however, the clustering coefficient is much higher for the movie actor network. the network characteristics and scaling exponents given by barabasi and albert ( 1999 ), indicates the scale - free behavior : size : 212 250 average degree : 28. 78 cutoff for power - law scaling : 900 clustering coefficient : 0. 79therefore, the underlying network has the scale - free degree distribution p ( k ) ~ k−γactor, with an exponent γactor = 2. 3 ± 0. 1 ( barabasi and albert, 1999 ), ( albert and barabasi, 2000 ). according to ( newman, strogatz, and watts, 2001 ), the movie actor network can be described by a bipartite graph.


the regularization term, or penalty, imposes a cost on the optimization function to make the optimal solution unique. implicit regularization is all other forms of regularization. this includes, for example, early stopping, using a robust loss function, and discarding outliers.


., + n, − n } { \ displaystyle l : v ( t ) \ to \ { + 1, - 1, + 2, - 2,..., + n, - n \ } } be a labeling of the vertices of t which is an odd function on s n − 1 { \ displaystyle s _ { n - 1 } }, i. e, l ( − v ) = − l ( v ) { \ displaystyle l ( - v ) = - l ( v ) } for every vertex v ∈ s n − 1 { \ displaystyle v \ in s _ { n - 1 } }. then tucker's lemma states that t contains a complementary edge - an edge ( a 1 - simplex ) whose vertices are labelled by the same number but with opposite signs.


all else being equal, an unbiased estimator is preferable to a biased estimator, although in practice, biased estimators ( with generally small bias ) are frequently used. when a biased estimator is used, bounds of the bias are calculated. a biased estimator may be used for various reasons : because an unbiased estimator does not exist without further assumptions about a population ; because an estimator is difficult to compute ( as in unbiased estimation of standard deviation ) ; because a biased estimator may be unbiased with respect to different measures of central tendency ; because a biased estimator gives a lower value of some loss function ( particularly mean squared error ) compared with unbiased estimators ( notably in shrinkage estimators ) ; or because in some cases being unbiased is too strong a condition, and the only unbiased estimators are not useful.


because it is impossible for banks to know every cheque that a customer writes and which may or may not be fraudulent, the onus is on the clients to make the bank aware of what cheques they write. these systems allow customers to upload their cheque files to the bank including the cheque number, the amount of money, and in some cases, the payee name. now, when a cheque is presented for payment, the bank scrubs it against the information on file.


in mathematics, the hurwitz problem ( named after adolf hurwitz ) is the problem of finding multiplicative relations between quadratic forms which generalise those known to exist between sums of squares in certain numbers of variables.


in the united states, " gangnam style " debuted at number 64 the billboard hot 100 in the week of september 22, 2012, with 61, 000 downloads sold, more than the total number of previous weeks ( 57, 000 ), becoming the second k - pop song to enter the chart behind the wonder girls'" nobody, " which spent a week at number 76 on the october 31, 2009 chart. the following week, the song rocketed to number 11 on the chart with 188, 000 downloads, seeing a sales increase of 210 % after psy appeared on various tv shows such as the ellen degeneres show and nbc's today. in its third week, it rose to number two on the chart, topping the hot digital songs chart with a 60 % increase to 301, 000 downloads sold and climbing to number nine on on - demand songs chart. after that, the song peaked at the runner - up spot for seven consecutive weeks behind maroon 5's " one more night, " failing to gain in enough radio audience to ascend to the summit, although it ruled hot digital songs for a fourth week and on - demand songs for a fifth week during that period.


in a network created by people analyzing their understanding of the word ( such as wordnet ) the links and decomposition structures of the network are few in number and kind, and include part of, kind of, and similar links. in automated ontologies the links are computed vectors without explicit meaning. various automated technologies are being developed to compute the meaning of words : latent semantic indexing and support vector machines, as well as natural language processing, artificial neural networks and predicate calculus techniques.


in mathematics and theoretical computer science, entropy compression is an information theoretic method for proving that a random process terminates, originally used by robin moser to prove an algorithmic version of the lovasz local lemma.


indeed, he would look favourably on an application for tenure by a young scientist who " got busy and found himself 43 coauthors. " in john quiggin's opinion, the social network analysis was not based on meaningful criteria, did not prove a conflict of interest and did not apply at the time of the 1998 and 1999 publications.


in mathematics, a classifying topos for some sort of structure is a topos t such that there is a natural equivalence between geometric morphisms from a cocomplete topos e to t and the category of models for the structure in e.


in the field of data compression, shannon coding, named after its creator, claude shannon, is a lossless data compression technique for constructing a prefix code based on a set of symbols and their probabilities ( estimated or measured ). it is suboptimal in the sense that it does not achieve the lowest possible expected code word length like huffman coding does, and never better than but sometimes equal to the shannon – fano coding ( fano's method ). the method was the first of its type, the technique was used to prove shannon's noiseless coding theorem in his 1948 article " a mathematical theory of communication ", and is therefore a centerpiece of the information age. shannon – fano coding methods gave rise to the field of information theory and without its contributions, the world would not have any of the many successors ; for example huffman coding, or arithmetic coding.


in modern mathematics, a common proof involves bezout's identity, which was unknown at euclid's time. bezout's identity states that if x and y are coprime integers ( i. e. they share no common divisors other than 1 and −1 ) there exist integers r and s such that r x + s y = 1. { \ displaystyle rx + sy = 1. } let a and n be coprime, and assume that n | ab.


in order to guarantee interoperability, dcf specifies the file system for image and sound files to be used on formatted dcf media ( like removable or non - removable memory ) as fat12, fat16, fat32, or exfat. media with a capacity of more than 2 gb must be formatted using fat32 or exfat. the filesystem in a digital camera contains a dcim ( digital camera images ) directory, which can contain multiple subdirectories with names such as " 123abcde " that consist of a unique directory number ( in the range 100... 999 ) and five alphanumeric characters, which may be freely chosen and often refer to a camera maker.


in mathematics, an ordered vector space or partially ordered vector space is a vector space equipped with a partial order that is compatible with the vector space operations.


in the 1980s the rca 1802 was used for many missions — like galileo. this mission and other missions started the trend away from custom built nasa cpus in spacecraft. the exploration of the inner and outer parts of the solar system would have to be done with existing ( civilian and military - aerospace ) cpus.


in mathematics, a function f : r n → r { \ displaystyle f : \ mathbb { r } ^ { n } \ rightarrow \ mathbb { r } } is said to be closed if for each α ∈ r { \ displaystyle \ alpha \ in \ mathbb { r } }, the sublevel set { x ∈ dom f | f ( x ) ≤ α } { \ displaystyle \ { x \ in { \ mbox { dom } } f \ vert f ( x ) \ leq \ alpha \ } } is a closed set. equivalently, if the epigraph defined by epi f = { ( x, t ) ∈ r n + 1 | x ∈ dom f, f ( x ) ≤ t } { \ displaystyle { \ mbox { epi } } f = \ { ( x, t ) \ in \ mathbb { r } ^ { n + 1 } \ vert x \ in { \ mbox { dom } } f, \ ; f ( x ) \ leq t \ } } is closed, then the function f { \ displaystyle f } is closed. this definition is valid for any function, but most used for convex functions. a proper convex function is closed if and only if it is lower semi - continuous. for a convex function which is not proper there is disagreement as to the definition of the closure of the function.


in mathematical logic, such concepts as primitive recursive functions and μ - recursive functions represent integer - valued functions of several natural variables or, in other words, functions on nn. godel numbering, defined on well - formed formulae of some formal language, is a natural - valued function. computability theory is essentially based on natural numbers and natural ( or integer ) functions on them.


note that the noise can be either stochastic or deterministic. alternatively the model can be expressed as p ω ( y ) = p ω ( m ) + p ω ( z ), { \ displaystyle p _ { \ omega } ( y ) = p _ { \ omega } ( m ) + p _ { \ omega } ( z ), } where z { \ displaystyle z } is an n × n { \ displaystyle n \ times n } matrix with entries z i j { \ displaystyle z _ { ij } } for ( i, j ) ∈ ω { \ displaystyle ( i, j ) \ in \ omega } assuming that ‖ p ω ( z ) ‖ f ≤ δ { \ displaystyle \ | p _ { \ omega } ( z ) \ | _ { f } \ leq \ delta } for some δ > 0 { \ displaystyle \ delta > 0 }. to recover the incomplete matrix, we try to solve the following optimization problem : min x ‖ x ‖ ∗ subject to ‖ p ω ( x − y ) ‖ f ≤ δ { \ displaystyle { \ begin { aligned } & { \ underset { x } { \ text { min } } } & \ | x \ | _ { * } \ \ & { \ text { subject to } } & \ | p _ { \ omega } ( x - y ) \ | _ { f } \ leq \ delta \ \ \ end { aligned } } } among all matrices consistent with the data, find the one with minimum nuclear norm. candes and plan have shown that this reconstruction is accurate.


in modern english, there are several conventions for abbreviations, and the choice may be confusing. the only rule universally accepted is that one should be consistent, and to make this easier, publishers express their preferences in a style guide. some questions which arise are shown below.


+ x 5 5! − x 7 7!


in telecommunications, the coverage of a radio station is the geographic area where the station can communicate. broadcasters and telecommunications companies frequently produce coverage maps to indicate to users the station's intended service area. coverage depends on several factors, such as orography ( i. e. mountains ) and buildings, technology, radio frequency and perhaps most importantly for two - way telecommunications the sensitivity and transmit efficiency of the consumer equipment. some frequencies provide better regional coverage, while other frequencies penetrate better through obstacles, such as buildings in cities.


in statistics, an expectation – maximization ( em ) algorithm is an iterative method to find ( local ) maximum likelihood or maximum a posteriori ( map ) estimates of parameters in statistical models, where the model depends on unobserved latent variables. the em iteration alternates between performing an expectation ( e ) step, which creates a function for the expectation of the log - likelihood evaluated using the current estimate for the parameters, and a maximization ( m ) step, which computes parameters maximizing the expected log - likelihood found on the e step. these parameter - estimates are then used to determine the distribution of the latent variables in the next e step.


in regards to implicit / automatic versus explicit proximity search, as of november 2008, most internet search engines only implement an implicit proximity search functionality. that is, they automatically rank those search results higher where the user keywords have a good " overall proximity score " in such results. if only two keywords are in the search query, this has no difference from an explicit proximity search which puts a near operator between the two keywords. however, if three or more than three keywords are present, it is often important for the user to specify which subsets of these keywords expect a proximity in search results.


assume this chain has stationary distribution π { \ displaystyle \ pi }. define q ( x, y ) = π ( x ) k ( x, y ) { \ displaystyle q ( x, y ) = \ pi ( x ) k ( x, y ) } and for a, b ⊂ x { \ displaystyle a, b \ subset x } define q ( a × b ) = x ∈ a, y ∈ b q ( x, y ). { \ displaystyle q ( a \ times b ) = \ sum _ { x \ in a, y \ in b } q ( x, y ). }


in strictly horological terms, " rating " a chronometer means that prior to the instrument entering service, the average rate of gaining or losing per day is observed and recorded on a rating certificate which accompanies the instrument. this daily rate is used in the field to correct the time indicated by the instrument to get an accurate time reading. even the best - made chronometer with the finest temperature compensation etc. exhibits two types of error, ( 1 ) random and ( 2 ) consistent. the quality of design and manufacture of the instrument keeps the random errors small. in principle, the consistent errors should be amenable to elimination by adjustment, but in practice it is not possible to make the adjustment so precisely that this error is completely eliminated, so the technique of rating is used. the rate will also change while the instrument is in service due to e. g. thickening of the oil, so on long expeditions the instrument's rate would be periodically checked against accurate time determined by astronomical observations.


in number theory, a multiplicative function is an arithmetic function f ( n ) of a positive integer n with the property that f ( 1 ) = 1 and whenever a and b are coprime. an arithmetic function f ( n ) is said to be completely multiplicative ( or totally multiplicative ) if f ( 1 ) = 1 and f ( ab ) = f ( a ) f ( b ) holds for all positive integers a and b, even when they are not coprime.


in the decentralized federated learning setting, the nodes are able to coordinate themselves to obtain the global model. this setup prevents single point failures as the model updates are exchanged only between interconnected nodes without the orchestration of the central server. nevertheless, the specific network topology may affect the performances of the learning process. see blockchain - based federated learning and the references therein.


this is called the " receiving party pays " model. in china, it was reported that both of its two operators will adopt the caller - pays approach as early as january 2007. one disadvantage of the receiving party pays systems is that phone owners keep their phones turned off to avoid receiving unwanted calls, which results in the total voice usage rates ( and profits ) in calling party pays countries outperform those in receiving party pays countries. to avoid the problem of users keeping their phone turned off, most receiving party pays countries have either switched to calling party pays, or their carriers offer additional incentives such as a large number of monthly minutes at a sufficiently discounted rate to compensate for the inconvenience. note that when a user roaming in another country, international roaming tariffs apply to all calls received, regardless of the model adopted in the home country.


in early days, the user space programs that wanted to use the graphical framebuffer were also responsible for providing the mode - setting operations, and therefore they needed to run with privileged access to the video hardware. in unix - type operating systems, the x server was the most prominent example, and its mode - setting implementation lived in the ddx driver for each specific type of video card. this approach, later referred as user space mode - setting or ums, poses several issues.


in parallel computing, an embarrassingly parallel workload or problem ( also called embarrassingly parallelizable, perfectly parallel, delightfully parallel or pleasingly parallel ) is one where little or no effort is needed to separate the problem into a number of parallel tasks. this is often the case where there is little or no dependency or need for communication between those parallel tasks, or for results between them. thus, these are different from distributed computing problems that need communication between tasks, especially communication of intermediate results. they are easy to perform on server farms which lack the special infrastructure used in a true supercomputer cluster. they are thus well suited to large, internet - based volunteer computing platforms such as boinc, and do not suffer from parallel slowdown.


the pair type is a special case of the dependent pair type, where the type b may depend on the instance picked from a. in many languages, product types take the form of a record type, for which the components of a tuple can be accessed by label. in languages that have algebraic data types, as in most functional programming languages, algebraic data types with one constructor are isomorphic to a product type. in the curry – howard correspondence, product types are associated with logical conjunction ( and ) in logic.


in system high mode of operation, all users must have : signed nda for all information on the system. proper clearance for all information on the system. formal access approval for all information on the system. a valid need to know for some information on the system. all users can access some data, based on their need to know.


in the double null chart for minkowski spacetime, d s 2 = − 2 d u d v + d x 2 + d y 2, − ∞ < u, v, x, y < ∞ { \ displaystyle ds ^ { 2 } = - 2 \, du \, dv + dx ^ { 2 } + dy ^ { 2 }, \ ; \ ; \ ; - \ infty


in einstein notation, covariant components are denoted with lower indices as in w = w i e i. { \ displaystyle \ mathbf { w } = w _ { i } \ mathbf { e } ^ { i }. }


combining 256 consecutive 20 - bit samples can increase the snr by a factor of 16, effectively adding 4 bits to the resolution and producing a single sample with 24 - bit resolution. the number of samples required to get n { \ displaystyle n } bits of additional data precision is number of samples = ( 2 n ) 2 = 2 2 n. { \ displaystyle { \ mbox { number of samples } } = ( 2 ^ { n } ) ^ { 2 } = 2 ^ { 2n }. } to get the mean sample scaled up to an integer with n { \ displaystyle n } additional bits, the sum of 2 2 n { \ displaystyle 2 ^ { 2n } } samples is divided by 2 n { \ displaystyle 2 ^ { n } } : scaled mean = i = 0 2 2 n − 1 2 n data i 2 2 n = i = 0 2 2 n − 1 data i 2 n.


in the area of tax policy, exchange of information is a critical tool in assuring compliance with tax codes. as the economy becomes increasingly globalized taxpayers gain greater freedom to move between countries and regions. tax authorities, however, are restrained by national borders. in order for governments to ensure the proper application of their tax laws, the free and accurate exchange of information is critical. the oecd centre for tax policy and administration works to improve flow of information in this area and establish a legal framework to facilitate it.


in mathematics, restriction of scalars ( also known as " weil restriction " ) is a functor which, for any finite extension of fields l / k and any algebraic variety x over l, produces another variety resl / kx, defined over k. it is useful for reducing questions about varieties over large fields to questions about more complicated varieties over smaller fields.


in mathematics, the maximum - minimums identity is a relation between the maximum element of a set s of n numbers and the minima of the 2n − 1 non - empty subsets of s. let s = { x1, x2,..., xn }. the identity states that max { x 1, x 2, …, x n } = i = 1 n x i − i < j min { x i, x j } + i < j < k min { x i, x j, x k } − + ( − 1 ) n + 1 min { x 1, x 2, …, x n }, { \ displaystyle { \ begin { aligned } \ max \ { x _ { 1 }, x _ { 2 }, \ ldots, x _ { n } \ } & = \ sum _ { i = 1 } ^ { n } x _ { i } - \ sum _ { i


in the context of computational musicology, lda has been used to discover tonal structures in different corpora.


in terms of mathematical optimization, dynamic programming usually refers to simplifying a decision by breaking it down into a sequence of decision steps over time. this is done by defining a sequence of value functions v1, v2,..., vn taking y as an argument representing the state of the system at times i from 1 to n. the definition of vn ( y ) is the value obtained in state y at the last time n. the values vi at earlier times i = n −1, n − 2,..., 2, 1 can be found by working backwards, using a recursive relationship called the bellman equation. for i = 2,..., n, vi−1 at any state y is calculated from vi by maximizing a simple function ( usually the sum ) of the gain from a decision at time i − 1 and the function vi at the new state of the system if this decision is made. since vi has already been calculated for the needed states, the above operation yields vi−1 for those states. finally, v1 at the initial state of the system is the value of the optimal solution. the optimal values of the decision variables can be recovered, one by one, by tracking back the calculations already performed.


in mathematics, a semigroup is a nonempty set together with an associative binary operation. a special class of semigroups is a class of semigroups satisfying additional properties or conditions. thus the class of commutative semigroups consists of all those semigroups in which the binary operation satisfies the commutativity property that ab = ba for all elements a and b in the semigroup. the class of finite semigroups consists of those semigroups for which the underlying set has finite cardinality.


but there are some efforts to characterize nonlinear systems, such as volterra and wiener series using polynomial integrals as the use of those methods naturally extend the signal into multi - dimensions. another example is the empirical mode decomposition method using hilbert transform instead of fourier transform for nonlinear multi - dimensional systems. this method is an empirical method and can be directly applied to data sets.


in some statically - typed languages such as boo and d, class type checking can be specified to occur at runtime rather than at compile time.


in some languages, for example english, there is often a similarity between clauses expressing an action or event in the passive voice and clauses expressing a state. for example, the string of words " the dog is fed " can have the following two different meanings : the dog is fed ( twice a day ). the dog is fed ( so we can leave now ). the additions in parentheses " force " the same string of words to clearly show only one of their two possible grammatical functions and the related meaning. in the first sentence, the combination of the auxiliary verb " is " and the past participle " fed " is a regular example of the construction of the passive voice in english.


some auxiliary information is needed in order to break symmetry. a standard assumption is that initially each node has a unique identifier, for example, from the set { 1, 2,..., n }. put otherwise, we assume that we are given an n - coloring.


it not only connects pots phone lines with the rest of the pstn, but also replaces dsl by connecting directly to ethernet wired into the home. asynchronous transfer mode is often the communications protocol used. cable tv has long carried multiplexed television channels, and late in the 20th century began offering the same services as telephone companies. iptv also depends on multiplexing.


in mathematics, a delannoy number d { \ displaystyle d } describes the number of paths from the southwest corner ( 0, 0 ) of a rectangular grid to the northeast corner ( m, n ), using only single steps north, northeast, or east. the delannoy numbers are named after french army officer and amateur mathematician henri delannoy. the delannoy number d ( m, n ) { \ displaystyle d ( m, n ) } also counts the number of global alignments of two sequences of lengths m { \ displaystyle m } and n { \ displaystyle n }, the number of points in an m - dimensional integer lattice or cross polytope which are at most n steps from the origin, and, in cellular automata, the number of cells in an m - dimensional von neumann neighborhood of radius n while the number of cells on a surface of an m - dimensional von neumann neighborhood of radius n is given with ( sequence a266213 in the oeis ).


based on the philosophical assumption of the strong church - turing thesis, a mathematical criterion for evaluation of evidence has been conjectured, with the criterion having a resemblance to the idea of occam's razor that the simplest comprehensive description of the evidence is most likely correct. it states formally, " the ideal principle states that the prior probability associated with the hypothesis should be given by the algorithmic universal probability, and the sum of the log universal probability of the model plus the log of the probability of the data given the model should be minimized. " however, some philosophers ( including richard boyd, mario bunge, john d. norton, and elliott sober ) have adopted a skeptical or deflationary view of the role of simplicity in science, arguing in various ways that its importance has been overemphasized. emphasis on hypothesis testing as the essence of science is prevalent among both scientists and philosophers.


the underlying assumption with descriptively close sets is that such sets contain elements that have location and measurable features such as colour and frequency of occurrence. the description of the element of a set is defined by a feature vector. comparison of feature vectors provides a basis for measuring the closeness of descriptively near sets.


in single - stage job scheduling problems, there are four main categories of machine environments : 1 : single - machine scheduling. there is a single machine. p : identical - machines scheduling. there are m { \ displaystyle m } parallel machines, and they are identical.


in philosophical ethics, the naturalistic fallacy is the claim that it is possible to give a reductive explanation of good, in terms of natural properties such as pleasant or desirable. the term was introduced by british philosopher g. e. moore in his 1903 book principia ethica. moore's naturalistic fallacy is closely related to the is – ought problem, which comes from david hume's a treatise of human nature ( 1738 – 40 ). however, unlike hume's view of the is – ought problem, moore ( and other proponents of ethical non - naturalism ) did not consider the naturalistic fallacy to be at odds with moral realism. the naturalistic fallacy should not be confused with the appeal to nature, which is exemplified by forms of reasoning such as " something is natural ; therefore, it is morally acceptable " or " this property is unnatural ; therefore, this property is undesirable. " such inferences are common in discussions of medicine, sexuality, environmentalism, gender roles, race, and carnism.


in statistics, additive smoothing, also called laplace smoothing or lidstone smoothing, is a technique used to smooth categorical data. given a set of observation counts x = ⟨ x 1, x 2, …, x d ⟩ { \ textstyle \ textstyle { \ mathbf { x } \ = \ \ left \ langle x _ { 1 }, \, x _ { 2 }, \, \ ldots, \, x _ { d } \ right \ rangle } } from a d { \ textstyle \ textstyle { d } } - dimensional multinomial distribution with n { \ textstyle \ textstyle { n } } trials, a " smoothed " version of the counts gives the estimator : θ ^ i = x i + α n + α d ( i = 1, …, d ), { \ displaystyle { \ hat { \ theta } } _ { i } = { \ frac { x _ { i } + \ alpha } { n + \ alpha d } } \ qquad ( i = 1, \ ldots, d ), } where the smoothed count x ^ i = n θ ^ i { \ textstyle \ textstyle { { \ hat { x } } _ { i } = n { \ hat { \ theta } } _ { i } } } and the " pseudocount " α > 0 is a smoothing parameter. α = 0 corresponds to no smoothing. ( this parameter is explained in § pseudocount below. )


in packed bcd, the number 127 is represented by 0001 0010 0111 1100 ( 127c ) and −127 is represented by 0001 0010 0111 1101 ( 127d ). burroughs systems used 1101 ( d ) for negative, and any other value is considered a positive sign value ( the processors will normalize a positive sign to 1100 ( c ) ). no matter how many bytes wide a word is, there is always an even number of nibbles because each byte has two of them.


in mathematics and computer science, the syntactic monoid m ( l ) { \ displaystyle m ( l ) } of a formal language l { \ displaystyle l } is the smallest monoid that recognizes the language l { \ displaystyle l }.


in 2001, thinsoft betwin offered a multiseat solution for windows, utilizing multiple graphics cards and peripherals attached to a single host pc. in 2002 a canadian company, userful corporation, released userful multiplier, a multiseat linux software solution that enables up to 10 users to simultaneously share one computer. earlier they worked on a kernel - based approach to a multi - station platform computer, but abandoned the idea due to a problem with multiple video card support. other solutions appeared in 2003, such svetoslav slavtchev, aivils stoss and james simmons worked, with the evdev and faketty approach modifying the linux kernel and letting more than one user independently use the same machine.


in mathematics, an integer matrix is a matrix whose entries are all integers. examples include binary matrices, the zero matrix, the matrix of ones, the identity matrix, and the adjacency matrices used in graph theory, amongst many others. integer matrices find frequent application in combinatorics.


the c0 control characters, being unaffected by the shift state of a 7 - bit code, were to always be represented in an 8 - bit code with the eighth bit unset. the consequently otherwise - unused bytes in the range 0x80 through 0x9f could be used for additional control codes, which would instead be represented as 0x1b 0x40 through 0x1b 0x5f ( esc @ through esc _ ) in a 7 - bit code. these additional control codes become known as the c1 control codes.


it can be proven that if for a transformation g ′ { \ displaystyle g ^ { \ prime } }, support set will also lie within g ′ g 0 { \ displaystyle g ^ { \ prime } g _ { 0 } }, then signature of i { \ displaystyle i } is invariant with respect to g ′ { \ displaystyle g ^ { \ prime } }. this theorem determines the range of transformations for which invariance is guaranteed to hold. one can see that the smaller is supp ( ⟨ i, g − 1 t k ⟩ ) { \ displaystyle \ operatorname { supp } ( \ langle i, g ^ { - 1 } t _ { k } \ rangle ) }, the larger is the range of transformations for which invariance is guaranteed to hold.


only one processor can access a block at a time. the following two algorithms solve the crew and erew problem if p ≤ b { \ displaystyle p \ leq b } processors write to the same block simultaneously. a first approach is to serialize the write operations. only one processor after the other writes to the block.


in some countries, crash type classification exists for statistical purpose so that a crash is counted in one type or another.


in an attempt to duplicate mills & boon's success in north america, harlequin improved their distribution and marketing system. by choosing to sell their books " where the women are, " they allowed many mass - market merchandisers and even supermarkets to sell the books, all of which were exactly 192 pages. harlequin then began a reader service, selling directly to readers who agreed to purchase a certain number of books each month.


{ \ displaystyle g _ { i } ( x _ { 0 } ) > 0. } equality constraints are always active.


for example, the following is an instruction for the super harvard architecture single - chip computer ( sharc ). in one cycle, it does a floating - point multiply, a floating - point add, and two autoincrement loads. all of this fits in one 48 - bit instruction : f12 = f0 * f4, f8 = f8 + f12, f0 = dm ( i0, m3 ), f4 = pm ( i8, m9 ) ; since the earliest days of computer architecture, some cpus have added several arithmetic logic units ( alus ) to run in parallel.


the set of prime numbers is not almost n { \ displaystyle \ mathbb { n } }, because there are infinitely many natural numbers that are not prime numbers. the set of transcendental numbers are almost r { \ displaystyle \ mathbb { r } }, because the algebraic real numbers form a countable subset of the set of real numbers ( which is uncountable ). the cantor set is uncountably infinite, but has lebesgue measure zero. so almost all real numbers in ( 0, 1 ) are members of the complement of the cantor set.


in phonology, an idiosyncratic property contrasts with a systematic regularity. while systematic regularities in the sound system of a language are useful for identifying phonological rules during analysis of the forms morphemes can take, idiosyncratic properties are those whose occurrence is not determined by those rules. for example, the fact that the english word cab starts with a / c / is an idiosyncratic property ; on the other hand that its vowel is longer than in the english word cap is a systematic regularity, as it arises from the fact that the final consonant is voiced rather than voiceless.


in statistics, sometimes the covariance matrix of a multivariate random variable is not known but has to be estimated. estimation of covariance matrices then deals with the question of how to approximate the actual covariance matrix on the basis of a sample from the multivariate distribution. simple cases, where observations are complete, can be dealt with by using the sample covariance matrix. the sample covariance matrix ( scm ) is an unbiased and efficient estimator of the covariance matrix if the space of covariance matrices is viewed as an extrinsic convex cone in rp×p ; however, measured using the intrinsic geometry of positive - definite matrices, the scm is a biased and inefficient estimator.


in software engineering, software aging is the tendency for software to fail or cause a system failure after running continuously for a certain time, or because of ongoing changes in systems surrounding the software. software aging has several causes, including the inability of old software to adapt to changing needs or changing technology platforms, and the tendency of software patches to introduce further errors. as the software gets older it becomes less well - suited to its purpose and will eventually stop functioning as it should. rebooting or reinstalling the software can act as a short - term fix.


primitive ideals are prime. the quotient of a ring by a left primitive ideal is a left primitive ring. for commutative rings the primitive ideals are maximal, and so commutative primitive rings are all fields.


in orthogonal range searching, the set s consists of n { \ displaystyle n } points in d { \ displaystyle d } dimensions, and the query consists of intervals in each of those dimensions. thus, the query consists of a multi - dimensional axis - aligned rectangle. with an output size of k { \ displaystyle k }, jon bentley used a k - d tree to achieve ( in big o notation ) o ( n ) { \ displaystyle o ( n ) } space and o ( n 1 − 1 d + k ) { \ displaystyle o { \ big ( } n ^ { 1 - { \ frac { 1 } { d } } } + k { \ big ) } } query time.


in mathematics and computer science, a stack - sortable permutation ( also called a tree permutation ) is a permutation whose elements may be sorted by an algorithm whose internal storage is limited to a single stack data structure. the stack - sortable permutations are exactly the permutations that do not contain the permutation pattern 231 ; they are counted by the catalan numbers, and may be placed in bijection with many other combinatorial objects with the same counting function including dyck paths and binary trees.


a set of intervals j is called a covering of p if each point in p is contained in at least one interval of q. the rainbow covering problem is the problem of finding a rainbow set q that is a covering of p. the problem is np - hard ( by reduction from linear sat ). a more general notion is conflict - free covering. in this problem : there is a set o of m objects, and a conflict - graph go on o. a subset q of o is called conflict - free if it is an independent set in go, that is, no two objects in q are connected by an edge in go.


in the beginning of a scenario, one might calculate the probability of a certain event. however, as soon as one gains more information about the scenario, one may need to re - calculate the probability accordingly. for example, when being told that a woman has two children, one might be interested in knowing if either of them is a girl, and if yes, what is probability that the other child is also a girl. considering the two events independently, one might expect that the probability that the other child is female is ½ ( 50 % ), but by building a probability space illustrating all possible outcomes, one would notice that the probability is actually only ⅓ ( 33 % ).


if bob measures in the computational basis, his only possible measurement is | ψ 00 ⟩ { \ displaystyle | \ psi _ { 00 } \ rangle }. this outcome is clearly consistent with the state having been | ψ 00 ⟩ { \ displaystyle | \ psi _ { 00 } \ rangle }, but it would also be a possible outcome if the state had been | ψ 01 ⟩ { \ displaystyle | \ psi _ { 01 } \ rangle }. if bob measures in the hadamard basis, either | ψ 01 ⟩ { \ displaystyle | \ psi _ { 01 } \ rangle } or | ψ 11 ⟩ { \ displaystyle | \ psi _ { 11 } \ rangle } could be measured, each with probability ½. if the outcome is | ψ 01 ⟩ { \ displaystyle | \ psi _ { 01 } \ rangle } then again this state is consistent with either starting state.


the most common example of a host is a pc but some cell phones and pdas also can be hosts. the hid protocol makes implementation of devices very simple. devices define their data packets and then present a " hid descriptor " to the host.


in some languages, like english, palatalization is allophonic. some phonemes have palatalized allophones in certain contexts, typically before front vowels and unpalatalized allophones elsewhere. because it is allophonic, palatalization of this type does not distinguish words and often goes unnoticed by native speakers. phonetic palatalization occurs in american english. stops are palatalized before the front vowel / i / and not palatalized in other cases.


in our initial formulation, introduce a binary variable x i { \ displaystyle x _ { i } } for i = 1, …, n { \ displaystyle i = 1, \ dots, n }, where x i = 1 { \ displaystyle x _ { i } = 1 } if facility i { \ displaystyle i } is open, and x i = 0 { \ displaystyle x _ { i } = 0 } otherwise. further introduce the variable y i j { \ displaystyle y _ { ij } } for i = 1, …, n { \ displaystyle i = 1, \ dots, n } and j = 1, …, m { \ displaystyle j = 1, \ dots, m } which represents the fraction of the demand d j { \ displaystyle d _ { j } } filled by facility i { \ displaystyle i }. the so - called capacitated facility location problem is then given by note that the second set of constraints ensures that if x i = 0 { \ displaystyle x _ { i } = 0 }, that is, facility i { \ displaystyle i } isn't open, then y i j = 0 { \ displaystyle y _ { ij } = 0 } for all j { \ displaystyle j }, that is, no demand for any customer can be filled from facility i { \ displaystyle i }.


in order to maintain the structure of the tango tree ( auxiliary trees correspond to preferred paths ), we must do some updating work whenever preferred children change as a result of searches. when a preferred child changes, the top part of a preferred path becomes detached from the bottom part ( which becomes its own preferred path ) and reattached to another preferred path ( which becomes the new bottom part ). in order to do this efficiently, we'll define cut and join operations on our auxiliary trees.


the very first attempt to devise an algorithmic language was undertaken in 1948 by k. zuse. his notation was quite general, but the proposal never attained the consideration it deserved. unable to continue building computers – which was also forbidden by the allied powers – zuse devoted his time to the development of a higher - level programming model and language.


reading accuracy is sometimes a problem with goniometers. issues with the intra - measure ( between measures ) and inter - tester ( between clinicians ) reliability may increase as the experience of the examiner decreases.


vehicles that carry commodities are further subdivided by number of axles and number of units, including both power and trailer units. the united states environmental protection agency ( us epa ) has developed a classification scheme used to compare fuel economy among similar vehicles. passenger vehicles are classified based on a vehicle's total interior passenger and cargo volumes. trucks are classified based upon their gross vehicle weight rating ( gvwr ). heavy - duty vehicles are not included within the epa scheme. certain cities in the united states in the 1920s chose to exempt electric - powered vehicles because officials believed those vehicles did not cause " substantial wear upon the pavements ".


note that the example below uses the c # null coalescing operator to guarantee error free invocation, where it could also have used a more mundane if... then... else. the following example only works when you do not care the existence of null, or you treat null and empty string the same. the assumption may not hold in other applications.


in the early days of computing, a few experimental soviet computers were built with balanced ternary instead of binary, the most famous being the setun, built by nikolay brusentsov and sergei sobolev. the notation has a number of computational advantages over traditional binary and ternary. particularly, the plus – minus consistency cuts down the carry rate in multi - digit multiplication, and the rounding – truncation equivalence cuts down the carry rate in rounding on fractions. in balanced ternary, the one - digit multiplication table remains one - digit and has no carry and the addition table has only two carries out of nine entries, compared to unbalanced ternary with one and three respectively. knuth wrote that " perhaps the symmetric properties and simple arithmetic of this number system will prove to be quite important some day, " noting that, the complexity of arithmetic circuitry for balanced ternary arithmetic is not much greater than it is for the binary system, and a given number requires only log 3 2 ≈ 63 % { \ displaystyle \ log _ { 3 } 2 \ approx 63 \ % } as many digit positions for its representation. "


the visitor1 class implements the operation ( visitelementb ( e : elementb ) ). the uml sequence diagram shows the run - time interactions : the client object traverses the elements of an object structure ( elementa, elementb ) and calls accept ( visitor ) on each element. first, the client calls accept ( visitor ) on elementa, which calls visitelementa ( this ) on the accepted visitor object. the element itself ( this ) is passed to the visitor so that it can " visit " elementa ( call operationa ( ) ). thereafter, the client calls accept ( visitor ) on elementb, which calls visitelementb ( this ) on the visitor that " visits " elementb ( calls operationb ( ) ).


in mathematics, set a is a subset of a set b if all elements of a are also elements of b ; b is then a superset of a. it is possible for a and b to be equal ; if they are unequal, then a is a proper subset of b. the relationship of one set being a subset of another is called inclusion ( or sometimes containment ). a is a subset of b may also be expressed as b includes ( or contains ) a or a is included ( or contained ) in b. a k - subset is a subset with k elements. the subset relation defines a partial order on sets. in fact, the subsets of a given set form a boolean algebra under the subset relation, in which the join and meet are given by intersection and union, and the subset relation itself is the boolean inclusion relation.


common mathematical expressions for a characterization of x in terms of p include " p is necessary and sufficient for x ", and " x holds if and only if p ". it is also common to find statements such as " property q characterizes y up to isomorphism ". the first type of statement says in different words that the extension of p is a singleton set, while the second says that the extension of q is a single equivalence class ( for isomorphism, in the given example — depending on how up to is being used, some other equivalence relation might be involved ).


in the following compilation, m is the length of the pattern, n the length of the searchable text, and k = | σ | is the size of the alphabet. 1. ^ asymptotic times are expressed using o, ω, and θ notation. 2. ^ used to implement the memmem and strstr search functions in the glibc and musl c standard libraries. 3. ^ can be extended to handle approximate string matching and ( potentially - infinite ) sets of patterns represented as regular languages. the boyer – moore string - search algorithm has been the standard benchmark for the practical string - search literature.


in statistical applications, many problems can be formulated in the following way. one is interested in the expectation of a response function g : r d → r { \ displaystyle g : \ mathbb { r } ^ { d } \ rightarrow \ mathbb { r } } applied to some random vector ( x 1, …, x d ) { \ displaystyle ( x _ { 1 }, \ dots, x _ { d } ) }. if we denote the cdf of this random vector with h { \ displaystyle h }, the quantity of interest can thus be written as e = r d g ( x 1, …, x d ) d h ( x 1, …, x d ). { \ displaystyle \ operatorname { e } \ left = \ int _ { \ mathbb { r } ^ { d } } g ( x _ { 1 }, \ dots, x _ { d } ) \, \ mathrm { d } h ( x _ { 1 }, \ dots, x _ { d } ). }


written multiplication is also based on the distributive law. second example ( with variables ) third example ( with two sums ) here the distributive law was applied twice, and it does not matter which bracket is first multiplied out. fourth examplehere the distributive law is applied the other way around compared to the previous examples. consider since the factor 6 a 2 b { \ displaystyle 6a ^ { 2 } b } occurs in all summands, it can be factored out. that is, due to the distributive law one obtains


in software engineering, software durability means the solution ability of serviceability of software and to meet user's needs for a relatively long time. software durability is important for user's satisfaction. for a software security to be durable, it must allow an organization to adjust the software to business needs that are constantly evolving, often in impulsive ways. durability of software depends on four characteristics mainly ; i. e. software trustworthiness, human trust for serviceability, software dependability and software usability. = = references = =


in mathematics, liouville's theorem, originally formulated by joseph liouville in 1833 to 1841, places an important restriction on antiderivatives that can be expressed as elementary functions. the antiderivatives of certain elementary functions cannot themselves be expressed as elementary functions. these are called nonelementary antiderivatives. a standard example of such a function is e − x 2, { \ displaystyle e ^ { - x ^ { 2 } }, } whose antiderivative is ( with a multiplier of a constant ) the error function, familiar from statistics.


in the hilbert space viewpoint, one considers an h { \ displaystyle h } - valued random element x { \ displaystyle x }, where h { \ displaystyle h } is a separable hilbert space such as the space of square - integrable functions l 2 { \ displaystyle l ^ { 2 } }. under the integrability condition that e ‖ x ‖ l 2 2 = e ( 0 1 | x ( t ) | 2 d t ) < ∞ { \ displaystyle \ mathbb { e } \ | x \ | _ { l ^ { 2 } } ^ { 2 } = \ mathbb { e } ( \ int _ { 0 } ^ { 1 } | x ( t ) | ^ { 2 } dt ) < \ infty }, one can define the mean of x { \ displaystyle x } as the unique element μ ∈ h { \ displaystyle \ mu \ in h } satisfying e ⟨ x, h ⟩ = ⟨ μ, h ⟩, h ∈ h. { \ displaystyle \ mathbb { e } \ langle x, h \ rangle = \ langle \ mu, h \ rangle, \ qquad h \ in h. } this formulation is the pettis integral but the mean can also be defined as bochner integral μ = e x { \ displaystyle \ mu = \ mathbb { e } x }.


in terms of independence, a finite matroid m { \ displaystyle m } is a pair ( e, i ) { \ displaystyle ( e, { \ mathcal { i } } ) }, where e { \ displaystyle e } is a finite set ( called the ground set ) and i { \ displaystyle { \ mathcal { i } } } is a family of subsets of e { \ displaystyle e } ( called the independent sets ) with the following properties : ( i1 ) the empty set is independent, i. e., ∅ ∈ i { \ displaystyle \ emptyset \ in { \ mathcal { i } } }. ( i2 ) every subset of an independent set is independent, i. e., for each a ′ ⊆ a ⊆ e { \ displaystyle a'\ subseteq a \ subseteq e }, if a ∈ i { \ displaystyle a \ in { \ mathcal { i } } } then a ′ ∈ i { \ displaystyle a'\ in { \ mathcal { i } } }. this is sometimes called the hereditary property, or the downward - closed property.


nevil maskelyne, the newly appointed astronomer royal who was on the board of longitude, started with mayer's tables and after his own experiments at sea trying out the lunar distance method, proposed annual publication of pre - calculated lunar distance predictions in an official nautical almanac for the purpose of finding longitude at sea. being very enthusiastic for the lunar distance method, maskelyne and his team of computers worked feverishly through the year 1766, preparing tables for the new nautical almanac and astronomical ephemeris. published first with data for the year 1767, it included daily tables of the positions of the sun, moon, and planets and other astronomical data, as well as tables of lunar distances giving the distance of the moon from the sun and nine stars suitable for lunar observations ( ten stars for the first few years ).


the set of all possible feature vectors constitutes a feature space. a common example of feature vectors appears when each image point is to be classified as belonging to a specific class. assuming that each image point has a corresponding feature vector based on a suitable set of features, meaning that each class is well separated in the corresponding feature space, the classification of each image point can be done using standard classification method. another and related example occurs when neural network - based processing is applied to images. the input data fed to the neural network is often given in terms of a feature vector from each image point, where the vector is constructed from several different features extracted from the image data. during a learning phase, the network can itself find which combinations of different features are useful for solving the problem at hand.


in producing, people must continually maintain their assets, replace assets, and consume things but they also can create more beyond those requirements, assuming sufficient productivity of labour. this social surplus product can be : destroyed, or wasted held in reserve, or hoarded consumed traded or otherwise transferred to or from others reinvestedthus, for a simple example, surplus seeds could be left to rot, stored, eaten, traded for other products, or sown on new fields. but if, for example, 90 people own 5 sacks of grain, and 10 people own 100 sacks of grain, it would be physically impossible for those 10 people to use all that grain themselves — most likely they would either trade that grain, or employ other people to farm it. since 5 sacks of grain are insufficient for 90 people, it is likely that the 90 people would be willing to work for the 10 people who own more grain than they can consume, in order to get some extra grain.


in some situations, there is a risk of losing track of block boundaries. this is often seen in large sections of code containing many compound statements nested to many levels of indentations. by the time the programmer scrolls to the bottom of a huge set of nested statements, they may have lost track of which control statements go where. however, overly - long code could have other causes, such as being too complex, and a programmer facing this problem might instead consider whether code refactoring would help in the longer term.


the validity of an argument is not a guarantee of the truth of its conclusion. a valid argument may have false premises that render it inconclusive : the conclusion of a valid argument with one or more false premises may be true or false. logic seeks to discover the forms that make arguments valid.


in the envy - free cake - cutting problem, a " cake " ( a heterogeneous divisible resource ) has to be divided among n partners with different preferences over parts of the cake. the cake has to be divided to n pieces such that : ( a ) each partner receives a single connected piece, and ( b ) each partner believes that his piece is ( weakly ) better than all other pieces. a protocol for solving this problem was developed by forest simmons in 1980, in a correspondence with michael starbird. it was first publicized by francis su in 1999. given a cut - set ( i. e. a certain partition of the cake to n pieces ), we say that a partner prefers a given piece if he believes that this piece is weakly better than all other pieces.


ℓ 2 { \ displaystyle \ ell _ { 2 } } ) counted with their multiplicities, augmented by adding a countable infinity of points of the diagonal { ( x, y ) ∈ r 2 : x = y } { \ displaystyle \ { ( x, y ) \ in \ mathbb { r } ^ { 2 } : x = y \ } }. the matching distance between ℓ 1 { \ displaystyle \ ell _ { 1 } } and ℓ 2 { \ displaystyle \ ell _ { 2 } } is given by d match ( ℓ 1, ℓ 2 ) = min σ max p ∈ c 1 δ ( p, σ ( p ) ) { \ displaystyle d _ { \ text { match } } ( \ ell _ { 1 }, \ ell _ { 2 } ) = \ min _ { \ sigma } \ max _ { p \ in c _ { 1 } } \ delta ( p, \ sigma ( p ) ) } where σ { \ displaystyle \ sigma } varies among all the bijections between c 1 { \ displaystyle c _ { 1 } } and c 2 { \ displaystyle c _ { 2 } } and δ ( ( x, y ), ( x ′, y ′ ) ) = min { max { | x − x ′ |, | y − y ′ | }, max { y − x 2, y ′ − x ′ 2 } }.


in n { \ displaystyle n } - dimensional space r n { \ displaystyle \ mathbb { r } ^ { n } }, uniform scaling by a factor v { \ displaystyle v } is accomplished by scalar multiplication with v { \ displaystyle v }, that is, multiplying each coordinate of each point by v { \ displaystyle v }. as a special case of linear transformation, it can be achieved also by multiplying each point ( viewed as a column vector ) with a diagonal matrix whose entries on the diagonal are all equal to v { \ displaystyle v }, namely v i { \ displaystyle vi }. non - uniform scaling is accomplished by multiplication with any symmetric matrix. the eigenvalues of the matrix are the scale factors, and the corresponding eigenvectors are the axes along which each scale factor applies.


in number theory, moessner's theorem or moessner's magic is related to an arithmetical algorithm to produce an infinite sequence of the exponents of positive integers 1 n, 2 n, 3 n, 4 n,, { \ displaystyle 1 ^ { n }, 2 ^ { n }, 3 ^ { n }, 4 ^ { n }, \ cdots ~, } with n ≥ 1, { \ displaystyle n \ geq 1 ~, } by recursively manipulating the sequence of integers algebraically. the algorithm was first published by alfred moessner in 1951 ; the first proof of its validity was given by oskar perron that same year. for example, for n = 2 { \ displaystyle n = 2 }, one can remove every even number, resulting in ( 1, 3, 5, 7 ) { \ displaystyle ( 1, 3, 5, 7 \ cdots ) }, and then add each odd number to the sum of all previous elements, providing ( 1, 4, 9, 16, ) = ( 1 2, 2 2, 3 2, 4 2 ) { \ displaystyle ( 1, 4, 9, 16, \ cdots ) = ( 1 ^ { 2 }, 2 ^ { 2 }, 3 ^ { 2 }, 4 ^ { 2 } \ cdots ) }.


in the category of sets, an exponential object z y { \ displaystyle z ^ { y } } is the set of all functions y → z { \ displaystyle y \ to z }. the map e v a l : ( z y × y ) → z { \ displaystyle \ mathrm { eval } \ colon ( z ^ { y } \ times y ) \ to z } is just the evaluation map, which sends the pair ( f, y ) { \ displaystyle ( f, y ) } to f ( y ) { \ displaystyle f ( y ) }. for any map g : x × y → z { \ displaystyle g \ colon x \ times y \ to z } the map λ g : x → z y { \ displaystyle \ lambda g \ colon x \ to z ^ { y } } is the curried form of g { \ displaystyle g } : λ g ( x ) ( y ) = g ( x, y ). { \ displaystyle \ lambda g ( x ) ( y ) = g ( x, y ). \, } a heyting algebra h { \ displaystyle h } is just a bounded lattice that has all exponential objects.


in that time, the linux console project also proposed an idea to use multiple independent consoles and then multiple independent keyboards and mice in a project called " backstreet ruby ". backstreet ruby is a kernel patch for the linux kernel. it is a back port to linux - 2. 4 of the ruby kernel tree.


in the nks framework, these themselves should be simple programs, and subject to the same goals and methodology. an extension of this idea is that the human mind is itself a computational system, and hence providing it with raw data in as effective a way as possible is crucial to research. wolfram believes that programs and their analysis should be visualized as directly as possible, and exhaustively examined by the thousands or more. since this new field concerns abstract rules, it can in principle address issues relevant to other fields of science. however, in general wolfram's idea is that novel ideas and mechanisms can be discovered in the computational universe, where they can be represented in their simplest forms, and then other fields can choose among these discoveries for those they find relevant.


in probability theory, dirichlet processes ( after the distribution associated with peter gustav lejeune dirichlet ) are a family of stochastic processes whose realizations are probability distributions. in other words, a dirichlet process is a probability distribution whose range is itself a set of probability distributions. it is often used in bayesian inference to describe the prior knowledge about the distribution of random variables — how likely it is that the random variables are distributed according to one or another particular distribution.


in some cases, a high - privilege application assumes that it would only be provided with input matching its interface specification, thus doesn't validate this input. then, an attacker may be able to exploit this assumption, in order to run unauthorized code with the application's privileges : some windows services are configured to run under the local system user account. a vulnerability such as a buffer overflow may be used to execute arbitrary code with privilege elevated to local system. alternatively, a system service that is impersonating a lesser user can elevate that user's privileges if errors are not handled correctly while the user is being impersonated ( e. g. if the user has introduced a malicious error handler ) under some legacy versions of the microsoft windows operating system, the all users screensaver runs under the local system account – any account that can replace the current screensaver binary in the file system or registry can therefore elevate privileges.


in the lp phase of slqp, the following linear program is solved : min d f ( x k ) + ∇ f ( x k ) t d s. t. b ( x k ) + ∇ b ( x k ) t d ≥ 0 c ( x k ) + ∇ c ( x k ) t d = 0. { \ displaystyle { \ begin { array } { rl } \ min \ limits _ { d } & f ( x _ { k } ) + \ nabla f ( x _ { k } ) ^ { t } d \ \ \ mathrm { s. t. } & b ( x _ { k } ) + \ nabla b ( x _ { k } ) ^ { t } d \ geq 0 \ \ & c ( x _ { k } ) + \ nabla c ( x _ { k } ) ^ { t } d = 0. \ end { array } } } let a k { \ displaystyle { \ cal { a } } _ { k } } denote the active set at the optimum d lp ∗ { \ displaystyle d _ { \ text { lp } } ^ { * } } of this problem, that is to say, the set of constraints that are equal to zero at d lp ∗ { \ displaystyle d _ { \ text { lp } } ^ { * } }. denote by b a k { \ displaystyle b _ { { \ cal { a } } _ { k } } } and c a k { \ displaystyle c _ { { \ cal { a } } _ { k } } } the sub - vectors of b { \ displaystyle b } and c { \ displaystyle c } corresponding to elements of a k { \ displaystyle { \ cal { a } } _ { k } }.


in order to increase the decimal division accuracy add as many zeros as required to the right of the dividend but still input it right justified and then proceed as with an integer division. it is important to know where the decimal point is, when you read the quotient ( some markers, first ivory and then metal, were usually sold with the machine and used for this purpose ).


the preconditioner matrix m has to be symmetric positive - definite and fixed, i. e., cannot change from iteration to iteration. if any of these assumptions on the preconditioner is violated, the behavior of the preconditioned conjugate gradient method may become unpredictable. an example of a commonly used preconditioner is the incomplete cholesky factorization.


in the calculus of constructions, denoted as λc in the cube or as λpω, : 130 these four features cohabit, so that both types and terms can depend on types and terms. the clear border that exists in λ→ between terms and types is somewhat abolished, as all types except the universal { \ displaystyle \ square } are themselves terms with a type.


in the cases below where n is an exponent, multiples of n are also proven, since a kn - th power is also an n - th power. where solutions involving a second power are alluded to below, they can be found specifically at fermat – catalan conjecture # known solutions. all cases of the form ( 2, 3, n ) or ( 2, n, 3 ) have the solution 23 + 1n = 32 which is referred below as the catalan solution. the case x = y = z ≥ 3 ( and thus the case gcd ( x, y, z ) ≥ 3 ) is fermat's last theorem, proven to have no solutions by andrew wiles in 1994.


in terms of kripke semantics, s5 is characterized by models where the accessibility relation is an equivalence relation : it is reflexive, transitive, and symmetric. determining the satisfiability of an s5 formula is an np - complete problem. the hardness proof is trivial, as s5 includes the propositional logic. membership is proved by showing that any satisfiable formula has a kripke model where the number of worlds is at most linear in the size of the formula.


by subtracting 1 2 i = 1 n v i { \ displaystyle { \ frac { 1 } { 2 } } \ sum _ { i = 1 } ^ { n } v _ { i } } from each possible subsum ( that is, by changing the origin and then scaling by a factor of 2 ), the littlewood – offord problem is equivalent to the problem of determining the number of sums of the form i = 1 n ε i v i { \ displaystyle \ sum _ { i = 1 } ^ { n } \ varepsilon _ { i } v _ { i } } that fall in the target set a, where ε i { \ displaystyle \ varepsilon _ { i } } takes the value 1 or −1. this makes the problem into a probabilistic one, in which the question is of the distribution of these random vectors, and what can be said knowing nothing more about the vi. = = references = =


in mathematics, an initial algebra is an initial object in the category of f - algebras for a given endofunctor f. this initiality provides a general framework for induction and recursion.


the probability measure is then defined by the function : so the full probability space which defines a fair coin is the triplet ( ω, f, p ) { \ displaystyle ( \ omega, { \ mathcal { f } }, p ) } as defined above. note that this is not a random variable because heads and tails don't have inherent numerical values like you might find on a fair two - valued die. a random variable adds the additional structure of assigning a numerical value to each outcome. common choices are ( h, t ) → ( 1, 0 ) { \ displaystyle ( h, t ) \ to ( 1, 0 ) } or ( h, t ) → ( 1, − 1 ) { \ displaystyle ( h, t ) \ to ( 1, - 1 ) }.


the generalized petersen graphs are non - strict unit distance graphs. an unsolved problem of paul erdos asks how many edges a unit distance graph on n { \ displaystyle n } vertices can have. the best known lower bound is slightly above linear in n { \ displaystyle n } — far from the upper bound, proportional to n 4 / 3 { \ displaystyle n ^ { 4 / 3 } }.


if different resulting states can occur, the selection of the respective resulting state can be modeled explicitly as a decision function using logical connectors. functions can be refined into another epc. in this case it is called a hierarchical function.


in mathematical optimization, total dual integrality is a sufficient condition for the integrality of a polyhedron. thus, the optimization of a linear objective over the integral points of such a polyhedron can be done using techniques from linear programming. a linear system a x ≤ b { \ displaystyle ax \ leq b }, where a { \ displaystyle a } and b { \ displaystyle b } are rational, is called totally dual integral ( tdi ) if for any c ∈ z n { \ displaystyle c \ in \ mathbb { z } ^ { n } } such that there is a feasible, bounded solution to the linear program max c t x a x ≤ b, { \ displaystyle { \ begin { aligned } & & \ max c ^ { \ mathrm { t } } x \ \ & & ax \ leq b, \ end { aligned } } } there is an integer optimal dual solution. edmonds and giles showed that if a polyhedron p { \ displaystyle p } is the solution set of a tdi system a x ≤ b { \ displaystyle ax \ leq b }, where b { \ displaystyle b } has all integer entries, then every vertex of p { \ displaystyle p } is integer - valued. thus, if a linear program as above is solved by the simplex algorithm, the optimal solution returned will be integer.


in numerical analysis, the weierstrass method or durand – kerner method, discovered by karl weierstrass in 1891 and rediscovered independently by durand in 1960 and kerner in 1966, is a root - finding algorithm for solving polynomial equations. in other words, the method can be used to solve numerically the equation f ( x ) = 0, where f is a given polynomial, which can be taken to be scaled so that the leading coefficient is 1.


in order to be executed by the system ( such as an operating system, firmware, or boot loader ), an executable file must conform to the system's application binary interface ( abi ). in simple interfaces, a file is executed by loading it into memory and jumping to the start of the address space and executing from there. in more complicated interfaces, executable files have additional metadata specifying a separate entry point. for example, in elf, the entry point is defined in the header's e _ entry field, which specifies the ( virtual ) memory address at which to start execution. in the gnu compiler collection, this field is set by the linker based on the _ start symbol.


whereas the sieve of eratosthenes marks off each non - prime for each of its prime factors, the sieve of pritchard avoids considering almost all non - prime numbers by building progressively larger wheels, which represent the pattern of numbers not divisible by any of the primes processed thus far. it thereby achieves a better asymptotic complexity, and was the first sieve with a running time sublinear in the specified bound. its asymptotic running - time has not been improved on, and it deletes fewer composites than any other known sieve. it was created in 1979 by paul pritchard. since pritchard has created a number of other sieve algorithms for finding prime numbers, the sieve of pritchard is sometimes singled out by being called the wheel sieve ( by pritchard himself ) or the dynamic wheel sieve.


in quantum information theory, a set of bases in hilbert space cd are are said to be mutually unbiased to mean, that, if a system is prepared in an eigen state of one of the bases, then all outcomes of the measurement with respect to the other basis are predicted to occur with an equal probability inexorably equal to 1 / d.


in particular, the corestriction onto the image always exists and it is sometimes simply called the corestriction of f { \ displaystyle f }. more generally, one can consider corestriction of a morphism in general categories with images.


the column assignment shows an assignment of n before entering a subsequent step. this possibly induces a reassignment of the other nodes p, g, u also. if something has been changed by the case, this is shown in the column group after.


however, in some cases, additional marks fulfil the role of diacritics, to differentiate distinct characters. such additional marks constitute glyphs. some characters such as " æ " in icelandic and the " ß " in german may be regarded as glyphs.


in number theory, dixon's factorization method ( also dixon's random squares method or dixon's algorithm ) is a general - purpose integer factorization algorithm ; it is the prototypical factor base method. unlike for other factor base methods, its run - time bound comes with a rigorous proof that does not rely on conjectures about the smoothness properties of the values taken by a polynomial. the algorithm was designed by john d. dixon, a mathematician at carleton university, and was published in 1981.


in phonology, segments are categorized into natural classes on the basis of their distinctive features. each feature is a quality or characteristic of the natural class, such as voice or manner. a unique combination of features defines a phoneme.


in order theory, arbitrary meets can be expressed in terms of arbitrary joins and vice versa ( for details, see completeness ( order theory ) ). in effect, this means that it is sufficient to require the existence of either all meets or all joins to obtain the class of all complete lattices. as a consequence, some authors use the terms complete meet - semilattice or complete join - semilattice as another way to refer to complete lattices. though similar on objects, the terms entail different notions of homomorphism, as will be explained in the below section on morphisms.


m flag ( 1 bit ) 1 means more fragments follow ; 0 means last fragment. identification ( 32 bits ) packet identification value, generated by the source node. needed for reassembly of the original packet.


in phonetics, labiodentals are consonants articulated with the lower lip and the upper teeth.


in the ims framework, it is required that once the callee is alerted, the chances of a session failure are minimum. an important source of failure is the inability to reserve network resources to support the session, so these resources should be allocated before the phone rings. however, in the ims, to reserve resources the network needs to know the callee's ip address, port and session parameters and therefore it is necessary that the initial offer / answer exchange to establish a session has started ( invite request ). in basic sip, this exchange eventually causes the callee to be alerted.


hence r = s = ∅. { \ displaystyle { \ mathcal { r } } \ neq { \ mathcal { s } } = \ emptyset \ ;. }


in mathematics there is the concept of proof of impossibility referring to problems impossible to solve. the difference between this impossibility and that of the no - go theorems is : a proof of impossibility states a category of logical proposition that may never be true ; a no - go theorem instead presents a sequence of events that may never occur.


in most multiprocessor systems, each processor schedules and controls itself, therefore there's no " supervisor " processor, and kernel data structures are globally shared ; sections of code that access those shared data structures are critical sections. this design choice is made to improve scaling, reliability and modularity. examples of such kernel data structure are ready list and communication channels. a " conflict " happens when more than one processor is trying to access the same resource ( a memory portion ) at the same time.


{ \ displaystyle + : =. } ⋅ : =. { \ displaystyle \ cdot : =. }


in the chart below, the carian letter is given, followed by the transcription. where the transcription differs from ipa, the phonetic value is given in brackets. many carian phonemes were represented by multiple letter forms in various locations.


sr shows that these concepts are all different aspects of the same physical quantity in much the same way that it shows space and time to be interrelated. consequently, another modification is the concept of the center of mass of a system, which is straightforward to define in classical mechanics but much less obvious in relativity – see relativistic center of mass for details. the equations become more complicated in the more familiar three - dimensional vector calculus formalism, due to the nonlinearity in the lorentz factor, which accurately accounts for relativistic velocity dependence and the speed limit of all particles and fields. however, they have a simpler and elegant form in four - dimensional spacetime, which includes flat minkowski space ( sr ) and curved spacetime ( gr ), because three - dimensional vectors derived from space and scalars derived from time can be collected into four vectors, or four - dimensional tensors. however, the six component angular momentum tensor is sometimes called a bivector because in the 3d viewpoint it is two vectors ( one of these, the conventional angular momentum, being an axial vector ).


in the united kingdom a migration authorisation code ( mac ) was a 17 to 19 - character unique identifier code used by dsl customers when they wish to switch internet service provider ( isp ). a mac is generated by the actual telecommunication provider ( most commonly bt ), identifies the local loop ( telephone line ) to be switched, and authorises the provider to switch the customer to the new isp. macs usually begin with " bbip ", " ftip ", " bbds ", or " bbdp ", and consist of 4 letters, 7 digits ( sometimes up to 9 ), a slash, 2 letters, 2 digits ( this indicates the day in the month the mac was issued ), and 1 final letter. ( for example : bbip87654321 / ab12c ).


typically an algorithm which solves a problem in polylogarithmic time in the network size is considered efficient in this model. another commonly used measure is the total number of bits transmitted in the network ( cf. communication complexity ). the features of this concept are typically captured with the congest ( b ) model, which is similarly defined as the local model, but where single messages can only contain b bits.


for ill - structured problems, on the other hand, it is not clear what steps need to be taken, i. e. there is no clear formula that would lead to success if followed correctly. in this case, the solution may sometimes come in a flash of insight in which the problem is suddenly seen in a new light. another way to categorize different forms of problem solving is by distinguishing between algorithms and heuristics.


in structural complexity theory, the berman – hartmanis conjecture is an unsolved conjecture named after leonard c. berman and juris hartmanis that states that all np - complete languages look alike, in the sense that they can be related to each other by polynomial time isomorphisms.


in the aerospace industry, equipment on - board aircraft must be tested in situ, or in place, to confirm everything functions properly as a system. individually, each piece may work but interference from nearby equipment may create unanticipated problems. special test equipment is available for this in situ testing. it can also refer to repairs made to the aircraft structure or flight controls while still in place.


this enables training very deep recurrent neural networks with a very long time span t. a later lstm version published in 2000 modulates the identity lstm connections by so - called forget gates such that their weights are not fixed to 1. 0 but can be learned. in experiments, the forget gates were initialized with positive bias weights, thus being opened, addressing the vanishing gradient problem. the highway network of may 2015 applies these principles to feedforward neural networks.


hypergraphs can be viewed as incidence structures. in particular, there is a bipartite " incidence graph " or " levi graph " corresponding to every hypergraph, and conversely, every bipartite graph can be regarded as the incidence graph of a hypergraph when it is 2 - colored and it is indicated which color class corresponds to hypergraph vertices and which to hypergraph edges. hypergraphs have many other names.


in the 1980s, charles forgy developed a successor to the rete algorithm named rete ii. unlike the original rete ( which is public domain ) this algorithm was not disclosed. rete ii claims better performance for more complex problems ( even orders of magnitude ), and is officially implemented in clips / r2, a c / + + implementation and in opsj, a java implementation in 1998.


in the internet engineering task force, two working groups in the operations & maintenance area deal with aspects of performance. the interprovider performance measurement ( ippm ) group focuses, as its name would suggest, on operational measurement of services. performance measurements on single routers, or narrowly defined systems of routers, are the province of the benchmarking working group ( bmwg ). rfc 2544 is the key bmwg document. a classic rfc 2544 benchmark uses half the router's ( i. e., the device under test ( dut ) ) ports for input of a defined load, and measures the time at which the outputs appear at the output ports.


an alternative direction is to aggregate word embeddings, such as those returned by word2vec, into sentence embeddings. the most straightforward approach is to simply compute the average of word vectors, known as continuous bag - of - words ( cbow ). however, more elaborate solutions based on word vector quantization have also been proposed. one such approach is the vector of locally aggregated word embeddings ( vlawe ), which demonstrated performance improvements in downstream text classification tasks.


in probability theory, a nonlinear expectation is a nonlinear generalization of the expectation. nonlinear expectations are useful in utility theory as they more closely match human behavior than traditional expectations. the common use of nonlinear expectations is in assessing risks under uncertainty. generally, nonlinear expectations are categorized into sub - linear and super - linear expectations dependent on the additive properties of the given sets. much of the study of nonlinear expectation is attributed to work of mathematicians within the past two decades.


more formally, a relatively well - defined usage refers to a conditional statement ( or a universal conditional statement ) with a false antecedent. one example of such a statement is " if tokyo is in france, then the eiffel tower is in bolivia ". such statements are considered vacuous truths, because the fact that the antecedent is false prevents using the statement to infer anything about the truth value of the consequent.


in morphology, taxonomy and other descriptive disciplines in which a term for such shapes is necessary, terms such as trapezoidal or trapeziform commonly are useful in descriptions of particular organs or forms.


in the case of semigroups, since the binary operation is required to satisfy only the associativity property the problem of classification is considered extremely difficult. descriptions of structures have been obtained for certain special classes of semigroups. for example, the structure of the sets of idempotents of regular semigroups is completely known.


in number theory, a gaussian integer is a complex number whose real and imaginary parts are both integers. the gaussian integers, with ordinary addition and multiplication of complex numbers, form an integral domain, usually written as z { \ displaystyle \ mathbf { z } } or z. { \ displaystyle \ mathbb { z }. } gaussian integers share many properties with integers : they form a euclidean domain, and have thus a euclidean division and a euclidean algorithm ; this implies unique factorization and many related properties.


in probability theory, a poisson process is a stochastic process of which the simplest case involves " occurrences " at random times, the waiting time until the next occurrence having a memoryless exponential distribution, and the number of " occurrences " in any time interval having a poisson distribution whose expected value is proportional to the length of the time interval. let xt be the number of " occurrences " before time t, and let tx be the waiting time until the xth " occurrence ". we seek the probability density function of the random variable tx. we use the probability mass function for the poisson distribution, which tells us that pr ( x t = x ) = ( λ t ) x e − λ t x!


in natural language processing, brown clustering or ibm clustering is a form of hierarchical clustering of words based on the contexts in which they occur, proposed by peter brown, william a. brown, vincent della pietra, peter de souza, jennifer lai, and robert mercer of ibm in the context of language modeling. the intuition behind the method is that a class - based language model ( also called cluster n - gram model ), i. e. one where probabilities of words are based on the classes ( clusters ) of previous words, is used to address the data sparsity problem inherent in language modeling. the method has been successfully used to improve parsing, domain adaptation, and name d entity recognition. jurafsky and martin give the example of a flight reservation system that needs to estimate the likelihood of the bigram " to shanghai ", without having seen this in a training set. the system can obtain a good estimate if it can cluster " shanghai " with other city names, then make its estimate based on the likelihood of phrases such as " to london ", " to beijing " and " to denver ".


in mathematics, the lehmer mean of a tuple x { \ displaystyle x } of positive real numbers, named after derrick henry lehmer, is defined as : l p ( x ) = k = 1 n x k p k = 1 n x k p − 1. { \ displaystyle l _ { p } ( \ mathbf { x } ) = { \ frac { \ sum _ { k = 1 } ^ { n } x _ { k } ^ { p } } { \ sum _ { k = 1 } ^ { n } x _ { k } ^ { p - 1 } } }. } the weighted lehmer mean with respect to a tuple w { \ displaystyle w } of positive weights is defined as : l p, w ( x ) = k = 1 n w k ⋅ x k p k = 1 n w k ⋅ x k p − 1. { \ displaystyle l _ { p, w } ( \ mathbf { x } ) = { \ frac { \ sum _ { k = 1 } ^ { n } w _ { k } \ cdot x _ { k } ^ { p } } { \ sum _ { k = 1 } ^ { n } w _ { k } \ cdot x _ { k } ^ { p - 1 } } }. } the lehmer mean is an alternative to power means for interpolating between minimum and maximum via arithmetic mean and harmonic mean.


so while these ad - hoc manufacturer - specific solutions were effective, they were not standardized, and there were no provisions for providing interoperability. this drew the attention of the vesa consortium and resulted in a proposal for a voluntary and royalty - free local bus standard in 1992. an additional benefit from this standardization ( beyond the primary goal of greater graphics card performance ) was that other devices could also be designed to utilize the performance offered from vlb ; notably, mass - storage controllers were offered for vlb, providing increased hard - disk performance. vlb bandwidth depended on the cpu's bus speed : it started at 100 mb / s for cpus with a 25 mhz bus, increased to 133 mb / s at 33 mhz and 160 mb / s at 40 mhz, and reached 200 mb / s at 50 mhz.


in regression analysis, it is also of interest to characterize the variation of the dependent variable around the regression function which can be described by a probability distribution. many techniques for carrying out regression analysis have been developed. familiar methods, such as linear regression, are parametric, in that the regression function is defined in terms of a finite number of unknown parameters that are estimated from the data ( e. g. using ordinary least squares ). nonparametric regression refers to techniques that allow the regression function to lie in a specified set of functions, which may be infinite - dimensional.


then let f : x × y → r ∪ { + ∞ } { \ displaystyle f : x \ times y \ to \ mathbb { r } \ cup \ { + \ infty \ } } be a perturbation function such that f ( x, 0 ) = f ( x ) { \ displaystyle f ( x, 0 ) = f ( x ) }. the duality gap is the difference given by inf x ∈ x − sup y ∗ ∈ y ∗ { \ displaystyle \ inf _ { x \ in x } - \ sup _ { y ^ { * } \ in y ^ { * } } } where f ∗ { \ displaystyle f ^ { * } } is the convex conjugate in both variables. in computational optimization, another " duality gap " is often reported, which is the difference in value between any dual solution and the value of a feasible but suboptimal iterate for the primal problem. this alternative " duality gap " quantifies the discrepancy between the value of a current feasible but suboptimal iterate for the primal problem and the value of the dual problem ; the value of the dual problem is, under regularity conditions, equal to the value of the convex relaxation of the primal problem : the convex relaxation is the problem arising replacing a non - convex feasible set with its closed convex hull and with replacing a non - convex function with its convex closure, that is the function that has the epigraph that is the closed convex hull of the original primal objective function. = = references = =


α = sup h ∈ h 0 p ( test rejects h 0 h ). { \ displaystyle \ alpha = \ sup _ { h \ in h _ { 0 } } p ( { \ text { test rejects } } h _ { 0 } \ mid h ). } a test is said to have significance level α { \ displaystyle \ alpha } if its size is less than or equal to α { \ displaystyle \ alpha }. in many cases the size and level of a test are equal. = = references = =


code elements 4 and 5 are transmitted by keys 4 and 5, and these are operated by the first two fingers of the left hand. " baudot's code became known as the international telegraph alphabet no. 1 ( ita1 ). it is no longer used.


in numerical linear algebra, the cuthill – mckee algorithm ( cm ), named after elizabeth cuthill and james mckee, is an algorithm to permute a sparse matrix that has a symmetric sparsity pattern into a band matrix form with a small bandwidth. the reverse cuthill – mckee algorithm ( rcm ) due to alan george and joseph liu is the same algorithm but with the resulting index numbers reversed. in practice this generally results in less fill - in than the cm ordering when gaussian elimination is applied. the cuthill mckee algorithm is a variant of the standard breadth - first search algorithm used in graph algorithms.


in recursive implementations of d & c algorithms, one must make sure that there is sufficient memory allocated for the recursion stack, otherwise, the execution may fail because of stack overflow. d & c algorithms that are time - efficient often have relatively small recursion depth. for example, the quicksort algorithm can be implemented so that it never requires more than log 2 n { \ displaystyle \ log _ { 2 } n } nested recursive calls to sort n { \ displaystyle n } items.


in the fair cake - cutting problem, the partners often have different entitlements. for example, the resource may belong to two shareholders such that alice holds 8 / 13 and george holds 5 / 13. this leads to the criterion of weighted proportionality ( wpr ) : there are several weights w i { \ displaystyle w _ { i } } that sum up to 1, and every partner i { \ displaystyle i } should receive at least a fraction w i { \ displaystyle w _ { i } } of the resource by their own valuation. in contrast, in the simpler proportional cake - cutting setting, the weights are equal : w i = 1 / n { \ displaystyle w _ { i } = 1 / n } for all i { \ displaystyle i } several algorithms can be used to find a wpr division.


using the load balancer, user can create systems that are responsive to user actions. apps in the cloud are run independently of each other. this allows multiple versions support of the same app and " soft migration " set up for moving users to updated versions of products. apps can be tested in the cloud by in an isolated environment run. this way, program errors will not affect the physical system or other apps.


a common case of the aba problem is encountered when implementing a lock - free data structure. if an item is removed from the list, deleted, and then a new item is allocated and added to the list, it is common for the allocated object to be at the same location as the deleted object due to mru memory allocation. a pointer to the new item is thus often equal to a pointer to the old item, causing an aba problem.


with the advent of multicore architectures, network processors can be used for higher layer ( l4 - l7 ) processing. additionally, traffic management, which is a critical element in l2 - l3 network processing and used to be executed by a variety of co - processors, has become an integral part of the network processor architecture, and a substantial part of its silicon area ( " real estate " ) is devoted to the integrated traffic manager. modern network processors are also equipped with low - latency high - throughput on - chip interconnection networks optimized for the exchange of small messages among cores ( few data words ). such networks can be used as an alternative facility for the efficient inter - core communication aside of the standard use of shared memory.


advances in lte and other technologies are rapidly improving the ability to transfer information over a wireless link at various combinations of speeds, distances, and non - line - of - sight conditions. " mobile service provisions " refers in part to the ability of subscribers to purchase mobile phone like services, as is often seen in co - marketing efforts between providers of landline services. it also reflects the ambition to gain wireless access on the go to voice, internet, and content / video without tethering to a network via cables.


in the " reserves first " model of money creation, a given reserve is lent out by a bank, then deposited at a bank ( possibly different ), which is then lent out again, the process repeating and the ultimate result being a geometric series.


in the 19th century, philologists devised a now classic classification of languages according to their morphology. some languages are isolating, and have little to no morphology ; others are agglutinative whose words tend to have many easily separable morphemes ( such as turkic languages ) ; others yet are inflectional or fusional because their inflectional morphemes are " fused " together ( like some indo - european languages such as pashto and russian ). that leads to one bound morpheme conveying multiple pieces of information. a standard example of an isolating language is chinese.


in mathematics — specifically, in probability theory — the concentration dimension of a banach space - valued random variable is a numerical measure of how " spread out " the random variable is compared to the norm on the space.


in the field of wi - fi ( wireless local area networks using the ieee 802. 11b and 802. 11g specification ), the term beacon signifies a specific data transmission from the wireless access point ( ap ), which carries the ssid, the channel number and security protocols such as wired equivalent privacy ( wep ) or wi - fi protected access ( wpa ). this transmission does not contain the link layer address of another wi - fi device, therefore it can be received by any lan client.


in statistics and information geometry, statistical distances measure the degree of difference between two probability distributions. there are many kinds of statistical distances, typically formalized as divergences ; these allow a set of probability distributions to be understood as a geometrical object called a statistical manifold. the most elementary is the squared euclidean distance, which is minimized by the least squares method ; this is the most basic bregman divergence. the most important in information theory is the relative entropy ( kullback – leibler divergence ), which allows one to analogously study maximum likelihood estimation geometrically ; this is an example of both an f - divergence and a bregman divergence ( and in fact the only example which is both ). statistical manifolds corresponding to bregman divergences are flat manifolds in the corresponding geometry, allowing an analog of the pythagorean theorem ( which holds for squared euclidean distance ) to be used for linear inverse problems in inference by optimization theory. other important statistical distances include the mahalanobis distance and the energy distance.


in proof theory, an area of mathematical logic, proof compression is the problem of algorithmically compressing formal proofs. the developed algorithms can be used to improve the proofs generated by automated theorem proving tools such as sat solvers, smt - solvers, first - order theorem provers and proof assistants.


these systems, however, gave a very poor sound quality. the first microphone that enabled proper voice telephony was the ( loose - contact ) carbon microphone.


in sound, smartphones and feature phones vary little. some audio - quality enhancing features, such as voice over lte and hd voice, have appeared and are often available on newer smartphones. sound quality can remain a problem due to the design of the phone, the quality of the cellular network and compression algorithms used in long - distance calls. audio quality can be improved using a voip application over wifi. cellphones have small speakers so that the user can use a speakerphone feature and talk to a person on the phone without holding it to their ear. the small speakers can also be used to listen to digital audio files of music or speech or watch videos with an audio component, without holding the phone close to the ear.


in mathematics, the van der corput inequality is a corollary of the cauchy – schwarz inequality that is useful in the study of correlations among vectors, and hence random variables. it is also useful in the study of equidistributed sequences, for example in the weyl equidistribution estimate. loosely stated, the van der corput inequality asserts that if a unit vector v { \ displaystyle v } in an inner product space v { \ displaystyle v } is strongly correlated with many unit vectors u 1, …, u n ∈ v { \ displaystyle u _ { 1 }, \ dots, u _ { n } \ in v }, then many of the pairs u i, u j { \ displaystyle u _ { i }, u _ { j } } must be strongly correlated with each other. here, the notion of correlation is made precise by the inner product of the space v { \ displaystyle v } : when the absolute value of ⟨ u, v ⟩ { \ displaystyle \ langle u, v \ rangle } is close to 1 { \ displaystyle 1 }, then u { \ displaystyle u } and v { \ displaystyle v } are considered to be strongly correlated. ( more generally, if the vectors involved are not unit vectors, then strong correlation means that | ⟨ u, v ⟩ | ≈ ‖ u ‖ ‖ v ‖ { \ displaystyle | \ langle u, v \ rangle | \ approx \ | u \ | \ | v \ | }. )


in practice, a large data set leads to a large k, and storing k may become a problem. one way to deal with this is to perform clustering on the dataset, and populate the kernel with the means of those clusters. since even this method may yield a relatively large k, it is common to compute only the top p eigenvalues and eigenvectors of the eigenvalues are calculated in this way.


in some models of phonology as well as morphophonology in the field of linguistics, the underlying representation ( ur ) or underlying form ( uf ) of a word or morpheme is the abstract form that a word or morpheme is postulated to have before any phonological rules have been applied to it. in contrast, a surface representation is the phonetic representation of the word or sound. the concept of an underlying representation is central to generative grammar. if more phonological rules apply to the same underlying form, they can apply wholly independently of each other or in a feeding or counterbleeding order. the underlying representation of a morpheme is considered to be invariable across related forms ( except in cases of suppletion ), despite alternations among various allophones on the surface.


+ 4! = 19. regardless of the parity of n, the last ( nth ) summand, n!, is given a positive sign, the ( n – 1 ) th summand is given a negative sign, and the signs of the lower - indexed summands are alternated accordingly.


compilers were updated to take advantage of these instructions. the benefits of semantically rich instructions with compact encodings can be seen in modern processors as well, particularly in the high - performance segment where caches are a central component ( as opposed to most embedded systems ). this is because these fast, but complex and expensive, memories are inherently limited in size, making compact code beneficial. of course, the fundamental reason they are needed is that main memories ( i. e., dynamic ram today ) remain slow compared to a ( high - performance ) cpu core.


{ \ displaystyle fg = \ lambda ( f, g ) + \ lambda ( g, f ). } for any appropriate functions f { \ displaystyle f } and h { \ displaystyle h } with h ( 0 ) = 0 { \ displaystyle h ( 0 ) = 0 }, it is the case that h ( f ) = λ ( f, h ′ ( f ) ) { \ displaystyle h ( f ) = \ lambda ( f, h'( f ) ) }. it should satisfy some form of the leibniz rule. a paraproduct may also be required to satisfy some form of holder's inequality.


in telecommunications, radio silence or emissions control ( emcon ) is a status in which all fixed or mobile radio stations in an area are asked to stop transmitting for safety or security reasons. the term " radio station " may include anything capable of transmitting a radio signal. a single ship, aircraft, spacecraft, or group of them may also maintain radio silence.


our modified model requires us to add two more instructions to the 7 post – turing instructions. the abbreviations that we will use are : in the cases of r, l, e, p0, and p1 after doing its task the machine continues on to the next instruction in numerical sequence ; ditto for the jumps if their tests fail. but, for brevity, our examples will only use three squares.


in more technical terms, let us assume that we have a theory described by a certain function z { \ displaystyle z } of the state variables { s i } { \ displaystyle \ { s _ { i } \ } } and a certain set of coupling constants { j k } { \ displaystyle \ { j _ { k } \ } }. this function may be a partition function, an action, a hamiltonian, etc. it must contain the whole description of the physics of the system. now we consider a certain blocking transformation of the state variables { s i } → { s ~ i } { \ displaystyle \ { s _ { i } \ } \ to \ { { \ tilde { s } } _ { i } \ } }, the number of s ~ i { \ displaystyle { \ tilde { s } } _ { i } } must be lower than the number of s i { \ displaystyle s _ { i } }. now let us try to rewrite the z { \ displaystyle z } function only in terms of the s ~ i { \ displaystyle { \ tilde { s } } _ { i } }.