numbers in s1 equals the sum of the numbers in s2. although the partition problem is np - complete, there is a pseudo - polynomial time dynamic programming solution, and there are heuristics that solve the problem in many instances, either optimally or approximately. for this reason, it has been called " the easiest hard problem ". there is an optimization version of the partition problem, which is to partition the multiset s into two subsets s1, s2 such that the difference between the sum of elements in s1 and the sum of elements in s2 is minimized. the optimization version is np - hard, but can be solved efficiently in practice. the partition problem is a special case of two related problems : in the subset sum problem, the goal is to find a subset of s whose sum is a certain target number t given as input ( the partition problem is the special case in which t is half the sum of s ).


a branch may have one incoming control flow and two or more outgoing control flows. when the condition is fulfilled, a branch activates exactly only one of the outgoing control flows and deactivates the others. the counterpart of a branch is a merge.


the service will then prompt the user to enter the dialed number of the party to be called. the disadvantage of this method of roaming is that the user will not be able to dial numbers directly from the handset. the advantage is that it works in almost all locations around the world since ussd is ubiquitous and free.


in the first half of the 20th century, telecommunication services developed progressively from completely manual setup of calls by operators called by subscribers, to automatic systems that could connect subscribers of the same local exchange through the use of telephone dials installed in each telephone. in the 1940s, the bell system in the united states and canada developed methods and technologies, called direct distance dialing and first implemented in 1951, that enabled telephone subscriber to dial long - distance telephone calls themselves without calling an operator. in the united kingdom, a similar technology called subscriber trunk dialling ( std ) was ready by 1958, when queen elizabeth ii, who was in bristol, publicised std by dialling edinburgh, the farthest distance a call could be directly dialled in the uk, on 5 december 1958. the std system was completed in 1979. the technology was extended when, from 8 march 1963, subscribers in london were able to directly dial paris using international direct dialling.


in the field of mathematical optimization, lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler problem. a solution to the relaxed problem is an approximate solution to the original problem, and provides useful information. the method penalizes violations of inequality constraints using a lagrange multiplier, which imposes a cost on violations. these added costs are used instead of the strict inequality constraints in the optimization. in practice, this relaxed problem can often be solved more easily than the original problem. the problem of maximizing the lagrangian function of the dual variables ( the lagrangian multipliers ) is the lagrangian dual problem.


{ \ displaystyle e = e = \ alpha + \ beta x _ { i } + e = \ alpha + \ beta x _ { i }. } the line of best fit for the bivariate dataset takes the form y = α + βx and is called the regression line. α and β correspond to the intercept and slope, respectively. in an experiment, the variable manipulated by an experimenter is something that is proven to work, called an independent variable.


in mathematics, the samuelson – berkowitz algorithm efficiently computes the characteristic polynomial of an n × n { \ displaystyle n \ times n } matrix whose entries may be elements of any unital commutative ring. unlike the faddeev – leverrier algorithm, it performs no divisions, so may be applied to a wider range of algebraic structures.


in the absence of parentheses, the parallel operator is defined as taking precedence over addition or subtraction, similar to multiplication.


in mathematics, the prime signature of a number is the multiset of ( nonzero ) exponents of its prime factorization. the prime signature of a number having prime factorization p 1 m 1 p 2 m 2 … p n m n { \ displaystyle p _ { 1 } ^ { m _ { 1 } } p _ { 2 } ^ { m _ { 2 } } \ dots p _ { n } ^ { m _ { n } } } is the multiset { m 1, m 2, …, m n } { \ displaystyle \ left \ { m _ { 1 }, m _ { 2 }, \ dots, m _ { n } \ right \ } }. for example, all prime numbers have a prime signature of { 1 }, the squares of primes have a prime signature of { 2 }, the products of 2 distinct primes have a prime signature of { 1, 1 } and the products of a square of a prime and a different prime ( e. g. 12, 18, 20,... ) have a prime signature of { 2, 1 }.


for example, individuals in a population can be assigned to compartments with labels – for example, s, i, or r, ( susceptible, infectious, or recovered ) and they progress between compartments. the order of the labels usually shows the flow patterns between the compartments ; for instance, sir means each individual is originally susceptible then changes to infectious and finally gets recovered and remained recovered ( immune ) forever. on the other hand, public health may apply some interventions such as vaccination or contact tracing to reduce the spread of an epidemic disease.


in statistics, a sum of squares due to lack of fit, or more tersely a lack - of - fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an f - test of the null hypothesis that says that a proposed model fits well. the other component is the pure - error sum of squares. the pure - error sum of squares is the sum of squared deviations of each value of the dependent variable from the average value over all observations sharing its independent variable value ( s ). these are errors that could never be avoided by any predictive equation that assigned a predicted value for the dependent variable as a function of the value ( s ) of the independent variable ( s ). the remainder of the residual sum of squares is attributed to lack of fit of the model since it would be mathematically possible to eliminate these errors entirely.


in multitasking computer operating systems, a daemon ( or ) is a computer program that runs as a background process, rather than being under the direct control of an interactive user. traditionally, the process names of a daemon end with the letter d, for clarification that the process is in fact a daemon, and for differentiation between a daemon and a normal computer program. for example, syslogd is a daemon that implements system logging facility, and sshd is a daemon that serves incoming ssh connections. in a unix environment, the parent process of a daemon is often, but not always, the init process.


the distinction arises because it is conventional to talk not about estimating fixed effects but rather about predicting random effects, but the two terms are otherwise equivalent. ( this is a bit strange since the random effects have already been " realized " ; they already exist. the use of the term " prediction " may be because in the field of animal breeding in which henderson worked, the random effects were usually genetic merit, which could be used to predict the quality of offspring ( robinson page 28 ) ).


complementary configuration occurs when multiple information sources supply different information about the same features. this strategy is used for fusing information at raw data level within decision - making algorithms.


effectiveness in using a system for controlling a continuous industrial process would generally be measured in very different terms to, say, effectiveness in using a text editor. thus, it can be difficult, if not impossible, to answer the question " is system a more usable than system b ", because the measures of effectiveness and efficiency may be very different. however, it can be argued that given a sufficiently high - level definition of subjective assessments of usability, comparisons can be made between systems.


in numerical linear algebra, the bartels – stewart algorithm is used to numerically solve the sylvester matrix equation a x − x b = c { \ displaystyle ax - xb = c }. developed by r. h. bartels and g. w.


there is specific verbal morphology — a particular form of the verb indicates passive voice. the problem arises with non - european languages. many constructions in these languages share at least one property with the canonical european passive, but not all. while it seems justified to call these constructions passive when comparing them to european languages'passive constructions, as a whole the passives of the world's languages do not share a single common feature.


in muscle physiology, physiological cross - sectional area ( pcsa ) is the area of the cross section of a muscle perpendicular to its fibers, generally at its largest point. it is typically used to describe the contraction properties of pennate muscles. it is not the same as the anatomical cross - sectional area ( acsa ), which is the area of the crossection of a muscle perpendicular to its longitudinal axis. in a non - pennate muscle the fibers are parallel to the longitudinal axis, and therefore pcsa and acsa coincide.


in telecommunications, 8b / 10b is a line code that maps 8 - bit words to 10 - bit symbols to achieve dc balance and bounded disparity, and at the same time provide enough state changes to allow reasonable clock recovery. this means that the difference between the counts of ones and zeros in a string of at least 20 bits is no more than two, and that there are not more than five ones or zeros in a row. this helps to reduce the demand for the lower bandwidth limit of the channel necessary to transfer the signal. an 8b / 10b code can be implemented in various ways with focus on different performance parameters.


they are infinite in number. they constitute the comparatively rare instances where the strict converse of fermat's little theorem does not hold. this fact precludes the use of that theorem as an absolute test of primality. the carmichael numbers form the subset k1 of the knodel numbers.


in this case, rather than simply counting through elements of the population and selecting every kth unit, we allocate each element a space along a number line according to its selection probability. we then generate a random start from a uniform distribution between 0 and 1, and move along the number line in steps of 1. example : we have a population of 5 units ( a to e ).


in relational databases, the information schema ( information _ schema ) is an ansi - standard set of read - only views that provide information about all of the tables, views, columns, and procedures in a database. it can be used as a source of the information that some databases make available through non - standard commands, such as : the show command of mysql the describe command of oracle's sql * plus the \ d command in psql ( postgresql's default command - line program ). = > select count ( table _ name ) from information _ schema. tables ; count - - - - - - - 99 ( 1 row ) = > select column _ name, data _ type, column _ default, is _ nullable from information _ schema. columns where table _ name ='alpha'; column _ name | data _ type | column _ default | is _ nullable - - - - - - - - - - - - - + - - - - - - - - - - - + - - - - - - - - - - - - - - - - + - - - - - - - - - - - - - foo | integer | | yes bar | character | | yes ( 2 rows ) = > select * from information _ schema. information _ schema _ catalog _ name ; catalog _ name - - - - - - - - - - - - - - johnd ( 1 row )


in software, semantic technology encodes meanings separately from data and content files, and separately from application code. this enables machines as well as people to understand, share and reason with them at execution time. with semantic technologies, adding, changing and implementing new relationships or interconnecting programs in a different way can be just as simple as changing the external model that these programs share. with traditional information technology, on the other hand, meanings and relationships must be predefined and " hard wired " into data formats and the application program code at design time.


in the european union the classifications for vehicle types are defined by : commission directive 2001 / 116 / ec of 20 december 2001, adapting to technical progress council directive 70 / 156 / eec on the approximation of the laws of the member states relating to the type - approval of motor vehicles and their trailers directive 2002 / 24 / ec of the european parliament and of the council of 18 march 2002 relating to the type - approval of two or three wheeled motor vehicles and repealing council directive 92 / 61 / eeceuropean community, is based on the community's wvta ( whole vehicle type - approval ) system. under this system, manufacturers can obtain certification for a vehicle type in one member state if it meets the ec technical requirements and then market it eu - wide with no need for further tests. total technical harmonization already has been achieved in three vehicle categories ( passenger cars, motorcycles, and tractors ) and soon will extend to other vehicle categories ( coaches and utility vehicles ). it is essential that european car manufacturers be ensured access to as large a market as possible. while the community type - approval system allows manufacturers to benefit fully from internal market opportunities, worldwide technical harmonization in the context of the united nations economic commission for europe ( unece ) offers a market beyond european borders.


in mathematics, the domain of a function is the set of inputs accepted by the function. it is sometimes denoted by dom ( f ) { \ displaystyle \ operatorname { dom } ( f ) } or dom f { \ displaystyle \ operatorname { dom } f }, where f is the function. in layman's terms, the domain of a function can generally be thought of as " what x can be ". more precisely, given a function f : x → y { \ displaystyle f \ colon x \ to y }, the domain of f is x. in modern mathematical language, the domain is part of the definition of a function rather than a property of it. in the special case that x and y are both subsets of r { \ displaystyle \ mathbb { r } }, the function f can be graphed in the cartesian coordinate system.


in mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of lie type, or one of 26 sporadic groups. the list below gives all finite simple groups, together with their order, the size of the schur multiplier, the size of the outer automorphism group, usually some small representations, and lists of all duplicates.


in the japanese kantenji braille, the standard 8 - dot braille patterns 567, 1567, 4567, and 14567 are the patterns related to braille pattern dots - 345, since the two additional dots of kantenji patterns 0345, 3457, and 03457 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


as blacks integrate to white communities they are perpetuating a system in which blacks are inferior to whites. blacks would continue to function in an environment of being second class citizens, he believes, never reaching equity to white citizens. carmichael therefore uses the concept of black nationalism to promote an equality that would begin to dismantle institutional racism.


in mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process. types of random trees include : uniform spanning tree, a spanning tree of a given graph in which each different tree is equally likely to be selected random minimal spanning tree, spanning trees of a graph formed by choosing random edge weights and using the minimum spanning tree for those weights random binary tree, binary trees with a given number of nodes, formed by inserting the nodes in a random order or by selecting all possible trees uniformly at random random recursive tree, increasingly labelled trees, which can be generated using a simple stochastic growth rule. treap or randomized binary search tree, a data structure that uses random choices to simulate a random binary tree for non - random update sequences rapidly exploring random tree, a fractal space - filling pattern used as a data structure for searching high - dimensional spaces brownian tree, a fractal tree structure created by diffusion - limited aggregation processes random forest, a machine - learning classifier based on choosing random subsets of variables for each tree and using the most frequent tree output as the overall classification branching process, a model of a population in which each individual has a random number of children


in mathematics, an operation is a function which takes zero or more input values ( also called " operands " or " arguments " ) to a well - defined output value. the number of operands is the arity of the operation. the most commonly studied operations are binary operations ( i. e., operations of arity 2 ), such as addition and multiplication, and unary operations ( i. e., operations of arity 1 ), such as additive inverse and multiplicative inverse. an operation of arity zero, or nullary operation, is a constant.


in the following, we state two equivalent forms of the theorem, and show their equivalence. later, we prove the theorem. this is done in the following steps : reducing the theorem to sentences ( formulas with no free variables ) in prenex form, i. e. with all quantifiers ( and ) at the beginning.


in the following, let x { \ displaystyle x } be a topological space, g, h { \ displaystyle g, h } topological groups and a group homomorphism : h → g { \ displaystyle \ phi \ colon h \ to g }.


in 1972, jurjen battjes, commissioned by the dutch technical advisory committee for flood defences, summarised the available research and provided a solid theoretical foundation. this work led to an improved version of hunt's formula, which explicitly included parameters for the angle of incidence of the waves, the effect of a berm, and the slope's roughness. however, the available experimental data on roughness and the berm were insufficient to establish a definitive formula.


the inequality is a limiting case of sobolev imbedding and can be stated as the following theorem : let ω { \ displaystyle \ omega } be a bounded domain in r n { \ displaystyle \ mathbb { r } ^ { n } } satisfying the cone condition. let m p = n { \ displaystyle mp = n } and p > 1 { \ displaystyle p > 1 }. set a ( t ) = exp ( t n / ( n − m ) ) − 1.


one of the biggest problems with this form of scientific fraud is that " university investigations into research misconduct are often inadequate, opaque and poorly conducted. they challenge the idea that institutions can police themselves on research integrity. " sometimes intentional fabrication can be difficult to distinguish from unintentional academic incompetence or malpractice.


as a result of being relatively close to the femtocell, the mobile phone ( user equipment ) expends significantly less power for communication with it, thus increasing battery life. they may also get better voice quality ( via hd voice ) depending on a number of factors such as operator / network support, customer contract / price plan, phone and operating system support. some carriers may also offer more attractive tariffs, for example discounted calls from home.


shortly after neo visits the oracle, morpheus is captured by agents who plan to hack into his mind. because morpheus, as a hovercraft captain, possesses access codes to the zion mainframe computer, the surviving members of the ship's crew are about to unplug morpheus from the matrix, without reconnecting his mind and body, a process that will kill him. neo and trinity, however, reenter the matrix to make a daring and successful rescue of morpheus. neo saves trinity from a helicopter crash, confirming morpheus'belief that neo is indeed the one. neo is eventually killed by agent smith shortly after the rescue, but revived as the one and returned to the nebuchadnezzar before the machines'sentinels can destroy the ship.


in mathematics, topology ( from the greek words τοπος,'place, location ', and λογος,'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing. a topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. the deformations that are considered in topology are homeomorphisms and homotopies.


in puzzle games, scores are usually gained by solving the puzzles quickly. higher scores can be gained by performing combos of puzzle solving. there is often a time bonus which can add extra points. the level number is often a multiplier on the points, so higher scores are possible on harder levels.


in quantum information theory, superdense coding ( also referred to as dense coding ) is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assumption of sender and receiver pre - sharing an entangled resource. in its simplest form, the protocol involves two parties, often referred to as alice and bob in this context, which share a pair of maximally entangled qubits, and allows alice to transmit two bits ( i. e., one of 00, 01, 10 or 11 ) to bob by sending only one qubit. this protocol was first proposed by charles h. bennett and stephen wiesner in 1970 ( though not published by them until 1992 ) and experimentally actualized in 1996 by klaus mattle, harald weinfurter, paul g. kwiat and anton zeilinger using entangled photon pairs. superdense coding can be thought of as the opposite of quantum teleportation, in which one transfers one qubit from alice to bob by communicating two classical bits, as long as alice and bob have a pre - shared bell pair. the transmission of two bits via a single qubit is made possible by the fact that alice can choose among four quantum gate operations to perform on her share of the entangled state.


manchester ship canal at latchford, stockton heath and lower walton in warrington, and also slightly further west at moore. near the eastern end of the canal in salford, the barton road swing bridge is adjacent to the barton swing aqueduct – a 234 - foot, 800 - ton trough holding some 800 tons of water ( retained by gates at either end ) swings so that it is at right angles to the bridgewater canal to allow ships to pass up the ship canal. myton swing bridge - road bridge in kingston upon hull oulton broad swing bridge – rail reedham swing bridge ( 52. 55887°n 1. 57237°e / 52. 55887 ; 1. 57237 ) – rail ross bridge, penzance sandwich toll bridge ( rebuilt 1892 ) selby swing bridge – rail somerleyton swing bridge trowse bridge at norwich.


{ \ displaystyle x. } remark.


the goal is for the referee to find an algorithm such that if the statement is true, there is a way for alice to win with probability greater than 3 / 4, and if the statement is false, there is a way for bob to win with probability greater than 3 / 4. this probability is equal to 1 - ε. in the language of complexity theory, a promise problem l = ( l yes, l no ) { \ displaystyle l = ( l _ { \ text { yes } }, l _ { \ text { no } } ) } has a classical refereed game ( classical rg ) if there exists a referee described by polynomial time randomized computation, such that 1. for each x ∈ l yes { \ displaystyle x \ in l _ { \ text { yes } } }, there is a strategy for alice to win with probability ≥ 3 / 4, and2. for each x ∈ l no { \ displaystyle x \ in l _ { \ text { no } } }, there is a strategy for bob to win with probability ≥ 3 / 4. it is known that rg = exp.


it should not be confused with the dot product ( projection product ). if two vectors have the same direction or have the exact opposite direction from each other ( that is, they are not linearly independent ), or if either one has zero length, then their cross product is zero. more generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides ; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths.


p ( if a, then b ) is normally interpreted not as an ordinary probability — not, specifically, as p ( a ′ ∨ b ) — but as the conditional probability of b given a, p ( b | a ) = p ( a ∧ b ) / p ( a ). this raises a question : what about a probability like p ( if a, then b, and if c, then d )? for this, there is no standard answer. what would be needed, for consistency, is a treatment of if - then as a binary operation, →, such that for conditional events a → b and c → d, p ( a → b ) = p ( b | a ), p ( c → d ) = p ( d | c ), and p ( ( a → b ) ∧ ( c → d ) ) is well - defined and reasonable. this treatment is what conditional event algebras try to provide.


in real social networks individuals exhibit a tendency to re - connect with past contacts ( ex. family, friends, co - workers, etc. ) rather than strangers. in 1970, mark granovetter examined this behaviour in the social networks of a group of workers and identified tie strength, a characteristic of social ties describing the frequency of contact between two individuals. from this comes the idea of strong and weak ties, where an individual's strong ties are those she has come into frequent contact with. link - centric preferential attachment aims to explain the mechanism behind strong and weak ties as a stochastic reinforcement process for old ties in agent - based modeling where nodes have long - term memory.


in the japanese kantenji braille, the standard 8 - dot braille patterns 378, 1378, 3478, and 13478 are the patterns related to braille pattern dots - 236, since the two additional dots of kantenji patterns 0236, 2367, and 02367 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


in optimal transport, a branch of mathematics, polar factorization of vector fields is a basic result due to brenier ( 1987 ), with antecedents of knott - smith ( 1984 ) and rachev ( 1985 ), that generalizes many existing results among which are the polar decomposition of real matrices, and the rearrangement of real - valued functions.


it is trained by repeatedly exposing it to examples of the problem and learning the significance ( weights ) of the input nodes. : 196 the neural network used by split _ up is said to generalise well if the output of the network is correct ( or nearly correct ) for examples not seen during training, which classifies it as an intelligent system. : 274


however, most prepaid phones now offer roaming using one of the following methods : the prepaid mobile phone user dials a " trigger " number from the foreign location using a ussd message which is not charged for while roaming. upon receipt of the ussd, the customer's operator will then return the call. when the service calls back, the user is being charged for the cost of the service from the credit available in the home network.


in part because the shannon capacity is difficult to compute, researchers have looked for other graph invariants that are easy to compute and that provide bounds on the shannon capacity.


in set theory, xy is the notation representing the set of all functions from y to x. as " 2 " can be defined as { 0, 1 } ( see, for example, von neumann ordinals ), 2s ( i. e., { 0, 1 } s ) is the set of all functions from s to { 0, 1 }. as shown above, 2s and the power set of s, p ( s ), are considered identical set - theoretically. this equivalence can be applied to the example above, in which s = { x, y, z }, to get the isomorphism with the binary representations of numbers from 0 to 2n − 1, with n being the number of elements in the set s or | s | = n. first, the enumerated set { ( x, 1 ), ( y, 2 ), ( z, 3 ) } is defined in which the number in each ordered pair represents the position of the paired element of s in a sequence of binary digits such as { x, y } = 011 ( 2 ) ; x of s is located at the first from the right of this sequence and y is at the second from the right, and 1 in the sequence means the element of s corresponding to the position of it in the sequence exists in the subset of s for the sequence while 0 means it does not. for the whole power set of s, we get : such a injective mapping from p ( s ) to integers is arbitrary, so this representation of all the subsets of s is not unique, but the sort order of the enumerated set does not change its cardinality.