in 1976, refinanced by the canada development corporation, it returned to operation as aes data, and went on to successfully market its brand of word processors worldwide until its demise in the mid - 1980s. its first office product, the aes - 90, combined for the first time a crt - screen, a floppy - disk and a microprocessor, that is, the very same winning combination that would be used by ibm for its pc seven years later. the aes - 90 software was able to handle french and english typing from the start, displaying and printing the texts side - by - side, a canadian government requirement.


in the following, expose ( v ) { \ displaystyle { \ text { expose } } ( v ) } extracts the left child l { \ displaystyle l }, key k { \ displaystyle k }, and right child r { \ displaystyle r } of node v { \ displaystyle v } into a tuple ( l, k, r ) { \ displaystyle ( l, k, r ) }. node ( l, k, r ) { \ displaystyle { \ text { node } } ( l, k, r ) } creates a node with left child l { \ displaystyle l }, key k { \ displaystyle k } and right child r { \ displaystyle r }. " s 1 | | s 2 { \ displaystyle s _ { 1 } | | s _ { 2 } } " means that two statements s 1 { \ displaystyle s _ { 1 } } and s 2 { \ displaystyle s _ { 2 } } can run in parallel.


in set theory language here, speak of a function class when f ⊂ a × c { \ displaystyle f \ subset a \ times c } and provenly ( a ∈ a ).! ( c ∈ c ). ⟨ a, c ⟩ ∈ f { \ displaystyle \ forall ( a \ in a ). \, \ exists!


nevertheless, the machine was air cooled, and would have been the fastest such machine on the market. the machine ran an early version of the mach kernel for multi - processor support. the compilers were designed to keep the processors as full as possible by reducing the number of branch delay slots, and did a particularly good job of it.


in mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem - proving technique for sentences in propositional logic and first - order logic. for propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsatisfiability, solving the ( complement of the ) boolean satisfiability problem. for first - order logic, resolution can be used as the basis for a semi - algorithm for the unsatisfiability problem of first - order logic, providing a more practical method than one following from godel's completeness theorem. the resolution rule can be traced back to davis and putnam ( 1960 ) ; however, their algorithm required trying all ground instances of the given formula. this source of combinatorial explosion was eliminated in 1965 by john alan robinson's syntactical unification algorithm, which allowed one to instantiate the formula during the proof " on demand " just as far as needed to keep refutation completeness. the clause produced by a resolution rule is sometimes called a resolvent.


in numerical analysis, pairwise summation, also called cascade summation, is a technique to sum a sequence of finite - precision floating - point numbers that substantially reduces the accumulated round - off error compared to naively accumulating the sum in sequence. although there are other techniques such as kahan summation that typically have even smaller round - off errors, pairwise summation is nearly as good ( differing only by a logarithmic factor ) while having much lower computational cost — it can be implemented so as to have nearly the same cost ( and exactly the same number of arithmetic operations ) as naive summation. in particular, pairwise summation of a sequence of n numbers xn works by recursively breaking the sequence into two halves, summing each half, and adding the two sums : a divide and conquer algorithm.


in real analysis, a branch of mathematics, a modulus of convergence is a function that tells how quickly a convergent sequence converges. these moduli are often employed in the study of computable analysis and constructive mathematics. if a sequence of real numbers x i { \ displaystyle x _ { i } } converges to a real number x { \ displaystyle x }, then by definition, for every real ε > 0 { \ displaystyle \ varepsilon > 0 } there is a natural number n { \ displaystyle n } such that if i > n { \ displaystyle i > n } then | x − x i | < ε { \ displaystyle \ left | x - x _ { i } \ right | < \ varepsilon }. a modulus of convergence is essentially a function that, given ε { \ displaystyle \ varepsilon }, returns a corresponding value of n { \ displaystyle n }.


example : slow memory diagram depicts a slow consistency example. the first process writes 1 to the memory location x and then it writes 1 to the memory location y. the second process reads 1 from y and it then reads 0 from x even though x was written before y. hutto, phillip w., and mustaque ahamad ( 1990 ) illustrate that by appropriate programming, slow memory ( consistency ) can be expressive and efficient. they mention that slow memory has two valuable properties ; locality and supporting reduction from atomic memory. they propose two algorithms to present the expressiveness of slow memory.


mersenne primes were studied in antiquity because of their close connection to perfect numbers : the euclid – euler theorem asserts a one - to - one correspondence between even perfect numbers and mersenne primes. many of the largest known primes are mersenne primes because mersenne numbers are easier to check for primality. as of 2023, 51 mersenne primes are known.


in the early 1970s, a noted nuclear scientist isadore perlman undertook the analysis of numerous cypriot ceramics sent to him by the swedish archaeologist, einar gherstad, when he pioneered high - precision methods of neutron activation analysis at the lawrence berkeley laboratory in the us. neutron activation analysis helps to determine the origin of ancient pottery and other artifacts through the analysis of the clay from which they were made. he was helped in the project by another noted scientist frank asaro. second millennium bc pottery from cyprus was one of the first archaeological projects that perlman and asaro undertook. the project of the origin of the then assumed second millennium palestinian bichrome ware was undertaken as part of the phd thesis of michal artzy.


in statistics, a hidden markov random field is a generalization of a hidden markov model. instead of having an underlying markov chain, hidden markov random fields have an underlying markov random field. suppose that we observe a random variable y i { \ displaystyle y _ { i } }, where i ∈ s { \ displaystyle i \ in s }. hidden markov random fields assume that the probabilistic nature of y i { \ displaystyle y _ { i } } is determined by the unobservable markov random field x i { \ displaystyle x _ { i } }, i ∈ s { \ displaystyle i \ in s }.


in mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. for example, 1200 = 2 4 ⋅ 3 1 ⋅ 5 2 = ( 2 ⋅ 2 ⋅ 2 ⋅ 2 ) ⋅ 3 ⋅ ( 5 ⋅ 5 ) = 5 ⋅ 2 ⋅ 5 ⋅ 2 ⋅ 3 ⋅ 2 ⋅ 2 = … { \ displaystyle 1200 = 2 ^ { 4 } \ cdot 3 ^ { 1 } \ cdot 5 ^ { 2 } = ( 2 \ cdot 2 \ cdot 2 \ cdot 2 ) \ cdot 3 \ cdot ( 5 \ cdot 5 ) = 5 \ cdot 2 \ cdot 5 \ cdot 2 \ cdot 3 \ cdot 2 \ cdot 2 = \ ldots } the theorem says two things about this example : first, that 1200 can be represented as a product of primes, and second, that no matter how this is done, there will always be exactly four 2s, one 3, two 5s, and no other primes in the product. the requirement that the factors be prime is necessary : factorizations containing composite numbers may not be unique ( for example, 12 = 2 ⋅ 6 = 3 ⋅ 4 { \ displaystyle 12 = 2 \ cdot 6 = 3 \ cdot 4 } ).


in order to further eliminate irrelevant links and search results, deeppeep uses the hierarchical form identification ( hifi ) framework that classifies links and search results based on the website's structure and content. unlike other forms of classification which solely relies on the web form labels for organization, hifi utilizes both the structure and content of the web form for classification. utilizing these two classifiers, hifi organizes the web forms in a hierarchical fashion which ranks the a web form's relevance to the target keyword.


in mathematics, specifically in abstract algebra, a torsion - free abelian group is an abelian group which has no non - trivial torsion elements ; that is, a group in which the group operation is commutative and the identity element is the only element with finite order. while finitely generated abelian groups are completely classified, not much is known about infinitely generated abelian groups, even in the torsion - free countable case.


lexical recognition is of particular value in the field of computer speech recognition, since the ability to build and search a network of semantically connected ideas would greatly increase the effectiveness of speech - recognition software. statistical models can be used to segment and align recorded speech to words or phones. applications include automatic lip - synch timing for cartoon animation, follow - the - bouncing - ball video sub - titling, and linguistic research. automatic segmentation and alignment software is commercially available.


in the context of complex networks, attack tolerance is the network's robustness meaning the ability to maintain the overall connectivity and diameter of the network as nodes are removed. several graph metrics have been proposed to predicate network robustness. algebraic connectivity is a graph metric that shows the best graph robustness among them.


in physics, a vector typically arises as the outcome of a measurement or series of measurements, and is represented as a list ( or tuple ) of numbers such as ( v 1, v 2, v 3 ). { \ displaystyle ( v _ { 1 }, v _ { 2 }, v _ { 3 } ). } the numbers in the list depend on the choice of coordinate system. for instance, if the vector represents position with respect to an observer ( position vector ), then the coordinate system may be obtained from a system of rigid rods, or reference axes, along which the components v1, v2, and v3 are measured.


we illustrate using the simple case of a one - dimensional parameter, but an analogous derivation holds more generally. in the one - dimensional case, we have p ( x ) = g ( η ) h ( x ) e η t ( x ). { \ displaystyle p ( x ) = g ( \ eta ) h ( x ) e ^ { \ eta t ( x ) }. }


every variable xi in the sequence is associated with a bernoulli trial or experiment. they all have the same bernoulli distribution. much of what can be said about the bernoulli process can also be generalized to more than two outcomes ( such as the process for a six - sided die ) ; this generalization is known as the bernoulli scheme. the problem of determining the process, given only a limited sample of bernoulli trials, may be called the problem of checking whether a coin is fair.


in telecommunication and data storage, manchester code ( also known as phase encoding, or pe ) is a line code in which the encoding of each data bit is either low then high, or high then low, for equal time. it is a self - clocking signal with no dc component. consequently, electrical connections using a manchester code are easily galvanically isolated.


others have attacked the problem from the database end, by defining an object - oriented data model for the database, and defining a database programming language that allows full programming capabilities as well as traditional query facilities. object databases suffered because of a lack of standardization : although standards were defined by odmg, they were never implemented well enough to ensure interoperability between products. nevertheless, object databases have been used successfully in many applications : usually specialized applications such as engineering databases or molecular biology databases rather than mainstream commercial data processing. however, object database ideas were picked up by the relational vendors and influenced extensions made to these products and indeed to the sql language. an alternative to translating between objects and relational databases is to use an object – relational mapping ( orm ) library.


other related phrasings include cumulative knowledge, collective knowledge or pooled knowledge. distributed knowledge is the union of all the knowledge of individuals in a community of agents. distributed knowledge differs from the concept of wisdom of the crowd, in that the latter is concerned with opinions, not knowledge.


in mathematics, the munn semigroup is the inverse semigroup of isomorphisms between principal ideals of a semilattice ( a commutative semigroup of idempotents ). munn semigroups are named for the scottish mathematician walter douglas munn ( 1929 – 2008 ).


in petroleum and natural gas extraction, a christmas tree, or " tree ", is an assembly of valves, casing spools, and fittings used to regulate the flow of pipes in an oil well, gas well, water injection well, water disposal well, gas injection well, condensate well, and other types of well.


a tone reproduction curve is applied to the electronic image prior to printing, so that the reflectance of the print closely approximates a proportionality to the luminance intent implied by the electronic image. it is easier to demonstrate the need for a trc using halftoned printing methods such as inkjet, or xerographic technologies. however, the need also applies to continuous - tone methods such as photographic paper printing.


in programming, several notations denote hexadecimal numbers, usually involving a prefix. the prefix 0x is used in c, which would denote this value as 0x7613. 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 some programming languages, const is a type qualifier ( a keyword applied to a data type ) that indicates that the data is read - only. while this can be used to declare constants, const in the c family of languages differs from similar constructs in other languages in being part of the type, and thus has complicated behavior when combined with pointers, references, composite data types, and type - checking. in other languages, the data is not in a single memory location, but copied at compile time on each use. languages which use it include c, c + +, d, javascript, julia, and rust.


in text databases, a document collection defined by a document by term d matrix ( of size m×n, where m is the number of documents and n is the number of terms ), the number of clusters can roughly be estimated by the formula m n t { \ displaystyle { \ tfrac { mn } { t } } } where t is the number of non - zero entries in d. note that in d each row and each column must contain at least one non - zero element.


that is ( after rewriting the expression with parentheses and in infix notation if necessary ), rearranging the parentheses in such an expression will not change its value. consider the following equations : even though the parentheses were rearranged on each line, the values of the expressions were not altered. since this holds true when performing addition and multiplication on any real numbers, it can be said that " addition and multiplication of real numbers are associative operations ".


for if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 ( and 7 itself is equal to 2 + 2 + 3 ). in 2013, harald helfgott released a proof of goldbach's weak conjecture. as of 2018, the proof is widely accepted in the mathematics community, but it has not yet been published in a peer - reviewed journal.


that a given psychological attribute is a continuous quantity is a logically coherent and empirically testable hypothesis. appearing in the next issue of the same journal were important papers by dana scott ( 1964 ), who proposed a hierarchy of cancellation conditions for the indirect testing of the solvability and archimedean axioms, and david krantz ( 1964 ) who connected the luce & tukey work to that of holder ( 1901 ). work soon focused on extending the theory of conjoint measurement to involve more than just two attributes.


in mathematics a p - group g { \ displaystyle g } is called power closed if for every section h { \ displaystyle h } of g { \ displaystyle g } the product of p k { \ displaystyle p ^ { k } } powers is again a p k { \ displaystyle p ^ { k } } th power. regular p - groups are an example of power closed groups. on the other hand, powerful p - groups, for which the product of p k { \ displaystyle p ^ { k } } powers is again a p k { \ displaystyle p ^ { k } } th power are not power closed, as this property does not hold for all sections of powerful p - groups. the power closed 2 - groups of exponent at least eight are described in ( mann 2005, th. 16 ).


in mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. a group that is not simple can be broken into two smaller groups, namely a nontrivial normal subgroup and the corresponding quotient group. this process can be repeated, and for finite groups one eventually arrives at uniquely determined simple groups, by the jordan – holder theorem. the complete classification of finite simple groups, completed in 2004, is a major milestone in the history of mathematics.


two nonsingular quadratic forms over f2 are isomorphic if and only if they have the same dimension and the same arf invariant. this fact was essentially known to leonard dickson ( 1901 ), even for any finite field of characteristic 2, and arf proved it for an arbitrary perfect field. the arf invariant is particularly applied in geometric topology, where it is primarily used to define an invariant of ( 4k + 2 ) - dimensional manifolds ( singly even - dimensional manifolds : surfaces ( 2 - manifolds ), 6 - manifolds, 10 - manifolds, etc. ) with certain additional structure called a framing, and thus the arf – kervaire invariant and the arf invariant of a knot. the arf invariant is analogous to the signature of a manifold, which is defined for 4k - dimensional manifolds ( doubly even - dimensional ) ; this 4 - fold periodicity corresponds to the 4 - fold periodicity of l - theory. the arf invariant can also be defined more generally for certain 2k - dimensional manifolds.


a tighter bound, was conjectured by hirschman and everett, proven in 1975 by w. beckner and in the same year interpreted as a generalized quantum mechanical uncertainty principle by białynicki - birula and mycielski. the equality holds in the case of gaussian distributions. note, however, that the above entropic uncertainty function is distinctly different from the quantum von neumann entropy represented in phase space.


in mid to late 2009 a tool named detect and eliminate computer acquired forensics ( decaf ) was announced by an uninvolved group of programmers. the tool would reportedly protect computers against cofee and render the tool ineffective. it alleged that it would provide real - time monitoring of cofee signatures on usb devices and in running applications and that when a cofee signature is detected, decaf would perform numerous user - defined processes. these included cofee log clearing, ejecting usb devices, and contamination or spoofing of mac addresses. on december 18, 2009, the decaf creators announced that the tool was a hoax and part of " a stunt to raise awareness for security and the need for better forensic tools ".


in modern multitasking environment, an application process usually has in its address space ( or spaces ) chunks of memory of following types : machine code, including : program's own code ( historically known as code segment or text segment ) ; shared libraries. data, including : initialized data ( data segment ) ; uninitialized ( but allocated ) variables ; run - time stack ; heap ; shared memory and memory mapped files. some parts of address space may be not mapped at all. some systems have a " split " memory architecture where machine code, constants, and data are in different locations, and may have different address sizes. for example, pic18 microcontrollers have a 21 - bit program counter to address machine code and constants in flash memory, and 12 - bit address registers to address data in sram.


in the case of two thieves and t colours, a fair split would require at most t cuts. if, however, only t − 1 cuts are available, hungarian mathematician gabor simonyi shows that the two thieves can achieve an almost fair division in the following sense. if the necklace is arranged so that no t - split is possible, then for any two subsets d1 and d2 of { 1, 2,..., t }, not both empty, such that d 1 ∩ d 2 = ∅ { \ displaystyle d _ { 1 } \ cap d _ { 2 } = \ varnothing }, a ( t − 1 ) - split exists such that : if colour i ∈ d 1 { \ displaystyle i \ in d _ { 1 } }, then partition 1 has more beads of colour i than partition 2 ; if colour i ∈ d 2 { \ displaystyle i \ in d _ { 2 } }, then partition 2 has more beads of colour i than partition 1 ; if colour i is in neither partition, both partitions have equally many beads of colour i. this means that if the thieves have preferences in the form of two " preference " sets d1 and d2, not both empty, there exists a ( t − 1 ) - split so that thief 1 gets more beads of types in his preference set d1 than thief 2 ; thief 2 gets more beads of types in her preference set d2 than thief 1 ; and the rest are equal.


in predicate logic, what is described in layman's terms as " something " can more specifically be regarded as existential quantification, that is, the predication of a property or relation to at least one member of the domain. it is a type of quantifier, a logical constant which is interpreted as " there exists, " " there is at least one, " or " for some. " it expresses that a propositional function can be satisfied by at least one member of a domain of discourse. in other terms, it is the predication of a property or relation to at least one member of the domain. it asserts that a predicate within the scope of an existential quantifier is true of at least one value of a predicate variable.


in the japanese kantenji braille, the standard 8 - dot braille patterns 358, 1358, 3458, and 13458 are the patterns related to braille pattern dots - 246, since the two additional dots of kantenji patterns 0246, 2467, and 02467 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


these scenarios will cause issues in the program running by providing false data. to prevent this, one method is that the entire data - structure can be kept under critical section so that only one operation is handled at a time. another method is locking the node in use under critical section, so that other operations do not use the same node. using critical section, thus, ensures that the code provides expected outputs.


in mathematics, a euclidean group is the group of ( euclidean ) isometries of a euclidean space e n { \ displaystyle \ mathbb { e } ^ { n } } ; that is, the transformations of that space that preserve the euclidean distance between any two points ( also called euclidean transformations ). the group depends only on the dimension n of the space, and is commonly denoted e ( n ) or iso ( n ). the euclidean group e ( n ) comprises all translations, rotations, and reflections of e n { \ displaystyle \ mathbb { e } ^ { n } } ; and arbitrary finite combinations of them. the euclidean group can be seen as the symmetry group of the space itself, and contains the group of symmetries of any figure ( subset ) of that space.


alessandro volta began investigating pneumatic chemistry in 1776 and argued that there were different types of inflammable air based on experiments on marsh gases. pneumatic chemists credited with discovering chemical elements include joseph priestley, henry cavendish, joseph black, daniel rutherford, and carl scheele. other individuals who investigated gases during this period include robert boyle, stephen hales, william brownrigg, antoine lavoisier, joseph louis gay - lussac, and john dalton.


the language they defined was known as cycl. after cycl, a number of ontology languages have been developed. most are declarative languages, and are either frame languages, or are based on first - order logic.


in the following identities, δ { \ displaystyle \ delta } is a derivation of a differential ring r. { \ displaystyle r. } : 76 if r ∈ r { \ displaystyle r \ in r } and c { \ displaystyle c } is a constant in r { \ displaystyle r } ( that is, δ c = 0 { \ displaystyle \ delta c = 0 } ), then if r ∈ r { \ displaystyle r \ in r } and u { \ displaystyle u } is a unit in r, { \ displaystyle r, } then if n { \ displaystyle n } is a nonnegative integer and r ∈ r { \ displaystyle r \ in r } then if u 1, …, u n { \ displaystyle u _ { 1 }, \ ldots, u _ { n } } are units in r, { \ displaystyle r, } and n 1, …, n n { \ displaystyle n _ { 1 }, \ ldots, n _ { n } } are integers, one has the logarithmic derivative identity :


monoidal categories can be seen as a generalization of these and other examples. every ( small ) monoidal category may also be viewed as a " categorification " of an underlying monoid, namely the monoid whose elements are the isomorphism classes of the category's objects and whose binary operation is given by the category's tensor product. a rather different application, of which monoidal categories can be considered an abstraction, is that of a system of data types closed under a type constructor that takes two types and builds an aggregate type ; the types are the objects and ⊗ { \ displaystyle \ otimes } is the aggregate constructor.


a probability function, p { \ displaystyle p }, which assigns each event in the event space a probability, which is a number between 0 and 1. in order to provide a sensible model of probability, these elements must satisfy a number of axioms, detailed in this article. in the example of the throw of a standard die, we would take the sample space to be { 1, 2, 3, 4, 5, 6 } { \ displaystyle \ { 1, 2, 3, 4, 5, 6 \ } }. for the event space, we could simply use the set of all subsets of the sample space, which would then contain simple events such as { 5 } { \ displaystyle \ { 5 \ } } ( " the die lands on 5 " ), as well as complex events such as { 2, 4, 6 } { \ displaystyle \ { 2, 4, 6 \ } } ( " the die lands on an even number " ).


in the java virtual machine, internal type signatures are used to identify methods and classes at the level of the virtual machine code. example : the method string string. substring ( int, int ) is represented in bytecode as ljava / lang / string. substring ( ii ) ljava / lang / string ;. the signature of the main method looks like this : and in the disassembled bytecode, it takes the form of lsome / package / main / main : ( [ ljava / lang / string ; ) v the method signature for the main ( ) method contains three modifiers : public indicates that the main ( ) method can be called by any object. static indicates that the main ( ) method is a class method. void indicates that the main ( ) method has no return value.


algorithms are needed for efficient computation of the statistics ( e. g., mean and variance ) of the modal parameters from the posterior distribution. unlike non - bayesian methods, the algorithms are often implicit and iterative. e. g., optimization algorithms may be involved in the determination of most probable value, which may not converge for poor quality data.


in the example graph shown, the algorithm is initially called with r = ø, p = { 1, 2, 3, 4, 5, 6 }, and x = ø. the pivot u should be chosen as one of the degree - three vertices, to minimize the number of recursive calls ; for instance, suppose that u is chosen to be vertex 2. then there are three remaining vertices in p \ n ( u ) : vertices 2, 4, and 6. the iteration of the inner loop of the algorithm for v = 2 makes a recursive call to the algorithm with r = { 2 }, p = { 1, 3, 5 }, and x = ø. within this recursive call, one of 1 or 5 will be chosen as a pivot, and there will be two second - level recursive calls, one for vertex 3 and the other for whichever vertex was not chosen as pivot. these two calls will eventually report the two cliques { 1, 2, 5 } and { 2, 3 }.


in mobile - telephone technology, the unipro protocol stack follows the architecture of the classical osi reference model. in unipro, the osi physical layer is split into two sublayers : layer 1 ( the actual physical layer ) and layer 1. 5 ( the phy adapter layer ) which abstracts from differences between alternative layer 1 technologies. the actual physical layer is a separate specification as the various phy options are reused in other mipi alliance specifications. the unipro specification itself covers layers 1. 5, 2, 3, 4 and the dme ( device management entity ).


in the field of multivariate statistics, kernel principal component analysis ( kernel pca ) is an extension of principal component analysis ( pca ) using techniques of kernel methods. using a kernel, the originally linear operations of pca are performed in a reproducing kernel hilbert space.


although much attention is focused on wcdma, the concept is applicable to all standards, including gsm, cdma2000, td - scdma, wimax and lte solutions. the use of femtocells allows network coverage in places where the signal to the main network cells might be too weak. furthermore, femtocells lower contention on the main network cells, by forming a connection from the end user, through an internet connection, to the operator's private network infrastructure elsewhere.


in mathematics, gradient descent ( also often called steepest descent ) is a first - order iterative optimization algorithm for finding a local minimum of a differentiable function. the idea is to take repeated steps in the opposite direction of the gradient ( or approximate gradient ) of the function at the current point, because this is the direction of steepest descent. conversely, stepping in the direction of the gradient will lead to a local maximum of that function ; the procedure is then known as gradient ascent. it is particularly useful in machine learning for minimizing the cost or loss function.


in mathematics, the class of l - matrices are those matrices whose off - diagonal entries are less than or equal to zero and whose diagonal entries are positive ; that is, an l - matrix l satisfies l = ( ℓ i j ) ; ℓ i i > 0 ; ℓ i j ≤ 0, i = j. { \ displaystyle l = ( \ ell _ { ij } ) ; \ quad \ ell _ { ii } > 0 ; \ quad \ ell _ { ij } \ leq 0, \ quad i \ neq j. }


in mathematics, the affine hull or affine span of a set s in euclidean space rn is the smallest affine set containing s, or equivalently, the intersection of all affine sets containing s. here, an affine set may be defined as the translation of a vector subspace. the affine hull aff ( s ) of s is the set of all affine combinations of elements of s, that is, aff ( s ) = { i = 1 k α i x i | k > 0, x i ∈ s, α i ∈ r, i = 1 k α i = 1 }. { \ displaystyle \ operatorname { aff } ( s ) = \ left \ { \ sum _ { i = 1 } ^ { k } \ alpha _ { i } x _ { i } \, { \ bigg | } \, k > 0, \, x _ { i } \ in s, \, \ alpha _ { i } \ in \ mathbb { r }, \, \ sum _ { i = 1 } ^ { k } \ alpha _ { i } = 1 \ right \ }. }


in programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. semantics assigns computational meaning to valid strings in a programming language syntax. it is closely related to, and often crosses over with, the semantics of mathematical proofs. semantics describes the processes a computer follows when executing a program in that specific language. this can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation.


in most practical contexts, a programming language involves a computer ; consequently, programming languages are usually defined and studied this way. programming languages differ from natural languages in that natural languages are only used for interaction between people, while programming languages also allow humans to communicate instructions to machines. the domain of the language is also worth consideration. markup languages like xml, html, or troff, which define structured data, are not usually considered programming languages.


vectors play an important role in physics : the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. many other physical quantities can be usefully thought of as vectors. although most of them do not represent distances ( except, for example, position or displacement ), their magnitude and direction can still be represented by the length and direction of an arrow. the mathematical representation of a physical vector depends on the coordinate system used to describe it. other vector - like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.


in recreational number theory, a primeval number is a natural number n for which the number of prime numbers which can be obtained by permuting some or all of its digits ( in base 10 ) is larger than the number of primes obtainable in the same way for any smaller natural number. primeval numbers were first described by mike keith. the first few primeval numbers are 1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, 1379, 10079, 10123, 10136, 10139, 10237, 10279, 10367, 10379, 12379, 13679,... ( sequence a072857 in the oeis ) the number of primes that can be obtained from the primeval numbers is 0, 1, 3, 4, 5, 7, 11, 14, 19, 21, 26, 29, 31, 33, 35, 41, 53, 55, 60, 64, 89, 96, 106,... ( sequence a076497 in the oeis ) the largest number of primes that can be obtained from a primeval number with n digits is 1, 4, 11, 31, 106, 402, 1953, 10542, 64905, 362451, 2970505,... ( sequence a076730 in the oeis ) the smallest n - digit number to achieve this number of primes is 2, 37, 137, 1379, 13679, 123479, 1234679, 12345679, 102345679


in standard logic, propositions are considered to be either true or false. in contradistinction, subjective logic assumes that humans cannot determine with absolute certainty whether a proposition about the real world is absolutely true or false. in subjective logic the posteriori probability estimates of binary events can be represented by beta distributions.


the design freedom of the time was very important because designers were very constrained by the cost of electronics, and only starting to explore how a computer could best be organized. some of the basic features introduced during this period included index registers ( on the ferranti mark 1 ), a return address saving instruction ( univac i ), immediate operands ( ibm 704 ), and detecting invalid operations ( ibm 650 ). by the end of the 1950s, commercial builders had developed factory - constructed, truck - deliverable computers.


limit theory helps in operational usage. for instance, in kbe derivation of a populated design ( geometrical objects, etc., similar concerns apply in shape theory ), equivalence assumptions allow convergence where potentially large, and perhaps even computationally indeterminate, solution sets are handled deftly. yet, in a chain of computation, downstream events may very well find some types of results from earlier resolutions of ramification as problematic for their own algorithms.


if the measure ρ is reducible with μ the associated reducer, then if f is square integrable for μ, and if g is square integrable for ρ and is orthogonal with p0 = 1 one has equivalence : f ( x ) = i g ( t ) − g ( x ) t − x ρ ( t ) d t g ( x ) = ( x − c 1 ) f ( x ) − t μ ( f ( x ) ) = φ ( x ) μ ( x ) ρ ( x ) f ( x ) − t ρ ( μ ( x ) ρ ( x ) f ( x ) ) { \ displaystyle f ( x ) = \ int _ { i } { \ frac { g ( t ) - g ( x ) } { t - x } } \ rho ( t ) dt \ leftrightarrow g ( x ) = ( x - c _ { 1 } ) f ( x ) - t _ { \ mu } ( f ( x ) ) = { \ frac { \ varphi ( x ) \ mu ( x ) } { \ rho ( x ) } } f ( x ) - t _ { \ rho } \ left ( { \ frac { \ mu ( x ) } { \ rho ( x ) } } f ( x ) \ right ) } c1 indicates the moment of order 1 of ρ and tρ the operator g ( x ) ↦ i g ( t ) − g ( x ) t − x ρ ( t ) d t. { \ displaystyle g ( x ) \ mapsto \ int _ { i } { \ frac { g ( t ) - g ( x ) } { t - x } } \ rho ( t ) \, dt. }


in mathematics, a de morgan algebra ( named after augustus de morgan, a british mathematician and logician ) is a structure a = ( a, ∨, ∧, 0, 1, ¬ ) such that : ( a, ∨, ∧, 0, 1 ) is a bounded distributive lattice, and ¬ is a de morgan involution : ¬ ( x ∧ y ) = ¬x ∨ ¬y and ¬¬x = x. ( i. e. an involution that additionally satisfies de morgan's laws ) in a de morgan algebra, the laws ¬x ∨ x = 1 ( law of the excluded middle ), and ¬x ∧ x = 0 ( law of noncontradiction ) do not always hold. in the presence of the de morgan laws, either law implies the other, and an algebra which satisfies them becomes a boolean algebra. remark : it follows that ¬ ( x ∨ y ) = ¬x ∧ ¬y, ¬1 = 0 and ¬0 = 1 ( e. g. ¬1 = ¬1 ∨ 0 = ¬1 ∨ ¬¬0 = ¬ ( 1 ∧ ¬0 ) = ¬¬0 = 0 ).


this says that the least significant n bits of k plus the remaining bits of k are equivalent to k modulo 2n−1. this equivalence can be used repeatedly until at most n bits remain. in this way, the remainder after dividing k by the mersenne number 2n−1 is computed without using division.


in radio or wireless telephony, private line is a term trademarked by motorola to describe an implementation of a continuous tone - coded squelch system ( ctcss ), a method of using low - frequency subaudible tones to share a single radio channel among multiple users. each user group would use a different low frequency tone. motorola's trade name, especially the abbreviation pl, has become a genericized trademark for the method.


in mathematics the discrete least squares meshless ( dlsm ) method is a meshless method based on the least squares concept. the method is based on the minimization of a least squares functional, defined as the weighted summation of the squared residual of the governing differential equation and its boundary conditions at nodal points used to discretize the domain and its boundaries.


in the following figure, the minimization problem on the left side of the equation is illustrated. one seeks to vary x such that the vertical distance between the convex and concave curves at x is as small as possible. the position of the vertical line in the figure is the ( approximate ) optimum. the next figure illustrates the maximization problem on the right hand side of the above equation.


by varying the weighting parameter b, one can trace out the entire contract curve : if b = 1 the problem is the same as the previous problem, and it identifies an efficient point at one edge of the lens formed by the indifference curves of the initial endowment ; if b = 0 all the weight is on person 2's utility instead of person 1's, and so the optimization identifies the efficient point on the other edge of the lens. as b varies smoothly between these two extremes, all the in - between points on the contract curve are traced out. note that the above optimizations are not ones that the two people would actually engage in, either explicitly or implicitly. instead, these optimizations are simply a way for the economist to identify points on the contract curve.


in the early 1980s, 1g was introduced as voice - only communication via " brick phones ". later in 1991, the development of 2g introduced short message service ( sms ) and multimedia messaging service ( mms ) capabilities, allowing picture messages to be sent and received between phones. in 1998, 3g was introduced to provide faster data - transmission speeds to support video calling and internet access. 4g was released in 2008 to support more demanding services such as gaming services, hd mobile tv, video conferencing, and 3d tv. 5g technology was initially released in 2019, but is still only available in certain areas.


in number theory, a wilson prime is a prime number p { \ displaystyle p } such that p 2 { \ displaystyle p ^ { 2 } } divides ( p − 1 )! + 1 { \ displaystyle ( p - 1 )! + 1 }, where "! { \ displaystyle! } " denotes the factorial function ; compare this with wilson's theorem, which states that every prime p { \ displaystyle p } divides ( p − 1 )!


then either the inner or outer circle participants – or the front or back line of desks – moves to the next space. following a brief settling - in period, the host starts the second round of meetings. in round robin speed networking, a participant would meet an average of 10 contacts during an hour - long event.


inverses are commonly used in groups — where every element is invertible, and rings — where invertible elements are also called units. they are also commonly used for operations that are not defined for all possible operands, such as inverse matrices and inverse functions.


planes are further subdivided into unicode blocks, which, unlike planes, do not have a fixed size. the 327 blocks defined in unicode 15. 0 cover 26 % of the possible code point space, and range in size from a minimum of 16 code points ( sixteen blocks ) to a maximum of 65, 536 code points ( supplementary private use area - a and - b, which constitute the entirety of planes 15 and 16 ). for future usage, ranges of characters have been tentatively mapped out for most known current and ancient writing systems.


with an attentive and planned assessment, a homeowner can spot many problems that cause energy losses and make decisions about possible energy efficiency upgrades. during a home energy audit it is important to have a checklist of areas that were inspected as well as problems identified. once the audit is completed, a plan for suggested actions needs to be developed.


in 1990, he asked " is there a double smoothly undulating integer? ", and he computed " all known replicating fibonacci digits less than one billion ". with his colleague john r. hendricks, he was the first to compute the smallest perfect ( nasik ) magic tesseract. the " pickover sequence " dealing with e and pi was named after him, as was the " cliff random number generator " and the pickover attractor, sometimes also referred to as the clifford attractor.


in probability theory and in particular in information theory, total correlation ( watanabe 1960 ) is one of several generalizations of the mutual information. it is also known as the multivariate constraint ( garner 1962 ) or multiinformation ( studeny & vejnarova 1999 ). it quantifies the redundancy or dependency among a set of n random variables.


most proofs of soundness are trivial. for example, in an axiomatic system, proof of soundness amounts to verifying the validity of the axioms and that the rules of inference preserve validity ( or the weaker property, truth ). if the system allows hilbert - style deduction, it requires only verifying the validity of the axioms and one rule of inference, namely modus ponens. ( and sometimes substitution ) soundness properties come in two main varieties : weak and strong soundness, of which the former is a restricted form of the latter.


in statistical hypothesis testing, a result has statistical significance when a result at least as " extreme " would be very infrequent if the null hypothesis were true. more precisely, a study's defined significance level, denoted by α { \ displaystyle \ alpha }, is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true ; and the p - value of a result, p { \ displaystyle p }, is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. the result is statistically significant, by the standards of the study, when p ≤ α { \ displaystyle p \ leq \ alpha }. the significance level for a study is chosen before data collection, and is typically set to 5 % or much lower — depending on the field of study. in any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone.


here " simple " indicates that the underlying type theory is the theory of simple types, also called the simple theory of types. leon chwistek and frank p. ramsey proposed this as a simplification of the complicated and clumsy ramified theory of types specified in the principia mathematica by alfred north whitehead and bertrand russell. simple types is sometimes also meant to exclude polymorphic and dependent types.


as many of these computers will give reduced privileges to ordinary users, it is possible that much of this has been done by network administrators. to some extent, this may be offset by better connectivity to home machines and increasing performance of home computers, especially those with gpus, which have also benefited other volunteer computing projects such as folding @ home. the spread of mobile computing devices provides another large resource for volunteer computing. for example, in 2012, piotr luszczek ( a former doctoral student of jack dongarra ) presented results showing that an ipad 2 matched the historical performance of a cray - 2 ( the fastest computer in the world in 1985 ) on an embedded linpack benchmark.


a fuzzbox ( or " fuzz box ” ) alters an audio signal until it is nearly a square wave and adds complex overtones by way of a frequency multiplier. a fuzz bass sound can be created by turning up the volume of a tube amp or transistor amp to the point that preamplifier tube ( or transistor preamp ) clipping " occurs. in practice, when a bass amp is " cranked " to its maximum volume, the fuzz tone will also include some power amplifier clipping. while some musicians seek out the additional " grit " provided by power amp clipping, audio engineers and bass technicians recommend avoiding power amp clipping, as it can blow speakers.


in contrast, the basis signals used to construct the signal subspace are identified empirically, and may for example be chirps, or particular characteristic shapes of transients after particular triggering events, rather than pure sinusoids. the wiener filter grades smoothly between linear components that are dominated by signal, and linear components that are dominated by noise. the noise components are filtered out, but not quite completely ; the signal components are retained, but not quite completely ; and there is a transition zone which is partly accepted. in contrast, the signal subspace approach represents a sharp cut - off : an orthogonal component either lies within the signal subspace, in which case it is 100 % accepted, or orthogonal to it, in which case it is 100 % rejected. this reduction in dimensionality, abstracting the signal into a much shorter vector, can be a particularly desired feature of the method. in the simplest case signal subspace methods assume white noise, but extensions of the approach to colored noise removal and the evaluation of the subspace - based speech enhancement for robust speech recognition have also been reported.


these handicap ratings where a player receives points can be denoted with an " r " in front, where the " r " indicates the player is receiving points. it is also possible to have a handicap system where the player owes point due to being higher - skilled, in which case the same two - number system is also used. these owed handicaps are denoted with an " o " in front that is short for " owed ".


it has been proved useful in recognizing targets ( i. e. battle tanks ) in infrared images of real scenes after training with synthetic images, since real images of those targets are scarce. due to the limitation of the training set, how realistic the synthetic images are matters a lot when it comes to recognize the real scenes test set. the overall cnn networks structure contains 7 convolution layers, 3 max pooling layers and a softmax layer as output.


the geometric mean of two numbers, a { \ displaystyle a } and b { \ displaystyle b }, is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a { \ displaystyle a } and b { \ displaystyle b }. similarly, the geometric mean of three numbers, a { \ displaystyle a }, b { \ displaystyle b }, and c { \ displaystyle c }, is the length of one edge of a cube whose volume is the same as that of a cuboid with sides whose lengths are equal to the three given numbers. the geometric mean is one of the three classical pythagorean means, together with the arithmetic mean and the harmonic mean. for all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between ( see inequality of arithmetic and geometric means. )


in mathematics, graphs are useful in geometry and certain parts of topology such as knot theory. algebraic graph theory has close links with group theory. algebraic graph theory has been applied to many areas including dynamic systems and complexity.


this could be simply presented in small cards or stories – the developers estimate the time needed for the implementation of each card. thus the work organization changes into self - pulling system – each morning during a stand - up meeting, each member of the team reviews what has been done yesterday, what is to be done today and tomorrow, and prompts for any inputs needed from colleagues or the customer. this requires transparency of the process, which is also beneficial for team communication. the myth underlying this principle is haste makes waste. however, lean implementation has shown that it is a good practice to deliver fast in order to see and analyze the output as early as possible.


in mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. although it is in fact a monoid, it is usually referred to as simply a semigroup. it is perhaps most easily understood as the syntactic monoid describing the dyck language of balanced pairs of parentheses. thus, it finds common applications in combinatorics, such as describing binary trees and associative algebras.


during the second quarter of 2004, it launched new low - power geode nx processors based on the k7 thoroughbred architecture with speeds of fanless processors 667 mhz and 1 ghz, and 1. 4 ghz processor with fan, of tdp 25 w. this technology is used in a variety of embedded systems ( casino slot machines and customer kiosks for instance ), several umpc designs in asia markets, as well as the olpc xo - 1 computer, an inexpensive laptop computer intended to be distributed to children in developing countries around the world. the geode lx processor was announced in 2005 and is said will continue to be available through 2015. amd has also introduced 64 - bit processors into its embedded product line starting with the amd opteron processor. leveraging the high throughput enabled through hypertransport and the direct connect architecture these server - class processors have been targeted at high - end telecom and storage applications.


in mathematics, a vertex cycle cover ( commonly called simply cycle cover ) of a graph g is a set of cycles which are subgraphs of g and contain all vertices of g. if the cycles of the cover have no vertices in common, the cover is called vertex - disjoint or sometimes simply disjoint cycle cover. this is sometimes known as exact vertex cycle cover. in this case the set of the cycles constitutes a spanning subgraph of g. a disjoint cycle cover of an undirected graph ( if it exists ) can be found in polynomial time by transforming the problem into a problem of finding a perfect matching in a larger graph. if the cycles of the cover have no edges in common, the cover is called edge - disjoint or simply disjoint cycle cover.


in china, the telecommunications regulations of the people's republic of china ( promulgated on 25 september 2000 ), stipulated the ministry of industry and information technology ( miit ) as the government department regulating all telecommunications related activities, including electronic commerce. on the same day, the administrative measures on internet information services were released, the first administrative regulations to address profit - generating activities conducted through the internet, and lay the foundation for future regulations governing e - commerce in china. on 28 august 2004, the eleventh session of the tenth npc standing committee adopted an electronic signature law, which regulates data message, electronic signature authentication and legal liability issues. it is considered the first law in china's e - commerce legislation. it was a milestone in the course of improving china's electronic commerce legislation, and also marks the entering of china's rapid development stage for electronic commerce legislation.


thus, in contrast to many monte carlo primality tests ( randomized algorithms that can return a false positive ), the primality testing algorithm based on proth's theorem is a las vegas algorithm, always returning the correct answer but with a running time that varies randomly. note that if a is chosen to be a quadratic nonresidue as described above, the runtime is constant, safe for the time spent on finding such a quadratic nonresidue. finding such a value is very fast compared to the actual test.


in certain physics applications such as in the computation of bands in a periodic volume, it is often a case that the elements of a matrix will be very complicated functions of frequency and wavenumber, and the matrix will be non - singular ( i. e., it has the inverse matrix. ) for most combinations of frequency and wavenumber, but will also be singular ( i. e., it does not have the inverse matrix. ) for certain specific combinations.


in the late 1990s and early 2000s, the market shifted for buyers, but since 2003 and 2004, it has been a strong seller's market, with net - back as the best estimation for prices.. research from global energy monitor in 2019 warned that up to us $ 1. 3 trillion in new lng export and import infrastructure currently under development is at significant risk of becoming stranded, as global gas risks becoming oversupplied, particularly if the united states and canada play a larger role. the current surge in unconventional oil and gas in the u. s. has resulted in lower gas prices in the u. s. this has led to discussions in asia'oil linked gas markets to import gas based on henry hub index.


the concept of notational associativity described here is related to, but different from, the mathematical associativity. an operation that is mathematically associative, by definition requires no notational associativity. ( for example, addition has the associative property, therefore it does not have to be either left associative or right associative. ) an operation that is not mathematically associative, however, must be notationally left -, right -, or non - associative. ( for example, subtraction does not have the associative property, therefore it must have notational associativity. )


in mathematics, a rotation map is a function that represents an undirected edge - labeled graph, where each vertex enumerates its outgoing neighbors. rotation maps were first introduced by reingold, vadhan and wigderson ( “ entropy waves, the zig - zag graph product, and new constant - degree expanders ”, 2002 ) in order to conveniently define the zig - zag product and prove its properties. given a vertex v { \ displaystyle v } and an edge label i { \ displaystyle i }, the rotation map returns the i { \ displaystyle i }'th neighbor of v { \ displaystyle v } and the edge label that would lead back to v { \ displaystyle v }.


in the japanese kantenji braille, the standard 8 - dot braille patterns 2678, 12678, 24678, and 124678 are the patterns related to braille pattern dots - 1356, since the two additional dots of kantenji patterns 01356, 13567, and 013567 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


the names of architectural styles ( as well as their adaptations ) varied between countries. many homes combined the elements of several different styles and are not easily distinguishable as one particular style or another.


those that remain are often used only in niche markets or as parts of other systems ; of the designs from these traditional vendors, only sparc and power have any significant remaining market. the arm architecture is illustrative of the adaptations made by risc vendors to respond to changing competitive circumstances, being first introduced to deliver higher performance in desktop computers such as the acorn archimedes, but also being introduced in embedded applications such as laser printer raster image processing. arm, in partnership with apple, developed a low - power design and then specialized in that market, which at the time was a niche. with the rise in mobile computing, especially after the introduction of the iphone, arm became the most widely used high - end cpu design in the market. competition between risc and conventional cisc approaches was also the subject of theoretical analysis in the early 1980s, leading, for example, to the iron law of processor performance.


so we take a sample of the k { \ displaystyle k }, get a sampling weight w ( k ) for all sampled k { \ displaystyle k }, and then sum up w ( k ) ⋅ y ( k ) { \ displaystyle w ( k ) \ cdot y ( k ) } for all sampled k { \ displaystyle k }. one property usually common to the weights w ( k ) { \ displaystyle w ( k ) } described here is that if we sum them over all sampled k { \ displaystyle k }, then this sum is an estimate of the total number of units k { \ displaystyle k } in the population ( for example, the total employment, or the total number of items ). because we have a sample, this estimate of the total number of units in the population will differ from the true population total.


in the client - to - gateway implementation, one or more servers are protected behind an accepting sdp host such that the accepting sdp host acts as a gateway between the clients and the protected servers. this implementation can be used inside an enterprise network to mitigate common lateral movement attacks such as server scanning, os and application vulnerability exploits, password cracking, man - in - the - middle, pass - the - hash ( pth ), and others. alternatively, it can be implemented on the internet to isolate protected servers from unauthorized users and mitigate attacks such as denial of service, os and application vulnerability exploits, password cracking, man - in - the - middle, and others.


in mathematics, in the field of group theory, a group is said to be strictly simple if it has no proper nontrivial ascendant subgroups. that is, g { \ displaystyle g } is a strictly simple group if the only ascendant subgroups of g { \ displaystyle g } are { e } { \ displaystyle \ { e \ } } ( the trivial subgroup ), and g { \ displaystyle g } itself ( the whole group ). in the finite case, a group is strictly simple if and only if it is simple. however, in the infinite case, strictly simple is a stronger property than simple.


if we assume that a function f : r n → r { \ displaystyle f \ colon { \ textbf { r } } ^ { n } \ to { \ textbf { r } } } is differentiable ( or even analytic ) in each variable separately, it is not true that f { \ displaystyle f } will necessarily be continuous. a counterexample in two dimensions is given by f ( x, y ) = x y x 2 + y 2. { \ displaystyle f ( x, y ) = { \ frac { xy } { x ^ { 2 } + y ^ { 2 } } }. } if in addition we define f ( 0, 0 ) = 0 { \ displaystyle f ( 0, 0 ) = 0 }, this function has well - defined partial derivatives in x { \ displaystyle x } and y { \ displaystyle y } at the origin, but it is not continuous at origin. ( indeed, the limits along the lines x = y { \ displaystyle x = y } and x = − y { \ displaystyle x = - y } are not equal, so there is no way to extend the definition of f { \ displaystyle f } to include the origin and have the function be continuous there. )


in order candidate for p after the current one c. valid ( p, c ) : check whether candidate c is a solution for p. output ( p, c ) : use the solution c of p as appropriate to the application. the next procedure must also tell when there are no more candidates for the instance p, after the current one c. a convenient way to do that is to return a " null candidate ", some conventional data value λ that is distinct from any real candidate. likewise the first procedure should return λ if there are no candidates at all for the instance p. the brute - force method is then expressed by the algorithm c ← first ( p ) while c = λ do if valid ( p, c ) then output ( p, c ) c ← next ( p, c ) end while for example, when looking for the divisors of an integer n, the instance data p is the number n. the call first ( n ) should return the integer 1 if n ≥ 1, or λ otherwise ; the call next ( n, c ) should return c + 1 if c < n, and λ otherwise ; and valid ( n, c ) should return true if and only if c is a divisor of n. ( in fact, if we choose λ to be n + 1, the tests n ≥ 1 and c < n are unnecessary. ) the brute - force search algorithm above will call output for every candidate that is a solution to the given instance p. the algorithm is easily modified to stop after finding the first solution, or a specified number of solutions ; or after testing a specified number of candidates, or after spending a given amount of cpu time.


as a result, the variance for the estimator in gan is usually much larger than that in wasserstein gan. see also figure 3 of. the problem with d j s { \ displaystyle d _ { js } } is much more severe in actual machine learning situations. consider training a gan to generate imagenet, a collection of photos of size 256 - by - 256.


in real mode or v86 mode, the size of a segment can range from 1 byte up to 65, 536 bytes ( using 16 - bit offsets ). the 16 - bit segment selector in the segment register is interpreted as the most significant 16 bits of a linear 20 - bit address, called a segment address, of which the remaining four least significant bits are all zeros. the segment address is always added to a 16 - bit offset in the instruction to yield a linear address, which is the same as physical address in this mode. for instance, the segmented address 06efh : 1234h ( here the suffix " h " means hexadecimal ) has a segment selector of 06efh, representing a segment address of 06ef0h, to which the offset is added, yielding the linear address 06ef0h + 1234h = 08124h.


in spite of its known drawbacks, one of the most widely used methods for community detection is modularity maximization. modularity is a benefit function that measures the quality of a particular division of a network into communities. the modularity maximization method detects communities by searching over possible divisions of a network for one or more that have particularly high modularity. since exhaustive search over all possible divisions is usually intractable, practical algorithms are based on approximate optimization methods such as greedy algorithms, simulated annealing, or spectral optimization, with different approaches offering different balances between speed and accuracy. a popular modularity maximization approach is the louvain method, which iteratively optimizes local communities until global modularity can no longer be improved given perturbations to the current community state. an algorithm that utilizes the reneel scheme, which is an example of the extremal ensemble learning ( eel ) paradigm, is currently the best modularity maximizing algorithm. the usefulness of modularity optimization is questionable, as it has been shown that modularity optimization often fails to detect clusters smaller than some scale, depending on the size of the network ( resolution limit ) ; on the other hand the landscape of modularity values is characterized by a huge degeneracy of partitions with high modularity, close to the absolute maximum, which may be very different from each other.


if n − 1 and m − 1 are coprime, on the other hand, the only two fixed points are the upper - left and lower - right corners of the matrix. the number of cycles of any length k > 1 is given by ( cate & twigg, 1977 ) : 1 k d | k μ ( k / d ) gcd ( n d − 1, m n − 1 ), { \ displaystyle { \ frac { 1 } { k } } \ sum _ { d | k } \ mu ( k / d ) \ gcd ( n ^ { d } - 1, mn - 1 ), } where μ is the mobius function and the sum is over the divisors d of k. furthermore, the cycle containing a = 1 ( i. e. the second element of the first row of the matrix ) is always a cycle of maximum length l, and the lengths k of all other cycles must be divisors of l ( cate & twigg, 1977 ). for a given cycle c, every element x ∈ c { \ displaystyle x \ in c } has the same greatest common divisor d = gcd ( x, m n − 1 ) { \ displaystyle d = \ gcd ( x, mn - 1 ) }.


in network routing, vcg mechanisms are a family of payment schemes based on the added value concept. the basic idea of a vcg mechanism in network routing is to pay the owner of each link or node ( depending on the network model ) that is part of the solution, its declared cost plus its added value. in many routing problems, this mechanism is not only strategyproof, but also the minimum among all strategyproof mechanisms. in the case of network flows, unicast or multicast, a minimum cost flow ( mcf ) in graph g is calculated based on the declared costs dk of each of the links and payment is calculated as follows : each link ( or node ) e k { \ displaystyle \ scriptstyle e _ { k } } in the mcf is paid p k = d k + m c f ( g − e k ) − m c f ( g ) { \ displaystyle p _ { k } = d _ { k } + mcf ( g - e _ { k } ) - mcf ( g ) }, where mcf ( g ) indicates the cost of the minimum cost flow in graph g and g − ek indicates graph g without the link ek.


in software development, linus's law is the assertion that " given enough eyeballs, all bugs are shallow ". the law was formulated by eric s. raymond in his essay and book the cathedral and the bazaar ( 1999 ), and was named in honor of linus torvalds. a more formal statement is : " given a large enough beta - tester and co - developer base, almost every problem will be characterized quickly and the fix obvious to someone. " presenting the code to multiple developers with the purpose of reaching consensus about its acceptance is a simple form of software reviewing. researchers and practitioners have repeatedly shown the effectiveness of reviewing processes in finding bugs and security issues.


the cantor set is an example of an uncountable set of lebesgue measure 0 which is not of strong measure zero. borel's conjecture states that every strong measure zero set is countable. it is now known that this statement is independent of zfc ( the zermelo – fraenkel axioms of set theory, which is the standard axiom system assumed in mathematics ). this means that borel's conjecture can neither be proven nor disproven in zfc ( assuming zfc is consistent ).


in modern computer systems, files are typically accessed using names ( filenames ). in some operating systems, the name is associated with the file itself. in others, the file is anonymous, and is pointed to by links that have names. in the latter case, a user can identify the name of the link with the file itself, but this is a false analogue, especially where there exists more than one link to the same file.


in the bijective base - 26 system one may use the latin alphabet letters " a " to " z " to represent the 26 digit values one to twenty - six. ( a = 1, b = 2, c = 3,..., z = 26 ) with this choice of notation, the number sequence ( starting from 1 ) begins a, b, c,..., x, y, z, aa, ab, ac,..., ax, ay, az, ba, bb, bc,... each digit position represents a power of twenty - six, so for example, the numeral abc represents the value 1 × 262 + 2 × 261 + 3 × 260 = 731 in base 10. many spreadsheets including microsoft excel use this system to assign labels to the columns of a spreadsheet, starting a, b, c,..., z, aa, ab,..., az, ba,..., zz, aaa, etc. for instance, in excel 2013, there can be up to 16384 columns ( 214 in binary code ), labeled from a to xfd. a variant of this system is used to name variable stars. it can be applied to any problem where a systematic naming using letters is desired, while using the shortest possible strings.


in qualitative research, there are many ways of analyzing data gathered in the field. one of the two most common methods of data analysis are thematic analysis and narrative analysis. as mentioned before, the type of analysis a researcher decides to use depends on the research question asked, the researcher's field, and the researcher's personal method of choice.


they include standard jtag ( ieee 1149. 1 ), cjtag ( ieee 1149. 7 ) and 4 - bit parallel trace interfaces ( mainly used for system traces ), supplemented by the arm - specific serial wire debug ( swd ) standard. mipi10 / 20 / 34 debug connectors became the standard for arm - based embedded designs. many embedded designs in the mobile space use high - speed parallel trace ports ( up to 600 megabits per second per pin ).


in the japanese kantenji braille, the standard 8 - dot braille patterns 2578, 12578, 24578, and 124578 are the patterns related to braille pattern dots - 1346, since the two additional dots of kantenji patterns 01346, 13467, and 013467 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


various broadcast relay stations can help to extend a station's area by retransmitting them on the same or another channel. what is usually called a repeater in amateur radio is called a broadcast translator ( different channel ) or booster ( same channel ) in american broadcasting, or the much broader category or rebroadcasters in canadian broadcasting ( which includes more than just the low - power broadcasting used in the u. s. ) boosters are used only within the broadcast range of the parent station, and serve the same function locally as regional and national single - frequency networks do in europe. distributed transmission has also undergone tests in the u. s., but to preserve stations'market share in their home media markets, these will be limited to the broadcast area of a single large station. satellite radio, which is designed for use without a dish, also uses ground repeaters in large cities due to the many obstructions their high - rise buildings cause to the many current and potential customers that are concentrated there.


in probability theory, an interacting particle system ( ips ) is a stochastic process ( x ( t ) ) t ∈ r + { \ displaystyle ( x ( t ) ) _ { t \ in \ mathbb { r } ^ { + } } } on some configuration space ω = s g { \ displaystyle \ omega = s ^ { g } } given by a site space, a countably - infinite - order graph g { \ displaystyle g } and a local state space, a compact metric space s { \ displaystyle s }. more precisely ips are continuous - time markov jump processes describing the collective behavior of stochastically interacting components. ips are the continuous - time analogue of stochastic cellular automata. among the main examples are the voter model, the contact process, the asymmetric simple exclusion process ( asep ), the glauber dynamics and in particular the stochastic ising model.


in physics, attempts have been made to explain stretched exponential behaviour as a linear superposition of simple exponential decays. this requires a nontrivial distribution of relaxation times, ρ ( u ), which is implicitly defined by alternatively, a distribution is used. ρ can be computed from the series expansion : for rational values of β, ρ ( u ) can be calculated in terms of elementary functions. but the expression is in general too complex to be useful except for the case β = 1 / 2 where figure 2 shows the same results plotted in both a linear and a log representation. the curves converge to a dirac delta function peaked at u = 1 as β approaches 1, corresponding to the simple exponential function. the moments of the original function can be expressed as the first logarithmic moment of the distribution of simple - exponential relaxation times is where eu is the euler constant.


the graph density of simple graphs is defined to be the ratio of the number of edges | e | with respect to the maximum possible edges. for undirected simple graphs, the graph density is : d = | e | ( | v | 2 ) = 2 | e | | v | ( | v | − 1 ) { \ displaystyle d = { \ frac { | e | } { \ binom { | v | } { 2 } } } = { \ frac { 2 | e | } { | v | ( | v | - 1 ) } } } for directed, simple graphs, the maximum possible edges is twice that of undirected graphs ( as there are two directions to an edge ) so the density is : d = | e | 2 ( | v | 2 ) = | e | | v | ( | v | − 1 ) { \ displaystyle d = { \ frac { | e | } { 2 { \ binom { | v | } { 2 } } } } = { \ frac { | e | } { | v | ( | v | - 1 ) } } } where e is the number of edges and v is the number of vertices in the graph.


in number theory, the selberg sieve is a technique for estimating the size of " sifted sets " of positive integers which satisfy a set of conditions which are expressed by congruences. it was developed by atle selberg in the 1940s.


non - interpolated string literals are sometimes referred to as " raw strings ", but this is distinct from " raw string " in the sense of escaping. for example, in python, a string prefixed with r or r has no escaping or interpolation, a normal string ( no prefix ) has escaping but no interpolation, and a string prefixed with f or f has escaping and interpolation. for example, the following perl code : produces the output : nancy said hello world to the crowd of people.


in the united states, a disclaimer must be conspicuous in the contract, such as in a different kind of print or font that makes it stand out. on the other hand, express warranty, or any affirmation of fact or promise to the buyer or description of the good, oral or written, can be negated or limited only if such disclaimers are reasonable. ucc § 2 - 316 ( 1 ) some jurisdictions, however, limit the ability of sellers or manufacturers to disclaim the implied warranty of merchantability or fitness, such as massachusetts. ( massachusetts general laws, chapter 106 : section 2 - 316a ).


meiser ( 1993 ) designed a fast algorithm to determine the face of an arrangement of hyperplanes containing an input point. another question about an arrangement in real space is to decide how many regions are simplices ( the n - dimensional generalization of triangles and tetrahedra ).


the first problem to address is to determine whether a given prime is elkies or atkin. in order to do so, we make use of modular polynomials, which come from the study of modular forms and an interpretation of elliptic curves over the complex numbers as lattices.


] _ { f } } which are composed by parallel computations. the ordinary denotation of α { \ displaystyle \ alpha } is simply whatever denotation it would have in a non - alternative - based system. the focus denotation of a constituent is typically the set of all ordinary denotations one could get by substituting a focused constituent for another expression of the same type.


this means that when something changes, previously unexchanged information needs to be exchanged, or two programs need to interoperate in a new way, the humans must get involved. off - line, the parties must define and communicate between them the knowledge needed to make the change, and then recode the data structures and program logic to accommodate it, and then apply these changes to the database and the application. then, and only then, can they implement the changes.


in some programming languages an operator may be ad hoc polymorphic, that is, have definitions for more than one kind of data, ( such as in java where the + operator is used both for the addition of numbers and for the concatenation of strings ). such an operator is said to be overloaded. in languages that support operator overloading by the programmer ( such as c + + ) but have a limited set of operators, operator overloading is often used to define customized uses for operators. in the example if order _ date > " 12 / 31 / 2011 " and order _ date < " 01 / 01 / 2013 " then continue else stop, the operators are : > ( greater than ), and and < ( less than ).


for every two objects a and b a set mor ( a, b ) of things called morphisms from a to b. if f is in mor ( a, b ), we write f : a → b. for every three objects a, b and c a binary operation mor ( a, b ) × mor ( b, c ) → mor ( a, c ) called composition of morphisms. the composition of f : a → b and g : b → c is written as g ∘ f or gf.


in the case of a simple attack, a firewall could have a simple rule added to deny all incoming traffic from the attackers, based on protocols, ports, or the originating ip addresses. more complex attacks will however be hard to block with simple rules : for example, if there is an ongoing attack on port 80 ( web service ), it is not possible to drop all incoming traffic on this port because doing so will prevent the server from serving legitimate traffic. additionally, firewalls may be too deep in the network hierarchy, with routers being adversely affected before the traffic gets to the firewall. also, many security tools still do not support ipv6 or may not be configured properly, so the firewalls often might get bypassed during the attacks.


in order to support user interaction with application directories, several files have special status.


where a member becomes aware that irregularities have occurred in relation to a client's tax affairs he should advise the client of the consequences, and the manner of disclosure. if necessary, appropriate specialist advice should be taken. where a client refuses to follow the advice of a member in relation to issues involving disclosure, the member should consider whether he should continue to act.


in mathematics, the spiral optimization ( spo ) algorithm is a metaheuristic inspired by spiral phenomena in nature. the first spo algorithm was proposed for two - dimensional unconstrained optimization based on two - dimensional spiral models. this was extended to n - dimensional problems by generalizing the two - dimensional spiral model to an n - dimensional spiral model. there are effective settings for the spo algorithm : the periodic descent direction setting and the convergence setting.


in the environment of convergent network, specific services with certain network technologies will receive different regulatory treatments. the 1996 act created distinct regulatory categories for services that are provided by different network technologies. besides the existing regulation framework for regulating telecommunications services and cable services in another title, the 1996 act defines a category of services, “ information services, ” that distinguished from “ telecommunications services ” and was not subject to either telephone or cable regulation. “ information services ” are consisted of the offering of a capability for generating, acquiring, storing, transforming, processing, retrieving, utilizing, or making available information via telecommunications.


however, over time, the weak verbs have become the normal form of verbs in all germanic languages, with most strong verbs being reassigned to the weak class. for example, in old english the verb to lock ( lucan ) was strong ( present tense ic luce'i lock ', past tense ic leac'i locked'), but has now become weak. this transition is ongoing. for example, the english verb to cleave currently exists in both a conservative strong form ( past tense i clove ) and an innovative weak form ( past tense i cleaved ).


this can happen if datasets are regional and / or demographically partitioned. for example, datasets containing images of animals vary significantly from country to country. concept drift ( same label, different features ) : local nodes may share the same labels but some of them correspond to different features at different local nodes.


in number theory, the green – tao theorem, proved by ben green and terence tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. in other words, for every natural number k, there exist arithmetic progressions of primes with k terms. the proof is an extension of szemeredi's theorem. the problem can be traced back to investigations of lagrange and waring from around 1770.


in the development of social networks, there has appeared a new economic phenomenon : doing business via social networks. for example, there are many users of wechat called wei - businessmen ( wechat businessman, a new form of e - commerce in wechat ) who sell products on wechat. doing business via social networks is not that easy. the identities of users in social networks are not the same as that in the real world.


in statistics and machine learning, the bias – variance tradeoff is the property of a model that the variance of the parameter estimated across samples can be reduced by increasing the bias in the estimated parameters. the bias – variance dilemma or bias – variance problem is the conflict in trying to simultaneously minimize these two sources of error that prevent supervised learning algorithms from generalizing beyond their training set : the bias error is an error from erroneous assumptions in the learning algorithm. high bias can cause an algorithm to miss the relevant relations between features and target outputs ( underfitting ). the variance is an error from sensitivity to small fluctuations in the training set. high variance may result from an algorithm modeling the random noise in the training data ( overfitting ). the bias – variance decomposition is a way of analyzing a learning algorithm's expected generalization error with respect to a particular problem as a sum of three terms, the bias, variance, and a quantity called the irreducible error, resulting from noise in the problem itself.


in statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values. it is a measure of the skewness of a random variable's distribution — that is, the distribution's tendency to " lean " to one side or the other of the mean. its calculation does not require any knowledge of the form of the underlying distribution — hence the name nonparametric. it has some desirable properties : it is zero for any symmetric distribution ; it is unaffected by a scale shift ; and it reveals either left - or right - skewness equally well. in some statistical samples it has been shown to be less powerful than the usual measures of skewness in detecting departures of the population from normality.


in mathematics, a markov information source, or simply, a markov source, is an information source whose underlying dynamics are given by a stationary finite markov chain.


lda can be generalized to multiple discriminant analysis, where c becomes a categorical variable with n possible states, instead of only two. analogously, if the class - conditional densities p ( x → c = i ) { \ displaystyle p ( { \ vec { x } } \ mid c = i ) } are normal with shared covariances, the sufficient statistic for p ( c x → ) { \ displaystyle p ( c \ mid { \ vec { x } } ) } are the values of n projections, which are the subspace spanned by the n means, affine projected by the inverse covariance matrix. these projections can be found by solving a generalized eigenvalue problem, where the numerator is the covariance matrix formed by treating the means as the samples, and the denominator is the shared covariance matrix. see “ multiclass lda ” above for details.


in the following scenario a web browser is developed using defense in depth - the browser developers receive security training the codebase is checked automatically using security analysis tools the browser is regularly audited by an internal security team... is occasionally audited by an external security team... is executed inside a sandbox


" abundancy " may also be expressed as σ − 1 ( n ) { \ displaystyle \ sigma _ { - 1 } ( n ) } where σ k { \ displaystyle \ sigma _ { k } } denotes a divisor function with σ k ( n ) { \ displaystyle \ sigma _ { k } ( n ) } equal to the sum of the k - th powers of the divisors of n. the numbers 1 through 5 are all solitary. the smallest " friendly number " is 6, forming for example, the " friendly " pair 6 and 28 with " abundancy " σ ( 6 ) / 6 = ( 1 + 2 + 3 + 6 ) / 6 = 2, the same as σ ( 28 ) / 28 = ( 1 + 2 + 4 + 7 + 14 + 28 ) / 28 = 2. the shared value 2 is an integer in this case but not in many other cases.


in mathematics and logic, ambiguity can be considered to be an instance of the logical concept of underdetermination — for example, x = y { \ displaystyle x = y } leaves open what the value of x is — while its opposite is a self - contradiction, also called inconsistency, paradoxicalness, or oxymoron, or in mathematics an inconsistent system — such as x = 2, x = 3 { \ displaystyle x = 2, x = 3 }, which has no solution. logical ambiguity and self - contradiction is analogous to visual ambiguity and impossible objects, such as the necker cube and impossible cube, or many of the drawings of m. c. escher.


in pharmacokinetics, a compartment is a defined volume of body fluids, typically of the human body, but also those of other animals with multiple organ systems. the meaning in this area of study is different from the concept of anatomic compartments, which are bounded by fasciae, the sheath of fibrous tissue that enclose mammalian organs. instead, the concept focuses on broad types of fluidic systems. this analysis is used in attempts to mathematically describe distribution of small molecules throughout organisms with multiple compartments.


in some languages, any gender markers have been so eroded over time ( possibly through deflexion ) that they are no longer recognizable. many german nouns, for example, do not indicate their gender through either meaning or form. in such cases a noun's gender must simply be memorized, and gender can be regarded as an integral part of each noun when considered as an entry in the speaker's lexicon. ( this is reflected in dictionaries, which typically indicate the gender of noun headwords where applicable. ) second - language learners are often encouraged to memorize a modifier, usually a definite article, in conjunction with each noun — for example, a learner of french may learn the word for " chair " as la chaise ( meaning " the chair " ) ; this carries the information that the noun is chaise, and that it is feminine ( because la is the feminine singular form of the definite article ).


other constituents ( such as oblique, genitive, and object of comparative ) are called nonterms ( n ). the predicate is marked ( p ). according to geoffrey k. pullum ( 1977 ), the gr hierarchy directly corresponds to the accessibility hierarchy : a schematic representation of a clause in this formalism might look like :


in the first series of experiments, experts in the use of the various techniques were tasked with both the creation of the index and its use against the sample queries. each system had its own concept about how a query should be structured, which would today be known as a query language. much of the criticism of the first experiments focused on whether the experiments were truly testing the systems, or the user's ability to translate the query into the query language. this led to the second series of experiments, cranfield 2, that considered the question of converting the query into the language. to do this, instead of considering the generation of the query as a black box, each step was broken down.


in politics, emergent democracy represents the rise of political structures and behaviors without central planning and by the action of many individual participants, especially when mediated by the internet. it has been likened to the democratic system of ancient greece in the sense that people could publicly participate as much or as little as they please, although a form of representation exists which is based on personal trust networks instead of party affiliations. more recently, american writer and researcher clay shirky has referred to this as " the power of organizing without organizations. "


let the set of neighbors of node u { \ displaystyle u } be denoted nbr ( u ) { \ displaystyle \ operatorname { nbr } ( u ) }. the average degree is then μ = 1 n u ∈ v | nbr ( u ) | = 2 m n ≥ 1 { \ displaystyle \ mu = { \ frac { 1 } { n } } \ sum _ { u \ in v } | \ operatorname { nbr } ( u ) | = { \ frac { 2m } { n } } \ geq 1 }. let the number of " friends of friends " of node u { \ displaystyle u } be denoted ff ( u ) = v ∈ nbr ( u ) | nbr ( v ) | { \ displaystyle \ operatorname { ff } ( u ) = \ sum _ { v \ in \ operatorname { nbr } ( u ) } | \ operatorname { nbr } ( v ) | }.


in most european countries the official accident statistics contain no information on rolling cars, only great britain can deliver official statistical data. regarding other sources, only a few accident databases on rollover accidents exist. although only less than 10 % of all vehicle accidents with severe injuries involve rollovers, approximately 25 % of all seriously injured occupants were involved in accidents where their car rolled. these numbers are currently increasing, as rollover frequency of several new vehicle types like mini vans, suv or mpv is a lot higher than for most conventional cars.


in mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. these groups were first studied by reinhold baer, who showed that a finite abelian group is capable if and only if it is a product of cyclic groups of orders n1,..., nk where ni divides ni + 1 and nk – 1 = nk.


in 2017, 2. 3 million out of kickstarter's 7. 9 million users had donated toward more than one project. traditionally, journalists are not involved in advertising and marketing. crowdfunding means that journalists are attracting funders while trying to remain independent, which may pose a conflict. therefore, being directly involved with financial aspects can call journalistic integrity and journalistic objectivity into question.


in signal processing, independent component analysis ( ica ) is a computational method for separating a multivariate signal into additive subcomponents. this is done by assuming that at most one subcomponent is gaussian and that the subcomponents are statistically independent from each other. ica is a special case of blind source separation. a common example application is the " cocktail party problem " of listening in on one person's speech in a noisy room.


in proof theory, particularly the proof theory of constructive mathematics based on the curry – howard correspondence, one often identifies a mathematical proposition with its set of proofs ( if any ). a given proposition may have many proofs, of course ; according to the principle of proof irrelevance, normally only the truth of the proposition matters, not which proof was used. however, the curry – howard correspondence can turn proofs into algorithms, and differences between algorithms are often important. so proof theorists may prefer to identify a proposition with a setoid of proofs, considering proofs equivalent if they can be converted into one another through beta conversion or the like.


in regards to the typology of neolithic adzes, initially two types were distinguished, when width exceeds thickness they were named flat adzes ( flachhacke ), when thickness exceeds width shoe - last adzes ( schuhleistenkeile ), or high adzes. within the latter group a distinction is sometimes made between intermediate flomborn adzes and the higher hinkelstein adzes ( buttler 1938 ; bakels 1987 ; merkel 1999 ). later, subdivisions were made on the basis of metric characteristics into two groups ( schietzel 1965 ), six groups ( modderman 1970, 184 ) and finally two groups again ( dohrn - ihmig 1983 ). all typologies were based on the width - height ratio, while modderman added the absolute dimension. the wide variation, from small to large and from flat to high adzes, certainly reflects a functional differentiation, but the various types do not appear to be of chronological significance.


these schemata are needed to link the pure category to sensed phenomenal appearances because the categories are, as kant says, heterogeneous with sense intuition. categories and sensed phenomena, however, do share one characteristic : time. succession is the form of sense impressions and also of the category of causality. therefore, time can be said to be the schema of categories or pure concepts of the understanding.


that is, at 16 byte intervals. since all segments are 64 kb long, this explains how overlap can occur between segments and why any location in the linear memory address space can be accessed with many segment : offset pairs. the actual location of the beginning of a segment in the linear address space can be calculated with segment×16.


this is computable in polynomial time as the determinant of a maximal principal submatrix of the laplacian matrix of g, an early result in algebraic graph theory known as kirchhoff ’ s matrix – tree theorem. likewise, the dimension of the bicycle space at t g ( − 1, − 1 ) { \ displaystyle t _ { g } ( - 1, - 1 ) } can be computed in polynomial time by gaussian elimination. for planar graphs, the partition function of the ising model, i. e., the tutte polynomial at the hyperbola h 2 { \ displaystyle h _ { 2 } }, can be expressed as a pfaffian and computed efficiently via the fkt algorithm. this idea was developed by fisher, kasteleyn, and temperley to compute the number of dimer covers of a planar lattice model.


full named - entity recognition is often broken down, conceptually and possibly also in implementations, as two distinct problems : detection of names, and classification of the names by the type of entity they refer to ( e. g. person, organization, or location ). the first phase is typically simplified to a segmentation problem : names are defined to be contiguous spans of tokens, with no nesting, so that " bank of america " is a single name, disregarding the fact that inside this name, the substring " america " is itself a name. this segmentation problem is formally similar to chunking.


in the 1920s, louis mordell posed a conjecture that implied that fermat's equation has at most a finite number of nontrivial primitive integer solutions, if the exponent n is greater than two. this conjecture was proved in 1983 by gerd faltings, and is now known as faltings's theorem.


in the event of a worst - case emergency, called a " design basis accident " in nrc regulations, the containment is designed to seal off and contain a meltdown. redundant systems are installed to prevent a meltdown, but as a matter of policy, one is assumed to occur and thus the requirement for a containment building. for design purposes, the reactor vessel's piping is assumed to be breached, causing a " loca " ( loss of coolant accident ) where the water in the reactor vessel is released to the atmosphere inside the containment and flashes into steam.


in probability theory, the zero - truncated poisson ( ztp ) distribution is a certain discrete probability distribution whose support is the set of positive integers. this distribution is also known as the conditional poisson distribution or the positive poisson distribution. it is the conditional probability distribution of a poisson - distributed random variable, given that the value of the random variable is not zero. thus it is impossible for a ztp random variable to be zero.


{ \ displaystyle \ chi'= \ sum _ { i = 1 } ^ { n } k _ { i } s _ { i } ^ { 2 }. } where k i { \ displaystyle k _ { i } } is a real positive number, typically k i = 1 ν i + 1 { \ displaystyle k _ { i } = { \ frac { 1 } { \ nu _ { i } + 1 } } }. in general, the probability distribution of χ'cannot be expressed analytically.


in order to overcome the volume size limit of fat16, while at the same time allowing dos real - mode code to handle the format, microsoft designed a new version of the file system, fat32, which supported an increased number of possible clusters, but could reuse most of the existing code, so that the conventional memory footprint was increased by less than 5 kb under dos. cluster values are represented by 32 - bit numbers, of which 28 bits are used to hold the cluster number.


for example, a common attack on asymmetric rsa relies on the fact that the encryption steps rely on the value of the key bits. every bit is processed with a square operation and then a multiplication operation if and only if the bit is equal to 1. an attacker with a clear trace can deduce the key simply by observing where the multiplication operations are performed.


in practice we have much fewer processors than the matrix elements. we can replace the matrix elements with submatrices, so that every processor processes more values. the scalar multiplication and addition become sequential matrix multiplication and addition. the width and height of the submatrices will be n = n / p { \ displaystyle n = n / { \ sqrt { p } } }.


in prehistoric time, quarter square multiplication involved floor function ; that some sources attribute to babylonian mathematics ( 2000 – 1600 bc ). antoine voisin published a table of quarter squares from 1 to 1000 in 1817 as an aid in multiplication. a larger table of quarter squares from 1 to 100000 was published by samuel laundy in 1856, and a table from 1 to 200000 by joseph blater in 1888. quarter square multipliers were used in analog computers to form an analog signal that was the product of two analog input signals. in this application, the sum and difference of two input voltages are formed using operational amplifiers.


it would be superseded by peripheral component interconnect ( pci ), starting at speeds of 133 mb / s ( 32 - bit at 33 mhz in the standard configuration ) thus for a short time, a market opening occurred where video card manufacturers and motherboard chipset makers created their own proprietary implementations of local buses to provide graphics cards direct access to the processor and system memory. this avoided the limitations of the isa bus while being less costly than a " licensed ibm mca machine ". it is important to note that at the time the cost to migrate to an mca architecture machine from an isa machine was substantial.