Operators had to maintain a steady rhythm, and the usual speed of operation was 30 words per minute.The table "shows the allocation of the Baudot code which was employed in the British Post Office for continental and inland services. A number of characters in the continental code are replaced by fractionals in the inland code. Code elements 1, 2 and 3 are transmitted by keys 1, 2 and 3, and these are operated by the first three fingers of the right hand.


The intent is to create standardized rules to maintain data integrity and enforce business rules throughout one or more related applications. Some industries use generalized data dictionaries as technical standards to ensure interoperability between systems. The real estate industry, for example, abides by a RESO's Data Dictionary to which the National Association of REALTORS mandates its MLSs comply with through its policy handbook. This intermediate mapping layer for MLSs' native databases is supported by software companies which provide API services to MLS organizations.


A different fairness notion, that can be guaranteed to more than 1/2 of the agents in each group, is the ordinal maximin-share approximation. For every integer c, there exists a ( 1 − 1 / 2 c − 1 ) {\displaystyle (1-1/2^{c-1})} -democratic 1-out-of-c MMS-fair allocation. These allocations can be found efficiently using a variant of round-robin item allocation, with weighted approval voting inside each group.


In more concrete terms, the uniform word problem can be expressed as a rewriting question, for literal strings. For a presentation P of a group G, P will specify a certain number of generators x, y, z, ...for G. We need to introduce one letter for x and another (for convenience) for the group element represented by x−1. Call these letters (twice as many as the generators) the alphabet Σ {\displaystyle \Sigma } for our problem. Then each element in G is represented in some way by a product abc ... pqrof symbols from Σ {\displaystyle \Sigma } , of some length, multiplied in G. The string of length 0 (null string) stands for the identity element e of G. The crux of the whole problem is to be able to recognise all the ways e can be represented, given some relations.


For example, a demand-side policy component may include placing public transit stops near development, in order to maximize walkability.Additionally, California state law requires minimum energy conservation levels for all new and/or existing development projects. The seller of a home is required to include information regarding energy conservation retrofitting and thermal insulation in the sales contract. : 133


In quantum computing, classical shadow is a protocol for predicting functions of a quantum state using only a logarithmic number of measurements. Given an unknown state ρ {\displaystyle \rho } , a tomographically complete set of gates U {\displaystyle U} (e.g Clifford gates), a set of M {\displaystyle M} observables { O i } {\displaystyle \{O_{i}\}} and a quantum channel M {\displaystyle M} (defined by randomly sampling from U {\displaystyle U} , applying it to ρ {\displaystyle \rho } and measuring the resulting state); predict the expectation values tr  ( O i ρ ) {\displaystyle \operatorname {tr} (O_{i}\rho )} . A list of classical shadows S {\displaystyle S} is created using ρ {\displaystyle \rho } , U {\displaystyle U} and M {\displaystyle M} by running a Shadow generation algorithm. When predicting the properties of ρ {\displaystyle \rho } , a Median-of-means estimation algorithm is used to deal with the outliers in S {\displaystyle S} .


In the first version of the AKS primality test paper, a conjecture about Sophie Germain primes is used to lower the worst-case complexity from O(log12n) to O(log6n). A later version of the paper is shown to have time complexity O(log7.5n) which can also be lowered to O(log6n) using the conjecture. Later variants of AKS have been proven to have complexity of O(log6n) without any conjectures or use of Sophie Germain primes.


In quantum mechanics, and especially quantum information and the study of open quantum systems, the trace distance T is a metric on the space of density matrices and gives a measure of the distinguishability between two states. It is the quantum generalization of the Kolmogorov distance for classical probability distributions.


The Finnish Pig Latin is called Kontinkieli ("container language"). After each word you add the word kontti "container", then switch the first syllables, So every sentence is converted to twice as many pseudo-words. For example,"wikipedia" ⟶ "wikipedia kontti" ⟶ "kokipedia wintti".


In mathematics, the multiplicity of a member of a multiset is the number of times it appears in the multiset. For example, the number of times a given polynomial has a root at a given point is the multiplicity of that root. The notion of multiplicity is important to be able to count correctly without specifying exceptions (for example, double roots counted twice).


Percentile scores and percentile ranks are often used in the reporting of test scores from norm-referenced tests, but, as just noted, they are not the same. For percentile ranks, a score is given and a percentage is computed. Percentile ranks are exclusive: if the percentile rank for a specified score is 90%, then 90% of the scores were lower. In contrast, for percentiles a percentage is given and a corresponding score is determined, which can be either exclusive or inclusive. The score for a specified percentage (e.g., 90th) indicates a score below which (exclusive definition) or at or below which (inclusive definition) other scores in the distribution fall.


In the 1990s, many of the notable early successes on statistical methods in natural-language programming (NLP) occurred in the field of machine translation, due especially to work at IBM Research. These systems were able to take advantage of existing multilingual textual corpora that had been produced by the Parliament of Canada and the European Union as a result of laws calling for the translation of all governmental proceedings into all official languages of the corresponding systems of government. There are corpora in non-European languages as well. For example, the National Institute for Japanese Language and Linguistics in Japan has built a number of corpora of spoken and written Japanese.


In statistics and in probability theory, distance correlation or distance covariance is a measure of dependence between two paired random vectors of arbitrary, not necessarily equal, dimension. The population distance correlation coefficient is zero if and only if the random vectors are independent. Thus, distance correlation measures both linear and nonlinear association between two random variables or random vectors. This is in contrast to Pearson's correlation, which can only detect linear association between two random variables. Distance correlation can be used to perform a statistical test of dependence with a permutation test. One first computes the distance correlation (involving the re-centering of Euclidean distance matrices) between two random vectors, and then compares this value to the distance correlations of many shuffles of the data.


A best-effort network or service does not support quality of service. An alternative to complex QoS control mechanisms is to provide high quality communication over a best-effort network by over-provisioning the capacity so that it is sufficient for the expected peak traffic load. The resulting absence of network congestion reduces or eliminates the need for QoS mechanisms.


In the algorithm, each sequence of concatenated strong characters is called a "run". A "weak" character that is located between two "strong" characters with the same orientation will inherit their orientation. A "weak" character that is located between two "strong" characters with a different writing direction will inherit the main context's writing direction (in an LTR document the character will become LTR, in an RTL document, it will become RTL).


In order theory, a discipline within mathematics, a critical pair is a pair of elements in a partially ordered set that are incomparable but that could be made comparable without requiring any other changes to the partial order. Formally, let P = (S, ≤) be a partially ordered set. Then a critical pair is an ordered pair (x, y) of elements of S with the following three properties: x and y are incomparable in P, for every z in S, if z < x then z < y, and for every z in S, if y < z then x < z.If (x, y) is a critical pair, then the binary relation obtained from P by adding the single relationship x ≤ y is also a partial order. The properties required of critical pairs ensure that, when the relationship x ≤ y is added, the addition does not cause any violations of the transitive property. A set R of linear extensions of P is said to reverse a critical pair (x, y) in P if there exists a linear extension in R for which y occurs earlier than x. This property may be used to characterize realizers of finite partial orders: A nonempty set R of linear extensions is a realizer if and only if it reverses every critical pair.


In mathematics, the Smith–Volterra–Cantor set (SVC), fat Cantor set, or ε-Cantor set is an example of a set of points on the real line that is nowhere dense (in particular it contains no intervals), yet has positive measure. The Smith–Volterra–Cantor set is named after the mathematicians Henry Smith, Vito Volterra and Georg Cantor. In an 1875 paper, Smith discussed a nowhere-dense set of positive measure on the real line, and Volterra introduced a similar example in 1881. The Cantor set as we know it today followed in 1883. The Smith–Volterra–Cantor set is topologically equivalent to the middle-thirds Cantor set.


For example, an 1871 census in the UK (the first of its kind, but personal data from other censuses dates back to 1841 and numerical data back to 1801) found the average male life expectancy as being 44, but if infant mortality is subtracted, males who lived to adulthood averaged 75 years. The present life expectancy in the UK is 77 years for males and 81 for females, while the United States averages 74 for males and 80 for females. Studies have shown that black American males have the shortest lifespans of any group of people in the US, averaging only 69 years (Asian-American females average the longest).


In mathematics, the notion of polyconvexity is a generalization of the notion of convexity for functions defined on spaces of matrices. Let Mm×n(K) denote the space of all m × n matrices over the field K, which may be either the real numbers R, or the complex numbers C. A function f: Mm×n(K) → R ∪ {±∞} is said to be polyconvex if A ↦ f ( A ) {\displaystyle A\mapsto f(A)} can be written as a convex function of the p × p subdeterminants of A, for 1 ≤ p ≤ min{m, n}. Polyconvexity is a weaker property than convexity. For example, the function f given by f ( A ) = { 1 det ( A ) , det ( A ) > 0 ; + ∞ , det ( A ) ≤ 0 ; {\displaystyle f(A)={\begin{cases}{\frac {1}{\det(A)}},&\det(A)>0;\\+\infty ,&\det(A)\leq 0;\end{cases}}} is polyconvex but not convex.


In mathematics, a ring class field is the abelian extension of an algebraic number field K associated by class field theory to the ring class group of some order O of the ring of integers of K.


The problem of determining whether a formula in propositional logic is satisfiable is decidable, and is known as the Boolean satisfiability problem, or SAT. In general, the problem of determining whether a sentence of first-order logic is satisfiable is not decidable. In universal algebra, equational theory, and automated theorem proving, the methods of term rewriting, congruence closure and unification are used to attempt to decide satisfiability. Whether a particular theory is decidable or not depends whether the theory is variable-free and on other conditions.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 2356, 12356, 23456, and 123456 are the patterns related to Braille pattern dots-1245, since the two additional dots of kantenji patterns 01245, 12457, and 012457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 2367, 12367, 23467, and 123467 are the patterns related to Braille pattern dots-1235, since the two additional dots of kantenji patterns 01235, 12357, and 012357 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


Unlike Javadoc tags, Java annotations can also be embedded in and read from Java class files generated by the Java compiler. This allows annotations to be retained by the Java virtual machine at run-time and read via reflection. It is possible to create meta-annotations out of the existing ones in Java.


In mathematical psychology and education theory, a knowledge space is a combinatorial structure used to formulate mathematical models describing the progression of a human learner. Knowledge spaces were introduced in 1985 by Jean-Paul Doignon and Jean-Claude Falmagne, and remain in extensive use in the education theory. Modern applications include two computerized tutoring systems, ALEKS and the defunct RATH.Formally, a knowledge space assumes that a domain of knowledge is a collection of concepts or skills, each of which must be eventually mastered.


In sociology of science, the graphism thesis is a proposition of Bruno Latour that graphs are important in science. Research has shown that one can distinguish between hard science and soft science disciplines based on the level of graph use, so it can be argued that there is a correlation between scientificity and visuality. Furthermore, natural sciences publications appear to make heavier use of graphs than mathematical and social sciences.It has been claimed that an example of a discipline that uses graphs heavily but is not at all scientific is technical analysis.


In mathematics, the notion of an (exact) dimension function (also known as a gauge function) is a tool in the study of fractals and other subsets of metric spaces. Dimension functions are a generalisation of the simple "diameter to the dimension" power law used in the construction of s-dimensional Hausdorff measure.


Given a linear system A x = b {\displaystyle \mathbf {A} \mathbf {x} =\mathbf {b} } where A is an n × n {\displaystyle n\times n} real symmetric sparse square matrix. The Cholesky factor L will typically suffer 'fill in', that is have more non-zeros than the upper triangle of A. We seek a permutation matrix P, so that the matrix P T A P {\displaystyle \mathbf {P} ^{T}\mathbf {A} \mathbf {P} } , which is also symmetric, has the least possible fill in its Cholesky factor. We solve the reordered system ( P T A P ) ( P T x ) = P T b .


Testing for failures such as ABA can be exceedingly difficult, because the problematic sequence of events is very rare. Model checking is an excellent way to uncover such problems. See for instance exercise 7.3.3 in "Modeling and analysis of communicating Systems".


In the agricultural industry, sodium polyacrylate is used to help plants retain moisture in the soil. It can act as a water reservoir for plants and is commonly used by florists to keep flowers fresh. Furthermore, the use of sodium polyacrylate for growing domestic fruit and vegetables has been approved by the U.S. Department of Agriculture.


In software engineering, many reuse metrics and models are metrics used to measure code reuse and reusability. A metric is a quantitative indicator of an attribute of a thing. A model specifies relationships among metrics.


In quantum computing, modular exponentiation appears as the bottleneck of Shor's algorithm, where it must be computed by a circuit consisting of reversible gates, which can be further broken down into quantum gates appropriate for a specific physical device. Furthermore, in Shor's algorithm it is possible to know the base and the modulus of exponentiation at every call, which enables various circuit optimizations.


Particularly in large software systems, any change to the source code may have unintended consequences, potentially introducing new bugs; thus, a code freeze helps ensure that a portion of the program that is known to work correctly will continue to do so. Code freezes are often employed in the final stages of development, when a particular release or iteration is being tested, but may also be used to prevent changes to one portion of a program while another is undergoing development. For example: "physics freeze" means no changes whatsoever will be permitted to the physics portion of the code.


In telecommunications, a message exchange pattern (MEP) describes the pattern of messages required by a communications protocol to establish or use a communication channel. The communications protocol is the format used to represent the message which all communicating parties agree on (or are capable to process). The communication channel is the infrastructure that enables messages to "travel" between the communicating parties. The message exchange patterns describe the message flow between parties in the communication process, there are two major message exchange patterns — a request–response pattern, and a one-way pattern.


In radio network protocols, leader election is often used as a first step to approach more advanced communication primitives, such as message gathering or broadcasts. The very nature of wireless networks induces collisions when adjacent nodes transmit at the same time; electing a leader allows to better coordinate this process. While the diameter D of a network is a natural lower bound for the time needed to elect a leader, upper and lower bounds for the leader election problem depend on the specific radio model studied.


In mathematics, differential refers to several related notions derived from the early days of calculus, put on a rigorous footing, such as infinitesimal differences and the derivatives of functions.The term is used in various branches of mathematics such as calculus, differential geometry, algebraic geometry and algebraic topology.


In probability, a singular distribution is a probability distribution concentrated on a set of Lebesgue measure zero, where the probability of each point in that set is zero.


Let G {\displaystyle G} be a group. Then the following is equivalent: G {\displaystyle G} is abelian. Every function on G {\displaystyle G} is a class function. All irreducible representations of G {\displaystyle G} have degree 1. {\displaystyle 1.}


In silico PCR refers to computational tools used to calculate theoretical polymerase chain reaction (PCR) results using a given set of primers (probes) to amplify DNA sequences from a sequenced genome or transcriptome.These tools are used to optimize the design of primers for target DNA or cDNA sequences. Primer optimization has two goals: efficiency and selectivity. Efficiency involves taking into account such factors as GC-content, efficiency of binding, complementarity, secondary structure, and annealing and melting point (Tm). Primer selectivity requires that the primer pairs not fortuitously bind to random sites other than the target of interest, nor should the primer pairs bind to conserved regions of a gene family.


In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is positive-definite. The conjugate gradient method is often implemented as an iterative algorithm, applicable to sparse systems that are too large to be handled by a direct implementation or other direct methods such as the Cholesky decomposition. Large sparse systems often arise when numerically solving partial differential equations or optimization problems.


A definition of distance between any two monads is defined and from this and probabilistic mathematical tools emerges a three-dimensional space.Axiomatic pregeometry by Perez, Bergliaffa, Romero and Vucetich An assortment of ontological presuppositions describes spacetime a result of relations between objectively existing entities. From presuppositions emerges the topology and metric of Minkowski spacetime.Cellular networks by Requardt Space is described by a graph with densely entangled sub-clusters of nodes (with differential states) and bonds (either vanishing at 0 or directed at 1). Rules describe the evolution of the graph from a chaotic patternless pre-Big Bang condition to a stable spacetime in the present.


Efforts to minimize leakage include the use of strained silicon, high-κ dielectrics, and/or stronger dopant levels in the semiconductor. Leakage reduction to continue Moore's law will not only require new material solutions but also proper system design. Certain types of semiconductor manufacturing defects exhibit themselves as increased leakage.


In the explanations below, any indication of a bit's position is counted from the right (least significant) side, advancing left. For example, the binary value 0001 (decimal 1) has zeroes at every position but the first (i.e., the rightmost) one.


Written test cases should include a description of the functionality to be tested, and the preparation required to ensure that the test can be conducted. A formal written test case is characterized by a known input and by an expected output, which is worked out before the test is executed. The known input should test a precondition and the expected output should test a postcondition.


In order to evaluate the methods a well understood family of languages is chosen, with a reliable dataset. This family is often the IE one but others have been used. After applying the methods to be compared to the database, the resulting trees are compared with the reference tree determined by traditional linguistic methods. The aim is to have no conflicts in topology, for example no missing sub-groups, and compatible dates. The families suggested for this analysis by Nichols and Warnow are Germanic, Romance, Slavic, Common Turkic, Chinese, and Mixe Zoque as well as older groups such as Oceanic and IE.


Any non-zero output indicates the offset error in the converter. That is, if the measurement of ground resulted in an output of 0.001 volts, one can assume that all measurements will be offset by the same amount and can subtract 0.001 from all subsequent results. Gain error can similarly be measured and corrected internally (again assuming that there is a constant gain error over the entire output range).


In mathematical finance, convexity refers to non-linearities in a financial model. In other words, if the price of an underlying variable changes, the price of an output does not change linearly, but depends on the second derivative (or, loosely speaking, higher-order terms) of the modeling function. Geometrically, the model is no longer flat but curved, and the degree of curvature is called the convexity.


In one restricted but very common sense of the term, a graph is an ordered pair G = ( V , E ) {\displaystyle G=(V,E)} comprising: V {\displaystyle V} , a set of vertices (also called nodes or points); E ⊆ { { x , y } ∣ x , y ∈ V and x ≠ y } {\displaystyle E\subseteq \{\{x,y\}\mid x,y\in V\;{\textrm {and}}\;x\neq y\}} , a set of edges (also called links or lines), which are unordered pairs of vertices (that is, an edge is associated with two distinct vertices).To avoid ambiguity, this type of object may be called precisely an undirected simple graph. In the edge { x , y } {\displaystyle \{x,y\}} , the vertices x {\displaystyle x} and y {\displaystyle y} are called the endpoints of the edge. The edge is said to join x {\displaystyle x} and y {\displaystyle y} and to be incident on x {\displaystyle x} and on y {\displaystyle y} . A vertex may exist in a graph and not belong to an edge.


Sanity testing and smoke testing avoid wasting time and effort by quickly determining whether an application is too flawed to merit more rigorous QA testing, but needs more developer debugging. Groups of sanity tests are often bundled together for automated unit testing of functions, libraries, or applications prior to merging development code into a testing or trunk version control branch, for automated building, or for continuous integration and continuous deployment.Another common usage of sanity test is to denote checks which are performed within programme code, usually on arguments to functions or returns therefrom, to see if the answers can be assumed to be correct. The more complicated the routine, the more important that its response be checked.


In telecommunication, the term security kernel has the following meanings: In computer and communications security, the central part of a computer or communications system hardware, firmware, and software that implements the basic security procedures for controlling access to system resources. A self-contained usually small collection of key security-related statements that (a) works as a part of an operating system to prevent unauthorized access to, or use of, the system and (b) contains criteria that must be met before specified programs can be accessed. Hardware, firmware, and software elements of a trusted computing base that implement the reference monitor concept.


In programming languages, name resolution can be performed either at compile time or at runtime. The former is called static name resolution, the latter is called dynamic name resolution. A somewhat common misconception is that dynamic typing implies dynamic name resolution. For example, Erlang is dynamically typed but has static name resolution.


In some languages, the gender of nouns can mostly be determined by physical (semantic) attributes, although there remain some nouns whose gender is not assigned in this way (Corbett calls this "semantic residue"). The world view (e.g. mythology) of the speakers may influence the division of categories. Zande has four genders: male human, female human, animal, and inanimate. However, there are about 80 nouns representing inanimate entities which are nonetheless animate in gender: heavenly objects (moon, rainbow), metal objects (hammer, ring), edible plants (sweet potato, pea), and non-metallic objects (whistle, ball).


In model checking, a subfield of computer science, a signal or timed state sequence is an extension of the notion of words in a formal language, in which letters are continuously emitted. While a word is traditionally defined as a function from a set of non-negative integers to letters, a signal is a function from a set of real numbers to letters. This allow the use of formalisms similar to the ones of automata theory to deal with continuous signals.


In proof complexity, a Frege system is a propositional proof system whose proofs are sequences of formulas derived using a finite set of sound and implicationally complete inference rules. Frege systems (more often known as Hilbert systems in general proof theory) are named after Gottlob Frege.


In mathematics, the minimum rank is a graph parameter mr  ( G ) {\displaystyle \operatorname {mr} (G)} for a graph G. It was motivated by the Colin de Verdière graph invariant.


In the United States, the National Weather Service gives out the advice "Turn Around, Don't Drown" for floods; that is, it recommends that people get out of the area of a flood, rather than trying to cross it. At the most basic level, the best defense against floods is to seek higher ground for high-value uses while balancing the foreseeable risks with the benefits of occupying flood hazard zones. : 22–23 Critical community-safety facilities, such as hospitals, emergency-operations centers, and police, fire, and rescue services, should be built in areas least at risk of flooding. Structures, such as bridges, that must unavoidably be in flood hazard areas should be designed to withstand flooding.


The receiving application may ask for this information to be retransmitted, possibly resulting in congestive collapse or unacceptable delays in the overall transmission. Errors Sometimes packets are corrupted due to bit errors caused by noise and interference, especially in wireless communications and long copper wires.


In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e., f P: O Y , f ( P ) → O X , P {\displaystyle f_{P}\colon {\mathcal {O}}_{Y,f(P)}\to {\mathcal {O}}_{X,P}} is a flat map for all P in X. A map of rings A → B {\displaystyle A\to B} is called flat if it is a homomorphism that makes B a flat A-module. A morphism of schemes is called faithfully flat if it is both surjective and flat.Two basic intuitions regarding flat morphisms are: flatness is a generic property; and the failure of flatness occurs on the jumping set of the morphism.The first of these comes from commutative algebra: subject to some finiteness conditions on f, it can be shown that there is a non-empty open subscheme Y ′ {\displaystyle Y'} of Y, such that f restricted to Y′ is a flat morphism (generic flatness). Here 'restriction' is interpreted by means of the fiber product of schemes, applied to f and the inclusion map of Y ′ {\displaystyle Y'} into Y. For the second, the idea is that morphisms in algebraic geometry can exhibit discontinuities of a kind that are detected by flatness. For instance, the operation of blowing down in the birational geometry of an algebraic surface, can give a single fiber that is of dimension 1 when all the others have dimension 0.


In the binary number system, each numerical digit has two possible states (0 or 1) and each successive digit represents an increasing power of two. Note: What follows is but one of several possible schemes for assigning the values 1, 2, 4, 8, 16, etc. to fingers, not necessarily the best. (see below the illustrations. ): The rightmost digit represents two to the zeroth power (i.e., it is the "ones digit"); the digit to its left represents two to the first power (the "twos digit"); the next digit to the left represents two to the second power (the "fours digit"); and so on.


For example, the graph query does the data inference through the connected relations, instead of repeated full search of the tables in relational database. KG facilitates the integration of new heterogeneous data by just adding new relationships between existing information and new entities. This facilitation is emphasized for the integration with existing popular linked open data source such as Wikidata.org.


We will also assume that all rings are unital, and all ring homomorphisms are unital. Many authors consider the more general concept of an associative algebra over a commutative ring R, instead of a field: An R-algebra is an R-module with an associative R-bilinear binary operation, which also contains a multiplicative identity. For examples of this concept, if S is any ring with center C, then S is an associative C-algebra.


Barbara Blackburn, who failed her QWERTY typing class in high school, first encountered the Dvorak layout in 1938 and then she quickly learned to achieve very high speeds of typing, also she occasionally toured giving speed-typing demonstrations during her secretarial career. She appeared on Late Night with David Letterman on January 24, 1985, but felt that Letterman made a spectacle of her.The recent emergence of several competitive typing websites has allowed fast typists on computer keyboards to emerge along with new records, though many of these are unverifiable. Some notable, verified records include 255 wpm on a one-minute, random-word test by a user under the username slekap and occasionally bailey, 213 wpm on a 1-hour, random-word test by Joshua Hu, 221 wpm average on 10 random quotes by Joshua Hu, and first place in the 2020 Ultimate Typing Championship by Anthony Ermollin based on an average of 180.88 wpm on texts of various lengths.


Region extraction: left and right hand detection based on a comparison between them. Characteristic extraction: location of the fingertips and to detect if it is a peak or a valley. To classify the point, peaks or valleys, these are transformed to 3D vectors, usually named pseudo vectors in the xy-plane, and then to compute the cross product.


A graph G is k-edge-choosable if every instance of list edge-coloring that has G as its underlying graph and that provides at least k allowed colors for each edge of G has a proper coloring. The edge choosability, or list edge colorability, list edge chromatic number, or list chromatic index, ch′(G) of graph G is the least number k such that G is k-edge-choosable. It is conjectured that it always equals the chromatic index.


In mathematics, the Cantor set is a set of points lying on a single line segment that has a number of unintuitive properties. It was discovered in 1874 by Henry John Stephen Smith and introduced by German mathematician Georg Cantor in 1883.Through consideration of this set, Cantor and others helped lay the foundations of modern point-set topology. The most common construction is the Cantor ternary set, built by removing the middle third of a line segment and then repeating the process with the remaining shorter segments.


In monolithic kernels, device drivers reside in the kernel. Thus, when a new peripheral is installed, unknown, untrusted code is inserted in the kernel. One bad line of code in a driver can bring down the system.


In the 2020s, concerns over ACs vulnerability to cyberattacks and data theft emerged.In 2018 and 2019 former Apple engineers were charged with stealing information related to Apple's self-driving car project. In 2021 the United States Department of Justice (DOJ) accused Chinese security officials of coordinating a hacking campaign to steal information from government entities, including research related to autonomous vehicles. China has prepared "the Provisions on Management of Automotive Data Security (Trial) to protect its own data".Cellular Vehicle-to-Everything technologies are based on 5G wireless networks. As of November 2022, the US Congress was considering the possibility that imported Chinese AC technology could facilitate espionage.


In older architectures, NMIs were used for interrupts which were typically never disabled because of the required response time. They were hidden signals. Examples include the floppy disk controller on the Amstrad PCW, the 8087 coprocessor on the x86 when used in the IBM PC or its compatibles (even though Intel recommended connecting it to a normal interrupt), and the Low Battery signal on the HP 95LX. In the original IBM PC, an NMI was triggered if a parity error was detected in system memory, or reported by an external device.


In numerical linear algebra, the alternating-direction implicit (ADI) method is an iterative method used to solve Sylvester matrix equations. It is a popular method for solving the large matrix equations that arise in systems theory and control, and can be formulated to construct solutions in a memory-efficient, factored form. It is also used to numerically solve parabolic and elliptic partial differential equations, and is a classic method used for modeling heat conduction and solving the diffusion equation in two or more dimensions. It is an example of an operator splitting method.


Internet protocols are designed for simplicity and modularity and fit into a coarse hierarchy of functional layers defined in the Internet Protocol Suite. The first two cooperating protocols, the Transmission Control Protocol (TCP) and the Internet Protocol (IP) resulted from the decomposition of the original Transmission Control Program, a monolithic communication protocol, into this layered communication suite. The OSI model was developed internationally based on experience with networks that predated the internet as a reference model for general communication with much stricter rules of protocol interaction and rigorous layering.


In probability and statistics, the inverse-chi-squared distribution (or inverted-chi-square distribution) is a continuous probability distribution of a positive-valued random variable. It is closely related to the chi-squared distribution. It arises in Bayesian inference, where it can be used as the prior and posterior distribution for an unknown variance of the normal distribution.


In statistical mechanics and mathematics, the Bethe lattice (also called a regular tree) is an infinite connected cycle-free graph where all vertices have the same number of neighbors. The Bethe lattice was introduced into the physics literature by Hans Bethe in 1935. In such a graph, each node is connected to z neighbors; the number z is called either the coordination number or the degree, depending on the field. Due to its distinctive topological structure, the statistical mechanics of lattice models on this graph are often easier to solve than on other lattices. The solutions are related to the often used Bethe ansatz for these systems.


In the Netherlands the then state-owned phone company PTT (now KPN) operated two platforms: Viditel (launched in 1980) and Videotex Nederland. From the user perspective the main difference between these systems was that Viditel used standard dial-in phone numbers where Videotex used premium-rate telephone numbers. For Viditel you needed a (paid) subscription and on top of that you paid for each page you visited. For Videotex services you normally didn't need a subscription nor was there the need to authenticate: you paid for the services via the premium rate of the modem-connection based on connection time, regardless of the pages or services you retrieved.


In multivariate statistics, if ε {\displaystyle \varepsilon } is a vector of n {\displaystyle n} random variables, and Λ {\displaystyle \Lambda } is an n {\displaystyle n} -dimensional symmetric matrix, then the scalar quantity ε T Λ ε {\displaystyle \varepsilon ^{T}\Lambda \varepsilon } is known as a quadratic form in ε {\displaystyle \varepsilon } .


Semantically textual data can be represented in binary format (e.g. when compressed or in certain formats that intermix various sorts of formatting codes, as in the doc format used by Microsoft Word); contrarily, image data is sometimes represented in textual format (e.g. the X PixMap image format used in the X Window System). 1 and 0 are nothing but just two different voltage levels. You can make the computer understand 1 for higher voltage and 0 for lower voltage.


Article 14 bis of the DADVSI law explicitly exempts from this regime the act of downloading a copyrighted work on a peer-to-peer network. This exemption is further extended to the act of making some copyrighted work available to the public without any commercial purpose, when this is an automatic result of the use of a peer-to-peer network for obtaining it; this clause was added because many peer-to-peer networks automatically make downloaded content available to other users, thus merely exempting downloads from the counterfeiting felony would not have been sufficient.


In the European Union, the treatment of VoIP service providers is a decision for each national telecommunications regulator, which must use competition law to define relevant national markets and then determine whether any service provider on those national markets has "significant market power" (and so should be subject to certain obligations). A general distinction is usually made between VoIP services that function over managed networks (via broadband connections) and VoIP services that function over unmanaged networks (essentially, the Internet).The relevant EU Directive is not clearly drafted concerning obligations that can exist independently of market power (e.g., the obligation to offer access to emergency calls), and it is impossible to say definitively whether VoIP service providers of either type are bound by them.


If the neighboring site is S, then let it become I. Repeat as long as there are S sites available.Making a list of I sites makes this run quickly. The net rate of infecting one neighbor over the rate of removal is λ = (1-c)/c. For the synchronous model, all sites are updated simultaneously (using two copies of the lattice) as in a cellular automaton.


In the following example, the text "Paul Schuster was born in Dresden" on a website will be annotated, connecting a person with their place of birth. The following HTML fragment shows how a small graph is being described, in RDFa-syntax using a schema.org vocabulary and a Wikidata ID: The example defines the following five triples (shown in Turtle syntax). Each triple represents one edge in the resulting graph: the first element of the triple (the subject) is the name of the node where the edge starts, the second element (the predicate) the type of the edge, and the last and third element (the object) either the name of the node where the edge ends or a literal value (e.g. a text, a number, etc.).


the first instance of "crypto" lines up with "abcdef" and the second instance lines up with "cdefab". The two instances will encrypt to different ciphertexts and the Kasiski examination will reveal nothing. However, with a 5-character keyword "abcde" (5 divides into 20): abcdeabcdeabcdeabcdeabcdeabcdeabc crypto is short for cryptography. both occurrences of "crypto" line up with "abcdea". The two instances will encrypt to the same ciphertext and the Kasiski examination will be effective.


In mathematics, the classic Möbius inversion formula is a relation between pairs of arithmetic functions, each defined from the other by sums over divisors. It was introduced into number theory in 1832 by August Ferdinand Möbius.A large generalization of this formula applies to summation over an arbitrary locally finite partially ordered set, with Möbius' classical formula applying to the set of the natural numbers ordered by divisibility: see incidence algebra.


Class 2 comprises mechanically propelled vehicles such as motorized wheelchairs and mobility scooters, limited to 4 mph. Class 3 consists mostly of mobility scooters. They are limited to 8 mph, with a further limiter set to 4 mph which must be enabled when used on a pavement.


These problems already trivially lie in co-NP. This was the first strong evidence that these problems are not NP-complete, since if they were, it would imply that NP is subset of co-NP, a result widely believed to be false; in fact, this was the first demonstration of a problem in NP intersect co-NP not known, at the time, to be in P. Producing certificates for the complement problem, to establish that a number is composite, is straightforward: it suffices to give a nontrivial divisor. Standard probabilistic primality tests such as the Baillie–PSW primality test, the Fermat primality test, and the Miller–Rabin primality test also produce compositeness certificates in the event where the input is composite, but do not produce certificates for prime inputs.


Depending on the author, such mappings may or may not be assumed to be linear, or to be defined on the whole space X . {\displaystyle X.} In computer science, it is synonymous with higher-order functions, that is, functions that take functions as arguments or return them.This article is mainly concerned with the second concept, which arose in the early 18th century as part of the calculus of variations.


(Conversation, in formal or informal settings is an example.) Written language, on the other hand, is the common mode used to convey objective information.Both vocal and sign languages are composed of words. In vocal languages, words are made up from a limited set of vowels and consonants, and often tone. In sign languages, words are made up from a limited set of shapes, orientations, locations movements of the hands, and often facial expressions; in both cases, the building blocks are called phonemes. In both vocal and sign languages, words are grammatically and prosodically linked into phrases, clauses, and larger units of discourse.


Interfaces are described in Microsoft Interface Definition Language. Type libraries can be viewed using various tools, such as the Microsoft OLE/COM Object Viewer (oleview.exe, part of the Microsoft Platform SDK) or the Object Browser in Visual Basic (up to version 6) and Visual Studio .NET. Type libraries are used to generate Proxy pattern/stub code for interoperating between COM and other platforms, such as Microsoft .NET and Java.


A system of equations is a subset E of the Cartesian product X∗ × X∗ of the free monoid (finite strings) over X with itself. The system E is satisfiable in S if there is a map f from X to S, which extends to a semigroup morphism f from X+ to S, such that for all (u,v) in E we have f(u) = f(v) in S. Such an f is a solution, or satisfying assignment, for the system E.Two systems of equations are equivalent if they have the same set of satisfying assignments. A system of equations if independent if it is not equivalent to a proper subset of itself. A semigroup is compact if every independent system of equations is finite.


To find an answer to this problem, a bipartite graph G' = (A ∪ B, E) is created where each flight has a copy in set A and set B. If the same plane can perform flight j after flight i, i∈A is connected to j∈B. A matching in G' induces a schedule for F and obviously maximum bipartite matching in this graph produces an airline schedule with minimum number of crews. As it is mentioned in the Application part of this article, the maximum cardinality bipartite matching is an application of maximum flow problem.


Silver proved the consistency of Chang's conjecture from the consistency of an ω1-Erdős cardinal. Hans-Dieter Donder showed a weak version of the reverse implication: if CC is not only consistent but actually holds, then ω2 is ω1-Erdős in K. More generally, Chang's conjecture for two pairs (α,β), (γ,δ) of cardinals is the claim that every model of type (α,β) for a countable language has an elementary submodel of type (γ,δ). The consistency of ( ω 3 , ω 2 ) ↠ ( ω 2 , ω 1 ) {\displaystyle (\omega _{3},\omega _{2})\twoheadrightarrow (\omega _{2},\omega _{1})} was shown by Laver from the consistency of a huge cardinal.


, then adding the transformed vectors. A v → + B v → = ( A + B ) v → {\displaystyle \mathbf {A} {\vec {v}}+\mathbf {B} {\vec {v}}=(\mathbf {A} +\mathbf {B} ){\vec {v}}\!} However, there are other operations that could also be considered addition for matrices, such as the direct sum and the Kronecker sum.


In mathematics, a Boolean function is a function whose arguments and result assume values from a two-element set (usually {true, false}, {0,1} or {-1,1}). Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic. Boolean functions are the subject of Boolean algebra and switching theory.A Boolean function takes the form f: { 0 , 1 } k → { 0 , 1 } {\displaystyle f:\{0,1\}^{k}\to \{0,1\}} , where { 0 , 1 } {\displaystyle \{0,1\}} is known as the Boolean domain and k {\displaystyle k} is a non-negative integer called the arity of the function. In the case where k = 0 {\displaystyle k=0} , the function is a constant element of { 0 , 1 } {\displaystyle \{0,1\}} .


This can be solved with a variant of Mahler and De Weger's lattice based analysis of N-adic numbers when N = 2 {\displaystyle N=2} ; by a variant of the Euclidean algorithm when N is prime; and in general by Xu's adaptation of the Berlekamp-Massey algorithm. If L is the size of the smallest FCSR that outputs the sequence (called the N-adic complexity of the sequence), then all these algorithms require a prefix of length about 2 L {\displaystyle 2L} to be successful and have quadratic time complexity.


In most reactor designs, as a safety measure, control rods are attached to the lifting machinery by electromagnets, rather than direct mechanical linkage. This means that in the event of power failure, or if manually invoked due to failure of the lifting machinery, the control rods fall automatically, under gravity, all the way into the pile to stop the reaction. A notable exception to this fail-safe mode of operation is the BWR, which requires hydraulic insertion in the event of an emergency shut-down, using water from a special tank under high pressure. Quickly shutting down a reactor in this way is called scramming.


It does not explicitly require the compiler to understand instruction names, as the compiler is only needed to substitute its register assignments, plus a few mov operations, to handle the input requirements. However, the user is prone to specifying clobbered registers incorrectly. The MSVC form of an embedded domain-specific language provides ease of writing, but it requires the compiler itself to know about opcode names and their clobbering properties, demanding extra attention in maintenance and porting.


Many sets that arise in mathematics do not allow a bijection to be established with {1, 2, ..., n} for any natural number n; these are called infinite sets, while those sets for which such a bijection does exist (for some n) are called finite sets. Infinite sets cannot be counted in the usual sense; for one thing, the mathematical theorems which underlie this usual sense for finite sets are false for infinite sets. Furthermore, different definitions of the concepts in terms of which these theorems are stated, while equivalent for finite sets, are inequivalent in the context of infinite sets.


In probability theory, Hoeffding's lemma is an inequality that bounds the moment-generating function of any bounded random variable. It is named after the Finnish–American mathematical statistician Wassily Hoeffding. The proof of Hoeffding's lemma uses Taylor's theorem and Jensen's inequality. Hoeffding's lemma is itself used in the proof of McDiarmid's inequality.


In probability theory and statistics, the Dirichlet process (DP) is one of the most popular Bayesian nonparametric models. It was introduced by Thomas Ferguson as a prior over probability distributions. A Dirichlet process D P ( s , G 0 ) {\displaystyle \mathrm {DP} \left(s,G_{0}\right)} is completely defined by its parameters: G 0 {\displaystyle G_{0}} (the base distribution or base measure) is an arbitrary distribution and s {\displaystyle s} (the concentration parameter) is a positive real number (it is often denoted as α {\displaystyle \alpha } ). According to the Bayesian paradigm these parameters should be chosen based on the available prior information on the domain.


In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share a birthday. The birthday paradox refers to the counterintuitive fact that only 23 people are needed for that probability to exceed 50%. The birthday paradox is a veridical paradox: it seems wrong at first glance but is, in fact, true. While it may seem surprising that only 23 individuals are required to reach a 50% probability of a shared birthday, this result is made more intuitive by considering that the birthday comparisons will be made between every possible pair of individuals.


Then: x  = ∑ k x k  , {\displaystyle x=\sum _{k}x_{k},\,} and y can be written as a sum of short convolutions: y  = ( ∑ k x k  ) ∗ h  = ∑ k ( x k  ∗ h  ) = ∑ k y k  , {\displaystyle {\begin{aligned}y=\left(\sum _{k}x_{k}\right)*h&=\sum _{k}\left(x_{k}*h\right)\\&=\sum _{k}y_{k},\end{aligned}}} where the linear convolution y k  ≜ x k  ∗ h  {\displaystyle y_{k}\ \triangleq \ x_{k}*h\,} is zero outside the region . And for any parameter N ≥ L + M − 1 , {\displaystyle N\geq L+M-1,\,} it is equivalent to the N-point circular convolution of x k  {\displaystyle x_{k}\,} with h  {\displaystyle h\,} in the region . The advantage is that the circular convolution can be computed more efficiently than linear convolution, according to the circular convolution theorem: where: DFTN and IDFTN refer to the Discrete Fourier transform and its inverse, evaluated over N discrete points, and L is customarily chosen such that N = L+M-1 is an integer power-of-2, and the transforms are implemented with the FFT algorithm, for efficiency.


In mathematics, a Relevance Vector Machine (RVM) is a machine learning technique that uses Bayesian inference to obtain parsimonious solutions for regression and probabilistic classification. The RVM has an identical functional form to the support vector machine, but provides probabilistic classification. It is actually equivalent to a Gaussian process model with covariance function: k ( x , x ′ ) = ∑ j = 1 N 1 α j φ ( x , x j ) φ ( x ′ , x j ) {\displaystyle k(\mathbf {x} ,\mathbf {x'} )=\sum _{j=1}^{N}{\frac {1}{\alpha _{j}}}\varphi (\mathbf {x} ,\mathbf {x} _{j})\varphi (\mathbf {x} ',\mathbf {x} _{j})} where φ {\displaystyle \varphi } is the kernel function (usually Gaussian), α j {\displaystyle \alpha _{j}} are the variances of the prior on the weight vector w ∼ N ( 0 , α − 1 I ) {\displaystyle w\sim N(0,\alpha ^{-1}I)} , and x 1 , … , x N {\displaystyle \mathbf {x} _{1},\ldots ,\mathbf {x} _{N}} are the input vectors of the training set.Compared to that of support vector machines (SVM), the Bayesian formulation of the RVM avoids the set of free parameters of the SVM (that usually require cross-validation-based post-optimizations). However RVMs use an expectation maximization (EM)-like learning method and are therefore at risk of local minima. This is unlike the standard sequential minimal optimization (SMO)-based algorithms employed by SVMs, which are guaranteed to find a global optimum (of the convex problem). The relevance vector machine was patented in the United States by Microsoft (patent expired September 4, 2019).


"B" routes are less significant routes, either as an alternative to an "A" or "M" route, or linking smaller population centres to larger regional centres, but without being a major through-route in the region. These are the major road links in areas without "A" routes. "C" routes link smaller settlements and towns to the rest of the major road network.


In multi-state models, the recurrent event processes of individuals are described by different states. The different states may describe the recurrence number, or whether the subject is at risk of recurrence. A change of state is called a transition (or an event) and is central in this framework, which is fully characterized through estimation of transition probabilities between states and transition intensities that are defined as instantaneous hazards of progression to one state, conditional on occupying another state.


(c) Overproduction of information. (d) Restricted capacity of the individual's brain which can lead to excessive specialization, with consequent dangers of degeneration. (e) A crisis precipitated by the creation of artificial intelligent beings.


In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into two or more isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network.


A blocking device (a duplexer), shut the receiver input when the transmitter pulsed. A Braun tube (a CRT) was used for displaying the range. The equipment was first tested at a NVA site at the Lübecker Bay near Pelzerhaken.


While not widely reported, it has been noted that the genre, or domain, of a text has an effect on the correlation obtained when using metrics. Coughlin (2003) reports that comparing the candidate text against a single reference translation does not adversely affect the correlation of metrics when working in a restricted domain text. Even if a metric correlates well with human judgment in one study on one corpus, this successful correlation may not carry over to another corpus.


In telecommunications, the base 10 definition of the unit (one million bits) is standard. In the semiconductor industry, it is still common practice to designate random-access memory (RAM), read-only memory (ROM) in a binary interpretation of the metric prefixes, such as the megabit, so that one megabit represents 220bits=1048576bits. For example, a single discrete DDR3 chip specified at "512 Mb" contains 229 bits = 536870912bits = 512 Mibit (approximately 536.87 Mbit) of storage, or 671088648-bit bytes, variously referred to as either 64 mebibytes or 64 (binary) megabytes. During the 16-bit game console era, the megabit (Mb) was a commonly used measure of the size (computer data storage capacity) of game cartridges.


In mathematics, a natural number a is a unitary divisor (or Hall divisor) of a number b if a is a divisor of b and if a and b a {\displaystyle {\frac {b}{a}}} are coprime, having no common factor other than 1. Thus, 5 is a unitary divisor of 60, because 5 and 60 5 = 12 {\displaystyle {\frac {60}{5}}=12} have only 1 as a common factor, while 6 is a divisor but not a unitary divisor of 60, as 6 and 60 6 = 10 {\displaystyle {\frac {60}{6}}=10} have a common factor other than 1, namely 2. 1 is a unitary divisor of every natural number.


In software engineering, the active record pattern is an architectural pattern. It is found in software that stores in-memory object data in relational databases. It was named by Martin Fowler in his 2003 book Patterns of Enterprise Application Architecture. The interface of an object conforming to this pattern would include functions such as Insert, Update, and Delete, plus properties that correspond more or less directly to the columns in the underlying database table.


In the algorithm as written above, there are two expensive operations during each iteration: the multiplication s × s, and the mod M operation. The mod M operation can be made particularly efficient on standard binary computers by observing that k ≡ ( k mod 2 n ) + ⌊ k / 2 n ⌋ ( mod 2 n − 1 ) . {\displaystyle k\equiv (k\,{\bmod {\,}}2^{n})+\lfloor k/2^{n}\rfloor {\pmod {2^{n}-1}}.}


In the United Kingdom, the Official Charts Company has included streaming into the UK Albums Chart since March 2015. The change was decided after the massive growth of streaming; the number of tracks streamed in the UK in a year doubled from 7.5 billion in 2013 to just under 15 billion in 2014. Under the new methodology, Official Charts Company takes the 12 most-streamed tracks from an album, with the top two songs being given lesser weight so that the figure will reflect the popularity of the album as a whole rather than of one or two successful singles. The adjusted total is divided by 1000 and added to the album sales figure.


In mathematics, the category of medial magmas, also known as the medial category, and denoted Med, is the category whose objects are medial magmas (that is, sets with a medial binary operation), and whose morphisms are magma homomorphisms (which are equivalent to homomorphisms in the sense of universal algebra). The category Med has direct products, so the concept of a medial magma object (internal binary operation) makes sense. As a result, Med has all its objects as medial objects, and this characterizes it. There is an inclusion functor from Set to Med as trivial magmas, with operations being the right projections (x, y) → y.An injective endomorphism can be extended to an automorphism of a magma extension—the colimit of the constant sequence of the endomorphism.


This allows the typesetter to distinguish sentence endings from abbreviations and to typeset them differently. Early versions of Troff, which only typeset in fixed-width fonts, would automatically add a second space between sentences, which were detected based on the combination of terminal punctuation and a line feed. In the April 2020 update, Microsoft Word started highlighting two spaces after a period as an error and offers a correction of one space.Multiple spaces are eliminated by default in most World Wide Web content, whether or not they are associated with sentences. There are options for preserving spacing, such as the CSS white-space property, and the tag.


In the broader sense of the term, game engines themselves can be described as middleware. In the context of video games, however, the term "middleware" is often used to refer to subsystems of functionality within a game engine. Some game middleware does only one thing but does it more convincingly or more efficiently than general purpose middleware. The four most widely used middleware packages that provide subsystems of functionality include RAD Game Tools' Bink, Firelight FMOD, Havok, and Scaleform GFx.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 367, 1367, 3467, and 13467 are the patterns related to Braille pattern dots-235, since the two additional dots of kantenji patterns 0235, 2357, and 02357 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


Jaccard is not cited in the paper, and it seems likely that the authors were not aware of it.Tanimoto goes on to define a "distance coefficient" based on this ratio, defined for bitmaps with non-zero similarity: T d ( X , Y ) = − log 2  ( T s ( X , Y ) ) {\displaystyle T_{d}(X,Y)=-\log _{2}(T_{s}(X,Y))} This coefficient is, deliberately, not a distance metric. It is chosen to allow the possibility of two specimens, which are quite different from each other, to both be similar to a third. It is easy to construct an example which disproves the property of triangle inequality.


In the case of reliability weights, the weights are normalized: V 1 = ∑ i = 1 N w i = 1. {\displaystyle V_{1}=\sum _{i=1}^{N}w_{i}=1.} (If they are not, divide the weights by their sum to normalize prior to calculating V 1 {\displaystyle V_{1}}: w i ′ = w i ∑ i = 1 N w i {\displaystyle w_{i}'={\frac {w_{i}}{\sum _{i=1}^{N}w_{i}}}} Then the weighted mean vector μ ∗ {\displaystyle \mathbf {\mu ^{*}} } can be simplified to μ ∗ = ∑ i = 1 N w i x i . {\displaystyle \mathbf {\mu ^{*}} =\sum _{i=1}^{N}w_{i}\mathbf {x} _{i}.}


In television, a similar idea is used to signal to a control room that a transition of some sort is about to occur on the broadcast (such as a commercial break). The most common type of television cue dot is the IBA style, used only in the United Kingdom, which consists of a small square in the top right corner of the screen, with black and white moving stripes. The other is a proprietary system used principally by the BBC (who do not air commercials). This version is a static square in the top left corner with a white-black-white pattern.


In mathematics, a symmetric Boolean function is a Boolean function whose value does not depend on the order of its input bits, i.e., it depends only on the number of ones (or zeros) in the input. For this reason they are also known as Boolean counting functions.There are 2n+1 symmetric n-ary Boolean functions. Instead of the truth table, traditionally used to represent Boolean functions, one may use a more compact representation for an n-variable symmetric Boolean function: the (n + 1)-vector, whose i-th entry (i = 0, ..., n) is the value of the function on an input vector with i ones. Mathematically, the symmetric Boolean functions correspond one-to-one with the functions that map n+1 elements to two elements, f: { 0 , 1 , .


A fundamental theorem due to Georg Cantor shows that it is possible for infinite sets to have different cardinalities, and in particular the cardinality of the set of real numbers is greater than the cardinality of the set of natural numbers. It is also possible for a proper subset of an infinite set to have the same cardinality as the original set—something that cannot happen with proper subsets of finite sets. There is a transfinite sequence of cardinal numbers: 0 , 1 , 2 , 3 , … , n , … ; ℵ 0 , ℵ 1 , ℵ 2 , … , ℵ α , … .


In the case of two explanatory variables, this indicator function was defined as yk when n = 1 and 1-yk when n = 0. This was convenient, but not necessary. Again, the optimum beta coefficients may be found by maximizing the log-likelihood function generally using numerical methods. A possible method of solution is to set the derivatives of the log-likelihood with respect to each beta coefficient equal to zero and solve for the beta coefficients: ∂ ℓ ∂ β n m = 0 = ∑ k = 1 K Δ ( n , y k ) x m k − ∑ k = 1 K p n ( x k ) x m k {\displaystyle {\frac {\partial \ell }{\partial \beta _{nm}}}=0=\sum _{k=1}^{K}\Delta (n,y_{k})x_{mk}-\sum _{k=1}^{K}p_{n}({\boldsymbol {x}}_{k})x_{mk}} where β n m {\displaystyle \beta _{nm}} is the m-th coefficient of the β n {\displaystyle {\boldsymbol {\beta }}_{n}} vector and x m k {\displaystyle x_{mk}} is the m-th explanatory variable of the k-th measurement. Once the beta coefficients have been estimated from the data, we will be able to estimate the probability that any subsequent set of explanatory variables will result in any of the possible outcome categories.


In optical mesh networks, nodes are junctions of fiber spans. Some nodes might contain highly sophisticated routing equipment— while others may be just a patch panel. Whatever the case, a node is a shared risk node group—because if the node fails, the failure affects all signals through that particular node.


Trace data generated and merged to a trace stream within the SoC can be streamed, via a dedicated unidirectional trace interface, off-chip to a trace analysis tool. The MIPI Debug Architecture provides specifications for both parallel and serial trace ports. The MIPI Parallel Trace Interface (MIPI PTI) specifies how to pass the trace data to multiple data pins and a clock pin (single-ended).


In polyalphabetic substitution ciphers where the substitution alphabets are chosen by the use of a keyword, the Kasiski examination allows a cryptanalyst to deduce the length of the keyword. Once the length of the keyword is discovered, the cryptanalyst lines up the ciphertext in n columns, where n is the length of the keyword. Then each column can be treated as the ciphertext of a monoalphabetic substitution cipher. As such, each column can be attacked with frequency analysis.


In non-fuzzy clustering (also known as hard clustering), data are divided into distinct clusters, where each data point can only belong to exactly one cluster. In fuzzy clustering, data points can potentially belong to multiple clusters. For example, an apple can be red or green (hard clustering), but an apple can also be red AND green (fuzzy clustering).


Since 2010, a new open source instruction set architecture (ISA), RISC-V, has been under development at the University of California, Berkeley, for research purposes and as a free alternative to proprietary ISAs. As of 2014, version 2 of the user space ISA is fixed. The ISA is designed to be extensible from a barebones core sufficient for a small embedded processor to supercomputer and cloud computing use with standard and chip designer–defined extensions and coprocessors. It has been tested in silicon design with the ROCKET SoC, which is also available as an open-source processor generator in the CHISEL language.


In mathematics, Legendre's formula gives an expression for the exponent of the largest power of a prime p that divides the factorial n!. It is named after Adrien-Marie Legendre. It is also sometimes known as de Polignac's formula, after Alphonse de Polignac.


In parallel to the development of the 1972 edition of ISO 646, which revised the standard to introduce the concept of national versions of the code in addition to the US-originated ASCII, work was also underway with the purpose of defining extension mechanisms for ASCII, applicable to both 7-bit and 8-bit environments, which would be published as ECMA-35 and ISO 2022.These mechanisms were designed so that any conformant 8-bit code could be converted to a corresponding 7-bit code, and vice versa. In a 7-bit environment, the Shift Out (SO) control would change the meaning of the 94 bytes 0x21 through 0x7E (i.e. the graphical codes, excluding the space) to invoke characters from an alternative set, and the Shift In (SI) control would change them back. In an 8-bit environment, instead of using shift codes, the eighth bit was set on a byte referencing the additional graphic character set. This meant that bytes 0xA1 through 0xFE were used for the additional graphic characters.


In mathematics, in the field of group theory, especially in the study of p-groups and pro-p-groups, the concept of powerful p-groups plays an important role. They were introduced in (Lubotzky & Mann 1987), where a number of applications are given, including results on Schur multipliers. Powerful p-groups are used in the study of automorphisms of p-groups (Khukhro 1998), the solution of the restricted Burnside problem (Vaughan-Lee 1993), the classification of finite p-groups via the coclass conjectures (Leedham-Green & McKay 2002), and provided an excellent method of understanding analytic pro-p-groups (Dixon et al. 1991).


In a "planned state" these work orders have estimates such as 2 electricians for 8 hours. These work orders have other attributes such as report date, priority, asset operational requirements, and safety concerns. These same organizations have a need to create weekly schedules.


In mathematics, an arithmetic group is a group obtained as the integer points of an algebraic group, for example S L 2 ( Z ) . {\displaystyle \mathrm {SL} _{2}(\mathbb {Z} ).} They arise naturally in the study of arithmetic properties of quadratic forms and other classical topics in number theory. They also give rise to very interesting examples of Riemannian manifolds and hence are objects of interest in differential geometry and topology. Finally, these two topics join in the theory of automorphic forms which is fundamental in modern number theory.


In modern computers many processes run at once. Active processes are placed in an array called a run queue, or runqueue. The run queue may contain priority values for each process, which will be used by the scheduler to determine which process to run next. To ensure each program has a fair share of resources, each one is run for some time period (quantum) before it is paused and placed back into the run queue.


Instead, the following heuristics are used. 1D partitioning: Every processor gets n / p {\displaystyle n/p} vertices and the corresponding outgoing edges. This can be understood as a row-wise or column-wise decomposition of the adjacency matrix.


4. Creating a model, likeness, analogy, metaphor, prototype or narrative which shows what the concept is about or how it is applied (isomorphism, simulation or successive approximation ). 5.


As another issue, for some programs, the method of taking the greatest lower bound at converging execution paths and adding corresponding down-coercion operations appears to be inadequate. For example, before the return 1 in the following program, all components x, y, and z of coord are initialized, but Strom's and Yemini's approach fails to recognize this, since each initialization of a struct component in the loop body has to be down-coerced at loop re-entry to meet the typestate of the very first loop entry, viz. ⊥. A related problem is that this example would require overloading of typestate transitions; for example, parse_int_attr("x",&coord->x) changes a typestate "no component initialized" to "x component initialized", but also "y component initialized" to "x and y component initialized".


Instead of simply “taking in” new information, one goes back to look at their understandings and pulls together information that was “triggered” and forms a new connection. This connection becomes tighter and one's understanding of a certain concept is solidified or “stable” (Pangaro, 2003).


If R is not a member of itself, then its definition entails that it is a member of itself; yet, if it is a member of itself, then it is not a member of itself, since it is the set of all sets that are not members of themselves. The resulting contradiction is Russell's paradox.


In the context of quantum information theory, the operators {Vi} are called the Kraus operators (after Karl Kraus) of Φ. Notice, given a completely positive Φ, its Kraus operators need not be unique. For example, any "square root" factorization of the Choi matrix CΦ = B∗B gives a set of Kraus operators. Let B ∗ =  , {\displaystyle B^{*}=,} where bi*'s are the row vectors of B, then C Φ = ∑ i = 1 n m b i b i ∗ . {\displaystyle C_{\Phi }=\sum _{i=1}^{nm}b_{i}b_{i}^{*}.}


All hardware architectures in common use are optimized for strict languages, so the best compilers for non-strict languages produce slower code than the best compilers for strict languages. Space complexity of non-strict programs is difficult to understand and predict.Strict programming languages are often associated with eager evaluation, and non-strict languages with lazy evaluation, but other evaluation strategies are possible in each case. The terms "eager programming language" and "lazy programming language" are often used as synonyms for "strict programming language" and "non-strict programming language" respectively. In many strict languages, some advantages of non-strict functions can be obtained through the use of macros or thunks.


In the early 2000s, many of the existing copyright laws were designed around printed books, magazines and newspapers. For example, copyright laws often set limits on how much of a book can be mechanically reproduced or copied. Electronic publishing raises new questions in relation to copyright, because if an e-book or e-journal is available online, millions of Internet users may be able to view a single electronic copy of the document, without any "copies" being made. Emerging evidence suggests that e-publishing may be more collaborative than traditional paper-based publishing; e-publishing often involves more than one author, and the resulting works are more accessible, since they are published online.


The probability of doing so in two draws depends on whether the first card drawn was replaced before the second drawing since without replacement there is one fewer card after the first card was drawn. The probabilities of the individual events (red, and club) are multiplied rather than added. The probability of drawing a red and a club in two drawings without replacement is then 26/52 × 13/51 × 2 = 676/2652, or 13/51.


Data elements are defined by the metamodel view and they are referred to by functional objects in other views.Functional viewpointFunctional Dataflow view – An abstract view that describes the functional elements in the system, their interactions, behavior, provided services, constraints and data flows among them. Defines which functions the system is capable of performing, regardless of how these functions are actually implemented. Functional Control view – Describes the control flows and interactions among functional elements within the system.


In queueing theory, a discipline within the mathematical theory of probability, a bulk queue (sometimes batch queue) is a general queueing model where jobs arrive in and/or are served in groups of random size. : vii Batch arrivals have been used to describe large deliveries and batch services to model a hospital out-patient department holding a clinic once a week, a transport link with fixed capacity and an elevator.Networks of such queues are known to have a product form stationary distribution under certain conditions. Under heavy traffic conditions a bulk queue is known to behave like a reflected Brownian motion.


Vadim Schechtman and Alexander Varchenko introduced a matrix indexed by the regions. The matrix element for the region R i {\displaystyle R_{i}} and R j {\displaystyle R_{j}} is given by the product of indeterminate variables a H {\displaystyle a_{H}} for every hyperplane H that separates these two regions. If these variables are specialized to be all value q, then this is called the q-matrix (over the Euclidean domain Q  {\displaystyle \mathbb {Q} } ) for the arrangement and much information is contained in its Smith normal form.


Franklin proved that the chromatic number of a graph embedded in the Klein bottle can be as large as 6 {\displaystyle 6} , but never exceeds 6 {\displaystyle 6} . Later it was proved in the works of Gerhard Ringel, J. W. T. Youngs, and other contributors that the complete graph with H ( S ) {\displaystyle H(S)} vertices can be embedded in the surface S {\displaystyle S} unless S {\displaystyle S} is the Klein bottle. This established that Heawood's bound could not be improved. For example, the complete graph on 7 {\displaystyle 7} vertices can be embedded in the torus as follows: The case of the sphere is the four-color conjecture, which was settled by Kenneth Appel and Wolfgang Haken in 1976.


Evaluation – Assesses the effectiveness of a public policy in terms of its perceived intentions and results. Policy actors attempt to determine whether the course of action is a success or failure by examining its impact and outcomes.Anderson's version of the stages model is the most common and widely recognised out of the models. However, it could also be seen as flawed.


There is a whole research branch dealing with all possible regularizations. In practice, one usually tries a specific regularization and then figures out the probability density that corresponds to that regularization to justify the choice. It can also be physically motivated by common sense or intuition. In machine learning, the data term corresponds to the training data and the regularization is either the choice of the model or modifications to the algorithm. It is always intended to reduce the generalization error, i.e. the error score with the trained model on the evaluation set and not the training data.One of the earliest uses of regularization is Tikhonov regularization, related to the method of least squares.


Two binary variables are considered positively associated if most of the data falls along the diagonal cells. In contrast, two binary variables are considered negatively associated if most of the data falls off the diagonal. If we have a 2×2 table for two random variables x and y where n11, n10, n01, n00, are non-negative counts of numbers of observations that sum to n, the total number of observations.


In telecommunications, a system that supports simultaneous voice and data (SVD) is one that can transceive both voice and primary data concurrently over one PSTN modem.


In mathematics, the Fibonacci numbers form a sequence defined recursively by: F n = { 0 n = 0 1 n = 1 F n − 1 + F n − 2 n > 1 {\displaystyle F_{n}={\begin{cases}0&n=0\\1&n=1\\F_{n-1}+F_{n-2}&n>1\end{cases}}} That is, after two starting values, each number is the sum of the two preceding numbers. The Fibonacci sequence has been studied extensively and generalized in many ways, for example, by starting with other numbers than 0 and 1, by adding more than two numbers to generate the next number, or by adding objects other than numbers.


In mathematics, the comparison test, sometimes called the direct comparison test to distinguish it from similar related tests (especially the limit comparison test), provides a way of deducing the convergence or divergence of an infinite series or an improper integral. In both cases, the test works by comparing the given series or integral to one whose convergence properties are known.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 5678, 15678, 45678, and 145678 are the patterns related to Braille pattern dots-3456, since the two additional dots of kantenji patterns 03456, 34567, and 034567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


A network or protocol that supports QoS may agree on a traffic contract with the application software and reserve capacity in the network nodes, for example during a session establishment phase. During the session it may monitor the achieved level of performance, for example the data rate and delay, and dynamically control scheduling priorities in the network nodes. It may release the reserved capacity during a tear down phase.


The reference validation mechanism must be Always invoked. Without this property, it is possible for the mechanism to not perform when intended, allowing an attacker to violate the security policy. The reference validation mechanism must be Tamper-proof.


In statically typed languages such as Go or ML, a variable also has a type, meaning that only certain kinds of values can be stored in it. For example, a variable of type "integer" is prohibited from storing text values. In dynamically typed languages such as Python, a variable's type is inferred by its value, and can change according to its value. In Common Lisp, both situations exist simultaneously: A variable is given a type (if undeclared, it is assumed to be T, the universal supertype) which exists at compile time.


In software architecture, a messaging pattern is an architectural pattern which describes how two different parts of an application, or different systems connect and communicate with each other. There are many aspects to the concept of messaging which can be divided in the following categories: hardware device messaging (telecommunications, computer networking, IoT, etc.) and software data exchange (the different data exchange formats and software capabilities of such data exchange). Despite the difference in the context, both categories exhibit common traits for data exchange.


In the context of hardware and software systems, formal verification is the act of proving or disproving the correctness of intended algorithms underlying a system with respect to a certain formal specification or property, using formal methods of mathematics.Formal verification can be helpful in proving the correctness of systems such as: cryptographic protocols, combinational circuits, digital circuits with internal memory, and software expressed as source code. The verification of these systems is done by providing a formal proof on an abstract mathematical model of the system, the correspondence between the mathematical model and the nature of the system being otherwise known by construction. Examples of mathematical objects often used to model systems are: finite-state machines, labelled transition systems, Petri nets, vector addition systems, timed automata, hybrid automata, process algebra, formal semantics of programming languages such as operational semantics, denotational semantics, axiomatic semantics and Hoare logic.


The first eight units were delivered to the office of the then Prime Minister, Pierre Elliot Trudeau, in February 1974. Despite these predecessors, Wang's product was a standout, and by 1978 it had sold more of these systems than any other vendor.The phrase "word processor" rapidly came to refer to CRT-based machines similar to the AES 90.


When analyzing a population, one of the main sources used to gather the required information is insurance by obtaining individual records that belong to a specific population. These are called mortality tables if they show death rates, and morbidity tables if they show various types of sickness or disability rates. The availability of computers and the proliferation of data gathering about individuals has made possible calculations that are more voluminous and intensive than those used in the past (i.e. they crunch more numbers) and it is more common to attempt to provide different tables for different uses, and to factor in a range of non-traditional behaviors (e.g. gambling, debt load) into specialized calculations utilized by some institutions for evaluating risk. This is particularly the case in non-life insurance (e.g. the pricing of motor insurance can allow for a large number of risk factors, which requires a correspondingly complex table of expected claim rates). However the expression "life table" normally refers to human survival rates and is not relevant to non-life insurance.


With the simple addition of the particle ni "at", for example, /hasiꜜni/ hàshí-nì "at the bridge" acquires a marked drop in pitch, while /hasini/ hàshi-ni "at the edge" does not. However, because the downstep occurs after the first mora of the accented syllable, a word with a final long accented syllable would contrast all three patterns even in isolation: an accentless word nihon, for example, would be pronounced , differently from either of the words above. In 2014, a study recording the electrical activity of the brain showed that native Japanese speakers mainly use context, rather than pitch accent information, to contrast between words that differ only in pitch.This property of the Japanese language allows for a certain type of pun, called dajare (駄洒落, だじゃれ), combining two words with the same or very similar sounds but different pitch accents and thus meanings.


Another strategy to deal with small sample size is to use a shrinkage estimator of the covariance matrix, which can be expressed mathematically as Σ = ( 1 − λ ) Σ + λ I {\displaystyle \Sigma =(1-\lambda )\Sigma +\lambda I\,} where I {\displaystyle I} is the identity matrix, and λ {\displaystyle \lambda } is the shrinkage intensity or regularisation parameter. This leads to the framework of regularized discriminant analysis or shrinkage discriminant analysis.Also, in many practical cases linear discriminants are not suitable. LDA and Fisher's discriminant can be extended for use in non-linear classification via the kernel trick.


In the SAME system, messages are constructed in four parts, the first and last of which are digital and the middle two are audio. The digital sections of a SAME message are AFSK data bursts, with individual bits lasting 1920 μs (1.92 ms) each, giving a bit rate of 5205⁄6 bits per second. A mark bit is four complete cycles of a sine wave, translating to a mark frequency of 20831⁄3 Hz, and a space bit is three complete sine wave cycles, making the space frequency 1562.5 Hz. The data is sent isochronously and encoded in 8-bit bytes with the most-significant bit of each ASCII byte set to zero. The least-significant bit of each byte is transmitted first, including the preamble. The data stream is bit and byte synchronized on the preamble.Since there is no error correction, the digital part of a SAME message is transmitted three times, so that decoders can pick "best two out of three" for each byte, thereby eliminating most errors which can cause an activation to fail.


In physics, the cluster decomposition property states that experiments carried out far from each other cannot influence each other. Usually applied to quantum field theory, it requires that vacuum expectation values of operators localized in bounded regions factorize whenever these regions becomes sufficiently distant from each other. First formulated by Eyvind H. Wichmann and James H. Crichton in 1963 in the context of the S-matrix, it was conjectured by Steven Weinberg that in the low energy limit the cluster decomposition property, together with Lorentz invariance and quantum mechanics, inevitably lead to quantum field theory. String theory satisfies all three of the conditions and so provides a counter-example against this being true at all energy scales.


In the OSI model, the definition of the application layer is narrower in scope. The OSI model defines the application layer as only the interface responsible for communicating with host-based and user-facing applications. OSI then explicitly distinguishes the functionality of two additional layers, the session layer and presentation layer, as separate levels below the application layer and above the transport layer. OSI specifies a strict modular separation of functionality at these layers and provides protocol implementations for each. In contrast, the Internet Protocol Suite compiles these functions into a single layer.


This algorithm was popular, but significantly more efficient algorithms exist. Algorithms based on the Newton–Raphson method are able to compute quadrature rules for significantly larger problem sizes. In 2014, Ignace Bogaert presented explicit asymptotic formulas for the Gauss–Legendre quadrature weights and nodes, which are accurate to within double-precision machine epsilon for any choice of n ≥ 21. This allows for computation of nodes and weights for values of n exceeding one billion.


Some used sign-magnitude arithmetic (-1 = 10001), or ones' complement (-1 = 11110), rather than modern two's complement arithmetic (-1 = 11111). Most computers used six-bit character sets because they adequately encoded Hollerith punched cards. It was a major revelation to designers of this period to realize that the data word should be a multiple of the character size. They began to design computers with 12-, 24- and 36-bit data words (e.g., see the TX-2). In this era, Grosch's law dominated computer design: computer cost increased as the square of its speed.


In statistical classification, two main approaches are called the generative approach and the discriminative approach. These compute classifiers by different approaches, differing in the degree of statistical modelling. Terminology is inconsistent, but three major types can be distinguished, following Jebara (2004): A generative model is a statistical model of the joint probability distribution P ( X , Y ) {\displaystyle P(X,Y)} on given observable variable X and target variable Y; A discriminative model is a model of the conditional probability P ( Y ∣ X = x ) {\displaystyle P(Y\mid X=x)} of the target Y, given an observation x; and Classifiers computed without using a probability model are also referred to loosely as "discriminative".The distinction between these last two classes is not consistently made; Jebara (2004) refers to these three classes as generative learning, conditional learning, and discriminative learning, but Ng & Jordan (2002) only distinguish two classes, calling them generative classifiers (joint distribution) and discriminative classifiers (conditional distribution or no distribution), not distinguishing between the latter two classes. Analogously, a classifier based on a generative model is a generative classifier, while a classifier based on a discriminative model is a discriminative classifier, though this term also refers to classifiers that are not based on a model.


The summation of an explicit sequence is denoted as a succession of additions. For example, summation of  is denoted 1 + 2 + 4 + 2, and results in 9, that is, 1 + 2 + 4 + 2 = 9. Because addition is associative and commutative, there is no need of parentheses, and the result is the same irrespective of the order of the summands.


In order to improve the optimisation of the valve timing for differing engine speeds and loads, the system is able to vary the timing and duration of the inlet valve opening. It achieves this by using a complex and finely machined mechanism to drive the inlet camshafts. This mechanism can accelerate and decelerate the rotational speed of the camshaft during different parts of its cycle. e.g. to produce longer opening duration, it slows the rotation during the valve open part of the cycle and speeds it up during the valve closed period.


Lingvo ". The search engine has learned to understand queries like “What is  in Spanish” and automatically translate them. It became possible to limit search results by region.


Even tiny measurement errors, when integrated, add up to an appreciable error known as "drift". For instance, the N-1 navigation system developed for the SM-64 Navaho cruise missile drifted at a rate of 1 nautical mile per hour, meaning that after a two-hour flight the INS would be indicating a position 2 nautical miles (3.7 km; 2.3 mi) away from its actual location. This was outside the desired accuracy of about half a mile.


In the above example of coin-tossing we explicitly assumed that each toss is an independent trial, and the probability of getting head or tail is always the same. Let X , X 1 , X 2 , … {\displaystyle X,X_{1},X_{2},\ldots } be independent and identically distributed (i.i.d.) random variables whose common distribution satisfies a certain growth condition. Then the following limit exists: lim N → ∞ 1 N ln  P ( M N > x ) = − I ( x ) {\displaystyle \lim _{N\to \infty }{\frac {1}{N}}\ln P(M_{N}>x)=-I(x)} .Here M N = 1 N ∑ i = 1 N X i {\displaystyle M_{N}={\frac {1}{N}}\sum _{i=1}^{N}X_{i}} ,as before.


In materials management, ABC analysis is an inventory categorisation technique. ABC analysis divides an inventory into three categories—"A items" with very tight control and accurate records, "B items" with less tightly controlled and good records, and "C items" with the simplest controls possible and minimal records. The ABC analysis provides a mechanism for identifying items that will have a significant impact on overall inventory cost, while also providing a mechanism for identifying different categories of stock that will require different management and controls. The ABC analysis suggests that inventories of an organization are not of equal value.


Reification data is often said to be made a first class object. Reification, at least partially, has been experienced in many languages to date: in early Lisp dialects and in current Prolog dialects, programs have been treated as data, although the causal connection has often been left to the responsibility of the programmer. In Smalltalk-80, the compiler from the source text to bytecode has been part of the run-time system since the very first implementations of the language.


Adding the constraint forces does not change the total energy, as the net work done by the constraint forces (taken over the set of particles that the constraints act on) is zero. Note that the sign on λ k {\displaystyle \lambda _{k}} is arbitrary and some references have an opposite sign. From integrating both sides of the equation with respect to the time, the constrained coordinates of particles at the time, t + Δ t {\displaystyle t+\Delta t} , are given, x i ( t + Δ t ) = x ^ i ( t + Δ t ) + ∑ k = 1 n λ k ∂ σ k ( t ) ∂ x i ( Δ t ) 2 m i − 1 , i = 1 … N {\displaystyle \mathbf {x} _{i}(t+\Delta t)={\hat {\mathbf {x} }}_{i}(t+\Delta t)+\sum _{k=1}^{n}\lambda _{k}{\frac {\partial \sigma _{k}(t)}{\partial \mathbf {x} _{i}}}\left(\Delta t\right)^{2}m_{i}^{-1},\quad i=1\ldots N} where x ^ i ( t + Δ t ) {\displaystyle {\hat {\mathbf {x} }}_{i}(t+\Delta t)} is the unconstrained (or uncorrected) position of the ith particle after integrating the unconstrained equations of motion.


In the UK, the Data Protection Act is used to ensure that personal data is accessible to those whom it concerns, and provides redress to individuals if there are inaccuracies. This is particularly important to ensure individuals are treated fairly, for example for credit checking purposes. The Data Protection Act states that only individuals and companies with legitimate and lawful reasons can process personal information and cannot be shared.


In telephony, an automated attendant (also auto attendant, auto-attendant, autoattendant, automatic phone menus, AA, or virtual receptionist) allows callers to be automatically transferred to an extension without the intervention of an operator/receptionist. Many AAs will also offer a simple menu system ("for sales, press 1, for service, press 2," etc.). An auto attendant may also allow a caller to reach a live operator by dialing a number, usually "0". Typically the auto attendant is included in a business's phone system such as a PBX, but some services allow businesses to use an AA without such a system. Modern AA services (which now overlap with more complicated interactive voice response or IVR systems) can route calls to mobile phones, VoIP virtual phones, other AAs/IVRs, or other locations using traditional land-line phones or voice message machines.


With 23 individuals, there are 23 × 22/2 = 253 pairs to consider, far more than half the number of days in a year. Real-world applications for the birthday problem include a cryptographic attack called the birthday attack, which uses this probabilistic model to reduce the complexity of finding a collision for a hash function, as well as calculating the approximate risk of a hash collision existing within the hashes of a given size of population.


In mathematics and physics, the centroid, also known as geometric center or center of figure, of a plane figure or solid figure is the arithmetic mean position of all the points in the surface of the figure. The same definition extends to any object in n-dimensional Euclidean space.In geometry, one often assumes uniform mass density, in which case the barycenter or center of mass coincides with the centroid. Informally, it can be understood as the point at which a cutout of the shape (with uniformly distributed mass) could be perfectly balanced on the tip of a pin.In physics, if variations in gravity are considered, then a center of gravity can be defined as the weighted mean of all points weighted by their specific weight. In geography, the centroid of a radial projection of a region of the Earth's surface to sea level is the region's geographical center.


During the 1980s, approaches to achieve inferential programming mostly involved techniques for logical inference. Today the term is sometimes used in connection with evolutionary computation techniques that enable a computer to evolve a solution in response to a problem posed as a fitness or reward function. In July 2022, GitHub Copilot was released, which is an example of inferential programming.


They have proved that when perfect noiseless recovery occurs, then matrix completion is stable vis a vis perturbations. The error is proportional to the noise level δ {\displaystyle \delta } . Therefore, when the noise level is small, the error is small.


If in addition p and q are congruent to 1 modulo 8, let p = c2 + 2d2 and q = C2 + 2D2. Then ( p | q ) 8 = ( q | p ) 8 = ( a B − b A | q ) 4 ( c D − d C | q ) 2 . {\displaystyle (p|q)_{8}=(q|p)_{8}=(aB-bA|q)_{4}(cD-dC|q)_{2}\ .}


In some of the academic literature, multiplication denoted by juxtaposition (also known as implied multiplication) is interpreted as having higher precedence than division, so that 1 ÷ 2n equals 1 ÷ (2n), not (1 ÷ 2)n. For example, the manuscript submission instructions for the Physical Review journals state that multiplication is of higher precedence than division, and this is also the convention observed in prominent physics textbooks such as the Course of Theoretical Physics by Landau and Lifshitz and the Feynman Lectures on Physics.This ambiguity is often exploited in internet memes such as "8÷2(2+2)", for which there are two conflicting interpretations: 8÷ = 1 and (2+2) = 16. The expression "6÷2(1+2)" also gained notoriety in the exact same manner, with the two interpretations resulting in the answers 1 and 9.Ambiguity can also be caused by the use of the slash symbol, '/', for division. The Physical Review submission instructions suggest to avoid expressions of the form a/b/c; ambiguity can be avoided by instead writing (a/b)/c or a/(b/c).