The Ganz factory in 1884 shipped the world's first five high-efficiency AC transformers. This first unit had been manufactured to the following specifications: 1,400 W, 40 Hz, 120:72 V, 11.6:19.4 A, ratio 1.67:1, one-phase, shell form.The ZBD patents included two other major interrelated innovations: one concerning the use of parallel connected, instead of series connected, utilization loads, the other concerning the ability to have high turns ratio transformers such that the supply network voltage could be much higher (initially 1400 V to 2000 V) than the voltage of utilization loads (100 V initially preferred). When employed in parallel connected electric distribution systems, closed-core transformers finally made it technically and economically feasible to provide electric power for lighting in homes, businesses and public spaces.


Additionally, a family of sets may be defined as a function from a set I {\displaystyle I} , known as the index set, to F {\displaystyle F} , in which case the sets of the family are indexed by members of I {\displaystyle I} . In some contexts, a family of sets may be allowed to contain repeated copies of any given member, and in other contexts it may form a proper class. A finite family of subsets of a finite set S {\displaystyle S} is also called a hypergraph. The subject of extremal set theory concerns the largest and smallest examples of families of sets satisfying certain restrictions.


Often an adjective is added for specifying the operation, such as in additive inverse, multiplicative inverse, and functional inverse. In this case (associative operation), an invertible element is an element that has an inverse. In a ring, an invertible element, also called a unit, is an element that is invertible under multiplication (this is not ambiguous, as every element is invertible under addition).


In the Euclidean space, the angle θ between two Euclidean vectors u and v is related to their dot product and their lengths by the formula This formula supplies an easy method to find the angle between two planes (or curved surfaces) from their normal vectors and between skew lines from their vector equations.


Between any two real numbers a < b, no matter how close they are to each other, there are always infinitely many other real numbers, and Cantor showed that they are as many as those contained in the whole set of real numbers. In other words, the open interval (a,b) is equinumerous with R . {\displaystyle \mathbb {R} .}


Many of these plants do not survive long, as they are often vandalized. An estimated 10,000 plants are mutilated each week by cutting off the lower leaves for barbacoa or destroying them completely to look for the edible white grubs or ant eggs that can inhabit them.A recent series of PBS travel shows feature pulque and say that it is once again a very popular drink and that there is a retro movement leading younger people seeking to establish their Mexican heritage to drink this beverage in large quantities. It has become a trendy drink among youth and back-to-your-roots types. The prohibition on female drinkers has also been lifted and co-ed pulquerias are now the norm.Also flavored syrups, seasonings and so on are now common with one pulqueria featured in the special offering 48 separate flavors.


Indeed, type T need not even have an implementation; it might be a purely abstract class. As another case in point, type Stack above is a behavioral subtype of type Bag even if type Bag's implementation exhibits FIFO behavior: what matters is that type Bag's specification does not specify which element is removed by method get. This also means that behavioral subtyping can be discussed only with respect to a particular (behavioral) specification for each type involved and that if the types involved have no well-defined behavioral specification, behavioral subtyping cannot be discussed meaningfully.


The end result of this process is to calculate a threshold value (of squared error) whereby observations with a squared error smaller than this threshold should be kept and observations with a squared error larger than this value should be removed (i.e., as an outlier). Because Peirce's criterion does not take observations, fitting parameters, or residual errors as an input, the output must be re-associated with the data. Taking the average of all the squared errors (i.e., the mean-squared error) and multiplying it by the threshold squared error (i.e., the output of this function) will result in the data-specific threshold value used to identify outliers. The following Python code returns x-squared values for a given N (first column) and n (top row) in Table 1 (m = 1) and Table 2 (m = 2) of Gould 1855. Due to the Newton-method of iteration, look-up tables, such as N versus log Q (Table III in Gould, 1855) and x versus log R (Table III in Peirce, 1852 and Table IV in Gould, 1855) are no longer necessary.


In mathematical optimization, the perturbation function is any function which relates to primal and dual problems. The name comes from the fact that any such function defines a perturbation of the initial problem. In many cases this takes the form of shifting the constraints.In some texts the value function is called the perturbation function, and the perturbation function is called the bifunction.


In the following example, the four bytes represent a KLV set where the key is one byte, the length field is one byte (or possibly BER - you cannot tell from the example), and the value is two bytes: a zero and a three. In your application you would have previously agreed to a) use one-byte keys and b) use one-byte length encoding. Also presumably the key value "42" would mean something to you, perhaps it indicates that the value bytes 0x00 and 0x03 are an integer representing the value of your bicycle's odometer.


In the United States, biomedical research containing human subjects is governed by a baseline standard of ethics known as The Common Rule, which aims to protect a subject's privacy by requiring "identifiers" such as name or address to be removed from collected data. A 2012 report by the Presidential Commission for the Study of Bioethical Issues stated, however, that "what constitutes 'identifiable' and 'de-identified' data is fluid and that evolving technologies and the increasing accessibility of data could allow de-identified data to become re-identified". In fact, research has already shown that it is "possible to discover a study participant's identity by cross-referencing research data about him and his DNA sequence …  genetic genealogy and public-records databases". This has led to calls for policy-makers to establish consistent guidelines and best practices for the accessibility and usage of individual genomic data collected by researchers.Privacy protections for genetic research participants were strengthened by provisions of the 21st Century Cures Act (H.R.34) passed on 7 December 2016 for which the American Society of Human Genetics (ASHG) commended Congress, Senator Warren and Senator Enzi.The Genetic Information Nondiscrimination Act of 2008 (GINA) protects the genetic privacy of the public, including research participants.


f ( x x ) ) . {\displaystyle {\textsf {Y}}=\lambda f.\ (\lambda x.f\ (x\ x))\ (\lambda x.f\ (x\ x))\ . }: 131 In functional programming, the Y combinator can be used to formally define recursive functions in a programming language that does not support recursion.


In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle c} can satisfy the equation a n + b n = c n {\displaystyle a^{n}+b^{n}=c^{n}} for any integer value of n {\displaystyle n} greater than two. This theorem was first conjectured by Pierre de Fermat in 1637 in the margin of a copy of Arithmetica, where he claimed that he had a proof that was too large to fit in the margin. The first successful proof was released in 1994 by Andrew Wiles, and formally published in 1995, after 358 years of effort by mathematicians. The unsolved problem stimulated the development of algebraic number theory in the 19th century, and the proof of the modularity theorem in the 20th century. It is among the most notable theorems in the history of mathematics, and prior to its proof it was in the Guinness Book of World Records for "most difficult mathematical problems".


In static typing, all expressions have their types determined before a program executes, typically at compile-time. For example, 1 and (2+2) are integer expressions; they cannot be passed to a function that expects a string or stored in a variable that is defined to hold dates.Statically-typed languages can be either manifestly typed or type-inferred. In the first case, the programmer must explicitly write types at certain textual positions (for example, at variable declarations). In the second case, the compiler infers the types of expressions and declarations based on context.


In software development, a signal can mean synchronous events (sequences of samples, video frames, etc., with constant sample rate or frame rate) rather than asynchronous events, while the word event and data flow is often used for asynchronous event queues, but this is by no means universal. This language was created in the 1950s Konrad Zuse. Especially in telecommunications, electrical engineering and signal processing, a digital signal is a sampled representation of an analog physical entity. In telecommunications, the term signalling means asynchronous phone call metadata information exchange, for example of telephone numbers. One application of synchronous signal programming is observer pattern.


Those are the only two "tenses" in Arabic (not counting أَمْر amr, command or imperative, which is traditionally considered as denoting future events.) To explicitly mark aspect, Arabic uses a variety of lexical and syntactic devices. Contemporary Arabic dialects are another matter.


The correspondence had been described, in a rather different form, much earlier by Robinson (Robinson 1938), in an attempt to prove the Littlewood–Richardson rule. The correspondence is often referred to as the Robinson–Schensted algorithm, although the procedure used by Robinson is radically different from the Schensted algorithm, and almost entirely forgotten.


The compartments are not described, though it is implied that each compartment is greater than the previous one and is joined based on one's merit. The first compartment is for Jewish martyrs, the second for those who drowned, the third for "Rabbi Johanan ben Zakkai and his disciples," the fourth for those whom the cloud of glory carried off, the fifth for penitents, the sixth for youths who have never sinned; and the seventh for the poor who lived decently and studied the Torah.In chapter two, Legends of the Jews gives a brief description of the lower Gan Eden. The tree of knowledge is a hedge around the tree of life, which is so vast that "it would take a man five hundred years to traverse a distance equal to the diameter of the trunk".


In statistics, alternative hypothesis is often denoted as Ha or H1. Hypotheses are formulated to compare in a statistical hypothesis test. In the domain of inferential statistics two rival hypotheses can be compared by explanatory power and predictive power.


The concept of F-statistics was developed during the 1920s by the American geneticist Sewall Wright, who was interested in inbreeding in cattle. However, because complete dominance causes the phenotypes of homozygote dominants and heterozygotes to be the same, it was not until the advent of molecular genetics from the 1960s onwards that heterozygosity in populations could be measured. F can be used to define effective population size.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 25678, 125678, 245678, and 1245678 are the patterns related to Braille pattern dots-13456, since the two additional dots of kantenji patterns 013456, 134567, and 0134567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


However, since only Alice knows b {\displaystyle b} , it makes it virtually impossible for either Bob or Eve to distinguish the states of the qubits. Bob proceeds to generate a string of random bits b ′ {\displaystyle b'} of the same length as b {\displaystyle b} , and uses those bits for his choice of basis when measuring the qubits transmitted by Alice. At this point, Bob announces publicly that he has received Alice's transmission.


In mathematics, the max–min inequality is as follows: For any function f: Z × W → R , {\displaystyle \ f:Z\times W\to \mathbb {R} \ ,} sup z ∈ Z inf w ∈ W f ( z , w ) ≤ inf w ∈ W sup z ∈ Z f ( z , w ) . {\displaystyle \sup _{z\in Z}\inf _{w\in W}f(z,w)\leq \inf _{w\in W}\sup _{z\in Z}f(z,w)\ .} When equality holds one says that f, W, and Z satisfies a strong max–min property (or a saddle-point property). The example function f ( z , w ) = sin  ( z + w ) {\displaystyle \ f(z,w)=\sin(z+w)\ } illustrates that the equality does not hold for every function. A theorem giving conditions on f, W, and Z which guarantee the saddle point property is called a minimax theorem.


Some languages, such as Haskell, do not substitute structurally in the case where an expected type is declared (i.e., not inferred), e.g., only substitute for functions that are signature-based polymorphic via type inference. Then it is not possible to accidentally subtype a non-inferred type, although it may still be possible to provide an explicit conversion to a non-inferred type, which is invoked implicitly. Structural subtyping is arguably more flexible than nominative subtyping, as it permits the creation of ad hoc types and protocols; in particular, it permits creation of a type which is a supertype of an existing type, without modifying the definition of the latter.


Honeytokens do not necessarily prevent any tampering with the data, but instead give the administrator a further measure of confidence in the data integrity. Honeytokens are fictitious words or records that are added to legitimate databases. They allow administrators to track data in situations they wouldn't normally be able to track, such as cloud-based networks.


In order to facilitate discussion, some notational conventions need explaining. The expression ϕ A , x , a ¯ = { x ∈ A: A ⊨ ϕ  } {\displaystyle \phi ^{A,x,{\bar {a}}}=\{x\in A\colon A\models \phi \}} for A an L-structure (or L-model) in a language L, φ an L-formula, and a ¯ {\displaystyle {\bar {a}}} a tuple of elements of the domain dom(A) of A. In other words, ϕ A , x , a ¯ {\displaystyle \phi ^{A,x,{\bar {a}}}} denotes a (monadic) property defined on dom(A). In general, where x is replaced by an n-tuple x ¯ {\displaystyle {\bar {x}}} of free variables, ϕ A , x ¯ , a ¯ {\displaystyle \phi ^{A,{\bar {x}},{\bar {a}}}} denotes an n-ary relation defined on dom(A). Each quantifier Q A {\displaystyle Q_{A}} is relativized to a structure, since each quantifier is viewed as a family of relations (between relations) on that structure.


L-matrices have the additional property that all diagonal entries are greater than zero. M-matrices have several equivalent definitions, one of which is as follows: a Z-matrix is an M-matrix if it is nonsingular and its inverse is nonnegative. All matrices that are both Z-matrices and P-matrices are nonsingular M-matrices. In the context of quantum complexity theory, these are referred to as stoquastic operators.


In statistics, a unit is one member of a set of entities being studied. It is the main source for the mathematical abstraction of a "random variable". Common examples of a unit would be a single person, animal, plant, manufactured item, or country that belongs to a larger collection of such entities being studied.


Moreover, Krüger rejects Davidson's claim that the argument can refute the correspondence theory of truth. Stephen Neale (1995) claims, controversially, that the most compelling version was suggested by Kurt Gödel (1944). These arguments are sometimes modified to support the alternative, and evidently stronger, conclusion that there is only one fact, or one true proposition, state of affairs, truth condition, truthmaker, and so on.


In the absence of all three lines of evidence mentioned above, linguistic substrata may be difficult to detect. Substantial indirect evidence is needed to infer the former existence of a substrate. The nonexistence of a substrate is difficult to show, and to avoid digressing into speculation, burden of proof must lie on the side of the scholar claiming the influence of a substrate. The principle of uniformitarianism and results from the study of human genetics suggest that many languages have formerly existed that have since then been replaced under expansive language families, such as Indo-European, Afro-Asiatic, Uralic or Bantu.


In mathematics and computer science, a string metric (also known as a string similarity metric or string distance function) is a metric that measures distance ("inverse similarity") between two text strings for approximate string matching or comparison and in fuzzy string searching. A requirement for a string metric (e.g. in contrast to string matching) is fulfillment of the triangle inequality. For example, the strings "Sam" and "Samuel" can be considered to be close. A string metric provides a number indicating an algorithm-specific indication of distance.


Increment 2c: Signed in January 2009. This extended the DII footprint into the above-Secret domain to support a number of key operations and intelligence initiatives.


In telecommunications, 5G is the fifth-generation technology standard for broadband cellular networks, which cellular phone companies began deploying worldwide in 2019, and is the successor to 4G networks which provide connectivity to most current cellphones. Like its predecessors, 5G networks are cellular networks, in which the service area is divided into small geographical areas called cells. All 5G wireless devices in a cell are connected to the Internet and telephone network by radio waves through a local antenna in the cell.


CFA was first developed by Jöreskog (1969) and has built upon and replaced older methods of analyzing construct validity such as the MTMM Matrix as described in Campbell & Fiske (1959).In confirmatory factor analysis, the researcher first develops a hypothesis about what factors they believe are underlying the measures used (e.g., "Depression" being the factor underlying the Beck Depression Inventory and the Hamilton Rating Scale for Depression) and may impose constraints on the model based on these a priori hypotheses. By imposing these constraints, the researcher is forcing the model to be consistent with their theory. For example, if it is posited that there are two factors accounting for the covariance in the measures, and that these factors are unrelated to each other, the researcher can create a model where the correlation between factor A and factor B is constrained to zero.


The speed at which an innovation spreads through a mass of people depends on how favorably an idea is perceived by the audience. Innovations that are ill matched with existing techniques are not as well accepted and diffused through the group. Social structures are naturally designed in a hierarchy; thus, different ideas follow different routes or courses in the hierarchy, depending on the type and source of an innovation.The study of the diffusion of innovations has led to advancements in awareness of three important aspects of social change: the qualities of an innovation which lead to successful diffusion, the effect of peer networking and conversations when it comes to spreading ideas, and the importance of various "user segments" (Robinson).


If the pulse contains more than one photon, then Eve can split off the extra photons and transmit the remaining single photon to Bob. This is the basis of the photon number splitting attack, where Eve stores these extra photons in a quantum memory until Bob detects the remaining single photon and Alice reveals the encoding basis. Eve can then measure her photons in the correct basis and obtain information on the key without introducing detectable errors.


More precisely, subresultants are defined for polynomials over any commutative ring R, and have the following property. Let φ be a ring homomorphism of R into another commutative ring S. It extends to another homomorphism, denoted also φ between the polynomials rings over R and S. Then, if P and Q are univariate polynomials with coefficients in R such that deg  ( P ) = deg  ( φ ( P ) ) {\displaystyle \deg(P)=\deg(\varphi (P))} and deg  ( Q ) = deg  ( φ ( Q ) ) , {\displaystyle \deg(Q)=\deg(\varphi (Q)),} then the subresultant polynomials and the principal subresultant coefficients of φ(P) and φ(Q) are the image by φ of those of P and Q. The subresultants have two important properties which make them fundamental for the computation on computers of the GCD of two polynomials with integer coefficients. Firstly, their definition through determinants allows bounding, through Hadamard inequality, the size of the coefficients of the GCD. Secondly, this bound and the property of good specialization allow computing the GCD of two polynomials with integer coefficients through modular computation and Chinese remainder theorem (see below).


The duality gap is the difference of the right and left hand sides of the inequality sup y ∗ ∈ Y ∗ − F ∗ ( 0 , y ∗ ) ≤ inf x ∈ X F ( x , 0 ) . {\displaystyle \sup _{y^{*}\in Y^{*}}-F^{*}\left(0,y^{*}\right)\leq \inf _{x\in X}F(x,0).} This principle is the same as weak duality. If the two sides are equal to each other, then the problem is said to satisfy strong duality. There are many conditions for strong duality to hold such as: F = F ∗ ∗ {\displaystyle F=F^{**}} where F {\displaystyle F} is the perturbation function relating the primal and dual problems and F ∗ ∗ {\displaystyle F^{**}} is the biconjugate of F {\displaystyle F} ; the primal problem is a linear optimization problem; Slater's condition for a convex optimization problem.


Given these, the following program unsoundly applies a function meant for integers to a Boolean value.The above program type checks using Hindley-Milner because c is given the type ∀ α . ( α → α ) r e f {\textstyle \forall \alpha . (\alpha \to \alpha )\ {\mathtt {ref}}} , which is then instantiated to be of the type ( i n t → i n t ) r e f {\textstyle ({\mathtt {int}}\to {\mathtt {int}})\ {\mathtt {ref}}} when typing the assignment c := (fn x => x + 1), and ( b o o l → b o o l ) r e f {\textstyle ({\mathtt {bool}}\to {\mathtt {bool}})\ {\mathtt {ref}}} ref when typing the dereference !c true.


Unconditionally secure ideal quantum coin flipping was shown impossible by Lo and Chau. Moreover, Lo showed that there cannot be unconditionally secure quantum protocols for one-out-of-two oblivious transfer and other secure two-party computations. However, unconditionally secure relativistic protocols for coin flipping and bit-commitment have been shown by Kent.


In number theory, the aliquot sum s(n) of a positive integer n is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, s ( n ) = ∑ d | n , d ≠ n d . {\displaystyle s(n)=\sum \nolimits _{d|n,\ d\neq n}d.} It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number.


In terms of the clinical evaluation, clinical features are the classification method


In number theory, a polite number is a positive integer that can be written as the sum of two or more consecutive positive integers. A positive integer which is not polite is called impolite. The impolite numbers are exactly the powers of two, and the polite numbers are the natural numbers that are not powers of two. Polite numbers have also been called staircase numbers because the Young diagrams which represent graphically the partitions of a polite number into consecutive integers (in the French notation of drawing these diagrams) resemble staircases. If all numbers in the sum are strictly greater than one, the numbers so formed are also called trapezoidal numbers because they represent patterns of points arranged in a trapezoid.The problem of representing numbers as sums of consecutive integers and of counting the number of representations of this type has been studied by Sylvester, Mason, Leveque, and many other more recent authors. The polite numbers describe the possible numbers of sides of the Reinhardt polygons.


It is the federal drug law that regulates manufacture, importation, possession, use, and distribution of controlled substances. The legislation classes these substances into five schedules, with varying qualifications for each schedule. The schedules are designated schedule I, schedule II, schedule III, schedule IV, and schedule V. Many drugs require a prescription, even though they are not a controlled substance.


The ResNet paper, however, provided strong experimental evidence of the benefits of going deeper than 20 layers. It argued that the identity mapping without modulation is crucial and mentioned that modulation in the skip connection can still lead to vanishing signals in forward and backward propagation (Section 3 in ). This is also why the forget gates of the 2000 LSTM were initially opened through positive bias weights: as long as the gates are open, it behaves like the 1997 LSTM.


In modern practice, a violation of the Compulsory Process Clause leads to the reversal of a conviction unless the original error is "harmless". This occurs because the exclusion of defense evidence can "significantly undermine fundamental elements of the  defense". The remedy is not automatic reversal only because not every Sixth Amendment error is automatically a Due Process error.


In mathematics, the incompressibility method is a proof method like the probabilistic method, the counting method or the pigeonhole principle. To prove that an object in a certain class (on average) satisfies a certain property, select an object of that class that is incompressible. If it does not satisfy the property, it can be compressed by computable coding. Since it can be generally proven that almost all objects in a given class are incompressible, the argument demonstrates that almost all objects in the class have the property involved (not just the average). To select an incompressible object is ineffective, and cannot be done by a computer program. However, a simple counting argument usually shows that almost all objects of a given class can be compressed by only a few bits (are incompressible).


If the distance is Euclidean distance, the rational quadratic covariance function is also isotropic. The rational quadratic covariance between two points separated by d distance units is given by C ( d ) = ( 1 + d 2 2 α k 2 ) − α {\displaystyle C(d)={\Bigg (}1+{\frac {d^{2}}{2\alpha k^{2}}}{\Bigg )}^{-\alpha }} where α and k are non-negative parameters of the covariance. == References ==


, A n ⊨ C {\displaystyle A_{1},A_{2},...,A_{n}\models C} . In other words, a system is sound when all of its theorems are tautologies. Soundness is among the most fundamental properties of mathematical logic.


In mathematics, a block matrix pseudoinverse is a formula for the pseudoinverse of a partitioned matrix. This is useful for decomposing or approximating many algorithms updating parameters in signal processing, which are based on the least squares method.


In most operating systems predating Unix, programs had to explicitly connect to the appropriate input and output devices. OS-specific intricacies caused this to be a tedious programming task. On many systems it was necessary to obtain control of environment settings, access a local file table, determine the intended data set, and handle hardware correctly in the case of a punch card reader, magnetic tape drive, disk drive, line printer, card punch, or interactive terminal. One of Unix's several groundbreaking advances was abstract devices, which removed the need for a program to know or care what kind of devices it was communicating with.


In social media, a story is a function in which the user tells a narrative or provides status messages and information in the form of short, time-limited clips from several automatically running sequences. A story is usually displayed on a user's profile page and thus represents an audiovisual extension to the text-based status function.


In statistics, asymptotic theory, or large sample theory, is a framework for assessing properties of estimators and statistical tests. Within this framework, it is often assumed that the sample size n may grow indefinitely; the properties of estimators and tests are then evaluated under the limit of n → ∞. In practice, a limit evaluation is considered to be approximately valid for large finite sample sizes too.


The first rod was then carried to the end of the third, an operation to be repeated 1,370 times. The final measurement gave the length of the base as 27,404.01 ft. (8,352 metres).


In number theory, the gcd-sum function, also called Pillai's arithmetical function, is defined for every n {\displaystyle n} by P ( n ) = ∑ k = 1 n gcd ( k , n ) {\displaystyle P(n)=\sum _{k=1}^{n}\gcd(k,n)} or equivalently P ( n ) = ∑ d ∣ n d φ ( n / d ) {\displaystyle P(n)=\sum _{d\mid n}d\varphi (n/d)} where d {\displaystyle d} is a divisor of n {\displaystyle n} and φ {\displaystyle \varphi } is Euler's totient function. it also can be written as P ( n ) = ∑ d ∣ n d τ ( d ) μ ( n / d ) {\displaystyle P(n)=\sum _{d\mid n}d\tau (d)\mu (n/d)} where, τ {\displaystyle \tau } is the divisor function, and μ {\displaystyle \mu } is the Möbius function. This multiplicative arithmetical function was introduced by the Indian mathematician Subbayya Sivasankaranarayana Pillai in 1933.


If prior distributions are available, then even an underdetermined system can be solved using the Bayesian MMSE estimator. In statistics, linear least squares problems correspond to a particularly important type of statistical model called linear regression which arises as a particular form of regression analysis. One basic form of such a model is an ordinary least squares model. The present article concentrates on the mathematical aspects of linear least squares problems, with discussion of the formulation and interpretation of statistical regression models and statistical inferences related to these being dealt with in the articles just mentioned. See outline of regression analysis for an outline of the topic.


Fibonacci actually lists several different methods for constructing Egyptian fraction representations. He includes the greedy method as a last resort for situations when several simpler methods fail; see Egyptian fraction for a more detailed listing of these methods. As Salzer (1948) details, the greedy method, and extensions of it for the approximation of irrational numbers, have been rediscovered several times by modern mathematicians, earliest and most notably by J. J. Sylvester (1880) A closely related expansion method that produces closer approximations at each step by allowing some unit fractions in the sum to be negative dates back to Lambert (1770). The expansion produced by this method for a number x {\displaystyle x} is called the greedy Egyptian expansion, Sylvester expansion, or Fibonacci–Sylvester expansion of x {\displaystyle x} . However, the term Fibonacci expansion usually refers, not to this method, but to representation of integers as sums of Fibonacci numbers.


In the context of forensic linguistics, author profiling is used to identify characteristics of the author of anonymous, pseudonymous or forged text, based on the author's use of the language. Through linguistic analysis, forensic linguists seek to identify the suspect's motivation and ideology, along with other class features, such as the suspect's ethnicity or profession. While this does not always lead to decisive author identification, such information can help law enforcement narrow the pool of suspects.In most cases, author profiling in the context of forensic linguistics involves a single text problem, in which there is either no or few comparison texts available and no external evidence that points to the author. Examples of text analysed by forensic linguists include blackmailing letters, confessions, testaments, suicide letters and plagiarised writing.


that minimizes the expected loss. This is known as a generalized Bayes rule with respect to π ( θ ) {\displaystyle \pi (\theta )\,\!} .


A matrix is said to be d-disjunct if no set of d columns has a boolean sum which is a superset of any other single column.The following relationships are "well-known": Every d + 1 ¯ {\displaystyle {\overline {d+1}}} -separable matrix is also d {\displaystyle d} -disjunct. Every d {\displaystyle d} -disjunct matrix is also d ¯ {\displaystyle {\overline {d}}} -separable. Every d ¯ {\displaystyle {\overline {d}}} -separable matrix is also d {\displaystyle d} -separable (by definition).


In mathematical physics, the ternary commutator is an additional ternary operation on a triple system defined by  = a b c − a c b − b a c + b c a + c a b − c b a . {\displaystyle =abc-acb-bac+bca+cab-cba.\,} Also called the ternutator or alternating ternary sum, it is a special case of the n-commutator for n = 3, whereas the 2-commutator is the ordinary commutator.


This results in a total of P {\displaystyle P} parallel block transfers. A second approach needs O ( log  ( P ) ) {\displaystyle O(\log(P))} parallel block transfers and an additional block for each processor. The main idea is to schedule the write operations in a binary tree fashion and gradually combine the data into a single block.


In production, research, retail, and accounting, a cost is the value of money that has been used up to produce something or deliver a service, and hence is not available for use anymore. In business, the cost may be one of acquisition, in which case the amount of money expended to acquire it is counted as cost. In this case, money is the input that is gone in order to acquire the thing. This acquisition cost may be the sum of the cost of production as incurred by the original producer, and further costs of transaction as incurred by the acquirer over and above the price paid to the producer.


Then, we adjust all weights W ( k ) {\displaystyle W(k)} by multiplying it by its benchmark factor F ( C ) {\displaystyle F(C)} , for its cell C {\displaystyle C} . The net result is that the estimated W {\displaystyle W}  will now equal the benchmark target total T {\displaystyle T} . But the more important benefit is that the estimate of the total of Y {\displaystyle Y}  will tend to be more accurate.


In mathematics, a Benz plane is a type of 2-dimensional geometrical structure, named after the German mathematician Walter Benz. The term was applied to a group of objects that arise from a common axiomatization of certain structures and split into three families, which were introduced separately: Möbius planes, Laguerre planes, and Minkowski planes.


By a similar argument, b − n = 1 / b n {\displaystyle b^{-n}=1/b^{n}} . The properties of fractional exponents also follow from the same rule. For example, suppose we consider b {\displaystyle {\sqrt {b}}} and ask if there is some suitable exponent, which we may call r {\displaystyle r} , such that b r = b {\displaystyle b^{r}={\sqrt {b}}} .


February 1, 1673, at a meeting of the Royal Society of London, he demonstrated his mechanical calculator. The curator of the experiments of the Society, Robert Hooke, carefully examined the device and even removed the back cover for this.


After finding that a few other networks, including some social and biological networks, also had heavy-tailed degree distributions, Barabási and Réka Albert coined the term "scale-free network" to describe the class of networks that exhibit a power-law degree distribution. However, studying seven examples of networks in social, economic, technological, biological, and physical systems, Amaral et al. were not able to find a scale-free network among these seven examples. Only one of these examples, the movie-actor network, had degree distribution P(k) following a power law regime for moderate k, though eventually this power law regime was followed by a sharp cutoff showing exponential decay for large k.Barabási and Réka Albert proposed a generative mechanism to explain the appearance of power-law distributions, which they called "preferential attachment" and which is essentially the same as that proposed by Price.


With the rise of digital distribution, distinctions have become more tenuous. The biggest digital music distributor, the iTunes Store, only accepts releases with three tracks or fewer that are less than ten minutes each as a singles (with longer releases being classified as EPs or albums). However, releases which don't fit these criteria have been promoted as singles by artists and labels elsewhere, such as on the Bandcamp storefront. Historically, when mainstream music was purchased via vinyl records, singles would be released double-sided, i.e. there was an A-side and a B-side, on which two songs would appear, one on each side.


{\displaystyle P=\{~\{1,2\},\{3,4\},\{5,6\},\ldots \}.} The deleted integer topology is defined by letting X = ⋃ n ∈ N ( n − 1 , n ) ⊆ R {\displaystyle X={\begin{matrix}\bigcup _{n\in \mathbb {N} }(n-1,n)\subseteq \mathbb {R} \end{matrix}}} and P = { ( 0 , 1 ) , ( 1 , 2 ) , ( 2 , 3 ) , … } . {\displaystyle P={\left\{(0,1),(1,2),(2,3),\ldots \right\}}.}


Kleene having switched from presenting his work in the terminology of Church-Kleene lambda definability, to that of Gödel-Kleene recursiveness (partial recursive functions). In this transition, Kleene modified Gödel's general recursive functions to allow for proofs of the unsolvability of problems in the Intuitionism of E. J. Brouwer. In his graduate textbook on logic, "Church's thesis" is introduced and basic mathematical results are demonstrated to be unrealizable.


Further, a mathematician's claim could be undermined by counter-claims that he had not truly invented an idea, but merely improved on someone else's idea, an improvement that required little skill, and was based on facts that were already known.A series of high-profile disputes about the scientific priority of the 17th century – the era that the American science historian D. Meli called "the golden age of the mud-slinging priority disputes" – is associated with the name Leibniz. The first of them occurred at the beginning of 1673, during his first visit to London, when in the presence of the famous mathematician John Pell he presented his method of approximating series by differences. To Pell's remark that this discovery had already been made by François Regnaud and published in 1670 in Lyon by Gabriel Mouton, Leibniz answered the next day.


A call setup procedure may fail due to a number of technical reasons. Such calls are classified as failed call attempts. In many practical cases, this definition needs to be further expanded with a number of detailed specifications describing which calls exactly are counted as successfully set up and which not.


So, these languages usually allow arbitrary new elements to be created at any time. This choice precludes the implementation of array types as array data structures. That is, those languages use array-like syntax to implement a more general associative array semantics, and must therefore be implemented by a hash table or some other search data structure.


Linear least squares problems are convex and have a closed-form solution that is unique, provided that the number of data points used for fitting equals or exceeds the number of unknown parameters, except in special degenerate situations. In contrast, non-linear least squares problems generally must be solved by an iterative procedure, and the problems can be non-convex with multiple optima for the objective function.


In the balanced assignment problem, both parts of the bipartite graph have the same number of vertices, denoted by n. One of the first polynomial-time algorithms for balanced assignment was the Hungarian algorithm. It is a global algorithm – it is based on improving a matching along augmenting paths (alternating paths between unmatched vertices). Its run-time complexity, when using Fibonacci heaps, is O ( m n + n 2 log  n ) {\displaystyle O(mn+n^{2}\log n)} , where m is a number of edges. This is currently the fastest run-time of a strongly polynomial algorithm for this problem.


The argument x does not belong to the function, but the two together make a whole (ib. p. 6 " (Russell 1903:505).)


In the decade preceding Unix, computers had grown enormously in power – to the point where computer operators were looking for new ways to get people to use their spare time on their machines. One of the major developments during this era was time-sharing, whereby a number of users would get small slices of computer time, at a rate at which it appeared they were each connected to their own, slower, machine.The development of time-sharing systems led to a number of problems. One was that users, particularly at universities where the systems were being developed, seemed to want to hack the system to get more CPU time.


Suppose that we estimate the regression model y = β 0 + β 1 x + u , {\displaystyle y=\beta _{0}+\beta _{1}x+u,\,} and obtain from this fitted model a set of values for u ^ {\displaystyle {\widehat {u}}} , the residuals. Ordinary least squares constrains these so that their mean is 0 and so, given the assumption that their variance does not depend on the independent variables, an estimate of this variance can be obtained from the average of the squared values of the residuals. If the assumption is not held to be true, a simple model might be that the variance is linearly related to independent variables.


A function f: D → R {\displaystyle f\colon D\to \mathbb {R} } is sequentially computable if, for every n {\displaystyle n} -tuplet ( { x i 1 } i = 1 ∞ , … { x i n } i = 1 ∞ ) {\displaystyle \left(\{x_{i\,1}\}_{i=1}^{\infty },\ldots \{x_{i\,n}\}_{i=1}^{\infty }\right)} of computable sequences of real numbers such that ( ∀ i ) ( x i 1 , … x i n ) ∈ D , {\displaystyle (\forall i)\quad (x_{i\,1},\ldots x_{i\,n})\in D\qquad ,} the sequence { f ( x i ) } i = 1 ∞ {\displaystyle \{f(x_{i})\}_{i=1}^{\infty }} is also computable. This article incorporates material from Computable real function on PlanetMath, which is licensed under the Creative Commons Attribution/Share-Alike License. == References ==


Thus, it is possible to exploit data transport level parallelism by scheduling several data transports in the same instruction. An addition operation can be executed in a TTA processor as follows: r1 -> ALU.operand1 r2 -> ALU.add.trigger ALU.result -> r3 The second move, a write to the second operand of the function unit called ALU, triggers the addition operation. This makes the result of addition available in the output port 'result' after the execution latency of the 'add'. The ports associated with the ALU may act as an accumulator, allowing creation of macro instructions that abstract away the underlying TTA:


In spoken Welsh, the word ddim (not) often occurs with a prefixed or mutated verb form that is negative in meaning: Dydy hi ddim yma (word-for-word, "Not-is she not here") expresses "She is not here" and Chaiff Aled ddim mynd (word-for-word, "Not-will-get Aled not go") expresses "Aled is not allowed to go". Negative correlatives can also occur with already negative verb forms. In literary Welsh, the mutated verb form is caused by an initial negative particle, ni or nid. The particle is usually omitted in speech but the mutation remains:  wyddai neb (word-for-word, " not-knew nobody") means "Nobody knew" and  chaiff Aled fawr o bres (word-for-word, " not-will-get Aled lots of money") means "Aled will not get much money". This is not usually regarded as three negative markers, however, because the negative mutation is really just an effect of the initial particle on the following word.


In sociology, structural cohesion is the conception of a useful formal definition and measure of cohesion in social groups. It is defined as the minimal number of actors in a social network that need to be removed to disconnect the group. It is thus identical to the question of the node connectivity of a given graph in discrete mathematics. The vertex-cut version of Menger's theorem also proves that the disconnection number is equivalent to a maximally sized group with a network in which every pair of persons has at least this number of separate paths between them.


In mathematics, a strong prime is a prime number with certain special properties. The definitions of strong primes are different in cryptography and number theory.


Hans Moravec wrote in 1988: I am confident that this bottom-up route to artificial intelligence will one day meet the traditional top-down route more than half way, ready to provide the real-world competence and the commonsense knowledge that has been so frustratingly elusive in reasoning programs. Fully intelligent machines will result when the metaphorical golden spike is driven uniting the two efforts. However, this is disputed.


In scholarly and scientific publishing, altmetrics are non-traditional bibliometrics proposed as an alternative or complement to more traditional citation impact metrics, such as impact factor and h-index. The term altmetrics was proposed in 2010, as a generalization of article level metrics, and has its roots in the #altmetrics hashtag. Although altmetrics are often thought of as metrics about articles, they can be applied to people, journals, books, data sets, presentations, videos, source code repositories, web pages, etc. Altmetrics use public APIs across platforms to gather data with open scripts and algorithms.


The goal is to find a maximum profit feasible solution. Mathematically the generalized assignment problem can be formulated as an integer program: maximize ∑ i = 1 m ∑ j = 1 n p i j x i j . subject to ∑ j = 1 n w i j x i j ≤ t i i = 1 , … , m ; ∑ i = 1 m x i j ≤ 1 j = 1 , … , n ; x i j ∈ { 0 , 1 } i = 1 , … , m , j = 1 , … , n ; {\displaystyle {\begin{aligned}{\text{maximize }}&\sum _{i=1}^{m}\sum _{j=1}^{n}p_{ij}x_{ij}.\\{\text{subject to }}&\sum _{j=1}^{n}w_{ij}x_{ij}\leq t_{i}&&i=1,\ldots ,m;\\&\sum _{i=1}^{m}x_{ij}\leq 1&&j=1,\ldots ,n;\\&x_{ij}\in \{0,1\}&&i=1,\ldots ,m,\quad j=1,\ldots ,n;\end{aligned}}}


In general, if P ( s i ) {\displaystyle \;P(s_{i})} is the probability that our system is in state s i {\displaystyle \;s_{i}} , P ( s 1 ) P ( s 2 ) = Ω R ( s 1 ) Ω R ( s 2 ) . {\displaystyle {\frac {P(s_{1})}{P(s_{2})}}={\frac {\Omega _{R}(s_{1})}{\Omega _{R}(s_{2})}}.} Since the entropy of the reservoir S R = k ln  Ω R {\displaystyle \;S_{R}=k\ln \Omega _{R}} , the above becomes P ( s 1 ) P ( s 2 ) = e S R ( s 1 ) / k e S R ( s 2 ) / k = e ( S R ( s 1 ) − S R ( s 2 ) ) / k .


The requirement that the convex set K {\displaystyle K} be compact can be weakened to give the following strengthened generalization version of the theorem. The property above is sometimes called quasicompactness or convex compactness. Compactness implies convex compactness because a topological space is compact if and only if every family of closed subsets having the finite intersection property (FIP) has non-empty intersection (that is, its kernel is not empty). The definition of convex compactness is similar to this characterization of compact spaces in terms of the FIP, except that it only involves those closed subsets that are also convex (rather than all closed subsets).


In mathematics and theoretical computer science, a constant-recursive sequence is an infinite sequence of numbers where each number in the sequence is equal to a fixed linear combination of one or more of its immediate predecessors. A constant-recursive sequence is also known as a linear recurrence sequence, linear-recursive sequence, linear-recurrent sequence, a C-finite sequence, or a solution to a linear recurrence with constant coefficients. The most famous example of a constant-recursive sequence is the Fibonacci sequence 0 , 1 , 1 , 2 , 3 , 5 , 8 , 13 , … {\displaystyle 0,1,1,2,3,5,8,13,\ldots } , in which each number is the sum of the previous two. The power of two sequence 1 , 2 , 4 , 8 , 16 , … {\displaystyle 1,2,4,8,16,\ldots } is also constant-recursive because each number is the sum of twice the previous number.


The analysis may also show one or more exception paths. An exception path is taken as the result of a fault condition. Use cases and the resulting interactions are commonly modeled in graphical languages such as the Unified Modeling Language (UML) or SysML.


{\displaystyle e(g^{a},g^{b})=e(g,g)^{ab}=e(g,g^{ab}).} Thus, if h = g a b {\displaystyle h=g^{ab}} , then the values e ( g a , g b ) {\displaystyle e(g^{a},g^{b})} and e ( g , h ) {\displaystyle e(g,h)} will be equal. Since this cryptographic assumption, essential to building ElGamal encryption and signatures, does not hold in this case, new assumptions are needed to build cryptography in symmetric bilinear groups. The DLIN assumption is a modification of Diffie-Hellman type assumptions to thwart the above attack.


Concrete datatypes have their representation as part of their name. Abstract datatypes are structures of concrete datatypes — with a new name assigned. For example, a list of integers could be called integer_list.


In order to do so, they applied the scientific method to human behavior. The first published study in the field was Norman Triplett's 1898 experiment on the phenomenon of social facilitation. These psychological experiments later went on to form the foundation of much of 20th century social psychological findings.


14. Identifying operational rules defining the use of the concept, which can be stated in a language and which cover all or most cases (material conditional). 15.


In probability theory, the matrix-exponential distribution is an absolutely continuous distribution with rational Laplace–Stieltjes transform. They were first introduced by David Cox in 1955 as distributions with rational Laplace–Stieltjes transforms.The probability density function is f ( x ) = α e x T s for x ≥ 0 {\displaystyle f(x)=\mathbf {\alpha } e^{x\,T}\mathbf {s} {\text{ for }}x\geq 0} (and 0 when x < 0), and the cumulative distribution function is F ( t ) = 1 − α e A t 1 {\displaystyle F(t)=1-\alpha e^{{\textbf {A}}t}{\textbf {1}}} where 1 is a vector of 1s and α ∈ R 1 × n , T ∈ R n × n , s ∈ R n × 1 . {\displaystyle {\begin{aligned}\alpha &\in \mathbb {R} ^{1\times n},\\T&\in \mathbb {R} ^{n\times n},\\s&\in \mathbb {R} ^{n\times 1}.\end{aligned}}} There are no restrictions on the parameters α, T, s other than that they correspond to a probability distribution. There is no straightforward way to ascertain if a particular set of parameters form such a distribution. The dimension of the matrix T is the order of the matrix-exponential representation.The distribution is a generalisation of the phase-type distribution.


In mathematics, the Halpern–Läuchli theorem is a partition result about finite products of infinite trees. Its original purpose was to give a model for set theory in which the Boolean prime ideal theorem is true but the axiom of choice is false. It is often called the Halpern–Läuchli theorem, but the proper attribution for the theorem as it is formulated below is to Halpern–Läuchli–Laver–Pincus or HLLP (named after James D. Halpern, Hans Läuchli, Richard Laver, and David Pincus), following Milliken (1979). Let d,r < ω, ⟨ T i: i ∈ d ⟩ {\displaystyle \langle T_{i}:i\in d\rangle } be a sequence of finitely splitting trees of height ω. Let ⋃ n ∈ ω ( ∏ i < d T i ( n ) ) = C 1 ∪ ⋯ ∪ C r , {\displaystyle \bigcup _{n\in \omega }\left(\prod _{i


In physics, the view of the universe and its workings as the ebb and flow of information was first observed by Wheeler. Consequently, two views of the world emerged: the first one proposes that the universe is a quantum computer, while the other one proposes that the system performing the simulation is distinct from its simulation (the universe). Of the former view, quantum-computing specialist Dave Bacon wrote, In many respects this point of view may be nothing more than a result of the fact that the notion of computation is the disease of our age—everywhere we look today we see examples of computers, computation, and information theory and thus we extrapolate this to our laws of physics. Indeed, thinking about computing as arising from faulty components, it seems as if the abstraction that uses perfectly operating computers is unlikely to exist as anything but a platonic ideal. Another critique of such a point of view is that there is no evidence for the kind of digitization that characterizes computers nor are there any predictions made by those who advocate such a view that have been experimentally confirmed.


Although more advanced algorithms such as simulated annealing or tabu search may give better results, in some situations hill climbing works just as well. Hill climbing can often produce a better result than other algorithms when the amount of time available to perform a search is limited, such as with real-time systems, so long as a small number of increments typically converges on a good solution (the optimal solution or a close approximation). At the other extreme, bubble sort can be viewed as a hill climbing algorithm (every adjacent element exchange decreases the number of disordered element pairs), yet this approach is far from efficient for even modest N, as the number of exchanges required grows quadratically. Hill climbing is an anytime algorithm: it can return a valid solution even if it's interrupted at any time before it ends.


The Workshop on Mechanized Metatheory is the main meeting of researchers participating in the challenge. The design of the POPLmark benchmark is guided by features common to reasoning about programming languages.


In probability theory, a random variable Y {\displaystyle Y} is said to be mean independent of random variable X {\displaystyle X} if and only if its conditional mean E ( Y | X = x ) {\displaystyle E(Y|X=x)} equals its (unconditional) mean E ( Y ) {\displaystyle E(Y)} for all x {\displaystyle x} such that the probability density/mass of X {\displaystyle X} at x {\displaystyle x} , f X ( x ) {\displaystyle f_{X}(x)} , is not zero. Otherwise, Y {\displaystyle Y} is said to be mean dependent on X {\displaystyle X} . Stochastic independence implies mean independence, but the converse is not true. ; moreover, mean independence implies uncorrelatedness while the converse is not true.


In mathematics, the Khintchine inequality, named after Aleksandr Khinchin and spelled in multiple ways in the Latin alphabet, is a theorem from probability, and is also frequently used in analysis. Heuristically, it says that if we pick N {\displaystyle N} complex numbers x 1 , … , x N ∈ C {\displaystyle x_{1},\dots ,x_{N}\in \mathbb {C} } , and add them together each multiplied by a random sign ± 1 {\displaystyle \pm 1} , then the expected value of the sum's modulus, or the modulus it will be closest to on average, will be not too far off from | x 1 | 2 + ⋯ + | x N | 2 {\displaystyle {\sqrt {|x_{1}|^{2}+\cdots +|x_{N}|^{2}}}} .


In ring theory, a branch of abstract algebra, a ring homomorphism is a structure-preserving function between two rings. More explicitly, if R and S are rings, then a ring homomorphism is a function f: R → S such that f is: addition preserving: f ( a + b ) = f ( a ) + f ( b ) {\displaystyle f(a+b)=f(a)+f(b)} for all a and b in R,multiplication preserving: f ( a b ) = f ( a ) f ( b ) {\displaystyle f(ab)=f(a)f(b)} for all a and b in R,and unit (multiplicative identity) preserving: f ( 1 R ) = 1 S {\displaystyle f(1_{R})=1_{S}} .Additive inverses and the additive identity are part of the structure too, but it is not necessary to require explicitly that they too are respected, because these conditions are consequences of the three conditions above. If in addition f is a bijection, then its inverse f−1 is also a ring homomorphism. In this case, f is called a ring isomorphism, and the rings R and S are called isomorphic.


In number theory, a multiplicative partition or unordered factorization of an integer n {\displaystyle n} is a way of writing n {\displaystyle n} as a product of integers greater than 1, treating two products as equivalent if they differ only in the ordering of the factors. The number n {\displaystyle n} is itself considered one of these products. Multiplicative partitions closely parallel the study of multipartite partitions, which are additive partitions of finite sequences of positive integers, with the addition made pointwise.


The Dow Jones Industrial Average and the S&P 500 primarily track U.S. markets, though some legacy international companies are included. The consumer price index tracks the variation in prices for different consumer goods and services over time in a constant geographical location and is integral to calculations used to adjust salaries, bond interest rates, and tax thresholds for inflation.


In statistical decision theory, where we are faced with the problem of estimating a deterministic parameter (vector) θ ∈ Θ {\displaystyle \theta \in \Theta } from observations x ∈ X , {\displaystyle x\in {\mathcal {X}},} an estimator (estimation rule) δ M {\displaystyle \delta ^{M}\,\!} is called minimax if its maximal risk is minimal among all estimators of θ {\displaystyle \theta \,\!} . In a sense this means that δ M {\displaystyle \delta ^{M}\,\!} is an estimator which performs best in the worst possible case allowed in the problem.


In mathematics, the graph Fourier transform is a mathematical transform which eigendecomposes the Laplacian matrix of a graph into eigenvalues and eigenvectors. Analogously to the classical Fourier transform, the eigenvalues represent frequencies and eigenvectors form what is known as a graph Fourier basis. The Graph Fourier transform is important in spectral graph theory. It is widely applied in the recent study of graph structured learning algorithms, such as the widely employed convolutional networks.


In other words, the "traditional spaces" are homogeneous spaces; but not for a uniquely determined group. Changing the group changes the appropriate geometric language. In today's language, the groups concerned in classical geometry are all very well known as Lie groups: the classical groups. The specific relationships are quite simply described, using technical language.


In negotiating a connection, an RTMP client sends and receives a data stream containing multiple elements, as a single command line. An on-demand stream typically includes the following elements:


In the experimental sciences, data collected from experiments are often visualized by a graph. For example, if one collects data on the speed of an object at certain points in time, one can visualize the data in a data table such as the following: Such a table representation of data is a great way to display exact values, but it can prevent the discovery and understanding of patterns in the values. In addition, a table display is often erroneously considered to be an objective, neutral collection or storage of the data (and may in that sense even be erroneously considered to be the data itself) whereas it is in fact just one of various possible visualizations of the data. Understanding the process described by the data in the table is aided by producing a graph or line chart of speed versus time.


Hence, it is not possible to carry out this computation in polynomial time on a Turing machine, but it is possible to compute it by polynomially many arithmetic operations. However, for the first condition, there are algorithms that run in a number of Turing machine steps bounded by a polynomial in the length of binary-encoded input, but do not take a number of arithmetic operations bounded by a polynomial in the number of input numbers.


6. The continuous envelope Env C A {\displaystyle {\text{Env}}_{\cal {C}}A} of a stereotype algebra A {\displaystyle A} is an envelope of A {\displaystyle A} in the category InvSteAlg {\displaystyle {\text{InvSteAlg}}} of all involutive stereotype algebras in the class DEpi {\displaystyle {\text{DEpi}}} of all dense epimorphisms in InvSteAlg {\displaystyle {\text{InvSteAlg}}} with respect to the class C ∗ {\displaystyle {\text{C}}^{*}} of all C*-algebras: Env C A = Env C ∗ DEpi A . {\displaystyle {\text{Env}}_{\cal {C}}A={\text{Env}}_{{\text{C}}^{*}}^{\text{DEpi}}A.}


Mathematically, h ( p , u ¯ ) = arg  min x ∑ i p i x i {\displaystyle h(p,{\bar {u}})=\arg \min _{x}\sum _{i}p_{i}x_{i}} s u b j e c t t o u ( x ) ≥ u ¯ {\displaystyle {\rm {subject~to}}\ \ u(x)\geq {\bar {u}}} .where h(p,u) is the Hicksian demand function, or commodity bundle demanded, at price vector p and utility level u ¯ {\displaystyle {\bar {u}}} . Here p is a vector of prices, and x is a vector of quantities demanded, so the sum of all pixi is total expenditure on all goods. (Note that if there is more than one vector of quantities that minimizes expenditure for the given utility, we have a Hicksian demand correspondence rather than a function.) Hicksian demand functions are useful for isolating the effect of relative prices on quantities demanded of goods, in contrast to Marshallian demand functions, which combine that with the effect of the real income of the consumer being reduced by a price increase, as explained below.


In mathematics, Lehmer's totient problem asks whether there is any composite number n such that Euler's totient function φ(n) divides n − 1. This is an unsolved problem. It is known that φ(n) = n − 1 if and only if n is prime. So for every prime number n, we have φ(n) = n − 1 and thus in particular φ(n) divides n − 1. D. H. Lehmer conjectured in 1932 that there are no composite numbers with this property.


The Hausdorff distance is the longest distance you can be forced to travel by an adversary who chooses a point in one of the two sets, from where you then must travel to the other set. In other words, it is the greatest of all the distances from a point in one set to the closest point in the other set. This distance was first introduced by Hausdorff in his book Grundzüge der Mengenlehre, first published in 1914, although a very close relative appeared in the doctoral thesis of Maurice Fréchet in 1906, in his study of the space of all continuous curves from  → R 3 {\displaystyle \to \mathbb {R} ^{3}} .


In statistics, the reduced chi-square statistic is used extensively in goodness of fit testing. It is also known as mean squared weighted deviation (MSWD) in isotopic dating and variance of unit weight in the context of weighted least squares.Its square root is called regression standard error, standard error of the regression, or standard error of the equation (see Ordinary least squares § Reduced chi-squared)


Naturality here means that there are natural isomorphisms between the pair of functors C ( F − , X ): D → S e t {\displaystyle {\mathcal {C}}(F-,X):{\mathcal {D}}\to \mathrm {Set} } and D ( − , G X ): D → S e t {\displaystyle {\mathcal {D}}(-,GX):{\mathcal {D}}\to \mathrm {Set} } for a fixed X {\displaystyle X} in C {\displaystyle {\mathcal {C}}} , and also the pair of functors C ( F Y , − ): C → S e t {\displaystyle {\mathcal {C}}(FY,-):{\mathcal {C}}\to \mathrm {Set} } and D ( Y , G − ): C → S e t {\displaystyle {\mathcal {D}}(Y,G-):{\mathcal {C}}\to \mathrm {Set} } for a fixed Y {\displaystyle Y} in D {\displaystyle {\mathcal {D}}} . The functor F {\displaystyle F} is called a left adjoint functor or left adjoint to G {\displaystyle G} , while G {\displaystyle G} is called a right adjoint functor or right adjoint to F {\displaystyle F} .


In the field of computer technology, it is known that using one-time authorization code (OTAC) through email, in a broad sense, and using one-time authorization code (OTAC) through web-application, in a professional sense. An email is one of the common ways of using OTACs. There are two main methods used. With the first method, a service provider sends a personalised one time URL to an authenticated email address e.g. @ucl.ac.uk; when the user clicks the URL, the server authenticates the user.


In mathematics and multivariate statistics, the centering matrix is a symmetric and idempotent matrix, which when multiplied with a vector has the same effect as subtracting the mean of the components of the vector from every component of that vector.


Various properties of relations are investigated. A relation R is reflexive if xRx holds for all x, and irreflexive if xRx holds for no x. It is symmetric if xRy always implies yRx, and asymmetric if xRy implies that yRx is impossible. It is transitive if xRy and yRz always implies xRz.


The decomposition process itself is called a Fourier transformation. Its output, the Fourier transform, is often given a more specific name, which depends on the domain and other properties of the function being transformed.


Additional performance can be wrung from systems by examining the instructions to find ones that operate on different types of data and adding units dedicated to that sort of data; this has led to the introduction of floating point units and, more recently, single instruction, multiple data (SIMD) units. The drawback to this approach is that it makes the CPU less generic; feeding the CPU with a program that uses almost all floating point instructions, for instance, will bog the FPUs while the other units sit idle. A more recent problem in modern CPU designs is the delay talking to the registers.


The comparison tree representing binary search has the fewest levels possible as every level above the lowest level of the tree is filled completely. Otherwise, the search algorithm can eliminate few elements in an iteration, increasing the number of iterations required in the average and worst case. This is the case for other search algorithms based on comparisons, as while they may work faster on some target values, the average performance over all elements is worse than binary search. By dividing the array in half, binary search ensures that the size of both subarrays are as similar as possible.


The implication is that it is the currency of the popularity that confers value, rather than any intrinsic quality of the music itself, or of popularity at previous times. If it is the case, a novelty in itself – though not necessarily all forms of novelty – is a key aspect of evaluation. In those cases, if a statement comparing two art forms does mention their respective states of novelty, there is no fallacy (e.g. "Song A is currently a much better bet for your party than song B. ").


In primary-based local-write protocols, primary copy moves between processes willing to perform an update. To update a data item, a process first moves it to its location. As a result, in this approach, successive write operations can be performed locally while each process can read their local copy of data items.


If function 1 does not send data to any of the other functions, the rest of the boxes to right of function 1 would be empty. If function 2 sends data to function 3 and function 5, then the data elements would be placed in the first and third boxes to the right of function 2. If any function sends data back to a previous function, then the associated box to the left of the function would have the data elements placed in it.


In survey methodology, systematic sampling is a statistical method involving the selection of elements from an ordered sampling frame. The most common form of systematic sampling is an equiprobability method. In this approach, progression through the list is treated circularly, with a return to the top once the list ends. The sampling starts by selecting an element from the list at random and then every kth element in the frame is selected, where k, is the sampling interval (sometimes known as the skip): this is calculated as: k = N n {\displaystyle k={\frac {N}{n}}} where n is the sample size, and N is the population size.


In the United States, trade secrets are not protected by law in the same manner as patents or trademarks. Historically, trademarks and patents are protected under federal statutes, the Lanham Act and Patent Act, respectively, while trade secrets are usually protected under state laws, and most states have enacted the Uniform Trade Secrets Act (UTSA), except for Massachusetts, New York, and North Carolina. However, since 2016 this situation changed with the enactment of the Defend Trade Secrets Act (DTSA), making trade secrets also protectable under a federal law. One of the differences between patents and trademarks, on the one hand, and trade secrets, on the other, is that a trade secret is protected only when the owner has taken reasonable measures to protect the information as a secret (see 18 U.S.C.


It is the amount by which some of the notes produced in Pythagorean tuning were flattened or sharpened to produce just minor and major thirds. In Pythagorean tuning, the only highly consonant intervals were the perfect fifth and its inversion, the perfect fourth. The Pythagorean major third (81:64) and minor third (32:27) were dissonant, and this prevented musicians from freely using triads and chords, forcing them to write music with relatively simple texture.


A number of key difficulties had been methodologically analyzed in the 1990s, including gradient diminishing and weak temporal correlation structure in the neural predictive models. All these difficulties were in addition to the lack of big training data and big computing power in these early days. Most speech recognition researchers who understood such barriers hence subsequently moved away from neural nets to pursue generative modeling approaches until the recent resurgence of deep learning starting around 2009–2010 that had overcome all these difficulties. Hinton et al. and Deng et al. reviewed part of this recent history about how their collaboration with each other and then with colleagues across four groups (University of Toronto, Microsoft, Google, and IBM) ignited a renaissance of applications of deep feedforward neural networks to speech recognition.


In medicine, the mean arterial pressure (MAP) is an average calculated blood pressure in an individual during a single cardiac cycle. Although methods of estimating MAP vary, a common calculation is to take one-third of the pulse pressure (the difference between the systolic and diastolic pressures), and add that amount to the diastolic pressure. A normal MAP is about 90 mmHg.MAP is altered by cardiac output and systemic vascular resistance. It is used clinically to estimate the risk of cardiovascular diseases, where a MAP of 90 mmHg or less is low risk, and a MAP of greater than 96 mmHg represents "stage one hypertension" with increased risk.


In the book, Moore argued that arrogance prevents humans from recognizing their kinship with nonhuman animals and grievously mistreating them, likening their "provincialist" attitude to chauvinism and racism: The denial by human animals of ethical relations to the rest of the animal world is a phenomenon not differing either in character or cause from the denial of ethical relations by a tribe, people, or race of human beings to the rest of the human world. : 276 Moore criticized the anthropocentrism of human beings, who "think of our acts toward non-human peoples  entirely from the human point of view. We never take the time to put ourselves in the places of our victims.


In natural language processing, deterministic parsing refers to parsing algorithms that do not backtrack. LR-parsers are an example. (This meaning of the words "deterministic" and "non-deterministic" differs from that used to describe nondeterministic algorithms.)


The AI then creates and executes whatever plan is calculated to maximize the value of its objective function. For example, AlphaZero chess has a simple objective function of "+1 if AlphaZero wins, -1 if AlphaZero loses". During the game, AlphaZero attempts to execute whatever sequence of moves it judges most likely to give the maximum value of +1. Similarly, a reinforcement learning system can have a "reward function" that allows the programmers to shape the AI's desired behavior. An evolutionary algorithm's behavior is shaped by a "fitness function".


In the following a brief description of applicable rules organized by source.


Sensitivity (or recall) is the ability of a test to correctly identify the people with disease. Specificity is the ability of the test to correctly identify those without the disease. Now presume two tests are performed on the same group of patients.


In number theory, a left-truncatable prime is a prime number which, in a given base, contains no 0, and if the leading ("left") digit is successively removed, then all resulting numbers are prime. For example, 9137, since 9137, 137, 37 and 7 are all prime. Decimal representation is often assumed and always used in this article. A right-truncatable prime is a prime which remains prime when the last ("right") digit is successively removed.


It allows one to deduce many properties of concrete computational complexity measures, such as time complexity or space complexity, from properties of axiomatically defined measures. In algorithmic information theory, the Kolmogorov complexity (also called descriptive complexity, algorithmic complexity or algorithmic entropy) of a string is the length of the shortest binary program that outputs that string. Minimum message length is a practical application of this approach.


In mathematics, the collage theorem characterises an iterated function system whose attractor is close, relative to the Hausdorff metric, to a given set. The IFS described is composed of contractions whose images, as a collage or union when mapping the given set, are arbitrarily close to the given set. It is typically used in fractal compression.


Since there are only countably many computable relations, there are also only countably many computable ordinals. Thus, ω 1 C K {\displaystyle \omega _{1}^{CK}} is countable. The computable ordinals are exactly the ordinals that have an ordinal notation in Kleene's O {\displaystyle {\mathcal {O}}} .


(See also partition function). This general result of the Gibbs algorithm is then a maximum entropy probability distribution. Statisticians identify such distributions as belonging to exponential families. == References ==


In numerical analysis, Stone's method, also known as the strongly implicit procedure or SIP, is an algorithm for solving a sparse linear system of equations. The method uses an incomplete LU decomposition, which approximates the exact LU decomposition, to get an iterative solution of the problem. The method is named after Harold S. Stone, who proposed it in 1968. The LU decomposition is an excellent general-purpose linear equation solver.


In the Deutsch–Jozsa problem, we are given a black box quantum computer known as an oracle that implements some function: f: { 0 , 1 } n → { 0 , 1 } {\displaystyle f\colon \{0,1\}^{n}\rightarrow \{0,1\}} The function takes n-bit binary values as input and produces either a 0 or a 1 as output for each such value. We are promised that the function is either constant (0 on all inputs or 1 on all inputs) or balanced (1 for exactly half of the input domain and 0 for the other half). The task then is to determine if f {\displaystyle f} is constant or balanced by using the oracle.


Several different clustering systems based on mutual information have been proposed. One is Marina Meilă's variation of information metric; another provides hierarchical clustering. Using genetic algorithms, a wide range of different fit-functions can be optimized, including mutual information. Also belief propagation, a recent development in computer science and statistical physics, has led to the creation of new types of clustering algorithms.


The data sources include, in particular: Revision Control, also known as version control. In this system every step of each individual developer is tracked for the entire life cycle of the software system. The data describes: “Which developer changed what when.” This data provides a basis for answering the question, “What effort or development cost has been invested in which areas of code?” Prominent revision control systems are Subversion, Git, Perforce, Mercurial, Synergy, ClearCase, … Software Test Systems.


In mathematics, the Miracle Octad Generator, or MOG, is a mathematical tool introduced by Rob T. Curtis for studying the Mathieu groups, binary Golay code and Leech lattice.


When considering race as a predictor for perceived popularity by asking a class how popular and important each other person is, African American students were rated most popular by their peers. Popularity in race was found to be correlated with athleticism, and because African Americans have a stereotype of being better at sports than individuals of other races, they are viewed as more popular. Additionally, White and Hispanic children were rated as more popular the better they succeeded in school and came from a higher socioeconomic background. No single factor can explain popularity, but instead the interaction between many factors such as race and athleticism vs. academics.


A Russell-style universe is a type whose terms are types. A Tarski-style universe is a type together with an interpretation operation allowing us to regard its terms as types.For example: The openendedness of Martin-Löf type theory is particularly manifest in the introduction of so-called universes. Type universes encapsulate the informal notion of reflection whose role may be explained as follows.


In the United States and Canada, callers pay the cost of connecting to the Gateway MSC of the subscriber's phone company, regardless of the actual location of the phone. As mobile numbers are given standard geographic numbers according to the North American Numbering Plan, callers pay the same to reach fixed phones and mobile phones in a given geographic area. Mobile subscribers pay for the connection time (typically using in-plan or prepaid minutes) for both incoming and outgoing calls. For outgoing calls, any long distance charges are billed as if they originate at the GMSC, even though it is the visiting MSC that completes the connection to the PSTN.


In number theory, the Fermat pseudoprimes make up the most important class of pseudoprimes that come from Fermat's little theorem.


Rules come in three types: formatting rules such as hiding or coloring a control, validation rules (e.g. allow only a nine-digit number), and action rules such as setting a field's value based on other fields. Rules can be triggered either by a user action such as clicking a button or by the evaluation of various conditions such as field values. For example, a conditional rule could be: "Set field 'Total' to 100 when field 'field1' is not blank".


In the context of a relational database, a row—also called a tuple—represents a single, implicitly structured data item in a table. In simple terms, a database table can be thought of as consisting of rows and columns. Each row in a table represents a set of related data, and every row in the table has the same structure. For example, in a table that represents companies, each row would represent a single company.


The work De musica by Johannes Cotto (also known as John Cotton or Johannes Afflighemensis) was illustrated with the blacksmith scene around 1250 by an anonymous book illuminator in the Cistercian Abbey of Aldersbach.Among the medieval music theorists who told the legend of the forge according to Boethius' version, were also Juan Gil de Zámora (Johannes Aegidius von Zamora), active in the late 13th and early 14th centuries, Johannes de Muris and Simon Tunstede in the 14th century, and Adam von Fulda on the threshold of the early modern period in the 15th century. As an opponent of the Pythagorean conception, which held that consonances were based on certain numerical ratios, Johannes de Grocheio emerged in the 13th century, starting from an Aristotelian perspective. Although he explicitly stated that Pythagoras had discovered the principles of music, and he told the legend of the forge citing Boethius, whom he considered trustworthy, he rejected the Pythagorean theory of consonance, which he wanted to reduce to a merely metaphorical expression.


In paleobotany, two terms were formerly used in the codes of nomenclature, "form genera" and "organ genera", to mean groups of fossils of a particular part of a plant, such as a leaf or seed, whose parent plant is not known because the fossils were preserved unattached to the parent plant. A later term "morphotaxa" also allows for differences in preservational state. These three terms have been replaced as of 2011 by provisions for "fossil-taxa" that are more similar to the provisions for other types of plants.Names given to organ genera could only be applied to the organs in question, and could not be extended to the entire organism. Fossil-taxon names can cover several parts of an organism, or several preservational states, but do not compete for priority with any names for the same organism that are based on a non-fossil type.The part of the plant was often, but not universally, indicated by the use of a suffix in the generic name: wood fossils may have generic names ending in -xylon leaf fossils generic names ending in -phyllum fruit fossils generic names ending in -carpon, -carpum or -carpus pollen fossils generic names ending in -pollis or -pollenoides.


In physical security and information security, access control (AC) is the selective restriction of access to a place or other resource, while access management describes the process. The act of accessing may mean consuming, entering, or using. Permission to access a resource is called authorization. Locks and login credentials are two analogous mechanisms of access control.


In statistics and econometrics, a distributed lag model is a model for time series data in which a regression equation is used to predict current values of a dependent variable based on both the current values of an explanatory variable and the lagged (past period) values of this explanatory variable.The starting point for a distributed lag model is an assumed structure of the form y t = a + w 0 x t + w 1 x t − 1 + w 2 x t − 2 + . . .


In the ARM processor architecture, 26-bit refers to the design used in the original ARM processors where the Program Counter (PC) and Processor Status Register (PSR) were combined into one 32-bit register (R15), the status flags filling the high 6 bits and the Program Counter taking up the lower 26 bits. In fact, because the program counter is always word-aligned the lowest two bits are always zero which allowed the designers to reuse these two bits to hold the processor's mode bits too. The four modes allowed were USR26, SVC26, IRQ26, FIQ26; contrast this with the 32 possible modes available when the program status was separated from the program counter in more recent ARM architectures.


There is no specific requirement for any particular transmission mode on the older bands, but in practice many legacy phones also have digital features such as DSSS and FHSS. Some cordless phones formerly advertised as 5.8 GHz actually transmit from base to phone on 5.8 GHz and transmit from phone to base on 2.4 GHz or 900 MHz, to conserve battery life. The 1.9 GHz band is used by the DECT 6.0 phone standard and is considered more secure than the other shared frequencies. The vast majority of new cordless phone devices sold in North America, whether connected by landline or to mobile phones (usually via Bluetooth), now use DECT 6.0. However, DECT 6.0's late start compared to DECT elsewhere has led to a large installed base of legacy cordless phones using other frequencies, many of which remain in use today despite increasingly common interference with the ever growing use of Wi-Fi, Bluetooth and other unlicensed digital radio standards, especially at 2.4 GHz and 5.8 GHz.


In mathematics, a tree is an undirected graph in which any two vertices are connected by exactly one simple path. Any connected graph without simple cycles is a tree. A tree data structure simulates a hierarchical tree structure with a set of linked nodes.


A 1983 anthology edited by Peter Achinstein provided a concise presentation by prominent philosophers on scientific evidence, including Carl Hempel (on the logic of confirmation), R. B. Braithwaite (on the structure of a scientific system), Norwood Russell Hanson (on the logic of discovery), Nelson Goodman (of grue fame, on a theory of projection), Rudolf Carnap (on the concept of confirming evidence), Wesley C. Salmon (on confirmation and relevance), and Clark Glymour (on relevant evidence). In 1990, William Bechtel provided four factors (clarity of the data, replication by others, consistency with results arrived at by alternative methods, and consistency with plausible theories of mechanisms) that biologists used to settle controversies about procedures and reliability of evidence.In 2001, Achinstein published his own book on the subject titled The Book of Evidence, in which, among other topics, he distinguished between four concepts of evidence: epistemic-situation evidence (evidence relative to a given epistemic situation), subjective evidence (considered to be evidence by a particular person at a particular time), veridical evidence (a good reason to believe that a hypothesis is true), and potential evidence (a good reason to believe that a hypothesis is highly probable). Achinstein defined all his concepts of evidence in terms of potential evidence, since any other kind of evidence must at least be potential evidence, and he argued that scientists mainly seek veridical evidence but they also use the other concepts of evidence, which rely on a distinctive concept of probability, and Achinstein contrasted this concept of probability with previous probabilistic theories of evidence such as Bayesian, Carnapian, and frequentist.Simplicity is one common philosophical criterion for scientific theories.


In statistics, Kruskal's most influential work is his seminal contribution to the formulation of multidimensional scaling. In computer science, his best known work is Kruskal's algorithm for computing the minimal spanning tree (MST) of a weighted graph. The algorithm first orders the edges by weight and then proceeds through the ordered list adding an edge to the partial MST provided that adding the new edge does not create a cycle. Minimal spanning trees have applications to the construction and pricing of communication networks.


The UNIVAC 1050 was an internally programmed computer with up to 32K of six-bit character memory, which was introduced in 1963. It was a one-address machine with 30-bit instructions, had a 4K operating system and was programmed in the PAL assembly language. The 1050 was used extensively by the U.S.


After contributions from other fields such as number theory and geometry, the group notion was generalized and firmly established around 1870. Modern group theory—an active mathematical discipline—studies groups in their own right. To explore groups, mathematicians have devised various notions to break groups into smaller, better-understandable pieces, such as subgroups, quotient groups and simple groups.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 2368, 12368, 23468, and 123468 are the patterns related to Braille pattern dots-1256, since the two additional dots of kantenji patterns 01256, 12567, and 012567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In natural and social science research, a protocol is most commonly a predefined procedural method in the design and implementation of an experiment. Protocols are written whenever it is desirable to standardize a laboratory method to ensure successful replication of results by others in the same laboratory or by other laboratories. Additionally, and by extension, protocols have the advantage of facilitating the assessment of experimental results through peer review. In addition to detailed procedures, equipment, and instruments, protocols will also contain study objectives, reasoning for experimental design, reasoning for chosen sample sizes, safety precautions, and how results were calculated and reported, including statistical analysis and any rules for predefining and documenting excluded data to avoid bias.Similarly, a protocol may refer to the procedural methods of health organizations, commercial laboratories, manufacturing plants, etc. to ensure their activities (e.g., blood testing at a hospital, testing of certified reference materials at a calibration laboratory, and manufacturing of transmission gears at a facility) are consistent to a specific standard, encouraging safe use and accurate results.Finally, in the field of social science, a protocol may also refer to a "descriptive record" of observed events or a "sequence of behavior" of one or more organisms, recorded during or immediately after an activity (e.g., how an infant reacts to certain stimuli or how gorillas behave in natural habitat) to better identify "consistent patterns and cause-effect relationships." These protocols may take the form of hand-written journals or electronically documented media, including video and audio capture.


In most practical cases, the stated prior data or testable information is given by a set of conserved quantities (average values of some moment functions), associated with the probability distribution in question. This is the way the maximum entropy principle is most often used in statistical thermodynamics. Another possibility is to prescribe some symmetries of the probability distribution. The equivalence between conserved quantities and corresponding symmetry groups implies a similar equivalence for these two ways of specifying the testable information in the maximum entropy method.


Semantic technologies are "meaning-centered". They involve but are not limited to the following areas of application: encoding/decoding of semantic representation, knowledge graphs of entities and their interrelationships, auto-recognition of topics and concepts, information and meaning extraction, semantic data integration, and taxonomies/classification.Given a question, semantic technologies can directly search topics, concepts, associations that span a vast number of sources. Semantic technologies provide an abstraction layer above existing IT technologies that enables bridging and interconnection of data, content, and processes. Second, from the portal perspective, semantic technologies can be thought of as a new level of depth that provides far more intelligent, capable, relevant, and responsive interaction than with information technologies alone. Semantic technologies would often leverage natural language processing and machine learning in order to extract topics, concepts, and associations between concepts in text.


In order to improve performance in a new instruction set architecture, the Cydrome processors were based on a very long instruction word (VLIW) containing instructions from parallel operations. Software pipelining in a custom Fortran compiler generated code that would run efficiently. The numeric processor used a 256 bit-wide instruction word with seven "fields". In most cases the compiler would find instructions that could run in parallel and place them together in a single word.


Some functional programming languages make explicit use of type constructors. A notable example is Haskell, in which all data type declarations are considered to declare type constructors, and basic types (or nullary type constructors) are called type constants. Type constructors may also be considered as parametric polymorphic data types.


In the Internet of things (IoT), 3GPP is going to submit evolution of NB-IoT and eMTC (LTE-M) as 5G technologies for the LPWA (Low Power Wide Area) use case.


Fermat's Last Theorem states that x k + y k = z k {\displaystyle x^{k}+y^{k}=z^{k}} is impossible in positive integers with k>2. The equation of a superellipse is | x / a | k + | y / b | k = 1 {\displaystyle |x/a|^{k}+|y/b|^{k}=1} . The squircle is the case k = 4 , a = b {\displaystyle k=4,a=b} .


A named identifier of each of the entities and their attributes that are represented in a database. A basic unit of information built on standard structures having a unique meaning and distinct units or values. In electronic record-keeping, a combination of characters or bytes referring to one separate item of information, such as name, address, or age.In the areas of databases and data systems more generally a data element is a concept forming part of a data model. As an element of data representation, a collection of data elements forms a data structure.


In order to understand a text, it is usually necessary to understand the spoken language associated with that text. In this way, writing systems are distinguished from many other symbolic communication systems. Once established, writing systems on the whole change more slowly than their spoken counterparts, and often preserve features and expressions which are no longer current in the spoken language. The great benefit of writing systems is their ability to maintain a persistent record of information expressed in a language, which can be retrieved independently of the initial act of formulation.


In mathematics, noncommutative projective geometry is a noncommutative analog of projective geometry in the setting of noncommutative algebraic geometry.


In the United Kingdom, South West Trains and Northern Rail have issued BlackBerry devices to guards in order to improve the communication between control, guards and passengers.In Canada, Toronto and many other municipalities within Canada have issued BlackBerry devices to most of its employees including but not limited to transportation, technical, water and operations inspection staff and all management staff in order to improve the communication between contracted construction companies, its winter maintenance operations and to assist and successfully organize multimillion-dollar contracts. The devices are the standard mobile device to receive e-mail redirected from GroupWise. As part of their Internet of Things endeavours, the company announced plans of moving into the shipping industry by adapting the smartphones devices to the communication necessities of freight containers.


In the field of control engineering, a map-based controller is a controller whose outputs are based on values derived from a pre-defined lookup table. The inputs to the controller are usually values taken from one or more sensors and are used to index the output values in the lookup table. By effectively placing the transfer function as discrete entries within a lookup table, engineers free to modify smaller sections or update the whole list of entries as required. == References ==


In parallel corpora single sentences in one language can be found translated into several sentences in the other and vice versa. Long sentences may be broken up, short sentences may be merged. There are even some languages that use writing systems without clear indication of a sentence end (for example, Thai). Sentence aligning can be performed through the Gale-Church alignment algorithm. Through this and other mathematical models efficient search and retrieval of the highest scoring sentence alignment is possible.


However, these models are derived under the concept that the respondent obtains some utility for each possible answer and gives the answer that provides the greatest utility. It might be more natural to think that the respondent has some latent measure or index associated with the question and answers in response to how high this measure is. Ordered logit and ordered probit models are derived under this concept.


In mathematics, −1 (negative one or minus one) is the additive inverse of 1, that is, the number that when added to 1 gives the additive identity element, 0. It is the negative integer greater than negative two (−2) and less than 0.


To receive the inversion of any prime, each number value is subtracted from 12 and the resulting number placed in the corresponding matrix cell (see twelve-tone technique). The retrograde inversion is the values of the inversion numbers read backwards. Therefore: A given prime zero (derived from the notes of Anton Webern's Concerto): 0, 11, 3, 4, 8, 7, 9, 5, 6, 1, 2, 10 The retrograde: 10, 2, 1, 6, 5, 9, 7, 8, 4, 3, 11, 0 The inversion: 0, 1, 9, 8, 4, 5, 3, 7, 6, 11, 10, 2 The retrograde inversion: 2, 10, 11, 6, 7, 3, 5, 4, 8, 9, 1, 0 More generally, a musical permutation is any reordering of the prime form of an ordered set of pitch classes or, with respect to twelve-tone rows, any ordering at all of the set consisting of the integers modulo 12.


In statistics and coding theory, a Hamming space (named after American mathematician Richard Hamming) is usually the set of all 2 N {\displaystyle 2^{N}} binary strings of length N. It is used in the theory of coding signals and transmission. More generally, a Hamming space can be defined over any alphabet (set) Q as the set of words of a fixed length N with letters from Q. If Q is a finite field, then a Hamming space over Q is an N-dimensional vector space over Q. In the typical, binary case, the field is thus GF(2) (also denoted by Z2).In coding theory, if Q has q elements, then any subset C (usually assumed of cardinality at least two) of the N-dimensional Hamming space over Q is called a q-ary code of length N; the elements of C are called codewords. In the case where C is a linear subspace of its Hamming space, it is called a linear code. A typical example of linear code is the Hamming code.


In practical use, inline assembly operating on values is rarely standalone as free-floating code. Since the programmer cannot predict what register a variable is assigned to, compilers typically provide a way to substitute them in as an extension. There are, in general, two types of inline assembly supported by C/C++ compilers: asm (or __asm__) in GCC. GCC uses a direct extension of the ISO rules: assembly code template is written in strings, with inputs, outputs, and clobbered registers specified after the strings in colons.