in this sense a feature structure is a list of key - value pairs. the value might be atomic or another feature structure. this leads to another notation for feature structures : the use of trees. in fact, some systems ( such as patr - ii ) use s - expressions to represent feature structures.


using the fee, it is possible to prove the following theorem : theorem : let y = f ( x ) { \ displaystyle y = f ( x ) } be an elementary transcendental function, that is the exponential function, or a trigonometric function, or an elementary algebraic function, or their superposition, or their inverse, or a superposition of the inverses. then s f ( n ) = o ( m ( n ) log 2 n ). { \ displaystyle s _ { f } ( n ) = o ( m ( n ) \ log ^ { 2 } n ). \, } here s f ( n ) { \ displaystyle s _ { f } ( n ) } is the complexity of computation ( bit ) of the function f ( x ) { \ displaystyle f ( x ) } with accuracy up to n { \ displaystyle n } digits, m ( n ) { \ displaystyle m ( n ) } is the complexity of multiplication of two n { \ displaystyle n } - digit integers.


in the java computer programming language, an annotation is a form of syntactic metadata that can be added to java source code. classes, methods, variables, parameters and java packages may be annotated. like javadoc tags, java annotations can be read from source files.


in software testing, error guessing is a test method in which test cases used to find bugs in programs are established based on experience in prior testing. the scope of test cases usually rely on the software tester involved, who uses past experience and intuition to determine what situations commonly cause software failure, or may cause errors to appear. typical errors include divide by zero, null pointers, or invalid parameters. error guessing has no explicit rules for testing ; test cases can be designed depending on the situation, either drawing from functional documents or when an unexpected / undocumented error is found while testing operations.


in native vocabulary, the fricatives and are allophones of a single phoneme / θ /. is used morpheme - initially, as in þak ('roof'), and before a voiceless consonant, as in maðkur ('worm'). is used intervocalically, as in iða ('vortex') and word - finally, as in bað ('bath'), although it is devoiced to before pause. some loanwords ( mostly from classical greek ) have introduced the phone in intervocalic environments, as in aþena ('athens'). the phone is actually a laminal voiceless alveolar non - sibilant fricative. the corresponding voiced phone is similar, but is apical rather than laminal ( ladefoged & maddieson 1996 ).


they were mode 5 stone tools, or microliths. he mentions neither westropp nor the mesolithic, however.


this reduces the complexity to o ( p2 log p log log p ) or o ( p2 ). an even more efficient multiplication algorithm, furer's algorithm, only needs p log p 2 o ( log ∗ p ) { \ displaystyle p \ log p \ 2 ^ { o ( \ log ^ { * } p ) } } time to multiply two p - bit numbers. by comparison, the most efficient randomized primality test for general integers, the miller – rabin primality test, requires o ( k n2 log n log log n ) bit operations using fft multiplication for an n - digit number, where k is the number of iterations and is related to the error rate.


in probability theory and statistics, the term markov property refers to the memoryless property of a stochastic process, which means that its future evolution is independent of its history. it is named after the russian mathematician andrey markov. the term strong markov property is similar to the markov property, except that the meaning of " present " is defined in terms of a random variable known as a stopping time. the term markov assumption is used to describe a model where the markov property is assumed to hold, such as a hidden markov model.


in the second place, the functional notion of nominal group differs from the formal notion of noun phrase because the first is anchored on the thing being described whereas the second is anchored on word classes. for that reason, one can analyse the nominal groups some friends and a couple of friends very similarly in terms of function : a thing / entity quantified in an imprecise fashion ; whereas one must recognise some friends as being a simple noun phrase and a couple of friends as being a noun phrase embedded in another noun phrase ( one noun phrase per noun ). in short, these notions are different even if formalists do not perceive them as different.


: 255 r. m. w. dixon has defined four criteria for determining whether a construction is a passive : it applies to underlying transitive clauses and forms a derived intransitive. the entity that is the patient or the object of the transitive verb in the underlying representation ( indicated as o in linguistic terminology ) becomes the core argument of the clause ( indicated as s, since the core argument is the subject of an intransitive ). the agent in the underlying representation ( indicated as a ) becomes a chomeur, a noun in the periphery that is not a core argument. it is marked by a non - core case or becomes part of an adpositional phrase, etc. this can be omitted, but there is always the option of including it. there is some explicit marking of the construction. dixon acknowledges that this excludes some constructions labeled as passive by some linguists.


in solving an underdetermined system of linear equations, the regularization term for the parameter vector is expressed in terms of the ℓ 1 { \ displaystyle \ ell _ { 1 } } norm ( taxicab geometry ) of the vector. this approach appears in the signal recovery framework called compressed sensing.


access to information is only possible if patients have given their prior consent. patients can view their medical records online ( authentication takes place via eid ) and allow access to the care providers. critics in the netherlands see the risk of abuse and invasion of privacy in the event of burglary of the system by crackers. in that case, very sensitive medical information can be exposed. such information is highly sensitive to privacy and can cause major harm to victims.


but most of the knowledge on this topic is not older than circa 1965 and the first computer algebra systems : when the long - known finite step algorithms were first put on computers, they turned out to be highly inefficient. the fact that almost any uni - or multivariate polynomial of degree up to 100 and with coefficients of a moderate size ( up to 100 bits ) can be factored by modern algorithms in a few minutes of computer time indicates how successfully this problem has been attacked during the past fifteen years. ( erich kaltofen, 1982 ) nowadays, modern algorithms and computers can quickly factor univariate polynomials of degree more than 1000 having coefficients with thousands of digits. for this purpose, even for factoring over the rational numbers and number fields, a fundamental step is a factorization of a polynomial over a finite field.


since function maximization subject to equality constraints is most conveniently done using a lagrangean expression of the problem, the score test can be equivalently understood as a test of the magnitude of the lagrange multipliers associated with the constraints where, again, if the constraints are non - binding at the maximum likelihood, the vector of lagrange multipliers should not differ from zero by more than sampling error. the equivalence of these two approaches was first shown by s. d. silvey in 1959, which led to the name lagrange multiplier test that has become more commonly used, particularly in econometrics, since breusch and pagan's much - cited 1980 paper. the main advantage of the score test over the wald test and likelihood - ratio test is that the score test only requires the computation of the restricted estimator. this makes testing feasible when the unconstrained maximum likelihood estimate is a boundary point in the parameter space. further, because the score test only requires the estimation of the likelihood function under the null hypothesis, it is less specific than the likelihood ratio test about the alternative hypothesis.


in statistics, a standard normal table, also called the unit normal table or z table, is a mathematical table for the values of φ, the cumulative distribution function of the normal distribution. it is used to find the probability that a statistic is observed below, above, or between values on the standard normal distribution, and by extension, any normal distribution. since probability tables cannot be printed for every normal distribution, as there are an infinite variety of normal distributions, it is common practice to convert a normal to a standard normal ( known as a z - score ) and then use the standard normal table to find probabilities.


in mathematics, the common logarithm is the logarithm with base 10. it is also known as the decadic logarithm and as the decimal logarithm, named after its base, or briggsian logarithm, after henry briggs, an english mathematician who pioneered its use, as well as standard logarithm. historically, it was known as logarithmus decimalis or logarithmus decadis. it is indicated by log ( x ), log10 ( x ), or sometimes log ( x ) with a capital l ( however, this notation is ambiguous, since it can also mean the complex natural logarithmic multi - valued function ).


assuming there is a trunk, merges from branches can be considered as " external " to the tree – the changes in the branch are packaged up as a patch, which is applied to head ( of the trunk ), creating a new revision without any explicit reference to the branch, and preserving the tree structure. thus, while the actual relations between versions form a dag, this can be considered a tree plus merges, and the trunk itself is a line. in distributed revision control, in the presence of multiple repositories these may be based on a single original version ( a root of the tree ), but there need not be an original root, and thus only a separate root ( oldest revision ) for each repository, for example, if two people starting working on a project separately. similarly in the presence of multiple data sets ( multiple projects ) that exchange data or merge, there is not a single root, though for simplicity one may think of one project as primary and the other as secondary, merged into the first with or without its own revision history.


in the axiomatic foundation for probability provided by measure theory, the expectation is given by lebesgue integration. the expected value of a random variable x is often denoted by e ( x ), e, or ex, with e also often stylized as e or e. { \ displaystyle \ mathbb { e }. }


patent us3541543 ) referred to as the " binary decoder ". this was the first time a read only memory had been made using mos transistors. by the late 1970s, mos rom devices had become the most common example of nonvolatile memory used to provide the storage of fixed programs in digital equipment such as calculators and microprocessor systems.


the exchange of messages may be carried out asynchronously, or may use a synchronous " rendezvous " style in which the sender blocks until the message is received. asynchronous message passing may be reliable or unreliable ( sometimes referred to as " send and pray " ). message - passing concurrency tends to be far easier to reason about than shared - memory concurrency, and is typically considered a more robust form of concurrent programming.


in statistics, the kth order statistic of a statistical sample is equal to its kth - smallest value. together with rank statistics, order statistics are among the most fundamental tools in non - parametric statistics and inference. important special cases of the order statistics are the minimum and maximum value of a sample, and ( with some qualifications discussed below ) the sample median and other sample quantiles. when using probability theory to analyze order statistics of random samples from a continuous distribution, the cumulative distribution function is used to reduce the analysis to the case of order statistics of the uniform distribution.


in signal processing, the fast folding algorithm ( staelin, 1969 ) is an efficient algorithm for the detection of approximately - periodic events within time series data. it computes superpositions of the signal modulo various window sizes simultaneously. the ffa is best known for its use in the detection of pulsars, as popularised by seti @ home and astropulse. it was also used by the breakthrough listen initiative during their 2023 investigation for periodic spectral signals campaign.


in class - based object - oriented programming, abstract types are implemented as abstract classes ( also known as abstract base classes ), and concrete types as concrete classes. in generic programming, the analogous notion is a concept, which similarly specifies syntax and semantics, but does not require a subtype relationship : two unrelated types may satisfy the same concept. often, abstract types will have one or more implementations provided separately, for example, in the form of concrete subtypes that can be instantiated. in object - oriented programming, an abstract class may include abstract methods or abstract properties that are shared by its subclasses. other names for language features that are ( or may be ) used to implement abstract types include traits, mixins, flavors, roles, or type classes.


pointed maps are the homomorphisms of these algebraic structures. the class of all pointed sets together with the class of all based maps form a category. in this category the pointed singleton sets ( { a }, a ) { \ displaystyle ( \ { a \ }, a ) } are initial objects and terminal objects, i. e. they are zero objects.


in the case of a scalar parameter, there are four principal types of alternative hypothesis : point. point alternative hypotheses occur when the hypothesis test is framed so that the population distribution under the alternative hypothesis is a fully defined distribution, with no unknown parameters ; such hypotheses are usually of no practical interest but are fundamental to theoretical considerations of statistical inference and are the basis of the neyman – pearson lemma. one - tailed directional. a one - tailed directional alternative hypothesis is concerned with the region of rejection for only one tail of the sampling distribution.


in statistics, the term " error " arises in two ways. firstly, it arises in the context of decision making, where the probability of error may be considered as being the probability of making a wrong decision and which would have a different value for each type of error. secondly, it arises in the context of statistical modelling ( for example regression ) where the model's predicted value may be in error regarding the observed outcome and where the term probability of error may refer to the probabilities of various amounts of error occurring.


the initial population is in this case randomly generated ( or created with a greedy algorithm ), and then enhanced through an iterative process. at each generation of the process, the whole population ( or a part of it ) is replaced by newly generated individuals ( often the best ones ). these techniques are called exploration - oriented methods, since their main ability resides in the diversification in the search space.


in response, kris mcdaniel has argued the weyl tile argument depends on accepting a " size thesis " which posits that the distance between two points is given by the number of tiles between the two points. however, as mcdaniel points out, the size thesis is not accepted for continuous spaces. thus, we might have reason not to accept the size thesis for discrete spaces.


for example, the result that the intersection of two subsemigroups of a semigroup t is a subsemigroup of t becomes valid even when the intersection is empty. when a semigroup is defined to have additional structure, the issue may not arise. for example, the definition of a monoid requires an identity element, which rules out the empty semigroup as a monoid.


.. a 1 b m, a 2 b 1,.


a property that is invariant under such deformations is a topological property. the following are basic examples of topological properties : the dimension, which allows distinguishing between a line and a surface ; compactness, which allows distinguishing between a line and a circle ; connectedness, which allows distinguishing a circle from two non - intersecting circles.


in statistics, d'agostino's k2 test, named for ralph d'agostino, is a goodness - of - fit measure of departure from normality, that is the test aims to gauge the compatibility of given data with the null hypothesis that the data is a realization of independent, identically distributed gaussian random variables. the test is based on transformations of the sample kurtosis and skewness, and has power only against the alternatives that the distribution is skewed and / or kurtic.


in number theory, berlekamp's root finding algorithm, also called the berlekamp – rabin algorithm, is the probabilistic method of finding roots of polynomials over a field z p { \ displaystyle \ mathbb { z } _ { p } }. the method was discovered by elwyn berlekamp in 1970 as an auxiliary to the algorithm for polynomial factorization over finite fields. the algorithm was later modified by rabin for arbitrary finite fields in 1979. the method was also independently discovered before berlekamp by other researchers.


page tables make it easier to allocate additional memory, as each new page can be allocated from anywhere in physical memory. on some systems a page table entry can also designate a page as read - only. some operating systems set up a different address space for each process, which provides hard memory protection boundaries.


in mathematics, more specifically point - set topology, a moore space is a developable regular hausdorff space. that is, a topological space x is a moore space if the following conditions hold : any two distinct points can be separated by neighbourhoods, and any closed set and any point in its complement can be separated by neighbourhoods. ( x is a regular hausdorff space. ) there is a countable collection of open covers of x, such that for any closed set c and any point p in its complement there exists a cover in the collection such that every neighbourhood of p in the cover is disjoint from c.


in the context of computability theory, a cost function is a computable function c : n × n → q ≥ 0. { \ displaystyle c : \ mathbb { n } \ times \ mathbb { n } \ to \ mathbb { q } ^ { \ geq 0 }. } for a computable approximation ⟨ a s ⟩ { \ displaystyle \ langle a _ { s } \ rangle } of δ 2 0 { \ displaystyle \ delta _ { 2 } ^ { 0 } } set a, such a function measures the cost c ( n, s ) of changing the approximation to a ( n ) at stage s. the first cost function construction was due to kucera and terwijn. they built a computably enumerable set that is low for martin - lof - randomness but not computable.


recall that the elementary discussion on maxima or minima for real - valued functions implies that if f { \ displaystyle f } is continuous on { \ displaystyle } and differentiable on ( a, b ) { \ displaystyle ( a, b ) }, then there is a point c { \ displaystyle c } in ( a, b ) { \ displaystyle ( a, b ) } such that f ( b ) − f ( a ) b − a = f ′ ( c ). { \ displaystyle { f ( b ) - f ( a ) \ over b - a } = f ^ { \ prime } ( c ). } for vector - valued functions with v { \ displaystyle v } a finite - dimensional normed space, there is no analogue of the equality above, indeed it fails.


in statistics, the term linear model is used in different ways according to the context. the most common occurrence is in connection with regression models and the term is often taken as synonymous with linear regression model. however, the term is also used in time series analysis with a different meaning. in each case, the designation " linear " is used to identify a subclass of models for which substantial reduction in the complexity of the related statistical theory is possible.


when storing and manipulating sparse matrices on a computer, it is beneficial and often necessary to use specialized algorithms and data structures that take advantage of the sparse structure of the matrix. specialized computers have been made for sparse matrices, as they are common in the machine learning field. operations using standard dense - matrix structures and algorithms are slow and inefficient when applied to large sparse matrices as processing and memory are wasted on the zeros. sparse data is by nature more easily compressed and thus requires significantly less storage. some very large sparse matrices are infeasible to manipulate using standard dense - matrix algorithms.


but by the mid - 1980s, the concepts had matured enough to be seen as commercially viable. commercial risc designs began to emerge in the mid - 1980s. the first mips r2000 appeared in january 1986, followed shortly thereafter by hewlett - packard's pa - risc in some of their computers. in the meantime, the berkeley effort had become so well known that it eventually became the name for the entire concept.


the function does not return a value and has to be called as a stand - alone function, e. g., function1 this function returns a result ( the number 5 ), and the call can be part of an expression, e. g., x + function2 ( ) this function converts a number between 0 and 6 into the initial letter of the corresponding day of the week, namely 0 to'm ', 1 to't ',..., 6 to's '. the result of calling it might be assigned to a variable, e. g., num _ day = function3 ( number ). this function does not return a value but modifies the variable whose address is passed as the parameter ; it would be called with " function4 ( variable _ to _ increment ) ".


order is particularly important in the theories of composition techniques originating in the 20th century such as the twelve - tone technique and serialism. analytical techniques such as set theory take care to distinguish between ordered and unordered collections. in traditional theory concepts like voicing and form include ordering ; for example, many musical forms, such as rondo, are defined by the order of their sections.


an object of ( s ↓ t ) { \ displaystyle ( s \ downarrow t ) } is called a morphism from s { \ displaystyle s } to t { \ displaystyle t } or a t { \ displaystyle t } - structured arrow with domain s { \ displaystyle s }. an object of ( s ↓ t ) { \ displaystyle ( s \ downarrow t ) } is called a morphism from s { \ displaystyle s } to t { \ displaystyle t } or a s { \ displaystyle s } - costructured arrow with codomain t { \ displaystyle t }. another special case occurs when both s { \ displaystyle s } and t { \ displaystyle t } are functors with domain 1 { \ displaystyle { \ textbf { 1 } } }. if s ( ∗ ) = a { \ displaystyle s ( * ) = a } and t ( ∗ ) = b { \ displaystyle t ( * ) = b }, then the comma category ( s ↓ t ) { \ displaystyle ( s \ downarrow t ) }, written ( a ↓ b ) { \ displaystyle ( a \ downarrow b ) }, is the discrete category whose objects are morphisms from a { \ displaystyle a } to b { \ displaystyle b }. an inserter category is a ( non - full ) subcategory of the comma category where a = b { \ displaystyle { \ mathcal { a } } = { \ mathcal { b } } } and f = g { \ displaystyle f = g } are required. the comma category can also be seen as the inserter of s ∘ π 1 { \ displaystyle s \ circ \ pi _ { 1 } } and t ∘ π 2 { \ displaystyle t \ circ \ pi _ { 2 } }, where π 1 { \ displaystyle \ pi _ { 1 } } and π 2 { \ displaystyle \ pi _ { 2 } } are the two projection functors out of the product category a × b { \ displaystyle { \ mathcal { a } } \ times { \ mathcal { b } } }.


in quantum information science, a classical information channel ( often called simply classical channel ) is a communication channel that can be used to transmit classical information ( as opposed to quantum channel which can transmit quantum information ). an example would be a light travelling over fiber optics lines or electricity travelling over phone lines. although classical channels cannot transmit quantum information by themselves, they can be useful in combination with quantum channels.


in mathematics, convex metric spaces are, intuitively, metric spaces with the property any " segment " joining two points in that space has other points in it besides the endpoints. formally, consider a metric space ( x, d ) and let x and y be two points in x. a point z in x is said to be between x and y if all three points are distinct, and d ( x, z ) + d ( z, y ) = d ( x, y ), { \ displaystyle d ( x, z ) + d ( z, y ) = d ( x, y ), \, } that is, the triangle inequality becomes an equality. a convex metric space is a metric space ( x, d ) such that, for any two distinct points x and y in x, there exists a third point z in x lying between x and y. metric convexity : does not imply convexity in the usual sense for subsets of euclidean space ( see the example of the rational numbers ) nor does it imply path - connectedness ( see the example of the rational numbers ) nor does it imply geodesic convexity for riemannian manifolds ( consider, for example, the euclidean plane with a closed disc removed ).


in mathematics, a basic algebraic operation is any one of the common operations of arithmetic, which include addition, subtraction, multiplication, division, raising to a whole number power, and taking roots ( fractional power ). these operations may be performed on numbers, in which case they are often called arithmetic operations. they may also be performed, in a similar way, on variables, algebraic expressions, and more generally, on elements of algebraic structures, such as groups and fields.


in most developed nations, all new developments are assessed for flood risks. the aim is to ensure flood risk is taken into account in all stages of the planning process to avoid inappropriate development in areas of high risk. when development is required in areas of high risk, structures should be built to flood - resistant standards and living or working areas should be raised well above the worst - case scenario flood levels. for existing structures in high - risk areas, funding should be allocated to i. e. raise the electrical wiring / sockets so any water that enters the home can not reach the electrics.


in mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain.


here the indices λ and μ are integer partitions and kλμ ( q, t ) is polynomial in the variables q and t. sometimes one considers single - variable versions of these polynomials that arise by setting q = 0, i. e., by considering the polynomial kλμ ( t ) = kλμ ( 0, t ). there are two slightly different versions of them, one called transformed kostka polynomials. the one - variable specializations of the kostka polynomials can be used to relate hall - littlewood polynomials pμ to schur polynomials sλ : s λ ( x 1, …, x n ) = μ k λ μ ( t ) p μ ( x 1, …, x n ; t ). { \ displaystyle s _ { \ lambda } ( x _ { 1 }, \ ldots, x _ { n } ) = \ sum _ { \ mu } k _ { \ lambda \ mu } ( t ) p _ { \ mu } ( x _ { 1 }, \ ldots, x _ { n } ; t ). \ } these polynomials were conjectured to have non - negative integer coefficients by foulkes, and this was later proved in 1978 by alain lascoux and marcel - paul schutzenberger.


if the column after determines exactly one case, this case is given as the subsequent one, otherwise there are question marks. the loop is contained in the sections from start _ d through " delete case d2 ", where the problem of rebalancing is escalated δ h = 1 { \ displaystyle \ delta h = 1 } level higher in the tree in that the parent p becomes the new current node n. so it takes maximally h { \ displaystyle h } iterations to repair the tree ( where h { \ displaystyle h } is the height of the tree ). because the probability of escalation decreases exponentially with each iteration the total rebalancing cost is constant on average, indeed amortized constant.


in order to solve the equation ln ( x ) = y { \ displaystyle \ ln ( x ) = y } the bkm algorithm takes advantage of a basic property of logarithms ln ( a b ) = ln ( a ) + ln ( b ) { \ displaystyle \ ln ( ab ) = \ ln ( a ) + \ ln ( b ) } using pi notation, this identity generalizes to ln ( k = 0 n a k ) = k = 0 n ln ( a k ) { \ displaystyle \ ln \ left ( \ prod _ { k = 0 } ^ { n } a _ { k } \ right ) = \ sum _ { k = 0 } ^ { n } \ ln ( a _ { k } ) } because any number can be represented by a product, this allows us to choose any set of values a k { \ displaystyle a _ { k } } which multiply to give the value we started with. in computer systems, it's much faster to multiply and divide by multiples of 2, but because not every number is a multiple of 2, using a k = 1 + 2 m { \ displaystyle a _ { k } = 1 + 2 ^ { m } } is a better option than a more simple choice of a k = 2 m { \ displaystyle a _ { k } = 2 ^ { m } }. since we want to start with large changes and get more accurate as k { \ displaystyle k } increases, we can more specifically use a k = 1 + 2 − k { \ displaystyle a _ { k } = 1 + 2 ^ { - k } }, allowing the product to approach any value between 1 and ~ 4. 768, depending on which subset of a k { \ displaystyle a _ { k } } we use in the final product.


in mathematics, especially in linear algebra and matrix theory, the vectorization of a matrix is a linear transformation which converts the matrix into a vector. specifically, the vectorization of a m × n matrix a, denoted vec ( a ), is the mn × 1 column vector obtained by stacking the columns of the matrix a on top of one another : here, a i, j { \ displaystyle a _ { i, j } } represents the element in the i - th row and j - th column of a, and the superscript t { \ displaystyle { } ^ { \ mathrm { t } } } denotes the transpose. vectorization expresses, through coordinates, the isomorphism r m × n : = r m ⊗ r n r m n { \ displaystyle \ mathbf { r } ^ { m \ times n } : = \ mathbf { r } ^ { m } \ otimes \ mathbf { r } ^ { n } \ cong \ mathbf { r } ^ { mn } } between these ( i. e., of matrices and vectors ) as vector spaces. for example, for the 2×2 matrix a = { \ displaystyle a = { \ begin { bmatrix } a & b \ \ c & d \ end { bmatrix } } }, the vectorization is vec ( a ) = { \ displaystyle \ operatorname { vec } ( a ) = { \ begin { bmatrix } a \ \ c \ \ b \ \ d \ end { bmatrix } } }. the connection between the vectorization of a and the vectorization of its transpose is given by the commutation matrix.


when that user places a call, the calling line id would be that of a los angeles number, although they are actually located in new york. this allows a call return without having to incur long distance calling charges. with cellphones, the biggest issue appears to be in the passing of calling line id information through the network. cellphone companies must support interconnecting trunks to a significant number of wireline and pstn access carriers.


in the electronics industry, embedded instrumentation refers to the integration of test and measurement instrumentation into semiconductor chips ( or integrated circuit devices ). embedded instrumentation differs from embedded system, which are electronic systems or subsystems that usually comprise the control portion of a larger electronic system. instrumentation embedded into chips ( embedded instrumentation ) is employed in a variety of electronic test applications, including validating and testing chips themselves, validating, testing and debugging the circuit boards where these chips are deployed, and troubleshooting systems once they have been installed in the field. a working group of the ieee ( institute of electrical and electronics engineers ) that is developing a standard for accessing embedded instruments ( the ieee 1687 internal jtag standard ) defines embedded instrumentation as follows : any logic structure within a device whose purpose is design for test ( dft ), design - for - debug ( dfd ), design - for - yield ( dfy ), test... there exists the widespread use of embedded instrumentation ( such as bist ( built - in self - test ) engines, complex i / o characterization and calibration, embedded timing instrumentation, etc. ).


in the united kingdom information about an individual's hiv status is kept confidential within the national health service. this is based in law, in the nhs constitution, and in key nhs rules and procedures. it is also outlined in every nhs employee's contract of employment and in professional standards set by regulatory bodies. the national aids trust's confidentiality in the nhs : your information, your rights outlines these rights.


in most modern digital cable systems the signals are encrypted, so cases of people obtaining illegal service are less common. the subscriber requires a set - top box provided by the cable company to decrypt and receive the cable signal. unlike the older analog set - top boxes, the digital set - top box will not function until the cable company activates it by sending it a unique activation key through the cable, which is sent only after the subscriber signs up. each set - top box is individually addressable, so a given box can be deactivated by command from the company if the subscriber fails to pay their bill ( this is sometimes colloquially referred to as a " bullet " ).


here, λ { \ displaystyle \ lambda } denotes the likelihood ratio, and the χ 2 { \ displaystyle \ chi ^ { 2 } } distribution has degrees of freedom equal to the difference in dimensionality of θ { \ displaystyle \ theta } and θ 0 { \ displaystyle \ theta _ { 0 } }, where θ { \ displaystyle \ theta } is the full parameter space and θ 0 { \ displaystyle \ theta _ { 0 } } is the subset of the parameter space associated with h 0 { \ displaystyle h _ { 0 } }. this result means that for large samples and a great variety of hypotheses, a practitioner can compute the likelihood ratio λ { \ displaystyle \ lambda } for the data and compare − 2 log ( λ ) { \ displaystyle - 2 \ log ( \ lambda ) } to the χ 2 { \ displaystyle \ chi ^ { 2 } } value corresponding to a desired statistical significance as an approximate statistical test. the theorem no longer applies when the true value of the parameter is on the boundary of the parameter space : wilks ’ theorem assumes that the ‘ true ’ but unknown values of the estimated parameters lie within the interior of the supported parameter space.


in numerical optimization, meta - optimization is the use of one optimization method to tune another optimization method. meta - optimization is reported to have been used as early as in the late 1970s by mercer and sampson for finding optimal parameter settings of a genetic algorithm. meta - optimization and related concepts are also known in the literature as meta - evolution, super - optimization, automated parameter calibration, hyper - heuristics, etc.


{ \ displaystyle \ sum _ { x = 0 } ^ { \ infty } { \ frac { \ mu ^ { x } } { x! } } c _ { n } ( x ; \ mu ) c _ { m } ( x ; \ mu ) = \ mu ^ { - n } e ^ { \ mu } n! \ delta _ { nm }, \ quad \ mu > 0. } they form a sheffer sequence related to the poisson process, similar to how hermite polynomials relate to the brownian motion.


in most indicating instruments, the accuracy is guaranteed to a certain percentage of full - scale reading. the limits of these deviations from the specified values are known as limiting errors or guarantee errors.


in the field of evaluation, and in particular educational evaluation, the joint committee on standards for educational evaluation has published three sets of standards for evaluations. the personnel evaluation standards was published in 1988, the program evaluation standards ( 2nd edition ) was published in 1994, and the student evaluation standards was published in 2003. each publication presents and elaborates a set of standards for use in a variety of educational settings. the standards provide guidelines for designing, implementing, assessing and improving the identified form of evaluation.


examples of such notations are : 3 + 4 { \ displaystyle 3 + 4 } : refers to the process of adding as well as the outcome of the process. n = 0 ∞ ( a n ) { \ displaystyle \ sum _ { n = 0 } ^ { \ infty } ( a _ { n } ) } : refers to the process of summing an infinite sequence, and to the outcome of the process. f ( x ) = 3 x + 2 { \ displaystyle f ( x ) = 3x + 2 } : refers to the process of mapping x to 3x + 2 as well as the outcome of that process, the function f { \ displaystyle f }.


by setting pi = λn / n, we see that this generalizes the usual poisson limit theorem. when λ n { \ displaystyle \ lambda _ { n } } is large a better bound is possible : k = 0 ∞ | pr ( s n = k ) − λ n k e − λ n k! | < 2 ( 1 ∧ 1 λ n ) ( i = 1 n p i 2 ).


various physical systems, such as crystals and the hydrogen atom, may be modelled by symmetry groups. thus group theory and the closely related representation theory have many important applications in physics, chemistry, and materials science. group theory is also central to public key cryptography.


in mathematics, the logarithmic integral function or integral logarithm li ( x ) is a special function. it is relevant in problems of physics and has number theoretic significance. in particular, according to the prime number theorem, it is a very good approximation to the prime - counting function, which is defined as the number of prime numbers less than or equal to a given value x { \ displaystyle x }.


in modern cryptography, null encryption ( or selecting null cipher or none cipher ) is choosing not to use encryption in a system where various encryption options are offered. when this option is used, the text is the same before and after encryption, which can be practical for testing / debugging, or authentication - only communication. in mathematics such a function is known as the identity function. examples of this are the " enull " and " anull " cipher suite in openssl, and the " null encryption algorithm " in ipsec.


, g, g + 1, g + 2, …. { \ displaystyle 1,?,?, \ dots,?, g, g + 1, g + 2, \ dots. } what we know about the?


in mathematics, the littlewood conjecture is an open problem ( as of may 2021 ) in diophantine approximation, proposed by john edensor littlewood around 1930. it states that for any two real numbers α and β, lim inf n → ∞ n ‖ n α ‖ ‖ n β ‖ = 0, { \ displaystyle \ liminf _ { n \ to \ infty } \ n \, \ vert n \ alpha \ vert \, \ vert n \ beta \ vert = 0, } where ‖ x ‖ : = min ( | x − x |, | x − x | ) { \ displaystyle \ vert x \ vert : = \ min ( | x - \ lfloor x \ rfloor |, | x - \ lceil x \ rceil | ) } is the distance to the nearest integer.


in plane geometry, the square root of 7 can be constructed via a sequence of dynamic rectangles, that is, as the largest diagonal of those rectangles illustrated here. the minimal enclosing rectangle of an equilateral triangle of edge length 2 has a diagonal of the square root of 7. due to the pythagorean theorem and legendre's three - square theorem, 7 { \ displaystyle { \ sqrt { 7 } } } is the smallest square root of a natural number that cannot be the distance between any two points of a cubic integer lattice ( or equivalently, the length of the space diagonal of a rectangular cuboid with integer side lengths ). 15 { \ displaystyle { \ sqrt { 15 } } } is the next smallest such number.


in the following diophantine equations, w, x, y, and z are the unknowns and the other letters are given constants :


in photography, a negative is an image, usually on a strip or sheet of transparent plastic film, in which the lightest areas of the photographed subject appear darkest and the darkest areas appear lightest. this reversed order occurs because the extremely light - sensitive chemicals a camera film must use to capture an image quickly enough for ordinary picture - taking are darkened, rather than bleached, by exposure to light and subsequent photographic processing. in the case of color negatives, the colors are also reversed into their respective complementary colors. typical color negatives have an overall dull orange tint due to an automatic color - masking feature that ultimately results in improved color reproduction. negatives are normally used to make positive prints on photographic paper by projecting the negative onto the paper with a photographic enlarger or making a contact print.


in probability theory and statistics, the empirical probability, relative frequency, or experimental probability of an event is the ratio of the number of outcomes in which a specified event occurs to the total number of trials, i. e., by means not of a theoretical sample space but of an actual experiment. more generally, empirical probability estimates probabilities from experience and observation. given an event a in a sample space, the relative frequency of a is the ratio m n, { \ displaystyle { \ tfrac { m } { n } }, } m being the number of outcomes in which the event a occurs, and n being the total number of outcomes of the experiment. in statistical terms, the empirical probability is an estimator or estimate of a probability. in simple cases, where the result of a trial only determines whether or not the specified event has occurred, modelling using a binomial distribution might be appropriate and then the empirical estimate is the maximum likelihood estimate. it is the bayesian estimate for the same case if certain assumptions are made for the prior distribution of the probability. if a trial yields more information, the empirical probability can be improved on by adopting further assumptions in the form of a statistical model : if such a model is fitted, it can be used to derive an estimate of the probability of the specified event


in programming practice, " snippet " refers narrowly to a portion of source code that is literally included by an editor program into a file, and is a form of copy and paste programming. this concrete inclusion is in contrast to abstraction methods, such as functions or macros, which are abstraction within the language. snippets are thus primarily used when these abstractions are not available or not desired, such as in languages that lack abstraction, or for clarity and absence of overhead.


since the text cursor's next key ( viz., the n key ) retained directional positioning information ( whether the up or down key was formerly pressed ), the dot macro ( the. key ) could then be used to place the text cursor on the next brace, given a suitable coding style. instead, inspecting the block boundaries using the % key can be used to enforce a coding standard.


here students are asked various questions prior to class, the instructor uses these responses to adapt his or her teaching to the students'prior knowledge and misconceptions. finally, there is a more research - intensive approach that involves interviewing students for the purpose of generating the items that will make up a concept inventory or other forms of diagnostic instruments. concept inventories require intensive validation efforts.


in the following transcriptions, diacritics may be used to distinguish between apical and laminal.


conversely, the smaller the base, the fewer pandigital numbers without redundant digits there are. 2 is the only such pandigital number in base 2, while there are more of these in base 10. sometimes, the term is used to refer only to pandigital numbers with no redundant digits.


in mathematics, more specifically in ring theory, a euclidean domain ( also called a euclidean ring ) is an integral domain that can be endowed with a euclidean function which allows a suitable generalization of the euclidean division of integers. this generalized euclidean algorithm can be put to many of the same uses as euclid's original algorithm in the ring of integers : in any euclidean domain, one can apply the euclidean algorithm to compute the greatest common divisor of any two elements. in particular, the greatest common divisor of any two elements exists and can be written as a linear combination of them ( bezout's identity ). also every ideal in a euclidean domain is principal, which implies a suitable generalization of the fundamental theorem of arithmetic : every euclidean domain is a unique factorization domain.


in telecommunication, a telecommunications service is a service provided by a telecommunications provider, or a specified set of user - information transfer capabilities provided to a group of users by a telecommunications system. the telecommunications service user is responsible for the information content of the message. the telecommunications service provider has the responsibility for the acceptance, transmission, and delivery of the message. for purposes of regulation by the federal communications commission under the u. s. communications act of 1934 and telecommunications act of 1996, the definition of telecommunications service is " the offering of telecommunications for a fee directly to the public, or to such classes of users as to be effectively available directly to the public, regardless of the facilities used. " telecommunications, in turn, is defined as " the transmission, between or among points specified by the user, of information of the user ’ s choosing, without change in the form or content of the information as sent and received. "


in reconfigurable computing and in supercomputing these terms refer to the data path width. the use of about one - bit wide processing elements like the configurable logic blocks ( clbs ) in an fpga is called fine - grained computing or fine - grained reconfigurability, whereas using wide data paths, such as, for instance, 32 bits wide resources, like microprocessor cpus or data - stream - driven data path units ( dpus ) like in a reconfigurable datapath array ( rdpa ) is called coarse - grained computing or coarse - grained reconfigurability.


in phonology and historical linguistics, cluster reduction is the simplification of consonant clusters in certain environments or over time. cluster reduction can happen in different languages, dialects of those languages, in world englishes, and as a part of language acquisition.


normally, model building codes have a 3 – 5 year update cycle. that is, a new edition of the building code comes out every 3 to 5 years. however, due to the length of time that it takes for a jurisdiction to review and approve a new code, the currently enforced version of the local code is often not the most recent edition of the model building code on which the adopted code is based.


in number theory, the gaussian moat problem asks whether it is possible to find an infinite sequence of distinct gaussian prime numbers such that the difference between consecutive numbers in the sequence is bounded. more colorfully, if one imagines the gaussian primes to be stepping stones in a sea of complex numbers, the question is whether one can walk from the origin to infinity with steps of bounded size, without getting wet. the problem was first posed in 1962 by basil gordon ( although it has sometimes been erroneously attributed to paul erdos ) and it remains unsolved. with the usual prime numbers, such a sequence is impossible : the prime number theorem implies that there are arbitrarily large gaps in the sequence of prime numbers, and there is also an elementary direct proof : for any n, the n − 1 consecutive numbers n! + 2, n!


in simulations with electric fields the most important characteristics of a test particle is its electric charge and its mass. in this situation it is often referred to as a test charge. similar to the case of classical gravitation, the electric field created by a point charge q is defined by e = k q r 2 r ^ { \ displaystyle { \ textbf { e } } = k { \ frac { q } { r ^ { 2 } } } { \ hat { r } } }, where k is the coulomb constant. multiplying this field by a test charge q test { \ displaystyle q _ { \ textrm { test } } } gives an electric force ( coulomb's law ) exerted by the field on a test charge. note that both the force and the electric field are vector quantities, so a positive test charge will experience a force in the direction of the electric field.


if the data exhibit a trend, the regression model is likely incorrect ; for example, the true function may be a quadratic or higher order polynomial. if they are random, or have no trend, but " fan out " - they exhibit a phenomenon called heteroscedasticity.


nightly builds also ensure that the build tools have not broken due to system updates, and are therefore often run whether any source code has changed or not. in contrast, continuous integration environments automatically rebuild the project whenever changes are checked in – often several times a day – and provide more immediate feedback ; however, they do not necessarily include nightly builds. as a result, compiler and tool updates may break the ability to compile older projects easily without warning.


in the 1970s, the american national bureau of standards ( nbs ), which was later renamed to the national institute of standards and technology ( nist ), defined a set of convenient numbers when it was developing procedures for metrication in the united states. an nbs technical note describes that system of convenient metric values as the 1 - 2 - 5 series in reverse, with assigned preferences for those numbers which are multiples of 5, 2, and 1 ( plus their powers of 10 ). linear dimensions above 100 mm were excluded ( because such measurements are defined by another set of rules ). a table of this 5, 2, 1 series can be seen below in the section " schedule of convenient numbers between 10 and 100 ". the nbs technical note also states that " basically, integers are more convenient than expressions which include decimal parts.


from the remaining n − n1 − n2 items choose n3 to label 3. again, this can be done ( n − n 1 − n 2 n 3 ) { \ displaystyle { \ tbinom { n - n _ { 1 } - n _ { 2 } } { n _ { 3 } } } } ways. multiplying the number of choices at each step results in : ( n n 1 ) ( n − n 1 n 2 ) ( n − n 1 − n 2 n 3 ) = n! ( n − n 1 )!


in mathematics, in the area of additive number theory, the erdos – fuchs theorem is a statement about the number of ways that numbers can be represented as a sum of elements of a given additive basis, stating that the average order of this number cannot be too close to being a linear function. the theorem is named after paul erdos and wolfgang heinrich johannes fuchs, who published it in 1956.


for some characters, like / ( u + 514c / u + 5151 ), either method can be used to display the different glyphs. in the following table, each row compares variants that have been assigned different code points.


the question arises what precisely a " class " is or should be. for dedekind and frege, a class is a distinct entity in its own right, a'unity'that can be identified with all those entities x that satisfy some propositional function f. ( this symbolism appears in russell, attributed there to frege : " the essence of a function is what is left when the x is taken away, i. e in the above instance, 2 ( ) 3 + ( ).


in the united states, most forms of censorship are self - imposed rather than enforced by the government. the government does not routinely censor material, although state and local governments often restrict what is provided in libraries and public schools. in addition, distribution, receipt, and transmission ( but not mere private possession ) of obscene material may be prohibited by law. furthermore, under fcc v. pacifica foundation, the fcc has the power to prohibit the transmission of indecent material over broadcast. additionally, critics of campaign finance reform in the united states say this reform imposes widespread restrictions on political speech.


in mathematical optimization, wolfe duality, named after philip wolfe, is type of dual problem in which the objective function and constraints are all differentiable functions. using this concept a lower bound for a minimization problem can be found because of the weak duality principle.


in the 1990s cook worked as a research assistant to stephen wolfram, assisting with work on wolfram's book, a new kind of science. among other things, he developed a proof showing that the rule 110 cellular automaton is turing - complete. cook presented his proof at the santa fe institute conference ca98 before the publishing of wolfram's book — an action that led wolfram research to accuse cook of violating his nda and resulted in the blocking of the publication of the proof in the conference proceedings. a new kind of science was released in 2002 with an outline of the proof. in 2004, cook published his proof in wolfram's journal complex systems.


the technique goes back as far as the 1960s having been used in ibm system / 360 model 91 and in cdc 6600. modern high - end desktop and workstation processors such as the amd ryzen threadripper series and the intel core i9 extreme edition lineup support quad - channel memory. server processors from the amd epyc series and the intel xeon platforms give support to memory bandwidth starting from quad - channel module layout to up to octa - channel layout. in march 2010, amd released socket g34 and magny - cours opteron 6100 series processors with support for quad - channel memory. in 2006, intel released chipsets that support quad - channel memory for its lga771 platform and later in 2011 for its lga2011 platform. microcomputer chipsets with even more channels were designed ; for example, the chipset in the alphastation 600 ( 1995 ) supports eight - channel memory, but the backplane of the machine limited operation to four channels.


in quantum teleportation, a sender wishes to transmit an arbitrary quantum state of a particle to a possibly distant receiver. quantum teleportation is able to achieve faithful transmission of quantum information by substituting classical communication and prior entanglement for a direct quantum channel. using teleportation, an arbitrary unknown qubit can be faithfully transmitted via a pair of maximally - entangled qubits shared between sender and receiver, and a 2 - bit classical message from the sender to the receiver. quantum teleportation requires a noiseless quantum channel for sharing perfectly entangled particles, and therefore entanglement distillation satisfies this requirement by providing the noiseless quantum channel and maximally entangled qubits.


in the example the majorities are all different, and this is what will usually happen when the number of voters is large. if ties are unlikely, then it does not matter much how they are resolved, so a random choice can be made. however this is not tideman's procedure, which is considerably more complicated. see his paper for details.


in the united states, the federal crime of witness tampering is defined by statute at 18 u. s. c. § 1512, which is entitled " tampering with a witness, victim, or an informant. " the statute is broad ; the justice manual notes that it " proscribes conduct intended to illegitimately affect the presentation of evidence in federal proceedings or the communication of information to federal law enforcement officers " and applies to tampering with witnesses in " proceedings before congress, executive departments, and administrative agencies, and to civil and criminal judicial proceedings, including grand jury proceedings. " witness tampering is a crime even if a proceeding is not actually pending, and even if the testimony sought to be influenced, delayed, or prevented would not be admissible in evidence.


in the first design of the altair, the parts needed to make a complete machine would not fit on a single motherboard, and the machine consisted of four boards stacked on top of each other with stand - offs. another problem facing roberts was that the parts needed to make a truly useful computer were not available, or would not be designed in time for the january launch date. so during the construction of the second model, he decided to build most of the machine on removable cards, reducing the motherboard to nothing more than an interconnect between the cards, a backplane. the basic machine consisted of five cards, including the cpu on one and memory on another.


for example, the ky fan - k - norm is the sum of first k singular values, the trace norm is the sum of all singular values, and the schatten norm is the pth root of the sum of the pth powers of the singular values. note that each norm is defined only on a special class of operators, hence s - numbers are useful in classifying different operators. in the finite - dimensional case, a matrix can always be decomposed in the form u σ v ∗ { \ displaystyle \ mathbf { u \ sigma v ^ { * } } }, where u { \ displaystyle \ mathbf { u } } and v ∗ { \ displaystyle \ mathbf { v ^ { * } } } are unitary matrices and σ { \ displaystyle \ mathbf { \ sigma } } is a rectangular diagonal matrix with the singular values lying on the diagonal. this is the singular value decomposition.


the full statement of vinogradov's theorem gives asymptotic bounds on the number of representations of an odd integer as a sum of three primes. the notion of " sufficiently large " was ill - defined in vinogradov's original work, but in 2002 it was shown that 101346 is sufficiently large. additionally numbers up to 1020 had been checked via brute force methods, thus only a finite number of cases to check remained before the odd goldbach conjecture would be proven or disproven. in 2013, harald helfgott proved goldbach's weak conjecture for all cases.


other means make use of the antenna pattern, which supports angular determination and phase discrimination. newer phones may also allow the tracking of the phone even when turned on but not active in a telephone call. this results from the roaming procedures that perform hand - over of the phone from one base station to another.


therefore, the principle of locality implies that an event at one point cannot cause a simultaneous result at another point. an event at point a { \ displaystyle a } cannot cause a result at point b { \ displaystyle b } in a time less than t = d / c { \ displaystyle t = d / c }, where d { \ displaystyle d } is the distance between the points and c { \ displaystyle c } is the speed of light in vacuum. bell test experiments show that quantum mechanics broadly violates the inequalities established in bell's theorem. according to some interpretations of quantum mechanics, this result implies that some quantum effects must be non - local.


in the 1970s the precalciner was pioneered in japan, and has subsequently become the equipment of choice for new large installations worldwide. the precalciner is a development of the suspension preheater. the philosophy is this : the amount of fuel that can be burned in the kiln is directly related to the size of the kiln. if part of the fuel necessary to burn the rawmix is burned outside the kiln, the output of the system can be increased for a given kiln size.


examples of tasks in mistrustful cryptography are commitment schemes and secure computations, the latter including the further examples of coin flipping and oblivious transfer. key distribution does not belong to the area of mistrustful cryptography. mistrustful quantum cryptography studies the area of mistrustful cryptography using quantum systems.


the new proof relied almost exclusively on the behavior of cyclotomic polynomials over finite fields. the new upper bound on time complexity was o ~ ( log ( n ) 10. 5 ) { \ displaystyle { \ tilde { o } } ( \ log ( n ) ^ { 10. 5 } ) }, later reduced using additional results from sieve theory to o ~ ( log ( n ) 7. 5 ) { \ displaystyle { \ tilde { o } } ( \ log ( n ) ^ { 7. 5 } ) }. in 2005, pomerance and lenstra demonstrated a variant of aks that runs in o ~ ( log ( n ) 6 ) { \ displaystyle { \ tilde { o } } ( \ log ( n ) ^ { 6 } ) } operations, leading to another updated version of the paper. agrawal, kayal and saxena proposed a variant which would run in o ~ ( log ( n ) 3 ) { \ displaystyle { \ tilde { o } } ( \ log ( n ) ^ { 3 } ) } if agrawal's conjecture were true ; however, a heuristic argument by pomerance and lenstra suggested that it is probably false.


natural deduction. every ( conditional ) line has exactly one asserted proposition on the right. sequent calculus.


in mathematics, the brunn – minkowski theorem ( or brunn – minkowski inequality ) is an inequality relating the volumes ( or more generally lebesgue measures ) of compact subsets of euclidean space. the original version of the brunn – minkowski theorem ( hermann brunn 1887 ; hermann minkowski 1896 ) applied to convex sets ; the generalization to compact nonconvex sets stated here is due to lazar lyusternik ( 1935 ).


another complication in applying lda and fisher's discriminant to real data occurs when the number of measurements of each sample ( i. e., the dimensionality of each data vector ) exceeds the number of samples in each class. in this case, the covariance estimates do not have full rank, and so cannot be inverted.


in statistics, a rank correlation is any of several statistics that measure an ordinal association — the relationship between rankings of different ordinal variables or different rankings of the same variable, where a " ranking " is the assignment of the ordering labels " first ", " second ", " third ", etc. to different observations of a particular variable. a rank correlation coefficient measures the degree of similarity between two rankings, and can be used to assess the significance of the relation between them. for example, two common nonparametric methods of significance that use rank correlation are the mann – whitney u test and the wilcoxon signed - rank test.


in hjelmslev's interpretation, there are no physical, psychological or other a priori principles that explain why languages are the way they are. cross - linguistic similarities on the expression plane depend on a necessity to express meaning ; conversely, cross - linguistic similarities on the content plane depend on the necessity to structure meaning potential according to the necessities of expression. " the linguist must be equally interested in the similarity and in the difference between languages, two complementary sides of the same thing.


the data is presented to the users in a common format. many programs aimed to aid in the creation of such warehouses are designed to be extremely versatile to allow for them to be implemented in diverse research projects. one advantage of this approach is that data is available for analysis at a single site, using a uniform schema.


in some languages, palatalization is used as a morpheme or part of a morpheme. in some cases, a vowel caused a consonant to become palatalized, and then this vowel was lost by elision. here, there appears to be a phonemic contrast when analysis of the deep structure shows it to be allophonic. in romanian, consonants are palatalized before / i /.


in reverse mathematics, one starts with a framework language and a base theory — a core axiom system — that is too weak to prove most of the theorems one might be interested in, but still powerful enough to develop the definitions necessary to state these theorems. for example, to study the theorem “ every bounded sequence of real numbers has a supremum ” it is necessary to use a base system that can speak of real numbers and sequences of real numbers. for each theorem that can be stated in the base system but is not provable in the base system, the goal is to determine the particular axiom system ( stronger than the base system ) that is necessary to prove that theorem.


the plain voiceless and voiced aspirated series would thus be replaced by just voiceless and voiced, with aspiration being a non - distinctive quality of both. that example of the application of linguistic typology to linguistic reconstruction has become known as the glottalic theory. it has a large number of proponents but is not generally accepted. the reconstruction of proto - sounds logically precedes the reconstruction of grammatical morphemes ( word - forming affixes and inflectional endings ), patterns of declension and conjugation and so on. the full reconstruction of an unrecorded protolanguage is an open - ended task.


the problem of edge coloring has also been studied in the distributed model. panconesi & rizzi ( 2001 ) achieve a ( 2δ − 1 ) - coloring in o ( δ + log * n ) time in this model. the lower bound for distributed vertex coloring due to linial ( 1992 ) applies to the distributed edge coloring problem as well.


in the rsa cryptosystem, bob might tend to use a small value of d, rather than a large random number to improve the rsa decryption performance. however, wiener ’ s attack shows that choosing a small value for d will result in an insecure system in which an attacker can recover all secret information, i. e., break the rsa system. this break is based on wiener ’ s theorem, which holds for small values of d. wiener has proved that the attacker may efficiently find d when d < 1 3 n 1 4 { \ displaystyle d < { \ frac { 1 } { 3 } } n ^ { \ frac { 1 } { 4 } } }. wiener's paper also presented some countermeasures against his attack that allow fast decryption. two techniques are described as follows.


" secure " phones are defined as " telephones that are approved by the u. s. government for the transmission of classified or sensitive voice communications. " in 2003, the fcc adopted rules to make digital wireless telephones compatible with hearing aids and cochlear implants.


in mathematics, a costas array can be regarded geometrically as a set of n points, each at the center of a square in an n×n square tiling such that each row or column contains only one point, and all of the n ( n − 1 ) / 2 displacement vectors between each pair of dots are distinct. this results in an ideal " thumbtack " auto - ambiguity function, making the arrays useful in applications such as sonar and radar. costas arrays can be regarded as two - dimensional cousins of the one - dimensional golomb ruler construction, and, as well as being of mathematical interest, have similar applications in experimental design and phased array radar engineering.


in the " sir " model, there are three states : susceptible ( s ) - - has not yet been infected, and has no immunity infected ( i ) - - currently " sick " and contagious to susceptible neighbors removed ( r ), where the removal from further participation in the process is assumed to be permanent, due to immunization or deathit is to be distinguished from the " sis " model, where sites recover without immunization, and are thus not " removed ". the asynchronous simulation of the model on a lattice is carried out as follows : pick a site. if it is i, then generate a random number x in ( 0, 1 ). if x < c then let i go to r. otherwise, pick one nearest neighbor randomly.


according to avery, calem, and canner in credit report accuracy and access to credit, " the parties that bear the costs of correcting errors or providing more timely and complete information may not receive much benefit from the improvement in accuracy. " the formula to calculate consumer credit scores by a consumer reporting agency is proprietary and considered a trade secret of the agency in the united states. some consumer reporting agencies in the united states provide two credit scores - an'educational'score to the consumer and a customary fico - like score to the lender or business. liz weston writes that some consumer advocates refer to these other credit scores as " fako scores " ( a play on acronym of fico ).


it shows whether what has been achieved is above or below expectation. secondly, it gives the planners a chance to learn, that is, to gather new general insight, for instance, regarding the strength and weakness of certain weapons or techniques of action. thirdly, this fact - finding should serve as a basis for correctly planning the next step. finally, it serves as a basis for modifying the " overall plan. "


this idea was " sharply " criticized by church. thus post in his 1936 paper was also discounting kurt godel's suggestion to church in 1934 – 1935 that the thesis might be expressed as an axiom or set of axioms. turing adds another definition, rosser equates all three : within just a short time, turing's 1936 – 1937 paper " on computable numbers, with an application to the entscheidungsproblem " appeared. in it he stated another notion of " effective computability " with the introduction of his a - machines ( now known as the turing machine abstract computational model ). and in a proof - sketch added as an " appendix " to his 1936 – 1937 paper, turing showed that the classes of functions defined by λ - calculus and turing machines coincided.


we would then like to choose a hypothesis that minimizes the expected risk : in most cases, we don't know the joint distribution of x n + 1, y n + 1 { \ displaystyle x _ { n + 1 }, \, y _ { n + 1 } } outright. in these cases, a common strategy is to choose the hypothesis that minimizes the empirical risk : under certain assumptions about the sequence of random variables x k, y k { \ displaystyle x _ { k }, \, y _ { k } } ( for example, that they are generated by a finite markov process ), if the set of hypotheses being considered is small enough, the minimizer of the empirical risk will closely approximate the minimizer of the expected risk as n { \ displaystyle n } grows large. this approach is called empirical risk minimization, or erm.


in the case where x 1, …, x m { \ displaystyle x _ { 1 }, \ dots, x _ { m } } are not known in advance, kedlaya and umans gave a data structure for evaluating polynomials over a finite field of size f q { \ displaystyle f _ { q } } in time ( log n ) o ( 1 ) ( log 2 q ) 1 + o ( 1 ) { \ displaystyle ( \ log n ) ^ { o ( 1 ) } ( \ log _ { 2 } q ) ^ { 1 + o ( 1 ) } } per evaluation after some initial preprocessing. this was shown by larsen to be essentially optimal. the idea is to transform p ( x ) { \ displaystyle p ( x ) } of degree n { \ displaystyle n } into a multivariate polynomial f ( x 1, x 2, …, x m ) { \ displaystyle f ( x _ { 1 }, x _ { 2 }, \ dots, x _ { m } ) }, such that p ( x ) = f ( x, x d, x d 2, …, x d m ) { \ displaystyle p ( x ) = f ( x, x ^ { d }, x ^ { d ^ { 2 } }, \ dots, x ^ { d ^ { m } } ) } and the individual degrees of f { \ displaystyle f } is at most d { \ displaystyle d }. since this is over mod q { \ displaystyle { \ bmod { q } } }, the largest value f { \ displaystyle f } can take ( over z { \ displaystyle \ mathbb { z } } ) is m = d m ( q − 1 ) d m { \ displaystyle m = d ^ { m } ( q - 1 ) ^ { dm } }.


in mathematics, milliken's tree theorem in combinatorics is a partition theorem generalizing ramsey's theorem to infinite trees, objects with more structure than sets. let t be a finitely splitting rooted tree of height ω, n a positive integer, and s t n { \ displaystyle \ mathbb { s } _ { t } ^ { n } } the collection of all strongly embedded subtrees of t of height n. in one of its simple forms, milliken's tree theorem states that if s t n = c 1 ∪... ∪ c r { \ displaystyle \ mathbb { s } _ { t } ^ { n } = c _ { 1 } \ cup... \ cup c _ { r } } then for some strongly embedded infinite subtree r of t, s r n ⊂ c i { \ displaystyle \ mathbb { s } _ { r } ^ { n } \ subset c _ { i } } for some i ≤ r. this immediately implies ramsey's theorem ; take the tree t to be a linear ordering on ω vertices. define s n = t s t n { \ displaystyle \ mathbb { s } ^ { n } = \ bigcup _ { t } \ mathbb { s } _ { t } ^ { n } } where t ranges over finitely splitting rooted trees of height ω. milliken's tree theorem says that not only is s n { \ displaystyle \ mathbb { s } ^ { n } } partition regular for each n < ω, but that the homogeneous subtree r guaranteed by the theorem is strongly embedded in t.


these categories are characterized by fundamental ontological concepts, including particularity and universality, abstractness and concreteness, or possibility and necessity. of special interest is the concept of ontological dependence, which determines whether the entities of a category exist on the most fundamental level.


one striking one is the result announced by dan goldston, janos pintz, and cem yıldırım, which shows ( assuming this conjecture ) that there are infinitely many pairs of primes which differ by at most 16. in november 2013, james maynard showed that subject to the elliott – halberstam conjecture, one can show the existence of infinitely many pairs of consecutive primes that differ by at most 12. in august 2014, polymath group showed that subject to the generalized elliott – halberstam conjecture, one can show the existence of infinitely many pairs of consecutive primes that differ by at most 6. without assuming any form of the conjecture, the lowest proven bound is 246.


linear - chain crfs have many of the same applications as conceptually simpler hidden markov models ( hmms ), but relax certain assumptions about the input and output sequence distributions. an hmm can loosely be understood as a crf with very specific feature functions that use constant probabilities to model state transitions and emissions. conversely, a crf can loosely be understood as a generalization of an hmm that makes the constant transition probabilities into arbitrary functions that vary across the positions in the sequence of hidden states, depending on the input sequence. notably, in contrast to hmms, crfs can contain any number of feature functions, the feature functions can inspect the entire input sequence x { \ displaystyle x } at any point during inference, and the range of the feature functions need not have a probabilistic interpretation.


each rule is defined to match a specific context. a context involves two pivots ( p { \ displaystyle p } and q { \ displaystyle q } ) and five clauses ( α { \ displaystyle \ alpha }, β { \ displaystyle \ beta }, γ { \ displaystyle \ gamma }, δ { \ displaystyle \ delta } and η { \ displaystyle \ eta } ). the structure of a context is shown in ( 1 ).


in programming languages and type theory, parametric polymorphism allows a single piece of code to be given a " generic " type, using variables in place of actual types, and then instantiated with particular types as needed. : 340 parametrically polymorphic functions and data types are sometimes called generic functions and generic datatypes, respectively, and they form the basis of generic programming. parametric polymorphism may be contrasted with ad hoc polymorphism.


for such a graph, with m { \ displaystyle m } edges and n { \ displaystyle n } vertices, the size of a minimum feedback arc set is always at least ( m 2 + m n ) / 2 n 2 { \ displaystyle ( m ^ { 2 } + mn ) / 2n ^ { 2 } }. there are infinitely many eulerian directed graphs for which this bound is tight. if a directed graph has n { \ displaystyle n } vertices, with at most three edges per vertex, then it has a feedback arc set of at most n / 3 { \ displaystyle n / 3 } edges, and some graphs require this many. if a directed graph has m { \ displaystyle m } edges, with at most four edges per vertex, then it has a feedback arc set of at most m / 3 { \ displaystyle m / 3 } edges, and some graphs require this many. = = references = =


in the 2016 / 2017 qs world university rankings® result tables, gist was ranked number 2 in the world in the category of citations per faculty. in the times higher education world university rankings 2014 – 2015, gist was ranked 96th in the world in the category of engineering & technology.


the only output from the programs was the patterns of lights on the panel. nevertheless, many were sold in this form. development was already underway on additional cards, including a paper tape reader for storage, additional ram cards, and an rs - 232 interface to connect to a proper teletype terminal.


when opening the airbrake disturbs the airfoil shape thereby slowing the mill. it was invented by german airplane engineer kurt bilau early in the twentieth century and became quite popular in germany where it was fitted to over 140 mills. a similar system was invented by a millwright by the name of van riet of goes where the leading edge and the airbrake together form a more complete airfoil.


{ \ displaystyle b _ { k } ^ { ( - k ) } \ sim ( k! ) ^ { 2 } { \ sqrt { \ frac { 1 } { k \ pi ( 1 - \ log 2 ) } } } \ left ( { \ frac { 1 } { \ log 2 } } \ right ) ^ { 2k + 1 }, \ quad { \ text { as } } k \ rightarrow \ infty. } for a positive integer n and a prime number p, the poly - bernoulli numbers satisfy b n ( − p ) ≡ 2 n ( mod p ), { \ displaystyle b _ { n } ^ { ( - p ) } \ equiv 2 ^ { n } { \ pmod { p } }, } which can be seen as an analog of fermat's little theorem. further, the equation b x ( − n ) + b y ( − n ) = b z ( − n ) { \ displaystyle b _ { x } ^ { ( - n ) } + b _ { y } ^ { ( - n ) } = b _ { z } ^ { ( - n ) } } has no solution for integers x, y, z, n > 2 ; an analog of fermat's last theorem. moreover, there is an analogue of poly - bernoulli numbers ( like bernoulli numbers and euler numbers ) which is known as poly - euler numbers.


in the equivalence of models of computability, a parallel is drawn between turing machines that do not terminate for certain inputs and an undefined result for that input in the corresponding partial recursive function. the unbounded search operator is not definable by the rules of primitive recursion as those do not provide a mechanism for " infinite loops " ( undefined values ).


in terms of descriptive complexity theory, np corresponds precisely to the set of languages definable by existential second - order logic ( fagin's theorem ). np can be seen as a very simple type of interactive proof system, where the prover comes up with the proof certificate and the verifier is a deterministic polynomial - time machine that checks it. it is complete because the right proof string will make it accept if there is one, and it is sound because the verifier cannot accept if there is no acceptable proof string.


in order to get a classical style reciprocity law from the hilbert reciprocity law π ( a, b ) p = 1, one needs to know the values of ( a, b ) p for p dividing n. explicit formulas for this are sometimes called explicit reciprocity laws.


2. inconsistency factors : features of the individual or the situation that can affect test scores but have nothing to do with the attribute being measured. these factors include : temporary but general characteristics of the individual : health, fatigue, motivation, emotional strain temporary and specific characteristics of individual : comprehension of the specific test task, specific tricks or techniques of dealing with the particular test materials, fluctuations of memory, attention or accuracy aspects of the testing situation : freedom from distractions, clarity of instructions, interaction of personality, etc. chance factors : luck in selection of answers by sheer guessing, momentary distractionsthe goal of estimating reliability is to determine how much of the variability in test scores is due to measurement errors and how much is due to variability in true scores ( true value ). a true score is the replicable feature of the concept being measured.


{ \ displaystyle \ delta \ left ( ( x, y ), ( x ', y') \ right ) = \ min \ left \ { \ max \ { | x - x'|, | y - y'| \ }, \ max \ left \ { { \ frac { y - x } { 2 } }, { \ frac { y'- x'} { 2 } } \ right \ } \ right \ }. } roughly speaking, the matching distance d match { \ displaystyle d _ { \ text { match } } } between two size functions is the minimum, over all the matchings between the cornerpoints of the two size functions, of the maximum of the l ∞ { \ displaystyle l _ { \ infty } } - distances between two matched cornerpoints. since two size functions can have a different number of cornerpoints, these can be also matched to points of the diagonal δ { \ displaystyle \ delta }. moreover, the definition of δ { \ displaystyle \ delta } implies that matching two points of the diagonal has no cost.


in metadata, a match report is a report that compares two distinct data dictionaries and creates a list of the data elements that have been identified as semantically equivalent.


the theorem is further generalized by carmichael's theorem. the theorem may be used to easily reduce large powers modulo n { \ displaystyle n }. for example, consider finding the ones place decimal digit of 7 222 { \ displaystyle 7 ^ { 222 } }, i. e. 7 222 ( mod 10 ) { \ displaystyle 7 ^ { 222 } { \ pmod { 10 } } }.


in some scenarios where the majority of files are shorter than half the block size, such as in a folder of small source code files or small bitmap images, tail packing can increase storage efficiency even more than twofold, compared to file systems without tail packing. this not only translates into conservation of disk space, but may also introduce performance increases, as due to higher locality of reference, less data has to be read, also translating into higher page cache efficiency. however, these advantages can be negated by the increased complexity of implementation. as of 2015, the most widely used read - write file systems with support for block suballocation are btrfs and freebsd ufs2 ( where it is called " block level fragmentation " ). reiserfs and reiser4 also support tail packing. several read - only file systems do not use blocks at all and are thus implicitly using space as efficiently as suballocating file systems ; such file systems double as archive formats.


in order to decide which clusters should be combined ( for agglomerative ), or where a cluster should be split ( for divisive ), a measure of dissimilarity between sets of observations is required. in most methods of hierarchical clustering, this is achieved by use of an appropriate distance d, such as the euclidean distance, between single observations of the data set, and a linkage criterion, which specifies the dissimilarity of sets as a function of the pairwise distances of observations in the sets. the choice of metric as well as linkage can have a major impact on the result of the clustering, where the lower level metric determines which objects are most similar, whereas the linkage criterion influences the shape of the clusters. for example, complete - linkage tends to produce more spherical clusters than single - linkage.


in this formulation, the statement is reviewed by leinster. a related example is discussed by leinster : the codensity monad of the inclusion of finite - dimensional vector spaces ( over a fixed field k { \ displaystyle k } ) into all vector spaces is the double dualization monad given by sending a vector space v { \ displaystyle v } to its double dual thus, in this example, the end formula mentioned above simplifies to considering ( in the notation above ) only one object d, { \ displaystyle d, } namely a one - dimensional vector space, as opposed to considering all objects in d. { \ displaystyle d. } adamek show that, in a number of situations, the codensity monad of the inclusion of finitely presented objects ( also known as compact objects ) is a double dualization monad with respect to a sufficiently nice cogenerating object.


in mathematics, specifically group theory, cauchy's theorem states that if g is a finite group and p is a prime number dividing the order of g ( the number of elements in g ), then g contains an element of order p. that is, there is x in g such that p is the smallest positive integer with xp = e, where e is the identity element of g. it is named after augustin - louis cauchy, who discovered it in 1845. the theorem is related to lagrange's theorem, which states that the order of any subgroup of a finite group g divides the order of g. cauchy's theorem implies that for any prime divisor p of the order of g, there is a subgroup of g whose order is p — the cyclic group generated by the element in cauchy's theorem. cauchy's theorem is generalized by sylow's first theorem, which implies that if pn is the maximal power of p dividing the order of g, then g has a subgroup of order pn ( and using the fact that a p - group is solvable, one can show that g has subgroups of order pr for any r less than or equal to n ).


in more general mathematical settings, the boltzmann distribution is also known as the gibbs measure. in statistics and machine learning, it is called a log - linear model. in deep learning, the boltzmann distribution is used in the sampling distribution of stochastic neural networks such as the boltzmann machine, restricted boltzmann machine, energy - based models and deep boltzmann machine. in deep learning, the boltzmann machine is considered to be one of the unsupervised learning models. in the design of boltzmann machine in deep learning, as the number of nodes are increased the difficulty of implementing in real time applications becomes critical, so a different type of architecture named restricted boltzmann machine is introduced.


in object - oriented programming languages, dynamic compilers are particularly good candidates for performing escape analysis. in traditional static compilation, method overriding can make escape analysis impossible, as any called method might be overridden by a version that allows a pointer to escape. dynamic compilers can perform escape analysis using the available information on overloading, and re - do the analysis when relevant methods are overridden by dynamic code loading. the popularity of the java programming language has made escape analysis a target of interest. java's combination of heap - only object allocation, built - in threading, the sun hotspot dynamic compiler, and openj9's just - in - time compiler ( jit ) creates a candidate platform for escape analysis related optimizations ( see escape analysis in java ). escape analysis is implemented in java standard edition 6. some jvms support a stronger variant of escape analysis called partial escape analysis that makes scalar replacement of an allocated object possible even if the object escapes in some paths of a function.


in probability theory and statistics, the noncentral beta distribution is a continuous probability distribution that is a noncentral generalization of the ( central ) beta distribution. the noncentral beta distribution ( type i ) is the distribution of the ratio x = χ m 2 ( λ ) χ m 2 ( λ ) + χ n 2, { \ displaystyle x = { \ frac { \ chi _ { m } ^ { 2 } ( \ lambda ) } { \ chi _ { m } ^ { 2 } ( \ lambda ) + \ chi _ { n } ^ { 2 } } }, } where χ m 2 ( λ ) { \ displaystyle \ chi _ { m } ^ { 2 } ( \ lambda ) } is a noncentral chi - squared random variable with degrees of freedom m and noncentrality parameter λ { \ displaystyle \ lambda }, and χ n 2 { \ displaystyle \ chi _ { n } ^ { 2 } } is a central chi - squared random variable with degrees of freedom n, independent of χ m 2 ( λ ) { \ displaystyle \ chi _ { m } ^ { 2 } ( \ lambda ) }. in this case, x beta ( m 2, n 2, λ ) { \ displaystyle x \ sim { \ mbox { beta } } \ left ( { \ frac { m } { 2 } }, { \ frac { n } { 2 } }, \ lambda \ right ) } a type ii noncentral beta distribution is the distribution of the ratio y = χ n 2 χ n 2 + χ m 2 ( λ ), { \ displaystyle y = { \ frac { \ chi _ { n } ^ { 2 } } { \ chi _ { n } ^ { 2 } + \ chi _ { m } ^ { 2 } ( \ lambda ) } }, } where the noncentral chi - squared variable is in the denominator only. if y { \ displaystyle y } follows the type ii distribution, then x = 1 − y { \ displaystyle x = 1 - y } follows a type i distribution.


in mathematics and computing, fibonacci coding is a universal code which encodes positive integers into binary code words. it is one example of representations of integers based on fibonacci numbers. each code word ends with " 11 " and contains no other instances of " 11 " before the end. the fibonacci code is closely related to the zeckendorf representation, a positional numeral system that uses zeckendorf's theorem and has the property that no number has a representation with consecutive 1s. the fibonacci code word for a particular integer is exactly the integer's zeckendorf representation with the order of its digits reversed and an additional " 1 " appended to the end.


in mathematics, a semigroup with two elements is a semigroup for which the cardinality of the underlying set is two. there are exactly five nonisomorphic semigroups having two elements : o2, the null semigroup of order two, lo2, the left zero semigroup of order two, ro2, the right zero semigroup of order two, ( { 0, 1 }, ∧ ) ( where " ∧ " is the logical connective " and " ), or equivalently the set { 0, 1 } under multiplication : the only semilattice with two elements and the only non - null semigroup with zero of order two, also a monoid, and ultimately the two - element boolean algebra, ( z2, + 2 ) ( where z2 = { 0, 1 } and " + 2 " is " addition modulo 2 " ), or equivalently ( { 0, 1 }, ⊕ ) ( where " ⊕ " is the logical connective " xor " ), or equivalently the set { −1, 1 } under multiplication : the only group of order two. the semigroups lo2 and ro2 are antiisomorphic. o2, ( { 0, 1 }, ∧ ) and ( z2, + 2 ) are commutative, and lo2 and ro2 are noncommutative. lo2, ro2 and ( { 0, 1 }, ∧ ) are bands.


in practice, results depend on choosing a good strategy for clustering the outcomes into classes. a huffman tree was used for this in google's word2vec models ( introduced in 2013 ) to achieve scalability. a second kind of remedies is based on approximating the softmax ( during training ) with modified loss functions that avoid the calculation of the full normalization factor. these include methods that restrict the normalization sum to a sample of outcomes ( e. g. importance sampling, target sampling ).


in mathematics, the legendre sieve, named after adrien - marie legendre, is the simplest method in modern sieve theory. it applies the concept of the sieve of eratosthenes to find upper or lower bounds on the number of primes within a given set of integers. because it is a simple extension of eratosthenes'idea, it is sometimes called the legendre – eratosthenes sieve.


in null - hypothesis significance testing, the p - value is the probability of obtaining test results at least as extreme as the result actually observed, under the assumption that the null hypothesis is correct. a very small p - value means that such an extreme observed outcome would be very unlikely under the null hypothesis. even though reporting p - values of statistical tests is common practice in academic publications of many quantitative fields, misinterpretation and misuse of p - values is widespread and has been a major topic in mathematics and metascience. in 2016, the american statistician association ( asa ) made a formal statement that " p - values do not measure the probability that the studied hypothesis is true, or the probability that the data were produced by random chance alone " and that " a p - value, or statistical significance, does not measure the size of an effect or the importance of a result " or " evidence regarding a model or hypothesis. " that said, a 2019 task force by asa has issued a statement on statistical significance and replicability, concluding with : " p - values and significance tests, when properly applied and interpreted, increase the rigor of the conclusions drawn from data. "


in statistical testing problems, one usually is not interested in the component vectors themselves, but rather in their squared lengths, or sum of squares. the degrees of freedom associated with a sum - of - squares is the degrees - of - freedom of the corresponding component vectors. the three - population example above is an example of one - way analysis of variance. the model, or treatment, sum - of - squares is the squared length of the second vector, sst = n ( x − m ) 2 + n ( y − m ) 2 + n ( z − m ) 2 { \ displaystyle { \ text { sst } } = n ( { \ bar { x } } - { \ bar { m } } ) ^ { 2 } + n ( { \ bar { y } } - { \ bar { m } } ) ^ { 2 } + n ( { \ bar { z } } - { \ bar { m } } ) ^ { 2 } } with 2 degrees of freedom.


in mathematical terms, quantum discord is defined in terms of the quantum mutual information. more specifically, quantum discord is the difference between two expressions which each, in the classical limit, represent the mutual information. these two expressions are : i ( a ; b ) = h ( a ) + h ( b ) − h ( a, b ) { \ displaystyle i ( a ; b ) = h ( a ) + h ( b ) - h ( a, b ) } j ( a ; b ) = h ( a ) − h ( a | b ) { \ displaystyle j ( a ; b ) = h ( a ) - h ( a | b ) } where, in the classical case, h ( a ) is the information entropy, h ( a, b ) the joint entropy and h ( a | b ) the conditional entropy, and the two expressions yield identical results. in the nonclassical case, the quantum physics analogy for the three terms are used – s ( ρa ) the von neumann entropy, s ( ρ ) the joint quantum entropy and s ( ρa | ρb ) a quantum generalization of conditional entropy ( not to be confused with conditional quantum entropy ), respectively, for probability density function ρ ; i ( ρ ) = s ( ρ a ) + s ( ρ b ) − s ( ρ ) { \ displaystyle i ( \ rho ) = s ( \ rho _ { a } ) + s ( \ rho _ { b } ) - s ( \ rho ) } j a ( ρ ) = s ( ρ b ) − s ( ρ b | ρ a ) { \ displaystyle j _ { a } ( \ rho ) = s ( \ rho _ { b } ) - s ( \ rho _ { b } | \ rho _ { a } ) } the difference between the two expressions defines the basis - dependent quantum discord d a ( ρ ) = i ( ρ ) − j a ( ρ ), { \ displaystyle { \ mathcal { d } } _ { a } ( \ rho ) = i ( \ rho ) - j _ { a } ( \ rho ), } which is asymmetrical in the sense that d a ( ρ ) { \ displaystyle { \ mathcal { d } } _ { a } ( \ rho ) } can differ from d b ( ρ ) { \ displaystyle { \ mathcal { d } } _ { b


} ( \ rho ) }.


in the context of it systems and data center management, a " workload " can be broadly defined as " the total requests made by users and applications of a system. " however, it is also possible to break down the entire workload of a given system into sets of self - contained units. such a self - contained unit constitutes a " workload " in the narrow sense : an integrated stack consisting of application, middleware, database, and operating system devoted to a specific computing task. typically, a workload is " platform agnostic, " meaning that it can run in physical, virtual or cloud computing environments. finally, a collection of related workloads which allow end users to complete a specific set of business tasks can be defined as a " business service. "


we say that ( x, l ) { \ displaystyle ( x, l ) } is : k - semistable if μ ( x, l ) ≥ 0 { \ displaystyle \ operatorname { \ mu } ( { \ mathcal { x } }, { \ mathcal { l } } ) \ geq 0 } for all test configurations ( x, l ) { \ displaystyle ( { \ mathcal { x } }, { \ mathcal { l } } ) } for ( x, l ) { \ displaystyle ( x, l ) }. k - stable if μ ( x, l ) ≥ 0 { \ displaystyle \ operatorname { \ mu } ( { \ mathcal { x } }, { \ mathcal { l } } ) \ geq 0 } for all test configurations ( x, l ) { \ displaystyle ( { \ mathcal { x } }, { \ mathcal { l } } ) } for ( x, l ) { \ displaystyle ( x, l ) }, and additionally μ ( x, l ) > 0 { \ displaystyle \ operatorname { \ mu } ( { \ mathcal { x } }, { \ mathcal { l } } ) > 0 } whenever ‖ ( x, l ) ‖ > 0 { \ displaystyle \ | ( { \ mathcal { x } }, { \ mathcal { l } } ) \ | > 0 }. k - polystable if ( x, l ) { \ displaystyle ( x, l ) } is k - semistable, and additionally whenever μ ( x, l ) = 0 { \ displaystyle \ operatorname { \ mu } ( { \ mathcal { x } }, { \ mathcal { l } } ) = 0 }, the test configuration ( x, l ) { \ displaystyle ( { \ mathcal { x } }, { \ mathcal { l } } ) } is a product configuration. k - unstable if it is not k - semistable.


in the broadest definition, document comparison can refer to any act of marking changes made between two versions of the same document and presenting those changes in a third document via a graphical user interface ( gui ). there are several variants in the types of changes registered through the process of document comparison. some programs limit comparison to solely text and table content in word processing documents, while others register changes made in spreadsheets and presentations, along with changes made in versions of pdf documents. certain programs also exist that compare changes made to objects like jpeg, tiff, bmp, png images embedded in documents, and plain text files.


e. g. the linux tool scanmem supports pie this way. for the configured memory offset the game trainer determines the load address as well and adds it back during run - time. the same method can be used for dynamic libraries as well.


its gps receiver compares the pgk's flight pattern to the coordinates of where it should hit, and the fins adjust its path to match where the round will actually impact. a fail safe exists where if the shell does not impact within 150 m ( 490 ft ) of the intended target, it will land but not explode ; the pgk " decides " five seconds after launch whether it expects to impact close enough to detonate. this safety feature is expected to give soldiers more confidence when calling in artillery support close to their position.


in mathematics, a trivial semigroup ( a semigroup with one element ) is a semigroup for which the cardinality of the underlying set is one. the number of distinct nonisomorphic semigroups with one element is one. if s = { a } is a semigroup with one element, then the cayley table of s is the only element in s is the zero element 0 of s and is also the identity element 1 of s. however not all semigroup theorists consider the unique element in a semigroup with one element as the zero element of the semigroup. they define zero elements only in semigroups having at least two elements. in spite of its extreme triviality, the semigroup with one element is important in many situations.


the case ( x, y, z ) = ( 3, 6, n ) and all its permutations were proven for n ≥ 3 by bennett, chen, dahmen and yazdani in 2014. the case ( x, y, z ) = ( 2n, 3, 4 ) and all its permutations were proven for n ≥ 2 by bennett, chen, dahmen and yazdani in 2014. the cases ( 5, 5, 7 ), ( 5, 5, 19 ), ( 7, 7, 5 ) and all their permutations were proven by sander r. dahmen and samir siksek in 2013.


in forro trios, where the only pitch instrument ( apart from the voice ) is the accordion ( which plays together with two percussionists ), the accordionist usually " puxa " ( " pulls " ) the next song as soon as the previous has finished. some album notations distinguish track listings through the use of symbols, such as a >, →, or / to indicate songs that flow seamlessly. the alternative rock band failure separates these musical transitions into individual tracks, which are simply given numerical distinctions such as segue 1. this system began with their 1996 album fantastic planet.


in pseudocode : if a < b then set c to true else set c to false in guarded command language : if a < b → c : = true a ≥ b → c : = false fi