in terms of a graph - based computational procedure, smiles is a string obtained by printing the symbol nodes encountered in a depth - first tree traversal of a chemical graph. the chemical graph is first trimmed to remove hydrogen atoms and cycles are broken to turn it into a spanning tree. where cycles have been broken, numeric suffix labels are included to indicate the connected nodes. parentheses are used to indicate points of branching on the tree. the resultant smiles form depends on the choices : of the bonds chosen to break cycles, of the starting atom used for the depth - first traversal, and of the order in which branches are listed when encountered.


in the execute stage, the instruction operations are carried out. instructions are delayed in this step until all of their operands are available, eliminating raw hazards. program correctness is maintained through effective address calculation to prevent hazards through memory. if one or more of the operands is not yet available then : wait for operand to become available on the cdb. when all operands are available, then : if the instruction is a load or store compute the effective address when the base register is available, and place it in the load / store buffer if the instruction is a load then : execute as soon as the memory unit is available else, if the instruction is a store then : wait for the value to be stored before sending it to the memory unit else, the instruction is an arithmetic logic unit ( alu ) operation then : execute the instruction at the corresponding functional unit


in the pinn framework, initial and boundary conditions are not analytically satisfied, thus they need to be included in the loss function of the network to be simultaneously learned with the differential equation ( de ) unknown functions. having competing objectives during the network's training can lead to unbalanced gradients while using gradient - based techniques, which causes pinns to often struggle to accurately learn the underlying de solution. this drawback is overcome by using functional interpolation techniques such as the theory of functional connections ( tfc )'s constrained expression, in the deep - tfc framework, which reduces the solution search space of constrained problems to the subspace of neural network that analytically satisfies the constraints. a further improvement of pinn and functional interpolation approach is given by the extreme theory of functional connections ( x - tfc ) framework, where a single - layer neural network and the extreme learning machine training algorithm are employed. x - tfc allows to improve the accuracy and performance of regular pinns, and its robustness and reliability are proved for stiff problems, optimal control, aerospace, and rarefied gas dynamics applications.


a more efficient version of the algorithm shortcuts these steps, instead replacing the larger of the two numbers by its remainder when divided by the smaller of the two ( with this version, the algorithm stops when reaching a zero remainder ). with this improvement, the algorithm never requires more steps than five times the number of digits ( base 10 ) of the smaller integer. this was proven by gabriel lame in 1844 ( lame's theorem ), and marks the beginning of computational complexity theory.


in the context modeling complexity the next - symbol predictions, of one or more statistical models, are combined or competing to yield a prediction that is based on events recorded in the past. the algorithmic information content derived from each symbol prediction can be used to compute algorithmic information profiles with a time proportional to the length of the sequence. the process has been applied to dna sequence analysis.


these coverings are called " caps ". depending on the method used for the shadow volume, the front end may be covered by the object itself, and the rear end may sometimes be omitted ( see depth pass below ).


in mathematics and computer science, graph edit distance ( ged ) is a measure of similarity ( or dissimilarity ) between two graphs. the concept of graph edit distance was first formalized mathematically by alberto sanfeliu and king - sun fu in 1983. a major application of graph edit distance is in inexact graph matching, such as error - tolerant pattern recognition in machine learning. the graph edit distance between two graphs is related to the string edit distance between strings. with the interpretation of strings as connected, directed acyclic graphs of maximum degree one, classical definitions of edit distance such as levenshtein distance, hamming distance and jaro – winkler distance may be interpreted as graph edit distances between suitably constrained graphs. likewise, graph edit distance is also a generalization of tree edit distance between rooted trees.


in mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. expressed algebraically, for quantities a { \ displaystyle a } and b { \ displaystyle b } with a > b > 0 { \ displaystyle a > b > 0 }, where the greek letter phi ( φ { \ displaystyle \ varphi } or { \ displaystyle \ phi } ) denotes the golden ratio. the constant φ { \ displaystyle \ varphi } satisfies the quadratic equation φ 2 = φ + 1 { \ displaystyle \ varphi ^ { 2 } = \ varphi + 1 } and is an irrational number with a value of the golden ratio was called the extreme and mean ratio by euclid, and the divine proportion by luca pacioli, and also goes by several other names. mathematicians have studied the golden ratio's properties since antiquity. it is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron.


in computability theory, a general recursive function is a partial function from the integers to the integers ; no algorithm can exist for deciding whether an arbitrary such function is in fact total. when arrow notation is used for functions, a partial function f { \ displaystyle f } from x { \ displaystyle x } to y { \ displaystyle y } is sometimes written as f : x y, { \ displaystyle f : x \ rightharpoonup y, } f : x → y, { \ displaystyle f : x \ nrightarrow y, } or f : x y. { \ displaystyle f : x \ hookrightarrow y. } however, there is no general convention, and the latter notation is more commonly used for inclusion maps or embeddings. specifically, for a partial function f : x y, { \ displaystyle f : x \ rightharpoonup y, } and any x ∈ x, { \ displaystyle x \ in x, } one has either : f ( x ) = y ∈ y { \ displaystyle f ( x ) = y \ in y } ( it is a single element in y ), or f ( x ) { \ displaystyle f ( x ) } is undefined. for example, if f { \ displaystyle f } is the square root function restricted to the integers f : z → n, { \ displaystyle f : \ mathbb { z } \ to \ mathbb { n }, } defined by : f ( n ) = m { \ displaystyle f ( n ) = m } if, and only if, m 2 = n, { \ displaystyle m ^ { 2 } = n, } m ∈ n, n ∈ z, { \ displaystyle m \ in \ mathbb { n }, n \ in \ mathbb { z }, } then f ( n ) { \ displaystyle f ( n ) } is only defined if n { \ displaystyle n } is a perfect square ( that is, 0, 1, 4, 9, 16, … { \ displaystyle 0, 1, 4, 9, 16, \ ldots } ). so f ( 25 ) = 5 { \ displaystyle f ( 25 ) = 5 } but f ( 26 ) { \ displaystyle f ( 26 ) } is undefined.


in the ascii version of the format, the vertices and faces are each described one to a line with the numbers separated by white space. in the binary version, the data is simply packed closely together at the endianness specified in the header and with the data types given in the property records. for the common property list... representation for polygons, the first number for that element is the number of vertices that the polygon has and the remaining numbers are the indices of those vertices in the preceding vertex list.


in phylogenetics, the metric is often used to compute a distance between two trees. the treedist program in the phylip suite offers this function, as does the raxml _ standard package, the dendropy python library ( under the name " symmetric difference metric " ), and r packages treedist ( ` robinsonfoulds ( ) ` function ) and phangorn ( ` treedist ( ) ` function ). for comparing groups of trees, the fastest implementations include hashrf and mrsrf. the robinson – foulds metric has also been used in quantitative comparative linguistics to compute distances between trees that represent how languages are related to each other.


in the 1980s and 1990s, a variety of svr4 versions of unix were available commercially for the x86 pc platform. however, the market for commercial unix on pcs declined after linux and bsd became widely available. in late 1994, eric s. raymond discontinued his pc - clone unix software buyer's guide on usenet, stating, " the reason i am dropping this is that i run linux now, and i no longer find the svr4 market interesting or significant. " in 1998, a confidential memo at microsoft stated, " linux is on track to eventually own the x86 unix market ", and further predicted, " i believe that linux – moreso than nt – will be the biggest threat to sco in the near future. " an infoworld article from 2001 characterized sco unixware as having a " bleak outlook " due to being " trounced " in the market by linux and solaris, and idc predicted that sco would " continue to see a shrinking share of the market ".


babai and szemeredi prove that every element of a finite group g has an slp of length o ( log2 | g | ) in every generating set. an efficient solution to the constructive membership problem is crucial to many group - theoretic algorithms. it can be stated in terms of slps as follows.


similarly for the generator in wasserstein gan. for wasserstein gan, d w g a n { \ displaystyle d _ { wgan } } has gradient 1 almost everywhere, while for gan, ln ( 1 − d ) { \ displaystyle \ ln ( 1 - d ) } has flat gradient in the middle, and steep gradient elsewhere.


in numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error. for example, suppose that the final result of a long, multi - step calculation can be safely rounded off to n decimal places. that is to say, the roundoff error introduced by this final roundoff makes a negligible contribution to the overall uncertainty. however, it is quite likely that it is not safe to round off the intermediate steps in the calculation to the same number of digits.


in mathematical logic, tarski's high school algebra problem was a question posed by alfred tarski. it asks whether there are identities involving addition, multiplication, and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high - school - level mathematics. the question was solved in 1980 by alex wilkie, who showed that such unprovable identities do exist.


in response to some of these variants, and to other feedback, the paper " primes is in p " was updated with a new formulation of the aks algorithm and of its proof of correctness. ( this version was eventually published in annals of mathematics. ) while the basic idea remained the same, r was chosen in a new manner, and the proof of correctness was more coherently organized.


in modern positional numbers systems, such as the decimal system, the digits and their positions in the representation of an integer, for example, 45, are a shorthand notation for a polynomial in the radix or base, in this case, 4 × 101 + 5 × 100. as another example, in radix 5, a string of digits such as 132 denotes the ( decimal ) number 1 × 52 + 3 × 51 + 2 × 50 = 42. this representation is unique. let b be a positive integer greater than 1.


for example, his f20 cores had 31 5 - bit instructions, which fit four to a 20 - bit word. risc chips now dominate the market for 32 - bit embedded systems. smaller risc chips are even growing common in the cost - sensitive 8 - bit embedded - system market.


in summary, backtracking line search ( and its modifications ) is a method which is easy to implement, is applicable for very general functions, has very good theoretical guarantee ( for both convergence to critical points and avoidance of saddle points ) and works well in practice. several other methods which have good theoretical guarantee, such as diminishing learning rates or standard gd with learning rate < 1 / l – both require the gradient of the objective function to be lipschitz continuous, turn out to be a special case of backtracking line search or satisfy armijo's condition. even though a priori one needs the cost function to be continuously differentiable to apply this method, in practice one can apply this method successfully also for functions which are continuously differentiable on a dense open subset such as f ( t ) = | t | { \ displaystyle f ( t ) = | t | } or f ( t ) = r e l u ( t ) = max { t, 0 } { \ displaystyle f ( t ) = relu ( t ) = \ max \ { t, 0 \ } }.


in the 1960s and 1970s, gallagher proved several results in large sieve methods in analytic number theory and simplified key ingredients used in the proof of the bombieri – vinogradov theorem. he also applied the large sieve to study the asymptotics of galois groups of monic integral polynomials of bounded height, improving on results by van der waerden. in 1971, he invented the larger sieve.


recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social, pathological and biological networks. for a survey on recent trends in computational methods and applications see buluc et al. ( 2013 ). two common examples of graph partitioning are minimum cut and maximum cut problems.


with the advent of high - speed computers, the minimization problem can be solved iteratively with adequate speed, and the communalities are calculated in the process, rather than being needed beforehand. the minres algorithm is particularly suited to this problem, but is hardly the only iterative means of finding a solution. if the solution factors are allowed to be correlated ( as in'oblimin'rotation, for example ), then the corresponding mathematical model uses skew coordinates rather than orthogonal coordinates.


in mathematics, computer science and logic, convergence is the idea that different sequences of transformations come to a conclusion in a finite amount of time ( the transformations are terminating ), and that the conclusion reached is independent of the path taken to get to it ( they are confluent ). more formally, a preordered set of term rewriting transformations are said to be convergent if they are confluent and terminating.


{ \ displaystyle \ left ( \ mathbf { p } ^ { t } \ mathbf { a } \ mathbf { p } \ right ) \ left ( \ mathbf { p } ^ { t } \ mathbf { x } \ right ) = \ mathbf { p } ^ { t } \ mathbf { b }. } the problem of finding the best ordering is an np - complete problem and is thus intractable, so heuristic methods are used instead.


in spectral graph theory, an eigenvalue of a graph is defined as an eigenvalue of the graph's adjacency matrix a { \ displaystyle a }, or ( increasingly ) of the graph's laplacian matrix due to its discrete laplace operator, which is either d − a { \ displaystyle d - a } ( sometimes called the combinatorial laplacian ) or i − d − 1 / 2 a d − 1 / 2 { \ displaystyle i - d ^ { - 1 / 2 } ad ^ { - 1 / 2 } } ( sometimes called the normalized laplacian ), where d { \ displaystyle d } is a diagonal matrix with d i i { \ displaystyle d _ { ii } } equal to the degree of vertex v i { \ displaystyle v _ { i } }, and in d − 1 / 2 { \ displaystyle d ^ { - 1 / 2 } }, the i { \ displaystyle i } th diagonal entry is 1 / deg ( v i ) { \ textstyle 1 / { \ sqrt { \ deg ( v _ { i } ) } } }. the k { \ displaystyle k } th principal eigenvector of a graph is defined as either the eigenvector corresponding to the k { \ displaystyle k } th largest or k { \ displaystyle k } th smallest eigenvalue of the laplacian. the first principal eigenvector of the graph is also referred to merely as the principal eigenvector. the principal eigenvector is used to measure the centrality of its vertices.


in the digital realm, there can be any number of conventional primary colors making up an image ; a channel in this case is extended to be the grayscale image based on any such conventional primary color. by extension, a channel is any grayscale image of the same dimension as and associated with the original image. channel is a conventional term used to refer to a certain component of an image. in reality, any image format can use any algorithm internally to store images.


the case where the classical communication is replaced by quantum communication was considered in. this is known as the fully quantum slepian - wolf theorem, since everything is sent down the quantum channel.


some important languages used in ogc - compliant systems are described in the following. xml stands for extensible markup language and is widely used for displaying and interpreting data from computers. thus the development of a web - based gi system requires several useful xml encodings that can effectively describe two - dimensional graphics such as maps svg and, at the same time, store and transfer simple features gml.


in statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model. the resulting fitted model can be used to summarize the data, to predict unobserved values from the same system, and to understand the mechanisms that may underlie the system. mathematically, linear least squares is the problem of approximately solving an overdetermined system of linear equations a x = b, where b is not an element of the column space of the matrix a. the approximate solution is realized as an exact solution to a x = b ', where b'is the projection of b onto the column space of a. the best approximation is then that which minimizes the sum of squared differences between the data values and their corresponding modeled values. the approach is called linear least squares since the assumed function is linear in the parameters to be estimated.


in preparation to the attack, weaknesses in the key schedule of ktantan that allows the 3 - subset mitm attack was identified. since only two key - bits are used each round, the diffusion of the key per round is small - the safety lies in the number of rounds. due to this structure of the key - schedule, it was possible to find a large number of consecutive rounds, which never utilized certain key - bits. more precisely, the authors of the attack found that : round 1 to 111 never uses the key - bits : k 32, k 39, k 44, k 61, k 66, k 75 { \ displaystyle k _ { 32 }, k _ { 39 }, k _ { 44 }, k _ { 61 }, k _ { 66 }, k _ { 75 } } round 131 to 254 never uses the key - bits : k 3, k 20, k 41, k 47, k 63, k 74 { \ displaystyle k _ { 3 }, k _ { 20 }, k _ { 41 }, k _ { 47 }, k _ { 63 }, k _ { 74 } } this characteristics of the key - schedule is used for staging the 3 - subset mitm attack, as we now are able to split the cipher into two blocks with independent key - bits. the parameters for the attack are thus : a 0 { \ displaystyle a _ { 0 } } = the keybits used by both blocks ( which means the rest 68 bits not mentioned above ) a 1 { \ displaystyle a _ { 1 } } = the keybits used only by the first block ( defined by round 1 - 111 ) a 2 { \ displaystyle a _ { 2 } } = the keybits used only by the second block ( defined by round 131 - 254 )


in mathematics, the mediant of two fractions, generally made up of four positive integers a c { \ displaystyle { \ frac { a } { c } } \ quad } and b d { \ displaystyle \ quad { \ frac { b } { d } } \ quad } is defined as a + b c + d. { \ displaystyle \ quad { \ frac { a + b } { c + d } }. } that is to say, the numerator and denominator of the mediant are the sums of the numerators and denominators of the given fractions, respectively.


the area of a square is equal to the product of two of its sides ( follows from 3 ). next, each top square is related to a triangle congruent with another triangle related in turn to one of two rectangles making up the lower square. the proof is as follows : let acb be a right - angled triangle with right angle cab.


in mathematical logic, formation rules are rules for describing which strings of symbols formed from the alphabet of a formal language are syntactically valid within the language. these rules only address the location and manipulation of the strings of the language. it does not describe anything else about a language, such as its semantics ( i. e. what the strings mean ). ( see also formal grammar ).


in mathematics, particularly in category theory, a morphism is a structure - preserving map from one mathematical structure to another one of the same type. the notion of morphism recurs in much of contemporary mathematics. in set theory, morphisms are functions ; in linear algebra, linear transformations ; in group theory, group homomorphisms ; in analysis and topology, continuous functions, and so on.


in some owl flavors like owl1 - dl, entities can be either classes or instances, but cannot be both. this limitations forbids metaclasses and metamodeling. this is not the case in the owl1 full flavor, but this allows the model to be computationally undecidable. in owl2, metaclasses can implemented with punning, that is a way to treat classes as if they were individuals. other approaches have also been proposed and used to check the properties of ontologies at a meta level.


the eigenvectors corresponding to the smaller eigenvalues will tend to be very sensitive to the exact choice of training data, and it is often necessary to use regularisation as described in the next section. if classification is required, instead of dimension reduction, there are a number of alternative techniques available.


computers usually solve square systems of linear equations using lu decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix. the lu decomposition was introduced by the polish astronomer tadeusz banachiewicz in 1938. to quote : " it appears that gauss and doolittle applied the method only to symmetric equations. more recent authors, for example, aitken, banachiewicz, dwyer, and crout … have emphasized the use of the method, or variations of it, in connection with non - symmetric problems … banachiewicz … saw the point … that the basic problem is really one of matrix factorization, or “ decomposition ” as he called it. " it's also referred to as lr decomposition ( factors into left and right triangular matrices ).


in optimization, a descent direction is a vector p ∈ r n { \ displaystyle \ mathbf { p } \ in \ mathbb { r } ^ { n } } that points towards a local minimum x ∗ { \ displaystyle \ mathbf { x } ^ { * } } of an objective function f : r n → r { \ displaystyle f : \ mathbb { r } ^ { n } \ to \ mathbb { r } }. computing x ∗ { \ displaystyle \ mathbf { x } ^ { * } } by an iterative method, such as line search defines a descent direction p k ∈ r n { \ displaystyle \ mathbf { p } _ { k } \ in \ mathbb { r } ^ { n } } at the k { \ displaystyle k } th iterate to be any p k { \ displaystyle \ mathbf { p } _ { k } } such that ⟨ p k, ∇ f ( x k ) ⟩ < 0 { \ displaystyle \ langle \ mathbf { p } _ { k }, \ nabla f ( \ mathbf { x } _ { k } ) \ rangle < 0 }, where ⟨, ⟩ { \ displaystyle \ langle, \ rangle } denotes the inner product. the motivation for such an approach is that small steps along p k { \ displaystyle \ mathbf { p } _ { k } } guarantee that f { \ displaystyle \ displaystyle f } is reduced, by taylor's theorem. using this definition, the negative of a non - zero gradient is always a descent direction, as ⟨ − ∇ f ( x k ), ∇ f ( x k ) ⟩ = − ⟨ ∇ f ( x k ), ∇ f ( x k ) ⟩ < 0 { \ displaystyle \ langle - \ nabla f ( \ mathbf { x } _ { k } ), \ nabla f ( \ mathbf { x } _ { k } ) \ rangle = - \ langle \ nabla f ( \ mathbf { x } _ { k } ), \ nabla f ( \ mathbf { x } _ { k } ) \ rangle < 0 }.


in mathematics, an interval contractor ( or contractor for short ) associated to a set x { \ displaystyle x } is an operator c { \ displaystyle c } which associates to a hyperrectangle { \ displaystyle } in r n { \ displaystyle { \ mathbf { r } } ^ { n } } another box c ( ) { \ displaystyle c ( ) } of r n { \ displaystyle { \ mathbf { r } } ^ { n } } such that the two following properties are always satisfied : c ( ) ⊂ { \ displaystyle c ( ) \ subset } ( contractance property ) c ( ) ∩ x = ∩ x { \ displaystyle c ( ) \ cap x = \ cap x } ( completeness property ) a contractor associated to a constraint ( such as an equation or an inequality ) is a contractor associated to the set x { \ displaystyle x } of all x { \ displaystyle x } which satisfy the constraint. contractors make it possible to improve the efficiency of branch - and - bound algorithms classically used in interval analysis.


in textbooks, channel length modulation in active mode usually is described using the shichman – hodges model, accurate only for old technology : where i d { \ displaystyle i _ { \ text { d } } } = drain current, k n ′ { \ displaystyle k'_ { n } } = technology parameter sometimes called the transconductance coefficient, w, l = mosfet width and length, v gs { \ displaystyle v _ { \ text { gs } } } = gate - to - source voltage, v th { \ displaystyle v _ { \ text { th } } } = threshold voltage, v ds { \ displaystyle v _ { \ text { ds } } } = drain - to - source voltage, v ds, sat = v gs − v th { \ displaystyle v _ { \ text { ds, sat } } = v _ { \ text { gs } } - v _ { \ text { th } } }, and λ = channel - length modulation parameter. in the classic shichman – hodges model, v th { \ displaystyle v _ { \ text { th } } } is a device constant, which reflects the reality of transistors with long channels.


in mathematics, a strictly convex space is a normed vector space ( x, | | | | ) for which the closed unit ball is a strictly convex set. put another way, a strictly convex space is one for which, given any two distinct points x and y on the unit sphere ∂b ( i. e. the boundary of the unit ball b of x ), the segment joining x and y meets ∂b only at x and y. strict convexity is somewhere between an inner product space ( all inner product spaces being strictly convex ) and a general normed space in terms of structure. it also guarantees the uniqueness of a best approximation to an element in x ( strictly convex ) out of a convex subspace y, provided that such an approximation exists. if the normed space x is complete and satisfies the slightly stronger property of being uniformly convex ( which implies strict convexity ), then it is also reflexive by milman - pettis theorem.


for high - dimensional data, many of the existing methods fail due to the curse of dimensionality, which renders particular distance functions problematic in high - dimensional spaces. this led to new clustering algorithms for high - dimensional data that focus on subspace clustering ( where only some attributes are used, and cluster models include the relevant attributes for the cluster ) and correlation clustering that also looks for arbitrary rotated ( " correlated " ) subspace clusters that can be modeled by giving a correlation of their attributes. examples for such clustering algorithms are clique and subclu. ideas from density - based clustering methods ( in particular the dbscan / optics family of algorithms ) have been adapted to subspace clustering ( hisc, hierarchical subspace clustering and dish ) and correlation clustering ( hico, hierarchical correlation clustering, 4c using " correlation connectivity " and eric exploring hierarchical density - based correlation clusters ).


in most post - soviet states dd. mm. yyyy format is used with dots as separators and with leading zeros. some, such as lithuania, have adopted the iso 8601 yyyy - mm - dd format ; previously a mixed standard with iso 8601 order but dots as separators was in use.


since this relaxation in us export restrictions, and because most personal computers connected to the internet include us - sourced web browsers such as firefox or internet explorer, almost every internet user worldwide has potential access to quality cryptography via their browsers ( e. g., via transport layer security ). the mozilla thunderbird and microsoft outlook e - mail client programs similarly can transmit and receive emails via tls, and can send and receive email encrypted with s / mime. many internet users do not realize that their basic application software contains such extensive cryptosystems. these browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally do not find it practical to do much to control distribution or use of cryptography of this quality, so even when such laws are in force, actual enforcement is often effectively impossible.


a suitable generalization of the first definition is : let d { \ displaystyle d } be a subset of r n. { \ displaystyle \ mathbb { r } ^ { n }. }


it is the smallest finite non - abelian group. a common example from physics is the rotation group so ( 3 ) in three dimensions ( for example, rotating something 90 degrees along one axis and then 90 degrees along a different axis is not the same as doing them in reverse order ). both discrete groups and continuous groups may be non - abelian. most of the interesting lie groups are non - abelian, and these play an important role in gauge theory.


finally, this generates two clearly different proposals : " cheap printer – expensive ink " or " expensive printer – cheap ink ". ultimately, the consumer decision depends on their reference interest rate or their time preference. from an economics viewpoint, there is a clear trade - off between cost per copy and cost of the printer.


in probability, statistics and related fields, a poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. the poisson point process is often called simply the poisson process, but it is also called a poisson random measure, poisson random point field or poisson point field. this point process has convenient mathematical properties, which has led to its being frequently defined in euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy, biology, ecology, geology, seismology, physics, economics, image processing, and telecommunications. the process is named after french mathematician simeon denis poisson despite poisson's never having studied the process. its name derives from the fact that if a collection of random points in some space forms a poisson process, then the number of points in a region of finite size is a random variable with a poisson distribution.


in the visual basic ( classic ) language, subprograms are termed functions or subs ( or methods when associated with a class ). visual basic 6 uses various terms called types to define what is being passed as a parameter. by default, an unspecified variable is registered as a variant type and can be passed as byref ( default ) or byval. also, when a function or sub is declared, it is given a public, private, or friend designation, which determines whether it can be accessed outside the module or project that it was declared in.


in the united states, each wireless network controls how their mdcs will be used. as such, when wireless customers call a mdc, they're call is routed to the end user that their carrier selects.


evaluating the cross - products : | e x e y e z − x a 0 0 0 r 0 0 | + | e x e y e z l − x a 0 0 0 r b 0 | = − x a r 0 e z + ( l − x a ) r b e z = 0. { \ displaystyle \ left | { \ begin { matrix } \ mathbf { e } _ { x } & \ mathbf { e } _ { y } & \ mathbf { e } _ { z } \ \ - x _ { a } & 0 & 0 \ \ 0 & r _ { 0 } & 0 \ end { matrix } } \ right | + \ left | { \ begin { matrix } \ mathbf { e } _ { x } & \ mathbf { e } _ { y } & \ mathbf { e } _ { z } \ \ l - x _ { a } & 0 & 0 \ \ 0 & r _ { b } & 0 \ end { matrix } } \ right | = - x _ { a } r _ { 0 } \, \ mathbf { e } _ { z } + ( l - x _ { a } ) r _ { b } \, \ mathbf { e } _ { z } = 0 \,. }


ask query used to provide a simple true / false result for a query on a sparql endpoint. describe query used to extract an rdf graph from the sparql endpoint, the content of which is left to the endpoint to decide, based on what the maintainer deems as useful information. each of these query forms takes a where block to restrict the query, although, in the case of the describe query, the where is optional. sparql 1. 1 specifies a language for updating the database with several new query forms.


in telecommunications, continuous tone - coded squelch system or ctcss is one type of in - band signaling that is used to reduce the annoyance of listening to other users on a shared two - way radio communication channel. it is sometimes referred to as tone squelch or pl for private line, a trademark of motorola. it does this by adding a low frequency audio tone to the voice. where more than one group of users is on the same radio frequency ( called co - channel users ), ctcss circuitry mutes those users who are using a different ctcss tone or no ctcss.


in the japanese kantenji braille, the standard 8 - dot braille patterns 23567, 123567, 234567, and 1234567 are the patterns related to braille pattern dots - 12345, since the two additional dots of kantenji patterns 012345, 123457, and 0123457 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


having established the necessary notions, the theorem is stated as follows. chomsky – schutzenberger theorem. if l { \ displaystyle l } is a context - free language admitting an unambiguous context - free grammar, and a k : = | l ∩ σ k | { \ displaystyle a _ { k } : = | l \ \ cap \ sigma ^ { k } | } is the number of words of length k { \ displaystyle k } in l { \ displaystyle l }, then g ( x ) = k = 0 ∞ a k x k { \ displaystyle g ( x ) = \ sum _ { k = 0 } ^ { \ infty } a _ { k } x ^ { k } } is a power series over n { \ displaystyle \ mathbb { n } } that is algebraic over q ( x ) { \ displaystyle \ mathbb { q } ( x ) }. proofs of this theorem are given by kuich & salomaa ( 1985 ), and by panholzer ( 2005 ).


given 2 1 × 0. 100 2 − 2 0 × 0. 111 2 { \ displaystyle 2 ^ { 1 } \ times 0. 100 _ { 2 } - 2 ^ { 0 } \ times 0. 111 _ { 2 } } we have to line up the binary points. this means we must add an extra digit to the first operand — a guard digit. this gives us 2 1 × 0. 1000 2 − 2 1 × 0. 0111 2 { \ displaystyle 2 ^ { 1 } \ times 0. 1000 _ { 2 } - 2 ^ { 1 } \ times 0. 0111 _ { 2 } }.


examples of phonemic or distinctive features are :, ( binary features ) and ( a unary feature ; also a place feature ). surface representations can be expressed as the result of rules acting on the features of the underlying representation. these rules are formulated in terms of transformations on features.


it is also possible to find a simultaneous embedding with fixed edges for any pair of a planar graph and a tree. it is an open question whether the existence of a simultaneous embedding with fixed edges for two given graphs can be tested in polynomial time. however, for three or more graphs, the problem is np - complete. when simultaneous embeddings with fixed edges do exist, they can be found in polynomial time for pairs of outerplanar graphs, and for biconnected graphs, i. e. pairs of graphs whose intersection is biconnected.


in number theory, fermat's last theorem ( sometimes called fermat's conjecture, especially in older texts ) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. the cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions. the proposition was first stated as a theorem by pierre de fermat around 1637 in the margin of a copy of arithmetica. fermat added that he had a proof that was too large to fit in the margin. although other statements claimed by fermat without proof were subsequently proven by others and credited as theorems of fermat ( for example, fermat's theorem on sums of two squares ), fermat's last theorem resisted proof, leading to doubt that fermat ever had a correct proof.


the analyst must learn the set of joint conditional opinions ω z | x y { \ displaystyle \ omega _ { z | xy } } in order to apply the deduction operator and derive the marginal opinion ω z ‖ x y { \ displaystyle \ omega _ { z \ | xy } } on the variable z { \ displaystyle z }. the conditional opinions express a conditional relationship between the parent variables and the child variable. the deduced opinion is computed as ω z ‖ x y = ω z | x y ω x y { \ displaystyle \ omega _ { z \ | xy } = \ omega _ { z | xy } \ circledcirc \ omega _ { xy } }.


in survey methodology, probability - proportional - to - size ( pps ) sampling is a sampling process where each element of the population ( of size n ) has some ( independent ) chance p i { \ displaystyle p _ { i } } to be selected to the sample when performing one draw. this p i { \ displaystyle p _ { i } } is proportional to some known quantity x i { \ displaystyle x _ { i } } so that p i = x i i = 1 n x i { \ displaystyle p _ { i } = { \ frac { x _ { i } } { \ sum _ { i = 1 } ^ { n } x _ { i } } } }. : 97 one of the cases this occurs in, as developed by hanson and hurwitz in 1943, is when we have several clusters of units, each with a different ( known upfront ) number of units, then each cluster can be selected with a probability that is proportional to the number of units inside it. : 250 so, for example, if we have 3 clusters with 10, 20 and 30 units each, then the chance of selecting the first cluster will be 1 / 6, the second would be 1 / 3, and the third cluster will be 1 / 2.


expectancy is defined as the individual's subjectively held probability that a given action will lead to a given outcome. it can range from zero to one, with one representing 100 % confidence in the outcome. for example, a person may entertain a given level of belief that they can make a foul shot in basketball or that an additional hour of study will improve their grade on an examination.


for each input command, a state - graph ( or statetable or extended finite state automaton ) is defined that provides a plan ( or procedure for making a plan ) for accomplishing the commanded task. the input command selects ( or causes to be generated ) an appropriate state - table, the execution of which generates a series of output commands to units at the next lower echelon. the library of state - tables contains a set of statesensitive procedural rules that identify all the task branching conditions and specify the corresponding state transition and output command parameters. the result of step 3 is that each organizational unit has for each input command a state - table of ordered production rules, each suitable for execution by an extended finite state automaton ( fsa ).


in mathematics, the arguments of the maxima ( abbreviated arg max or argmax ) are the points, or elements, of the domain of some function at which the function values are maximized. in contrast to global maxima, which refers to the largest outputs of a function, arg max refers to the inputs, or arguments, at which the function outputs are as large as possible.


in order to explain the verifier - based definition of np, consider the subset sum problem : assume that we are given some integers, { −7, −3, −2, 5, 8 }, and we wish to know whether some of these integers sum up to zero. here the answer is " yes ", since the integers { −3, −2, 5 } corresponds to the sum ( −3 ) + ( −2 ) + 5 = 0. to answer whether some of the integers add to zero we can create an algorithm that obtains all the possible subsets. as the number of integers that we feed into the algorithm becomes larger, both the number of subsets and the computation time grows exponentially.


in the following, let m be a g - module.


in statistics and in machine learning, a linear predictor function is a linear function ( linear combination ) of a set of coefficients and explanatory variables ( independent variables ), whose value is used to predict the outcome of a dependent variable. this sort of function usually comes in linear regression, where the coefficients are called regression coefficients. however, they also occur in various types of linear classifiers ( e. g. logistic regression, perceptrons, support vector machines, and linear discriminant analysis ), as well as in various other models, such as principal component analysis and factor analysis. in many of these models, the coefficients are referred to as " weights ".


in sociolinguistics, a register is a variety of language used for a particular purpose or particular communicative situation. for example, when speaking officially or in a public setting, an english speaker may be more likely to follow prescriptive norms for formal usage than in a casual setting, for example, by pronouncing words ending in - ing with a velar nasal instead of an alveolar nasal ( e. g., walking rather than walkin'), choosing words that are considered more " formal " ( such as father vs. dad or child vs. kid ), and refraining from using words considered nonstandard, such as ain't and y'all. as with other types of language variation, there tends to be a spectrum of registers rather than a discrete set of obviously distinct varieties — numerous registers can be identified, with no clear boundaries between them. discourse categorization is a complex problem, and even according to the general definition of register given above ( language variation defined by use rather than user ), there are cases where other kinds of language variation, such as regional or age dialect, overlap.


according to paul a. sabatier, the model has " outlived its usefulness " and should be replaced. the model's issues have led to a paradoxical situation in which current research and updated versions of the model continue to rely on the framework created by anderson. but the very concept of the stages model has been discredited, which attacks the cycle's status as a heuristic. due to these problems, alternative and newer versions of the model have aimed to create a more comprehensive view of the policy cycle.


748 if random vector x is elliptically distributed, then so is dx for any matrix d with full row rank. thus any linear combination of the components of x is elliptical ( though not necessarily with the same elliptical distribution ), and any subset of x is elliptical. : p. 748


in mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included. dilworth ( 1940 ) was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts. the axioms defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an exchange axiom, antimatroids are defined instead by an anti - exchange axiom, from which their name derives. antimatroids can be viewed as a special case of greedoids and of semimodular lattices, and as a generalization of partial orders and of distributive lattices. antimatroids are equivalent, by complementation, to convex geometries, a combinatorial abstraction of convex sets in geometry. antimatroids have been applied to model precedence constraints in scheduling problems, potential event sequences in simulations, task planning in artificial intelligence, and the states of knowledge of human learners.


angles cbd and fba are both right angles ; therefore angle abd equals angle fbc, since both are the sum of a right angle and angle abc. since ab is equal to fb, bd is equal to bc and angle abd equals angle fbc, triangle abd must be congruent to triangle fbc. since a - k - l is a straight line, parallel to bd, then rectangle bdlk has twice the area of triangle abd because they share the base bd and have the same altitude bk, i. e., a line normal to their common base, connecting the parallel lines bd and al. ( lemma 2 ) since c is collinear with a and g, and this line is parallel to fb, then square bagf must be twice in area to triangle fbc.


in mathematics, the gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius r { \ displaystyle r }. this number is approximated by the area of the circle, so the real problem is to accurately bound the error term describing how the number of points differs from the area. the first progress on a solution was made by carl friedrich gauss, hence its name.


in recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. the basic polygon is often ( but not necessarily ) a convex plane - filling polygon, such as a square or a triangle. more specific names have been given to polyforms resulting from specific basic polygons, as detailed in the table below. for example, a square basic polygon results in the well - known polyominoes.


in spite of its apparently paradoxical nature, the phenomenon is real, and can be explained as a consequence of the general mathematical properties of social networks. the mathematics behind this are directly related to the arithmetic - geometric mean inequality and the cauchy – schwarz inequality. formally, feld assumes that a social network is represented by an undirected graph g = ( v, e ), where the set v of vertices corresponds to the people in the social network, and the set e of edges corresponds to the friendship relation between pairs of people. that is, he assumes that friendship is a symmetric relation : if x is a friend of y, then y is a friend of x. the friendship between x and y is therefore modeled by the edge { x, y }, and the number of friends an individual has corresponds to a vertex's degree. the average number of friends of a person in the social network is therefore given by the average of the degrees of the vertices in the graph.


this is one example where some upper bound helps in proving lower bounds ; the construction of a circuit given by baur and strassen implies a lower bound for more general polynomials. the lack of ability to prove lower bounds brings us to consider simpler models of computation. some examples are : monotone circuits ( in which all the field elements are nonnegative real numbers ), constant depth circuits, and multilinear circuits ( in which every gate computes a multilinear polynomial ). these restricted models have been studied extensively and some understanding and results were obtained.


in quantum information theory, the no low - energy trivial state ( nlts ) conjecture is a precursor to a quantum pcp theorem ( qpcp ) and posits the existence of families of hamiltonians with all low - energy states of non - trivial complexity. an nlts proof would be a consequence of one aspect of qpcp problems – the inability to certify an approximation of local hamiltonians via np completeness. in other words, an nlts proof would be one consequence of the qma complexity of qpcp problems. on a high level, if proved, nlts would be one property of the non - newtonian complexity of quantum computation.


in terms of metrics that the qa & ux manager work with, this task mainly is about collecting and analyze data an about game and gamer activity in relation to a particular game. in terms of the communication characterized parts of the work the qa & ux manager do, this is often done in relation with meetings with the development team and where the qa & ux manager pass on his or her knowledge and data to the development team. = = references = =


in order to qualify for protection, a work must be an expression with a degree of originality, and it must be in a fixed medium, such as written down on paper or recorded digitally. the idea itself is not protected. that is, a copy of someone else's original idea is not infringing unless it copies that person's unique, tangible expression of the idea. some of these limitations, especially regarding what qualifies as original, are embodied only in case law ( judicial precedent ), rather than in statutes.


in statistics, a generalized linear model ( glm ) is a flexible generalization of ordinary linear regression. the glm generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. generalized linear models were formulated by john nelder and robert wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and poisson regression.


in number theory, ramanujan's sum, usually denoted cq ( n ), is a function of two positive integer variables q and n defined by the formula c q ( n ) = 1 ≤ a ≤ q ( a, q ) = 1 e 2 π i a q n, { \ displaystyle c _ { q } ( n ) = \ sum _ { 1 \ leq a \ leq q \ atop ( a, q ) = 1 } e ^ { 2 \ pi i { \ tfrac { a } { q } } n }, } where ( a, q ) = 1 means that a only takes on values coprime to q. srinivasa ramanujan mentioned the sums in a 1918 paper. in addition to the expansions discussed in this article, ramanujan's sums are used in the proof of vinogradov's theorem that every sufficiently large odd number is the sum of three primes.


in the example above, the algorithm was guided by the conditional expectation of a random variable f { \ displaystyle f }. in some cases, instead of an exact conditional expectation, an upper bound ( or sometimes a lower bound ) on some conditional expectation is used instead. this is called a pessimistic estimator.


in model theory, definable sets are important objects of study. for instance, in n { \ displaystyle \ mathbb { n } } the formula u v ( w ( x × w = u × v ) → ( w ( x × w = u ) ∨ w ( x × w = v ) ) ) ∧ x = 0 ∧ x = 1 { \ displaystyle \ forall u \ forall v ( \ exists w ( x \ times w = u \ times v ) \ rightarrow ( \ exists w ( x \ times w = u ) \ lor \ exists w ( x \ times w = v ) ) ) \ land x \ neq 0 \ land x \ neq 1 } defines the subset of prime numbers, while the formula y ( 2 × y = x ) { \ displaystyle \ exists y ( 2 \ times y = x ) } defines the subset of even numbers. in a similar way, formulas with n free variables define subsets of m n { \ displaystyle { \ mathcal { m } } ^ { n } }. for example, in a field, the formula y = x × x { \ displaystyle y = x \ times x } defines the curve of all ( x, y ) { \ displaystyle ( x, y ) } such that y = x 2 { \ displaystyle y = x ^ { 2 } }.


the u. s. securities and exchange commission issued a statement in 1984 with the goal of reminding companies that securities fraud also applies to " statements that can reasonably be expected to reach investors and the trading markets ". several companies have been accused in court of using knowingly false announcements to gain market advantage. in 1969, the united states justice department accused ibm of doing this in the case united states v. ibm.


this generalized definition implies that the above - mentioned geometric entities are a special kind of vectors, as they are elements of a special kind of vector space called euclidean space. this particular article is about vectors strictly defined as arrows in euclidean space. when it becomes necessary to distinguish these special vectors from vectors as defined in pure mathematics, they are sometimes referred to as geometric, spatial, or euclidean vectors.


then, the current non - integer solution is no longer feasible to the relaxation. this process is repeated until an optimal integer solution is found.


its worst - case roundoff errors grow asymptotically as at most o ( ε log n ), where ε is the machine precision ( assuming a fixed condition number, as discussed below ). in comparison, the naive technique of accumulating the sum in sequence ( adding each xi one at a time for i = 1,..., n ) has roundoff errors that grow at worst as o ( εn ). kahan summation has a worst - case error of roughly o ( ε ), independent of n, but requires several times more arithmetic operations. if the roundoff errors are random, and in particular have random signs, then they form a random walk and the error growth is reduced to an average of o ( ε log n ) { \ displaystyle o ( \ varepsilon { \ sqrt { \ log n } } ) } for pairwise summation. a very similar recursive structure of summation is found in many fast fourier transform ( fft ) algorithms, and is responsible for the same slow roundoff accumulation of those ffts.


in the 1980s, the revolution of the personal computer and the popularity of computer bulletin board systems ( bbses ) ( accessed via modem ) created an influx of tech - savvy users. these bbses became popular for computer hackers and others interested in the technology, and served as a medium for previously scattered independent phone phreaks to share their discoveries and experiments. this not only led to unprecedented collaboration between phone phreaks, but also spread the notion of phreaking to others who took it upon themselves to study, experiment with, or exploit the telephone system. this was also at a time when the telephone company was a popular subject of discussion in the us, as the monopoly of at & t corporation was forced into divestiture.


in telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. this repertoire of signals is usually called a constrained code in data storage systems. some signals are more prone to error than others as the physics of the communication channel or storage medium constrains the repertoire of signals that can be used reliably. common line encodings are unipolar, polar, bipolar, and manchester code.


there are differing views as to exactly what phonemes are and how a given language should be analyzed in phonemic ( or phonematic ) terms. however, a phoneme is generally regarded as an abstraction of a set ( or equivalence class ) of speech sounds ( phones ) that are perceived as equivalent to each other in a given language. for example, the english k sounds in the words kill and skill are not identical ( as described below ), but they are distributional variants of a single phoneme / k /.


in numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. for a quadratic function f ( x ) { \ displaystyle \ displaystyle f ( x ) } f ( x ) = ‖ a x − b ‖ 2, { \ displaystyle \ displaystyle f ( x ) = \ | ax - b \ | ^ { 2 }, } the minimum of f { \ displaystyle f } is obtained when the gradient is 0 : ∇ x f = 2 a t ( a x − b ) = 0 { \ displaystyle \ nabla _ { x } f = 2a ^ { t } ( ax - b ) = 0 }. whereas linear conjugate gradient seeks a solution to the linear equation a t a x = a t b { \ displaystyle \ displaystyle a ^ { t } ax = a ^ { t } b }, the nonlinear conjugate gradient method is generally used to find the local minimum of a nonlinear function using its gradient ∇ x f { \ displaystyle \ nabla _ { x } f } alone. it works when the function is approximately quadratic near the minimum, which is the case when the function is twice differentiable at the minimum and the second derivative is non - singular there. given a function f ( x ) { \ displaystyle \ displaystyle f ( x ) } of n { \ displaystyle n } variables to minimize, its gradient ∇ x f { \ displaystyle \ nabla _ { x } f } indicates the direction of maximum increase.


in probability theory, gauss's inequality ( or the gauss inequality ) gives an upper bound on the probability that a unimodal random variable lies more than any given distance from its mode. let x be a unimodal random variable with mode m, and let τ 2 be the expected value of ( x − m ) 2. ( τ 2 can also be expressed as ( μ − m ) 2 + σ 2, where μ and σ are the mean and standard deviation of x. ) then for any positive value of k, pr ( | x − m | > k ) ≤ { ( 2 τ 3 k ) 2 if k ≥ 2 τ 3 1 − k τ 3 if 0 ≤ k ≤ 2 τ 3. { \ displaystyle \ pr ( | x - m | > k ) \ leq { \ begin { cases } \ left ( { \ frac { 2 \ tau } { 3k } } \ right ) ^ { 2 } & { \ text { if } } k \ geq { \ frac { 2 \ tau } { \ sqrt { 3 } } } \ \ 1 - { \ frac { k } { \ tau { \ sqrt { 3 } } } } & { \ text { if } } 0 \ leq k \ leq { \ frac { 2 \ tau } { \ sqrt { 3 } } }. \ end { cases } } } the theorem was first proved by carl friedrich gauss in 1823.


sometimes the stress of the 0 is made different from a letter o in some way, although many fonts do not do this. high - quality typesetting generally prefers text figures in body text : they integrate better with lowercase letters and small capitals, unlike runs of lining figures. lining figures are called for in all - capitals settings ( hence the alternative name titling figures ), and may work better in tables and spreadsheets. although many conventional typefaces have both types of numerals in full, early digital fonts only had one or the other ( with the exception of those used by professional printers ).


for ν = 1 { \ displaystyle \ nu = 1 } the student's t distribution t ν { \ displaystyle t _ { \ nu } } becomes the standard cauchy distribution, whereas for ν → ∞ { \ displaystyle \ nu \ rightarrow \ infty } it becomes the standard normal distribution n ( 0, 1 ) { \ displaystyle n ( 0, 1 ) }. the student's t - distribution plays a role in a number of widely used statistical analyses, including student's t - test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. in the form of the location - scale t - distribution l s t ( μ, τ 2, ν ) { \ displaystyle lst ( \ mu, \ tau ^ { 2 }, \ nu ) } it generalizes the normal distribution and also arises in the bayesian analysis of data from a normal family as a compound distribution when marginalizing over the variance parameter.


an incomplete cholesky factorization is given by a sparse lower triangular matrix k that is in some sense close to l. the corresponding preconditioner is kk *. one popular way to find such a matrix k is to use the algorithm for finding the exact cholesky decomposition in which k has the same sparsity pattern as a ( any entry of k is set to zero if the corresponding entry in a is also zero ). this gives an incomplete cholesky factorization which is as sparse as the matrix a.


in the 1990s, specialized computers were released where two computers that each had their own memory controller could be networked at such a low level that the software run could use the memory, or cpu of either computer as if they were one unit. with amd's release of the opteron, and intel's corresponding cpu, systems that share more than one memory controller in a single system have become common in applications that require the power of more than one common desktop. for these systems schemes like non - uniform memory architecture are used. channels are the highest - level structure at the local memory controller level. modern computers can have two, three or even more channels.


in mathematics, logic and computer science, a formal language ( a set of finite sequences of symbols taken from a fixed alphabet ) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language. equivalently, a formal language is recursive if there exists a turing machine that, when given a finite sequence of symbols as input, always halts and accepts it if it belongs to the language and halts and rejects it otherwise. in theoretical computer science, such always - halting turing machines are called total turing machines or algorithms ( sipser 1997 ).


in order to understand the public's opinion on youth marketing, one must be able to understand the experiences that each generation has been exposed to while growing up. generation y is very similar to the baby boomer generation especially at different points in life. so it is essential to see what experiences each generation has experienced while growing up. but different formative experiences affect each person of generation y. for example, the events that made the biggest impression on members of generation y who graduated from school in 2000 were columbine, the war in kosovo, and princess diana's death.


the written test is usually done at a computerized learning center and results are available immediately. the oral and practical exams include questions about common rigging practices. the practical test consists of inspecting and repacking 20 reserves, along with hand sewing and a simple machine - sewn patch on a canopy.


in the russian federation, a state secret ( государственная таина ) is information protected by the state on its military, foreign policy, economic, intelligence, counterintelligence, operational and investigative and other activities, dissemination of which could harm state security.


in probability and statistics, the hellinger distance ( closely related to, although different from, the bhattacharyya distance ) is used to quantify the similarity between two probability distributions. it is a type of f - divergence. the hellinger distance is defined in terms of the hellinger integral, which was introduced by ernst hellinger in 1909. it is sometimes called the jeffreys distance.


in mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete : an optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set. a problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found. they can include constrained problems and multimodal problems.


this scheme, a type of virtual memory, allows in - memory data not currently in use to be moved to secondary storage and back in a way which is transparent to applications, to increase overall memory capacity. on some systems, a request for virtual storage may allocate a block of virtual addresses for which no page frames have been assigned, and the system will only assign and initialize page frames when page faults occur. on some systems a guard page may be used, either for error detection or to automatically grow data structures. on some systems, the page fault mechanism is also used for executable space protection such as w ^ x.


295 ). skolem's paradox is that every countable axiomatisation of set theory in first - order logic, if it is consistent, has a model that is countable. this appears contradictory because it is possible to prove, from those same axioms, a sentence that intuitively says ( or that precisely says in the standard model of the theory ) that there exist sets that are not countable.


in practice, bitstreams are not used directly to encode bytestreams ; a communication channel may use a signalling method that does not directly translate to bits ( for instance, by transmitting signals of multiple frequencies ) and typically also encodes other information such as framing and error correction together with its data.


in recent years, neural networks have generated a great deal of interest by outperforming traditional methods on longstanding problems across many fields. machine learning, and by extension neural networks, have been used in many facets of mri — for instance, speeding up image reconstruction, or improving reconstruction quality when working with a lack of data. neural networks have also been used in motion artifact correction thanks to their ability to learn visual information from data, as well as infer underlying, latent representations in data.


in the united states, the director of the cybersecurity and infrastructure security agency ( cisa ), jen easterly, described the exploit as " one of the most serious i've seen in my entire career, if not the most serious ", explaining that hundreds of millions of devices were affected and advising vendors to prioritize software updates. civilian agencies contracted by the united states government had until 24 december 2021 to patch vulnerabilities. on 4 january, the federal trade commission ( ftc ) stated its intent to pursue companies that fail to take reasonable steps to update used log4j software.


decoding, determining the probability of a given label sequence y { \ displaystyle y } given x { \ displaystyle x }. inference, determining the most likely label sequence y { \ displaystyle y } given x { \ displaystyle x }. the conditional dependency of each y i { \ displaystyle y _ { i } } on x { \ displaystyle x } is defined through a fixed set of feature functions of the form f ( i, y i − 1, y i, x ) { \ displaystyle f ( i, y _ { i - 1 }, y _ { i }, x ) }, which can be thought of as measurements on the input sequence that partially determine the likelihood of each possible value for y i { \ displaystyle y _ { i } }. the model assigns each feature a numerical weight and combines them to determine the probability of a certain value for y i { \ displaystyle y _ { i } }.


in recent years, as the general population has become more e - mail savvy, the lines have blurred somewhat between face - to - face and e - mail communication. e - mail is now thought of as a verbal tool, with its capacity to enable immediate feedback, leverage natural language, and embed emotion via acronyms and emoticons. however, there is a downside of e - mail : volume overload. emails often have large unnecessary quantities of information which is non - job essential and / or spam.


moreover, this factorization is unique up to the order of the factors. although integer factorization is a sort of inverse to multiplication, it is much more difficult algorithmically, a fact which is exploited in the rsa cryptosystem to implement public - key cryptography. polynomial factorization has also been studied for centuries.


in mathematics, the theory of latin squares is an active research area with many open problems. as in other areas of mathematics, such problems are often made public at professional conferences and meetings. problems posed here appeared in, for instance, the loops ( prague ) conferences and the milehigh ( denver ) conferences.


in the distributed memory model, the usual approach is to partition the vertex set v { \ displaystyle v } of the graph into p { \ displaystyle p } sets v 0, …, v p − 1 { \ displaystyle v _ { 0 }, \ dots, v _ { p - 1 } }. here, p { \ displaystyle p } is the amount of available processing elements ( pe ). the vertex set partitions are then distributed to the pes with matching index, additionally to the corresponding edges. every pe has its own subgraph representation, where edges with an endpoint in another partition require special attention.


in most eqa schemes, laboratories receive scores for their results. the most popular score is the z - score, also called standard deviation index ( sdi ). the score is given per analyte and per test item.


( i3 ) if a { \ displaystyle a } and b { \ displaystyle b } are two independent sets ( i. e., each set is independent ) and a { \ displaystyle a } has more elements than b { \ displaystyle b }, then there exists x ∈ a b { \ displaystyle x \ in a \ backslash b } such that b ∪ { x } { \ displaystyle b \ cup \ { x \ } } is in i { \ displaystyle { \ mathcal { i } } }. this is sometimes called the augmentation property or the independent set exchange property. the first two properties define a combinatorial structure known as an independence system ( or abstract simplicial complex ). actually, assuming ( i2 ), property ( i1 ) is equivalent to the fact that at least one subset of e { \ displaystyle e } is independent, i. e., i = ∅ { \ displaystyle { \ mathcal { i } } \ neq \ emptyset }.


the emergence of affordable consumer telephony devices with advanced features such as last number redial and preprogrammed numbers paralleled phone industry deregulation and the breakup of the bell system in the early 1980s. while speed dial technology had been invented nearly a decade earlier by bell labs, it did not become a consumer product until deregulation. previously, connecting non - at & t handsets was generally prohibited and most phones were leased devices ( similar to residential broadband routers ).


the main cabinet of the minicomputer was the 6000 cpu, housing the computer's main z80a microprocessor and nine expansion slots ( none populated by default ) ; the 6000 cpu - 1, with a second z80a processor seven expansion slots and a floppy disk drive ; and the 6000 cpu - 2, which has two such disk drives and a third z80a processor. each cabinet houses 64 kb of ram with parity. optional was a video board, additional disk controllers, a mass - storage controller board for hard disks and tape drives ( the latter making use of the board's integrated parallel interface ), a dual - channel rs - 232 serial interface board, and a serial communication interface board with support for asynchronous, synchronous, and bit - oriented communications protocols.


in order to avoid this problem, additional framing bits are added to either end of every byte, typically one bit on either side known as the " start and stop bits ". this guarantees at least one 1 - to - 0 transition for every byte, more than enough to keep the clocks locked. however, these bits also expand every 8 bits of data ( one byte ) to 10 bits, an overhead of 20 %.


in mathematics and theoretical computer science, analysis of boolean functions is the study of real - valued functions on { 0, 1 } n { \ displaystyle \ { 0, 1 \ } ^ { n } } or { − 1, 1 } n { \ displaystyle \ { - 1, 1 \ } ^ { n } } ( such functions are sometimes known as pseudo - boolean functions ) from a spectral perspective. the functions studied are often, but not always, boolean - valued, making them boolean functions. the area has found many applications in combinatorics, social choice theory, random graphs, and theoretical computer science, especially in hardness of approximation, property testing, and pac learning.


in some system distributions, sudo has largely supplanted the default use of a distinct superuser login for administrative tasks, most notably in some linux distributions as well as apple's macos. this allows for more secure logging of admin commands and prevents some exploits.


in case of any failure, the destination switches onto the alternative path / route. this architecture is simple for implementation and results fast restoration. its major drawback is the wastage of bandwidth, since no traffic travels through the redundant path.


in politics, rankings focus on the comparison of economic, social, environmental and governance performance of countries. in relation to credit standing, the ranking of a security refers to where that particular security would stand in a wind up of the issuing company, i. e., its seniority in the company's capital structure. for instance, capital notes are subordinated securities ; they would rank behind senior debt in a wind up. in other words, the holders of senior debt would be paid out before subordinated debt holders received any funds.


in order to accurately measure longitude, the precise time of a sextant sighting ( down to the second, if possible ) must be recorded. each second of error is equivalent to 15 seconds of longitude error, which at the equator is a position error of. 25 of a nautical mile, about the accuracy limit of manual celestial navigation. the spring - driven marine chronometer is a precision timepiece used aboard ship to provide accurate time for celestial observations. a chronometer differs from a spring - driven watch principally in that it contains a variable lever device to maintain even pressure on the mainspring, and a special balance designed to compensate for temperature variations. a spring - driven chronometer is set approximately to greenwich mean time ( gmt ) and is not reset until the instrument is overhauled and cleaned, usually at three - year intervals.


furthermore, they may develop undesirable emergent goals that may be hard to detect before the system is in deployment, where it faces new situations and data distributions. today, these problems affect existing commercial systems such as language models, robots, autonomous vehicles, and social media recommendation engines. some ai researchers argue that more capable future systems will be more severely affected since these problems partially result from the systems being highly capable. many leading ai scientists such as geoffrey hinton and stuart russell argue that ai is approaching superhuman capabilities and could endanger human civilization if misaligned. ai alignment is a subfield of ai safety, the study of how to build safe ai systems. other subfields of ai safety include robustness, monitoring, and capability control. research challenges in alignment include instilling complex values in ai, developing honest ai, scalable oversight, auditing and interpreting ai models, and preventing emergent ai behaviors like power - seeking. alignment research has connections to interpretability research, ( adversarial ) robustness, anomaly detection, calibrated uncertainty, formal verification, preference learning, safety - critical engineering, game theory, algorithmic fairness, and the social sciences, among others.


the meaning of a sentence is conveyed if the truth conditions for the sentence are understood. additionally, there are many sentences that are understood although their truth condition is uncertain. one popular argument for this view is that some sentences are necessarily true — that is, they are true whatever happens to obtain. all such sentences have the same truth conditions, but arguably do not thereby have the same meaning. likewise, the sets { x : x is alive } and { x : x is alive and x is not a rock } are identical — they have precisely the same members — but presumably the sentences " nixon is alive " and " nixon is alive and is not a rock " have different meanings.


the rage 128 used an 8 kb buffer to store texels that were used by the 3d engine. in order to improve performance even more, ati engineers also incorporated an 8 kb pixel cache used to write pixels back to the frame buffer. 8 million transistors, 0. 25 micrometer fabrication 3d feature set hardware support for vertex arrays, fog and fog table support alpha blending, vertex and z - based fog, video textures, texture lighting single clock bilinear and trilinear texture filtering and texture compositing perspective - correct mip - mapped texturing with chroma - key support vertex and z - based reflections, shadows, spotlights, 1. 00 biasing hidden surface removal using 16, 24, or 32 - bit z - buffering gouraud and specular shaded polygons line and edge anti - aliasing, bump mapping, 8 - bit stencil buffer 250 mhz ramdac, agp 2×


an example is google's pagerank algorithm. the principal eigenvector of a modified adjacency matrix of the world wide web graph gives the page ranks as its components.


in parallel computing, the geometric arithmetic parallel processor ( gapp ), invented by polish mathematician włodzimierz holsztynski in 1981, was patented by martin marietta and is now owned by silicon optix, inc. the gapp's network topology is a mesh - connected array of single - bit simd processing elements ( pes ), where each pe can communicate with its neighbor to the north, east, south, and west. each cell has its own memory. the space of addresses is the same for all cells. the data travels from the cell memories to the cell registers, and in the opposite direction, in parallel.


in mathematics, lazard's universal ring is a ring introduced by michel lazard in lazard ( 1955 ) over which the universal commutative one - dimensional formal group law is defined. there is a universal commutative one - dimensional formal group law over a universal commutative ring defined as follows. we let f ( x, y ) { \ displaystyle f ( x, y ) } be x + y + i, j c i, j x i y j { \ displaystyle x + y + \ sum _ { i, j } c _ { i, j } x ^ { i } y ^ { j } } for indeterminates c i, j { \ displaystyle c _ { i, j } }, and we define the universal ring r to be the commutative ring generated by the elements c i, j { \ displaystyle c _ { i, j } }, with the relations that are forced by the associativity and commutativity laws for formal group laws.


in physics and geometry, there are two closely related vector spaces, usually three - dimensional but in general of any finite dimension. position space ( also real space or coordinate space ) is the set of all position vectors r in euclidean space, and has dimensions of length ; a position vector defines a point in space. ( if the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle. ) momentum space is the set of all momentum vectors p a physical system can have ; the momentum vector of a particle corresponds to its motion, with units of −1.


the triples result in the graph shown in the given figure. one of the advantages of using uniform resource identifiers ( uris ) is that they can be dereferenced using the http protocol. according to the so - called linked open data principles, such a dereferenced uri should result in a document that offers further data about the given uri.


for an input x { \ displaystyle \ mathbf { x } } from source x { \ displaystyle x }, only the syndrome given by s = h x { \ displaystyle \ mathbf { s } = \ mathbf { h } \ mathbf { x } } is transmitted, which is 3 bits. with received y { \ displaystyle \ mathbf { y } } and s { \ displaystyle \ mathbf { s } }, suppose there are two inputs x 1 { \ displaystyle \ mathbf { x _ { 1 } } } and x 2 { \ displaystyle \ mathbf { x _ { 2 } } } with same syndrome s { \ displaystyle \ mathbf { s } }. that means h x 1 = h x 2 { \ displaystyle \ mathbf { h } \ mathbf { x _ { 1 } } = \ mathbf { h } \ mathbf { x _ { 2 } } }, which is h ( x 1 − x 2 ) = 0 { \ displaystyle \ mathbf { h } ( \ mathbf { x _ { 1 } } - \ mathbf { x _ { 2 } } ) = 0 }.


in mathematical logic, an uninterpreted function or function symbol is one that has no other property than its name and n - ary form. function symbols are used, together with constants and variables, to form terms. the theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or the empty theory, being the theory having an empty set of sentences ( in analogy to an initial algebra ). theories with a non - empty set of equations are known as equational theories. the satisfiability problem for free theories is solved by syntactic unification ; algorithms for the latter are used by interpreters for various computer languages, such as prolog. syntactic unification is also used in algorithms for the satisfiability problem for certain other equational theories, see unification ( computer science ).


) ^ { 2 } } } = \ prod \ limits _ { k = 1 } ^ { n } { \ frac { n + k } { k } } { \ text { for all } } n \ geq 0. } they are called central since they show up exactly in the middle of the even - numbered rows in pascal's triangle. the first few central binomial coefficients starting at n = 0 are : 1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620,... ; ( sequence a000984 in the oeis )


it is called the wooley integer semigroup and members of this semigroup are called wooley integers. similarly, the set of integers in w is itself a multiplicative semigroup. it is called the wild integer semigroup and members of this semigroup are called wild numbers.


in natural languages, an indicative conditional is a conditional sentence such as " if leona is at home, she isn't in paris ", whose grammatical form restricts it to discussing what could be true. indicatives are typically defined in opposition to counterfactual conditionals, which have extra grammatical marking which allows them to discuss eventualities which are no longer possible. indicatives are a major topic of research in philosophy of language, philosophical logic, and linguistics. open questions include which logical operation indicatives denote, how such denotations could be composed from their grammatical form, and the implications of those denotations for areas including metaphysics, psychology of reasoning, and philosophy of mathematics.


in statistics, a weighted median of a sample is the 50 % weighted percentile. it was first proposed by f. y. edgeworth in 1888. like the median, it is useful as an estimator of central tendency, robust against outliers. it allows for non - uniform statistical weights related to, e. g., varying precision measurements in the sample.


{ \ displaystyle \ mathbf { \ lambda } _ { j } = - \ mathbf { j } ^ { - 1 } \ left. } after each iteration, the unconstrained particle positions are updated using x ^ i ( t + δ t ) ← x ^ i ( t + δ t ) + k = 1 n λ k ∂ σ k ∂ x i ( δ t ) 2 m i − 1. { \ displaystyle { \ hat { \ mathbf { x } } } _ { i } ( t + \ delta t ) \ leftarrow { \ hat { \ mathbf { x } } } _ { i } ( t + \ delta t ) + \ sum _ { k = 1 } ^ { n } \ lambda _ { k } { \ frac { \ partial \ sigma _ { k } } { \ partial \ mathbf { x } _ { i } } } \ left ( \ delta t \ right ) ^ { 2 } m _ { i } ^ { - 1 }. }


mcgee and prusak ( 1993 ) noted that core competencies are not what an organization owns, but rather what it knows. bartlett ( 1999 ) indicates that empowerment is not possible in an autocratic organization, that networks cannot be sustained in fixed hierarchical structure, and that learning is not possible in an environment constrained by rigid policies and procedures. davenport ( 1997 ) used an information ecology approach, in which he explored the use and abuse of information in the context of infighting, resource hoarding, and political battles as well as appropriate management in such a context. simard ( 2000 ) states that knowledge is inextricably linked to organizational mandates. some providers strive for objectivity, others selectively disseminate information and knowledge, while still others use information to further their agenda. users must understand that information is not innocent, and that all information is not created equal.


a fractional weighted version of the conjecture, posed by jack edmonds and rick giles, was refuted by alexander schrijver. the lucchesi – younger theorem states that the minimum size of a dijoin, in any given directed graph, equals the maximum number of disjoint dicuts that can be found in the graph. the minimum weight dijoin in a weighted graph can be found in polynomial time, and is a special case of the submodular flow problem. in planar graphs, dijoins and feedback arc sets are dual concepts. the dual graph of a directed graph, embedded in the plane, is a graph with a vertex for each face of the given graph, and a dual edge between two dual vertices when the corresponding two faces are separated by an edge.


in the case where v = w { \ displaystyle v = w }, a linear map is called a linear endomorphism. sometimes the term linear operator refers to this case, but the term " linear operator " can have different meanings for different conventions : for example, it can be used to emphasize that v { \ displaystyle v } and w { \ displaystyle w } are real vector spaces ( not necessarily with v = w { \ displaystyle v = w } ), or it can be used to emphasize that v { \ displaystyle v } is a function space, which is a common convention in functional analysis. sometimes the term linear function has the same meaning as linear map, while in analysis it does not. a linear map from v to w always maps the origin of v to the origin of w. moreover, it maps linear subspaces in v onto linear subspaces in w ( possibly of a lower dimension ) ; for example, it maps a plane through the origin in v to either a plane through the origin in w, a line through the origin in w, or just the origin in w. linear maps can often be represented as matrices, and simple examples include rotation and reflection linear transformations. in the language of category theory, linear maps are the morphisms of vector spaces.


the primary achievement of ludics is the discovery of a relationship between two natural, but distinct notions of type, or proposition. the first view, which might be termed the proof - theoretic or gentzen - style interpretation of propositions, says that the meaning of a proposition arises from its introduction and elimination rules. focalization refines this viewpoint by distinguishing between positive propositions, whose meaning arises from their introduction rules, and negative propositions, whose meaning arises from their elimination rules.


in solvent extraction, a distribution ratio is often quoted as a measure of how well - extracted a species is. the distribution ratio ( kd ) is equal to the concentration of a solute in the organic phase divided by its concentration in the aqueous phase. depending on the system, the distribution ratio can be a function of temperature, the concentration of chemical species in the system, and a large number of other parameters. note that d is related to the δg of the extraction process.


in standard gematria ( mispar hechrechi ), each letter is given a numerical value between 1 and 400, as shown in the following table. in mispar gadol, the five final letters are given their own values, ranging from 500 to 900. it is possible that this well - known cipher was used to conceal other more hidden ciphers in jewish texts. for instance, a scribe may discuss a sum using the'standard gematria'cipher, but may intend the sum to be checked with a different secret cipher. a mathematical formula for finding a letter's corresponding number in mispar gadol is : f ( x ) = 10 x − 1 9 × ( ( x − 1 mod 9 ) + 1 ), { \ displaystyle f ( x ) = 10 ^ { \ left \ lfloor { \ frac { x - 1 } { 9 } } \ right \ rfloor } \ times ( ( x - 1 \ mod 9 ) + 1 ), } where x is the position of the letter in the language letters index ( regular order of letters ), and the floor and modulo functions are used.


in software engineering, test design is the activity of deriving and specifying test cases from test conditions to test software.


in some cases, a page fault may indicate a software bug, which can be prevented by using memory protection as one of key benefits of an mmu : an operating system can use it to protect against errant programs by disallowing access to memory that a particular program should not have access to. typically, an operating system assigns each program its own virtual address space. an paged mmu also mitigates the problem of external fragmentation of memory. after blocks of memory have been allocated and freed, the free memory may become fragmented ( discontinuous ) so that the largest contiguous block of free memory may be much smaller than the total amount.


in the case of equality constraints, this theorem is proved with the calculus of variations and lagrange multipliers. the constraints can be written as − ∞ ∞ f j ( x ) p ( x ) d x = a j { \ displaystyle \ int _ { - \ infty } ^ { \ infty } f _ { j } ( x ) p ( x ) dx = a _ { j } } we consider the functional j ( p ) = − ∞ ∞ p ( x ) ln p ( x ) d x − η 0 ( − ∞ ∞ p ( x ) d x − 1 ) − j = 1 n λ j ( − ∞ ∞ f j ( x ) p ( x ) d x − a j ) { \ displaystyle j ( p ) = \ int _ { - \ infty } ^ { \ infty } p ( x ) \ ln { p ( x ) } dx - \ eta _ { 0 } \ left ( \ int _ { - \ infty } ^ { \ infty } p ( x ) dx - 1 \ right ) - \ sum _ { j = 1 } ^ { n } \ lambda _ { j } \ left ( \ int _ { - \ infty } ^ { \ infty } f _ { j } ( x ) p ( x ) dx - a _ { j } \ right ) } where η 0 { \ displaystyle \ eta _ { 0 } } and λ j, j ≥ 1 { \ displaystyle \ lambda _ { j }, j \ geq 1 } are the lagrange multipliers. the zeroth constraint ensures the second axiom of probability.


optimizing the fsse results in a compromise between fairness ( especially avoiding scheduling starvation ) and achieving high spectral efficiency. if the cost of each user is known, in terms of consumed resources per transferred information bit, the fsse measure may be redefined to reflect proportional fairness. in a proportional fair system, this " proportionally fair shared spectrum efficiency " ( or " fairly shared radio resource cost " ) is maximized. this policy is less fair since " expensive " users are given lower throughput than others, but still scheduling starvation is avoided.


all the preferences cast by voters are awarded the points associated with their rank position. then, all the points for each option are tallied and the one with the most points is the winner. where a few winners ( w ) are instead required following the count, the w highest - ranked options are selected. positional voting is not only a means of identifying a single winner but also a method for converting sets of individual preferences ( ranked ballots ) into one collective and fully rank - ordered set. it is possible and legitimate for options to be tied in this resultant set ; even in first place.


the circuit will not function when the path delay exceeds the clock cycle delay so modifying the circuit to remove the timing failure ( and eliminate the critical path ) is an important part of the logic design engineer's task. critical path also defines the maximum delay in all the multiple register - to - register paths, and it must not be greater than the clock cycle time. after meeting the timing closure, one way to improve the circuit performance is to insert a register in between the combinational path of the critical path.


in the field of calculus of variations in mathematics, the method of lagrange multipliers on banach spaces can be used to solve certain infinite - dimensional constrained optimization problems. the method is a generalization of the classical method of lagrange multipliers as used to find extrema of a function of finitely many variables.


in natural language processing, latent dirichlet allocation ( lda ) is a bayesian network ( and, therefore, a generative statistical model ) that explains a set of observations through unobserved groups, and each group explains why some parts of the data are similar. the lda is an example of a bayesian topic model. in this, observations ( e. g., words ) are collected into documents, and each word's presence is attributable to one of the document's topics. each document will contain a small number of topics.


on mechanical dutch typewriters, there is a key that produces'ij'( in a single letterspace, located directly to the right of the l ). however, this is not the case on modern computer keyboards. in many word puzzles, such as lingo, ij fills one square, but in others, such as scrabble, ij fills two squares.


the examples within the position paper are just " examples " of current carrier practices for illustration purposes, but do not reflect any official oftel regulation. the main networks often agree to unlock handsets for a charge, either at the end of a contract or, for prepaid handsets, after several months. some blackberry handsets supplied by vodafone ( e. g., storm ) are examples of a uk carrier not offering unlocking codes.


a set of acronyms are commonly used : pmdr ( premotor dorsal, rostral ), pmdc, pmvr, pmvc. some researchers use a different terminology. field 7 or f7 denotes pmdr ; f2 = pmdc ; f5 = pmvr ; f4 = pmvc.


the set of values of η for which the function f x ( x ; η ) { \ displaystyle f _ { x } ( x ; \ eta ) } is integrable is called the natural parameter space. it can be shown that the natural parameter space is always convex. a ( η ) is called the log - partition function because it is the logarithm of a normalization factor, without which f x ( x ; θ ) { \ displaystyle f _ { x } ( x ; \ theta ) } would not be a probability distribution : a ( η ) = log ( x h ( x ) exp ( η ( θ ) ⋅ t ( x ) ) d x ) { \ displaystyle a ( \ eta ) = \ log \ left ( \ int _ { x } h ( x ) \, \ exp ( \ eta ( \ theta ) \ cdot t ( x ) ) \, \ mathrm { d } x \ right ) } the function a is important in its own right, because the mean, variance and other moments of the sufficient statistic t ( x ) can be derived simply by differentiating a ( η ). for example, because log ( x ) is one of the components of the sufficient statistic of the gamma distribution, e { \ displaystyle \ operatorname { \ mathcal { e } } } can be easily determined for this distribution using a ( η ). technically, this is true because k ( u η ) = a ( η + u ) − a ( η ), { \ displaystyle k \ left ( u \ mid \ eta \ right ) = a ( \ eta + u ) - a ( \ eta ) \,, } is the cumulant generating function of the sufficient statistic.


in statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted. for example, the numerical data 3. 4, 5. 1, 2. 6, 7. 3 are observed, the ranks of these data items would be 2, 3, 1 and 4 respectively. for example, the ordinal data hot, cold, warm would be replaced by 3, 1, 2.


in mathematics, real trees ( also called r { \ displaystyle \ mathbb { r } } - trees ) are a class of metric spaces generalising simplicial trees. they arise naturally in many mathematical contexts, in particular geometric group theory and probability theory. they are also the simplest examples of gromov hyperbolic spaces.


in some cases, storefronts and aggregates have intervened to stop review bombs and delete the negative reviews. in february 2019, rotten tomatoes announced that it would no longer accept user reviews for a film until after its official release. in 2017, valve added review histograms to steam user review scores to show how these change over time ; according to valve's alden kroll, this can help a potential purchaser of a game recognize a short term review bomb that is not indicative of the game itself, compared to a game that has a long tail of bad reviews. kroll said they did not want to silence the ability of users to leave reviews but recognized they needed to highlight phenomena like review bombs to aid customers. in march 2019, valve stated that it would employ a new system to detect spikes of negative " off - topic " reviews on games : if it is determined that they were the result of a review bomb campaign, the time period will be flagged, and all reviews made during that period ( whether negative or positive ) will be excluded from the user rating displayed for a game.


in mathematics, the bareiss algorithm, named after erwin bareiss, is an algorithm to calculate the determinant or the echelon form of a matrix with integer entries using only integer arithmetic ; any divisions that are performed are guaranteed to be exact ( there is no remainder ). the method can also be used to compute the determinant of matrices with ( approximated ) real entries, avoiding the introduction of any round - off errors beyond those already present in the input.


in the japanese kantenji braille, the standard 8 - dot braille patterns 35678, 135678, 345678, and 1345678 are the patterns related to braille pattern dots - 23456, since the two additional dots of kantenji patterns 023456, 234567, and 0234567 are placed above the base 6 - dot cell, instead of below, as in standard 8 - dot braille.


this jni interface pointer can be stored, but remains valid only in the current thread. other threads must first call attachcurrentthread ( ) to attach themselves to the vm and obtain a jni interface pointer. once attached, a native thread works like a regular java thread running within a native method.


in probability theory, foster's theorem, named after gordon foster, is used to draw conclusions about the positive recurrence of markov chains with countable state spaces. it uses the fact that positive recurrent markov chains exhibit a notion of " lyapunov stability " in terms of returning to any state while starting from it within a finite time interval.


in networking, packets are the key foundation for scheduling. there are many different types of packet travelling around network core every day, and they are treated totally different. for example, voice and video packets have higher priority than normal packets. in order to manage and distribute packet effectively, network devices also use input queue to determine which packet will be transmitted first.


in the counter - counter mode, the cascaded cipher uses full - strength aes - 128 in counter mode to generate a secure key stream and supplies this key - stream to a reduced round serpent also operating in counter mode to encrypt each plaintext block. to increase performance, each inner key stream block is reused several times to encrypt multiple blocks.


in theory some measures of guarantee that an obtained solution solves the original problem with reasonable accuracy. typically in applications only the first stage optimal solution x ∗ { \ displaystyle x ^ { * } } has a practical value since almost always a " true " realization of the random data will be different from the set of constructed ( generated ) scenarios. suppose ξ { \ displaystyle \ xi } contains d { \ displaystyle d } independent random components, each of which has three possible realizations ( for example, future realizations of each random parameters are classified as low, medium and high ), then the total number of scenarios is k = 3 d { \ displaystyle k = 3 ^ { d } }. such exponential growth of the number of scenarios makes model development using expert opinion very difficult even for reasonable size d { \ displaystyle d }. the situation becomes even worse if some random components of ξ { \ displaystyle \ xi } have continuous distributions.


through her attempts to solve fermat's last theorem, germain developed a result now known as germain's theorem which states that if p is an odd prime and 2p + 1 is also prime, then p must divide x, y, or z. otherwise, x n + y n = z n { \ textstyle x ^ { n } + y ^ { n } \ neq z ^ { n } }. this case where p does not divide x, y, or z is called the first case. sophie germain ’ s work was the most progress achieved on fermat ’ s last theorem at that time.


next, set the first vector v1 = u1. then, we set u2 = v2 - proju1v2. this process is repeated to for k vectors, with the final vector being uk = vk - σ ( j = 1 ) ( k - 1 ) projukvk.