In the case of measurement error, one wishes to discard them or use statistics that are robust to outliers, while in the case of heavy-tailed distributions, they indicate that the distribution has high skewness and that one should be very cautious in using tools or intuitions that assume a normal distribution. A frequent cause of outliers is a mixture of two distributions, which may be two distinct sub-populations, or may indicate 'correct trial' versus 'measurement error'; this is modeled by a mixture model. In most larger samplings of data, some data points will be further away from the sample mean than what is deemed reasonable.


In mathematics, especially order theory, a weak ordering is a mathematical formalization of the intuitive notion of a ranking of a set, some of whose members may be tied with each other. Weak orders are a generalization of totally ordered sets (rankings without ties) and are in turn generalized by (strictly) partially ordered sets and preorders.There are several common ways of formalizing weak orderings, that are different from each other but cryptomorphic (interconvertable with no loss of information): they may be axiomatized as strict weak orderings (strictly partially ordered sets in which incomparability is a transitive relation), as total preorders (transitive binary relations in which at least one of the two possible relations exists between every pair of elements), or as ordered partitions (partitions of the elements into disjoint subsets, together with a total order on the subsets). In many cases another representation called a preferential arrangement based on a utility function is also possible. Weak orderings are counted by the ordered Bell numbers. They are used in computer science as part of partition refinement algorithms, and in the C++ Standard Library.


In quantum information theory, a quantum channel is a communication channel which can transmit quantum information, as well as classical information. An example of quantum information is the state of a qubit. An example of classical information is a text document transmitted over the Internet.


In mathematics, the square root of a matrix extends the notion of square root from numbers to matrices. A matrix B is said to be a square root of A if the matrix product BB is equal to A.Some authors use the name square root or the notation A1/2 only for the specific case when A is positive semidefinite, to denote the unique matrix B that is positive semidefinite and such that BB = BTB = A (for real-valued matrices, where BT is the transpose of B). Less frequently, the name square root may be used for any factorization of a positive semidefinite matrix A as BTB = A, as in the Cholesky factorization, even if BB ≠ A. This distinct meaning is discussed in Positive definite matrix § Decomposition.


In some languages and programming environments, the use of a case or switch statement is considered superior to an equivalent series of if else if statements because it is: Easier to debug (e.g. setting breakpoints on code vs. a call table, if the debugger has no conditional breakpoint capability) Easier for a person to read Easier to understand, and consequently easier to maintain Fixed depth: a sequence of "if else if" statements may yield deep nesting, making compilation more difficult (especially in automatically generated code) Easier to verify that all values are handled. Compilers can issue a warning if some enum values are not handled.Additionally, an optimized implementation may execute much faster than the alternative, because it is often implemented by using an indexed branch table. For example, deciding program flow based on a single character's value, if correctly implemented, is vastly more efficient than the alternative, reducing instruction path lengths considerably.


In mathematics, the Chinese monoid is a monoid generated by a totally ordered alphabet with the relations cba = cab = bca for every a ≤ b ≤ c. An algorithm similar to Schensted's algorithm yields characterisation of the equivalence classes and a cross-section theorem. It was discovered by Duchamp & Krob (1994) during their classification of monoids with growth similar to that of the plactic monoid, and studied in detail by Julien Cassaigne, Marc Espie, Daniel Krob, Jean-Christophe Novelli, and Florent Hivert in 2001.The Chinese monoid has a regular language cross-section a ∗ ( b a ) ∗ b ∗ ( c a ) ∗ ( c b ) ∗ c ∗ ⋯ {\displaystyle a^{*}\ (ba)^{*}b^{*}\ (ca)^{*}(cb)^{*}c^{*}\cdots } and hence polynomial growth of dimension n ( n + 1 ) 2 {\displaystyle {\frac {n(n+1)}{2}}} .The Chinese monoid equivalence class of a permutation is the preimage of an involution under the map w ↦ w ∘ w − 1 {\displaystyle w\mapsto w\circ w^{-1}} where ∘ {\displaystyle \circ } denotes the product in the Iwahori-Hecke algebra with q s = 0 {\displaystyle q_{s}=0} .


In some countries' online banking, the bank sends to the user a numbered list of OTPs that is printed on paper. Other banks send plastic cards with actual OTPs obscured by a layer that the user has to scratch off to reveal a numbered OTP. For every online transaction, the user is required to enter a specific OTP from that list. Some systems ask for the numbered OTPs sequentially, others pseudorandomly choose an OTP to be entered.


In order to discuss the continuous-time Markov decision process, we introduce two sets of notations: If the state space and action space are finite, S {\displaystyle {\mathcal {S}}}: State space; A {\displaystyle {\mathcal {A}}}: Action space; q ( i ∣ j , a ) {\displaystyle q(i\mid j,a)}: S × A → △ S {\displaystyle {\mathcal {S}}\times {\mathcal {A}}\rightarrow \triangle {\mathcal {S}}} , transition rate function; R ( i , a ) {\displaystyle R(i,a)}: S × A → R {\displaystyle {\mathcal {S}}\times {\mathcal {A}}\rightarrow \mathbb {R} } , a reward function.If the state space and action space are continuous, X {\displaystyle {\mathcal {X}}}: state space; U {\displaystyle {\mathcal {U}}}: space of possible control; f ( x , u ) {\displaystyle f(x,u)}: X × U → △ X {\displaystyle {\mathcal {X}}\times {\mathcal {U}}\rightarrow \triangle {\mathcal {X}}} , a transition rate function; r ( x , u ) {\displaystyle r(x,u)}: X × U → R {\displaystyle {\mathcal {X}}\times {\mathcal {U}}\rightarrow \mathbb {R} } , a reward rate function such that r ( x ( t ) , u ( t ) ) d t = d R ( x ( t ) , u ( t ) ) {\displaystyle r(x(t),u(t))\,dt=dR(x(t),u(t))} , where R ( x , u ) {\displaystyle R(x,u)} is the reward function we discussed in previous case.


Examples are cell phones, which transmit and receive the two sides of a phone conversation using radio waves to a cell tower, cordless phones in which both the phone handset and the base station have transceivers to communicate both sides of the conversation, and land mobile radio systems like walkie-talkies and CB radios. Another large use is in wireless modems in mobile networked computer devices such laptops, pads, and cellphones, which both transmit digital data to and receive data from a wireless router. Aircraft carry automated microwave transceivers called transponders which, when they are triggered by microwaves from an air traffic control radar, transmit a coded signal back to the radar to identify the aircraft. Satellite transponders in communication satellites receive digital telecommunication data from a satellite ground station, and retransmit it to another ground station.


To form the product of two 8-bit integers, for example, the digital device forms the sum and difference, looks both quantities up in a table of squares, takes the difference of the results, and divides by four by shifting two bits to the right. For 8-bit integers the table of quarter squares will have 29−1=511 entries (one entry for the full range 0..510 of possible sums, the differences using only the first 256 entries in range 0..255) or 29−1=511 entries (using for negative differences the technique of 2-complements and 9-bit masking, which avoids testing the sign of differences), each entry being 16-bit wide (the entry values are from (0²/4)=0 to (510²/4)=65025). The quarter square multiplier technique has benefited 8-bit systems that do not have any support for a hardware multiplier. Charles Putney implemented this for the 6502.


In the fourth year of his degree course Richard's research project led him to using Oxford's Ferranti Mercury computer to solve integrals. During a fellowship year in France at Centre de Mécanique Ondulatoire Appliquée, he was able to use more powerful computers. Returning to Oxford, he worked on ab initio computations and applied computational techniques to solving quantum mechanical problems in theoretical chemistry, in particular studying spin-orbit coupling. His influential paper Third age of quantum chemistry (1979) marked the development of computational techniques for theoretical analysis whose precision equaled or surpassed experimental results.


By offering a quantity discount for a larger quantity purchased the seller is able to capture some of the consumer surplus but not all. This is because diminishing marginal utility may mean the consumer would not be willing to purchase an additional unit without a discount since the marginal utility received from the good or service is no longer greater than price. However, by offering a discount the seller can capture some of consumers surplus by encouraging them to purchase an additional unit at a discounted price.


Optimization will generally focus on improving just one or two aspects of performance: execution time, memory usage, disk space, bandwidth, power consumption or some other resource. This will usually require a trade-off – where one factor is optimized at the expense of others. For example, increasing the size of cache improves run time performance, but also increases the memory consumption.


In telecommunications, effective transmission rate (average rate of transmission, effective speed of transmission) is the rate at which information is processed by a transmission facility. The effective transmission rate is calculated as (a) the measured number of units of data, such as bits, characters, blocks, or frames, transmitted during a significant measurement time interval divided by (b) the measurement time interval. The effective transmission rate is usually expressed as a number of units of data per unit time, such as bits per second or characters per second.


In statistical decision theory, an admissible decision rule is a rule for making a decision such that there is no other rule that is always "better" than it (or at least sometimes better and never worse), in the precise sense of "better" defined below. This concept is analogous to Pareto efficiency.


In statistics, the standard score is the number of standard deviations by which the value of a raw score (i.e., an observed value or data point) is above or below the mean value of what is being observed or measured. Raw scores above the mean have positive standard scores, while those below the mean have negative standard scores. It is calculated by subtracting the population mean from an individual raw score and then dividing the difference by the population standard deviation.


The presumed difficulty of this problem is important for the algorithms used in cryptography such as RSA public-key encryption and the RSA digital signature. Many areas of mathematics and computer science have been brought to bear on the problem, including elliptic curves, algebraic number theory, and quantum computing. In 2019, Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé and Paul Zimmermann factored a 240-digit (795-bit) number (RSA-240) utilizing approximately 900 core-years of computing power.


In mathematics, an iterated function is a function X → X (that is, a function from some set X to itself) which is obtained by composing another function f: X → X with itself a certain number of times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying a given function is fed again in the function as input, and this process is repeated. For example on the image on the right: L = F {\displaystyle {\mathit {F}}\,} ( K ), M = F ∘ F {\displaystyle {\mathit {F}}\,\circ {\mathit {F}}\,} ( K ) = F 2 {\displaystyle {\mathit {F}}\;^{2}\,} ( K ),with the circle‑shaped symbol of function composition.Iterated functions are objects of study in computer science, fractals, dynamical systems, mathematics and renormalization group physics.


In mathematical logic, Craig's theorem (also known as Craig's trick) states that any recursively enumerable set of well-formed formulas of a first-order language is (primitively) recursively axiomatizable. This result is not related to the well-known Craig interpolation theorem, although both results are named after the same logician, William Craig.


In regional testing, 20 to 50 µL of liquid stimulus is presented to the anterior and posterior tongue using a pipette, soaked filter-paper disks, or cotton swabs. In whole mouth testing, small quantities (2-10 mL) of solution are administered, and the patient is asked to swish the solution around in the mouth.Threshold tests for sucrose (sweet), citric acid (sour), sodium chloride (salty), and quinine or caffeine (bitter) are frequently performed with natural stimuli. One of the most frequently used techniques is the "three-drop test."


In the 1960s a metrication program was initiated in most English-speaking countries, resulting in either the partial or total displacement of the imperial system or the US customary system of measure in those countries. The current status of imperial and US customary units, as summarised by NIST, is that "the SI metric system is now the official system of units in the United Kingdom, while the customary units are still predominantly used in the United States".The situation is however not as clear-cut as this. In the United States, for example, the metric system is the predominant system of measure in certain fields such as automobile manufacture even though customary units are used in aircraft manufacture. In the United Kingdom, metric units are required for almost all regulated use of units of measure except for a few specifically exempt areas such as road signs, speedometers and draught beer. Metrication is also all but complete in the Commonwealth countries of Australia, India, New Zealand and South Africa; metrication in Canada has displaced the imperial system in many areas.The imperial and US customary systems of measurement use the SI for their formal definitions, the yard being defined as 0.9144 metres exactly, the pound avoirdupois as 0.45359237 kilograms exactly while both systems of measure share the definition of the second.


In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a field and its absolute Galois group. It is an interdisciplinary subject as it uses tools from algebraic number theory, arithmetic geometry, algebraic geometry, model theory, the theory of finite groups and of profinite groups.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 256, 1256, 2456, and 12456 are the patterns related to Braille pattern dots-145, since the two additional dots of kantenji patterns 0145, 1457, and 01457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


An element of order 6 in the group S5 can be written in cycle notation as (1 2) (3 4 5). Note that the same argument applies to the number 6, that is, g(6) = 6. There are arbitrarily long sequences of consecutive numbers n, n + 1, …, n + m on which the function g is constant.The integer sequence g(0) = 1, g(1) = 1, g(2) = 2, g(3) = 3, g(4) = 4, g(5) = 6, g(6) = 6, g(7) = 12, g(8) = 15, ... (sequence A000793 in the OEIS) is named after Edmund Landau, who proved in 1902 that lim n → ∞ ln  ( g ( n ) ) n ln  ( n ) = 1 {\displaystyle \lim _{n\to \infty }{\frac {\ln(g(n))}{\sqrt {n\ln(n)}}}=1} (where ln denotes the natural logarithm).


In the UNL approach, information conveyed by natural language is represented sentence by sentence as a hypergraph composed of a set of directed binary labeled links (referred to as relations) between nodes or hypernodes (the Universal Words, or simply UWs), which stand for concepts. UWs can also be annotated with attributes representing context information. As an example, the English sentence ‘The sky was blue? !’ can be represented in UNL as follows: In the example above, sky(icl>natural world) and blue(icl>color), which represent individual concepts, are UWs; "aoj" (= attribute of an object) is a directed binary semantic relation linking the two UWs; and "@def", "@interrogative", "@past", "@exclamation" and "@entry" are attributes modifying UWs.


For a dijoin in the given graph, the corresponding set of edges forms a directed cut in the dual graph, and vice versa. This relationship between these two problems allows the feedback arc set problem to be solved efficiently for planar graphs, even though it is NP-hard for other types of graphs. == References ==


In professional usage, digital cameras offer many advantages in speed, precision, flexibility, ease, and cost. Immediacy: image review and deletion are possible immediately; lighting and composition can be assessed immediately, which ultimately conserves storage space. Faster workflow: management (color and file), manipulation, and printing tools are more versatile than conventional film processes. However, batch processing of RAW files can be time-consuming, even on a fast computer.


In the Reiner–Stanton–White paper, the following example is given: Let α be a composition of n, and let W(α) be the set of all words of length n with αi letters equal to i. A descent of a word w is any index j such that w j > w j + 1 {\displaystyle w_{j}>w_{j+1}} . Define the major index maj  ( w ) {\displaystyle \operatorname {maj} (w)} on words as the sum of all descents. The triple ( X n , C n − 1 , 1  q  q ) {\displaystyle (X_{n},C_{n-1},{\frac {1}{_{q}}}\left_{q})} exhibit a cyclic sieving phenomenon, where X n {\displaystyle X_{n}} is the set of non-crossing (1,2)-configurations of .


In probability theory, the central limit theorem states conditions under which the average of a sufficiently large number of independent random variables, each with finite mean and variance, will be approximately normally distributed.Directional statistics is the subdiscipline of statistics that deals with directions (unit vectors in Rn), axes (lines through the origin in Rn) or rotations in Rn. The means and variances of directional quantities are all finite, so that the central limit theorem may be applied to the particular case of directional statistics.This article will deal only with unit vectors in 2-dimensional space (R2) but the method described can be extended to the general case.


This makes the reliable modification of static memory values more complex. The load address has to be determined and subtracted from a found memory address to obtain a static memory offset. This offset is often exactly the address of the static variable within the PIE binary.


Additionally, both of these services allow browsing of their classifications, via Westlaw's West Key Numbers or Lexis' Headnotes. Though these two search algorithms are proprietary and secret, it is known that they employ manual classification of text (though this may be computer-assisted).These systems can help overcome the majority of problems inherent in legal information retrieval systems, in that manual classification has the greatest chances of identifying landmark cases and understanding the issues that arise in the text. In one study, ontological searching resulted in a precision rate of 82% and a recall rate of 97% among legal professionals. The legal texts included, however, were carefully controlled to just a few areas of law in a specific jurisdiction.The major drawback to this approach is the requirement of using highly skilled legal professionals and large amounts of time to classify texts. As the amount of text available continues to increase, some have stated their belief that manual classification is unsustainable.


I am her. Subject + Verb (transitive) + Indirect Object + Direct ObjectExample: She made me a pie.This clause pattern is a derivative of S+V+O, transforming the object of a preposition into an indirect object of the verb, as the example sentence in transformational grammar is actually "She made a pie for me". Subject + Verb (transitive) + Object + Object ComplementExample: They made him happy.They did not make "him", and they did not make "happy"; they made "him happy"—the object and its complement form a syntactical unit.Sentences – which are composed of these clauses, in either "dependent" or "independent" form – also have patterns, as explained below.


In logics with double negation elimination (where ¬ ¬ x ≡ x {\displaystyle \lnot \lnot x\equiv x} ) the complementary literal or complement of a literal l {\displaystyle l} can be defined as the literal corresponding to the negation of l {\displaystyle l} . We can write l ¯ {\displaystyle {\bar {l}}} to denote the complementary literal of l {\displaystyle l} . More precisely, if l ≡ x {\displaystyle l\equiv x} then l ¯ {\displaystyle {\bar {l}}} is ¬ x {\displaystyle \lnot x} and if l ≡ ¬ x {\displaystyle l\equiv \lnot x} then l ¯ {\displaystyle {\bar {l}}} is x {\displaystyle x} .


In performance testing, it is often crucial for the test conditions to be similar to the expected actual use. However, in practice this is hard to arrange and not wholly possible, since production systems are subjected to unpredictable workloads. Test workloads may mimic occurrences in the production environment as far as possible, but only in the simplest systems can one exactly replicate this workload variability. Loosely-coupled architectural implementations (e.g.: SOA) have created additional complexities with performance testing. To truly replicate production-like states, enterprise services or assets that share a common infrastructure or platform require coordinated performance testing, with all consumers creating production-like transaction volumes and load on shared infrastructures or platforms. Because this activity is so complex and costly in money and time, some organizations now use tools to monitor and simulate production-like conditions (also referred as "noise") in their performance testing environments (PTE) to understand capacity and resource requirements and verify / validate quality attributes.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 23568, 123568, 234568, and 1234568 are the patterns related to Braille pattern dots-12456, since the two additional dots of kantenji patterns 012456, 124567, and 0124567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


As in the case of groups or magmas, the semigroup operation need not be commutative, so x·y is not necessarily equal to y·x; a well-known example of an operation that is associative but non-commutative is matrix multiplication. If the semigroup operation is commutative, then the semigroup is called a commutative semigroup or (less often than in the analogous case of groups) it may be called an abelian semigroup. A monoid is an algebraic structure intermediate between semigroups and groups, and is a semigroup having an identity element, thus obeying all but one of the axioms of a group: existence of inverses is not required of a monoid.


In the 19th century, research into the subject started to intensify. Notable developments in this century include the work of Hans Christian Ørsted who discovered in 1820 that an electric current produces a magnetic field that will deflect a compass needle, of William Sturgeon who, in 1825 invented the electromagnet, of Joseph Henry and Edward Davy who invented the electrical relay in 1835, of Georg Ohm, who in 1827 quantified the relationship between the electric current and potential difference in a conductor, of Michael Faraday (the discoverer of electromagnetic induction in 1831), and of James Clerk Maxwell, who in 1873 published a unified theory of electricity and magnetism in his treatise Electricity and Magnetism.In 1782, Georges-Louis Le Sage developed and presented in Berlin probably the world's first form of electric telegraphy, using 24 different wires, one for each letter of the alphabet. This telegraph connected two rooms. It was an electrostatic telegraph that moved gold leaf through electrical conduction.


In order to reduce encryption or signature verification time, it is useful to use a small public exponent ( e {\displaystyle e} ). In practice, common choices for e {\displaystyle e} are 3, 17 and 65537 ( 2 16 + 1 ) {\displaystyle (2^{16}+1)} . These values for e are Fermat primes, sometimes referred to as F 0 , F 2 {\displaystyle F_{0},F_{2}} and F 4 {\displaystyle F_{4}} respectively ( F x = 2 2 x + 1 ) {\displaystyle (F_{x}=2^{2^{x}}+1)} . They are chosen because they make the modular exponentiation operation faster.


The blinking of the text cursor is usually temporarily suspended when it is being moved; otherwise, the cursor may change position when it is not visible, making its location difficult to follow. The concept of a blinking cursor can be attributed to Charles Kiesling Sr. via US Patent 3531796, filed in August 1967.Some interfaces use an underscore or thin vertical bar to indicate that the user is in insert mode, a mode where text will be inserted in the middle of the existing text, and a larger block to indicate that the user is in overtype mode, where inserted text will overwrite existing text. In this way, a block cursor may be seen as a piece of selected text one character wide, since typing will replace the text "in" the cursor with the new text.


When any two indices are interchanged, equal or not, the symbol is negated: If any two indices are equal, the symbol is zero. When all indices are unequal, we have: where p (called the parity of the permutation) is the number of pairwise interchanges of indices necessary to unscramble i1, i2, ..., in into the order 1, 2, ..., n, and the factor (−1)p is called the sign, or signature of the permutation. The value ε1 2 ... n must be defined, else the particular values of the symbol for all permutations are indeterminate.


In multivariate statistics, spectral clustering techniques make use of the spectrum (eigenvalues) of the similarity matrix of the data to perform dimensionality reduction before clustering in fewer dimensions. The similarity matrix is provided as an input and consists of a quantitative assessment of the relative similarity of each pair of points in the dataset. In application to image segmentation, spectral clustering is known as segmentation-based object categorization.


What stopping rule minimizes the expected rank of the selected observation, and what is its corresponding value?The general solution to this full-information expected rank problem is unknown. The major difficulty is that the problem is fully history-dependent, that is, the optimal rule depends at every stage on all preceding values, and not only on simpler sufficient statistics of these. Only bounds are known for the limiting value v as n goes to infinity, namely 1.908 < v < 2.329. It is known that there is some room to improve the lower bound by further computations for a truncated version of the problem. It is still not known how to improve on the upper bound which stems from the subclass of memoryless threshold rules.


Since the posterior mean is cumbersome to calculate, the form of the MMSE estimator is usually constrained to be within a certain class of functions. Linear MMSE estimators are a popular choice since they are easy to use, easy to calculate, and very versatile. It has given rise to many popular estimators such as the Wiener–Kolmogorov filter and Kalman filter.


In the 2010s, software has become a key business differentiator. As a result, organizations now expect software development teams to deliver more, and more innovative, software within shorter delivery cycles. To meet these demands, teams have turned to lean approaches, such as Agile, DevOps, and Continuous Delivery, to try to speed up the systems development life cycle (SDLC). After accelerating other aspects of the delivery pipeline, teams typically find that their testing process is preventing them from achieving the expected benefits of their SDLC acceleration initiative.


Interaction between 32-bit addresses and two loop control instructions, BXH and BXLE that treated their arguments as signed numbers when doing comparisons (and which was said to be the reason TSS used 31-bit addressing on the Model 67). : 26, note 85 Input from key initial Model 67 sites, which had debated the alternatives during the initial system design period, and had recommended 31 bits (instead of the 32-bit design that was ultimately chosen at the time). : 8–9, note 21 Certain machine instructions in this 31-bit addressing mode alter the addressing mode bit.


In the dynamic topic model, only W t , d , n {\displaystyle W_{t,d,n}} is observable. Learning the other parameters constitutes an inference problem. Blei and Lafferty argue that applying Gibbs sampling to do inference in this model is more difficult than in static models, due to the nonconjugacy of the Gaussian and multinomial distributions. They propose the use of variational methods, in particular, the Variational Kalman Filtering and the Variational Wavelet Regression.


). Roughly speaking, δ {\displaystyle \delta \,\!} minimizes this expectation of expected loss (i.e., is a Bayes rule) if and only if it minimizes the expected loss for each x ∈ X {\displaystyle x\in {\mathcal {X}}} separately (i.e., is a generalized Bayes rule).


In mathematics, the Lévy metric is a metric on the space of cumulative distribution functions of one-dimensional random variables. It is a special case of the Lévy–Prokhorov metric, and is named after the French mathematician Paul Lévy.


For each ordinal α {\displaystyle \alpha } , ℵ α + 1 {\displaystyle \aleph _{\alpha +1}} is the least cardinal number greater than ℵ α {\displaystyle \aleph _{\alpha }} . The cardinality of the natural numbers is denoted aleph-null ( ℵ 0 {\displaystyle \aleph _{0}} ), while the cardinality of the real numbers is denoted by " c {\displaystyle {\mathfrak {c}}} " (a lowercase fraktur script "c"), and is also referred to as the cardinality of the continuum. Cantor showed, using the diagonal argument, that c > ℵ 0 {\displaystyle {\mathfrak {c}}>\aleph _{0}} .


fppf stands for fidèlement plate de présentation finie, and in this topology, a morphism of affine schemes is a covering morphism if it is faithfully flat and of finite presentation. fpqc stands for fidèlement plate et quasi-compacte, and in this topology, a morphism of affine schemes is a covering morphism if it is faithfully flat. In both categories, a covering family is defined be a family which is a cover on Zariski open subsets.


passport, are by law one of the few primary documents for proving U.S. citizenship. These certificates are normally not carried on a day-to-day basis; instead, they are used to procure other documents, such as a passport or driver's license, which are then carried and used as a primary means of identification.


In mathematics, a local language is a formal language for which membership of a word in the language can be determined by looking at the first and last symbol and each two-symbol substring of the word. Equivalently, it is a language recognised by a local automaton, a particular kind of deterministic finite automaton.Formally, a language L over an alphabet A is defined to be local if there are subsets R and S of A and a subset F of A×A such that a word w is in L if and only if the first letter of w is in R, the last letter of w is in S and no factor of length 2 in w is in F. This corresponds to the regular expression ( R A ∗ ∩ A ∗ S ) ∖ A ∗ F A ∗ . {\displaystyle (RA^{*}\cap A^{*}S)\setminus A^{*}FA^{*}\ .} More generally, a k-testable language L is one for which membership of a word w in L depends only on the prefix, suffix and the set of factors of w of length k; a language is locally testable if it is k-testable for some k. A local language is 2-testable.


We merely abstain from both assumptions. . .


In order to decouple the real-time operating system platform from the application software, ARINC 653 defines an API called APplication EXecutive (APEX). Each application software is called a partition and has its own memory space. It also has a dedicated time slot allocated by the APEX API. Within each partition, multitasking is allowed.


In mathematics, economics, and computer science, the lattice of stable matchings is a distributive lattice whose elements are stable matchings. For a given instance of the stable matching problem, this lattice provides an algebraic description of the family of all solutions to the problem. It was originally described in the 1970s by John Horton Conway and Donald Knuth.By Birkhoff's representation theorem, this lattice can be represented as the lower sets of an underlying partially ordered set. The elements of this set can be given a concrete structure as rotations, with cycle graphs describing the changes between adjacent stable matchings in the lattice.


In 1847 Gabriel Lamé announced a solution of Fermat's Last Theorem for all n > 2 {\displaystyle n>2} ; that is, that the Fermat equation has no solutions in nonzero integers, but it turned out that his solution hinged on the assumption that the cyclotomic ring Z  {\displaystyle \mathbb {Z} } is a UFD. Ernst Kummer had shown three years before that this was not the case already for n = 23 {\displaystyle n=23} (the full, finite list of values for which Z  {\displaystyle \mathbb {Z} } is a UFD is now known). At the same time, Kummer developed powerful new methods to prove Fermat's Last Theorem at least for a large class of prime exponents n {\displaystyle n} using what we now recognize as the fact that the ring Z  {\displaystyle \mathbb {Z} } is a Dedekind domain.


In realtime scheduling algorithms for periodic jobs, an acceptance test is needed before accepting a sporadic job with a hard deadline. One of the simplest acceptance tests for a sporadic job is calculating the amount of slack time between the release time and deadline of the job.


However, this naming scheme was quite temporary, lasting for a few years during the early 1980s.Although the 8086 was primarily developed for embedded systems and small multi-user or single-user computers, largely as a response to the successful 8080-compatible Zilog Z80, the x86 line soon grew in features and processing power. Today, x86 is ubiquitous in both stationary and portable personal computers, and is also used in midrange computers, workstations, servers, and most new supercomputer clusters of the TOP500 list. A large amount of software, including a large list of x86 operating systems are using x86-based hardware.


In the STAR, new instructions essentially wrote the loops for the user. The user told the machine where in memory the list of numbers was stored, then fed in a single instruction a(1..1000000) = addv b(1..1000000), c(1..1000000). At first glance it appears the savings are limited; in this case the machine fetches and decodes only a single instruction instead of 1,000,000, thereby saving 1,000,000 fetches and decodes, perhaps one-fourth of the overall time. The real savings are not so obvious.


Property is in a person's presence when it is within the area of their immediate control. The property has to be close enough to the victim's person that the victim could have prevented its taking if he/she had not been placed in fear or intimidation.by force or threat of force – the use of force or threat of force is the defining element of robbery. For there to be robbery there must be "force or fear" in perpetrating the theft.


Some of these databases may be shared among several companies, each paying every time a name is "extracted". It is for this reason that mobile telephone callers may appear as "WIRELESS CALLER", or the central office location of the number. If the call originates on a POTS line (a standard loop-start line), then caller ID is provided by the service provider's local switch.


The application of biotechnology to basic science (for example through the Human Genome Project) has also dramatically improved our understanding of biology and as our scientific knowledge of normal and disease biology has increased, our ability to develop new medicines to treat previously untreatable diseases has increased as well.Genetic testing allows the genetic diagnosis of vulnerabilities to inherited diseases, and can also be used to determine a child's parentage (genetic mother and father) or in general a person's ancestry. In addition to studying chromosomes to the level of individual genes, genetic testing in a broader sense includes biochemical tests for the possible presence of genetic diseases, or mutant forms of genes associated with increased risk of developing genetic disorders. Genetic testing identifies changes in chromosomes, genes, or proteins.


In the 19th century it became a common technique to gain insight into integer solutions of polynomial equations using rings of algebraic numbers of higher degree. For instance, fix a positive integer m {\displaystyle m} . In the attempt to determine which integers are represented by the quadratic form x 2 + m y 2 {\displaystyle x^{2}+my^{2}} , it is natural to factor the quadratic form into ( x + − m y ) ( x − − m y ) {\displaystyle (x+{\sqrt {-m}}y)(x-{\sqrt {-m}}y)} , the factorization taking place in the ring of integers of the quadratic field Q ( − m ) {\displaystyle \mathbb {Q} ({\sqrt {-m}})} . Similarly, for a positive integer n {\displaystyle n} the polynomial z n − y n {\displaystyle z^{n}-y^{n}} (which is relevant for solving the Fermat equation x n + y n = z n {\displaystyle x^{n}+y^{n}=z^{n}} ) can be factored over the ring Z  {\displaystyle \mathbb {Z} } , where ζ n {\displaystyle \zeta _{n}} is a primitive n-th root of unity.


In mathematics, convergence tests are methods of testing for the convergence, conditional convergence, absolute convergence, interval of convergence or divergence of an infinite series ∑ n = 1 ∞ a n {\displaystyle \sum _{n=1}^{\infty }a_{n}} .


in the interpretation above, the only partition of { 1 , 2 , 3 } {\textstyle \{1,2,3\}} into 1 set can have its set ordered in 6 ways: L ( 3 , 2 ) {\textstyle L(3,2)} is equal to 6, because there are six partitions of { 1 , 2 , 3 } {\textstyle \{1,2,3\}} into two ordered parts: L ( n , n ) {\textstyle L(n,n)} is always 1 because the only way to partition { 1 , 2 , … , n } {\textstyle \{1,2,\ldots ,n\}} into n {\displaystyle n} non-empty subsets results in subsets of size 1, that can only be permuted in one way. In the more recent literature, Karamata–Knuth style notation has taken over. Lah numbers are now often written as


The intuitive meaning of a stack is that it is a fibred category such that "all possible gluings work". The specification of gluings requires a definition of coverings with regard to which the gluings can be considered. It turns out that the general language for describing these coverings is that of a Grothendieck topology. Thus a stack is formally given as a fibred category over another base category, where the base has a Grothendieck topology and where the fibred category satisfies a few axioms that ensure existence and uniqueness of certain gluings with respect to the Grothendieck topology.


It is a sharper bound than the first- or second-moment-based tail bounds such as Markov's inequality or Chebyshev's inequality, which only yield power-law bounds on tail decay. However, when applied to sums the Chernoff bound requires the random variables to be independent, a condition that is not required by either Markov's inequality or Chebyshev's inequality (although Chebyshev's inequality does require the random variables to be pairwise independent). The Chernoff bound is related to the Bernstein inequalities. It is also used to prove Hoeffding's inequality, Bennett's inequality, and McDiarmid's inequality.


This language became quite popular in the early 1980s, and thus may also have been instrumental in spreading the style outside PARC. Upper camel case (or "Pascal case") is used in Wolfram Language in computer algebraic system Mathematica for predefined identifiers. User defined identifiers should start with a lower case letter. This avoids the conflict between predefined and user defined identifiers both today and in all future versions. C# variable names are recommended to follow the lower camel case convention.


Properties of time-aggregated network snapshots are able to be studied in terms of F ( x ) {\displaystyle F(x)} . For example, since each node j {\displaystyle j} after T {\displaystyle T} timesteps will have on average m η x i T {\displaystyle m\eta x_{i}T} outgoing links, the degree distribution after T {\displaystyle T} timesteps in the time-aggregated network will be related to the activity-potential distribution by P T ( k ) ∝ F ( k m η T ) . {\displaystyle P_{T}(k)\propto F\left({\frac {k}{m\eta T}}\right).} Spreading behavior according to the SIS epidemic model was investigated on activity-driven networks, and the following condition was derived for large-scale outbreaks to be possible: β λ > 2 ⟨ a ⟩ ⟨ a ⟩ + ⟨ a 2 ⟩ , {\displaystyle {\frac {\beta }{\lambda }}>{\frac {2\langle a\rangle }{\langle a\rangle +{\sqrt {\langle a^{2}\rangle }}}},} where β {\displaystyle \beta } is the per-contact transmission probability, λ {\displaystyle \lambda } is the per-timestep recovery probability, and ( ⟨ a ⟩ {\displaystyle \langle a\rangle } , ⟨ a 2 ⟩ {\displaystyle \langle a^{2}\rangle } ) are the first and second moments of the random activity-rate a j {\displaystyle a_{j}} .


In the 17th century Conrad Henfling writing to Leibniz about music theory and the tuning of musical instruments makes use of the Euclidean algorithm in his reasoning.Viggo Brun investigated the use of Euclidean Algorithm in terms of constructing scales up to 4 different size intervals. Erv Wilson explored both using ratios andscale steps of which Kraig Grady applied torhythms within long meters.


In principle, it would be possible to inflate the number of bytes in an encoding by padding the code point with leading 0s. To encode the euro sign € from the above example in four bytes instead of three, it could be padded with leading 0s until it was 21 bits long – 000 000010 000010 101100, and encoded as 11110000 10000010 10000010 10101100 (or F0 82 82 AC in hexadecimal). This is called an overlong encoding.


His device was the foundation for further developments in analog computing.The differential analyser, a mechanical analog computer designed to solve differential equations by integration using wheel-and-disc mechanisms, was conceptualized in 1876 by James Thomson, the brother of the more famous Lord Kelvin. He explored the possible construction of such calculators, but was stymied by the limited output torque of the ball-and-disk integrators. In a differential analyzer, the output of one integrator drove the input of the next integrator, or a graphing output.


In anti addition, two substituents are added to opposite sides (or faces) of a double bond or triple bond, once again resulting in a decrease in bond order and increase in number of substituents. The classical example of this is bromination (any halogenation) of alkenes. An anti addition reaction results in a trans-isomer of the products, as the substituents are on opposite faces of the bond.


In order to achieve the required amount of 'testing volume' needed to validate real-world testing, three points must be considered: System accuracy Federal and/or state health and safety guidelines and/or standards Economic viability based on the first two points.Once a particular portable emissions system has been identified and pronounced as accurate, the next step is to ensure that the worker(s) are properly protected from work hazards associated with the task(s) being performed in the use of the testing equipment. For example, typical functions for a worker may be to transport the equipment to the jobsite (i.e. car, truck, train, or plane), carry the equipment to the jobsite, and lift the equipment into position.


In some literature articles, the terms "mechanism of action" and "mode of action" are used interchangeably, typically referring to the way in which the drug interacts and produces a medical effect. However, in actuality, a mode of action describes functional or anatomical changes, at the cellular level, resulting from the exposure of a living organism to a substance. This differs from a mechanism of action since it is a more specific term that focuses on the interaction between the drug itself and an enzyme or receptor and its particular form of interaction, whether through inhibition, activation, agonism, or antagonism. Furthermore, the term "mechanism of action" is the main term that is primarily used in pharmacology, whereas "mode of action" will more often appear in the field of microbiology or certain aspects of biology.


In most computer programming languages, a while loop is a control flow statement that allows code to be executed repeatedly based on a given Boolean condition. The while loop can be thought of as a repeating if statement.


In statistics, combinatorial data analysis (CDA) is the study of data sets where the order in which objects are arranged is important. CDA can be used either to determine how well a given combinatorial construct reflects the observed data, or to search for a suitable combinatorial construct that does fit the data.


In some situations, the set of edges that are required is different from the edges in the graph. This is modeled by the Rural Postman Problem (RPP), where the required edges are a subset of the system of edges.


In mathematics, a bipartite matroid is a matroid all of whose circuits have even size.


In the 1950, Waldo Tobler published a paper titled "Automation and Cartography" that established the first use case for computers as aids in cartography. In this paper, Tobler established what he referred to as a "map in–map out" (MIMO) system, which facilitated digitization of traditional maps, changing them, and reproducing them. The MIMO system, while simple, established the use of computers for map making in the literature and set the stage for more advanced Geographic information systems in later years by geographers such as Roger Tomlinson.


This is typically done with polynomial or rational (ratio of polynomials) approximations. The objective is to make the approximation as close as possible to the actual function, typically with an accuracy close to that of the underlying computer's floating point arithmetic. This is accomplished by using a polynomial of high degree, and/or narrowing the domain over which the polynomial has to approximate the function. Narrowing the domain can often be done through the use of various addition or scaling formulas for the function being approximated. Modern mathematical libraries often reduce the domain into many tiny segments and use a low-degree polynomial for each segment.


A learning process that involves a method of reward and punishment must be in place that will select desirable patterns in the mind. This whole process, Turing mentions, to a large extent is similar to that of evolution by natural selection where the similarities are: Structure of the child machine = hereditary material Changes of the child machine = mutations Natural selection = judgment of the experimenterFollowing this discussion Turing addresses certain specific aspects of the learning machine: Nature of inherent complexity: The child machine could either be one that is as simple as possible, merely maintaining consistency with general principles, or the machine could be one with a complete system of logical inference programmed into it.


Hence the result by Cole and Vishkin raised the question of whether there is a constant-time distributed algorithm for 3-coloring an n-cycle. Linial (1992) showed that this is not possible: any deterministic distributed algorithm requires Ω(log* n) communication steps to reduce an n-coloring to a 3-coloring in an n-cycle. The technique by Cole and Vishkin can be applied in arbitrary bounded-degree graphs as well; the running time is poly(Δ) + O(log* n).


In mathematics and its applications, the mean square is normally defined as the arithmetic mean of the squares of a set of numbers or of a random variable.It may also be defined as the arithmetic mean of the squares of the deviations between a set of numbers and a reference value (e.g., may be a mean or an assumed mean of the data), in which case it may be known as mean square deviation. When the reference value is the assumed true value, the result is known as mean squared error. A typical estimate for the sample variance from a set of sample values x i {\displaystyle x_{i}} uses a divisor of the number of values minus one, n-1, rather than n as in a simple quadratic mean, and this is still called the "mean square" (e.g. in analysis of variance): s 2 = 1 n − 1 ∑ ( x i − x ¯ ) 2 {\displaystyle s^{2}=\textstyle {\frac {1}{n-1}}\sum (x_{i}-{\bar {x}})^{2}} The second moment of a random variable, E ( X 2 ) {\displaystyle E(X^{2})} is also called the mean square. The square root of a mean square is known as the root mean square (RMS or rms), and can be used as an estimate of the standard deviation of a random variable. == References ==


The Besicovitch inequality asserts that The inequality can be generalized in the following way. Given an n-dimensional Riemannian manifold M with connected boundary and a smooth map f: M →  n {\displaystyle f:M\rightarrow ^{n}} , such that the restriction of f to the boundary of M is a degree 1 map onto ∂  n {\displaystyle \partial ^{n}} , define Then ∏ i d i ≥ V o l ( M ) {\displaystyle \prod _{i}d_{i}\geq Vol(M)} . The Besicovitch inequality was used to prove systolic inequalities on surfaces.


In order theory a better-quasi-ordering or bqo is a quasi-ordering that does not admit a certain type of bad array. Every better-quasi-ordering is a well-quasi-ordering.


The chromatic polynomial, a polynomial whose values at integer arguments give the number of colorings of the graph with that many colors. The dichromatic polynomial, a 2-variable generalization of the chromatic polynomial The flow polynomial, a polynomial whose values at integer arguments give the number of nowhere-zero flows with integer flow amounts modulo the argument. The (inverse of the) Ihara zeta function, defined as a product of binomial terms corresponding to certain closed walks in a graph. The Martin polynomial, used by Pierre Martin to study Euler tours The matching polynomials, several different polynomials defined as the generating function of the matchings of a graph. The reliability polynomial, a polynomial that describes the probability of remaining connected after independent edge failures The Tutte polynomial, a polynomial in two variables that can be defined (after a small change of variables) as the generating function of the numbers of connected components of induced subgraphs of the given graph, parameterized by the number of vertices in the subgraph.


In mathematics and computer algebra, factorization of polynomials or polynomial factorization expresses a polynomial with coefficients in a given field or in the integers as the product of irreducible factors with coefficients in the same domain. Polynomial factorization is one of the fundamental components of computer algebra systems. The first polynomial factorization algorithm was published by Theodor von Schubert in 1793. Leopold Kronecker rediscovered Schubert's algorithm in 1882 and extended it to multivariate polynomials and coefficients in an algebraic extension.


Individual U.S. states set their own policies for state and local government employees (i.e. public sector employees).


In molecular biology, a batch effect occurs when non-biological factors in an experiment cause changes in the data produced by the experiment. Such effects can lead to inaccurate conclusions when their causes are correlated with one or more outcomes of interest in an experiment. They are common in many types of high-throughput sequencing experiments, including those using microarrays, mass spectrometers, and single-cell RNA-sequencing data. They are most commonly discussed in the context of genomics and high-throughput sequencing research, but they exist in other fields of science as well.


In number theory, Bertrand's postulate is a theorem stating that for any integer n > 3 {\displaystyle n>3} , there always exists at least one prime number p {\displaystyle p} with n < p < 2 n − 2. {\displaystyle n 1 {\displaystyle n>1} , there is always at least one prime p {\displaystyle p} such that n < p < 2 n . {\displaystyle n


Laws issue out a command to their constituents which can be realized as an action. When forming a legal contract, speech acts can be made when people are making or accepting an offer. Considering the theory of freedom of speech, some speech acts may not be legally protected. For example, a death threat is a type of speech act and is considered to exist outside of the protection of freedom of speech as it is treated as a criminal act.


In mathematics, especially linear algebra, an M-matrix is a Z-matrix with eigenvalues whose real parts are nonnegative. The set of non-singular M-matrices are a subset of the class of P-matrices, and also of the class of inverse-positive matrices (i.e. matrices with inverses belonging to the class of positive matrices). The name M-matrix was seemingly originally chosen by Alexander Ostrowski in reference to Hermann Minkowski, who proved that if a Z-matrix has all of its row sums positive, then the determinant of that matrix is positive.


Since functional programming languages, by definition, support function literals, which can also be stored in records, records types with subtyping provide some of the features of object-oriented programming. Typically, functional programming languages also provide some, usually restricted, form of parametric polymorphism. In a theoretical setting, it is desirable to study the interaction of the two features; a common theoretical setting is system F<:.


As well as log2, an alternative notation for the binary logarithm is lb (the notation preferred by ISO 31-11 and ISO 80000-2). Historically, the first application of binary logarithms was in music theory, by Leonhard Euler: the binary logarithm of a frequency ratio of two musical tones gives the number of octaves by which the tones differ. Binary logarithms can be used to calculate the length of the representation of a number in the binary numeral system, or the number of bits needed to encode a message in information theory.


In recent years commercial ADNs have begun to include application firewall functionality to further secure applications during the delivery process. This is a hotly debated subject with many security professionals arguing that the functionality included in an application firewall are unnecessary and should be handled by the application while others consider employing as much security as possible, regardless of position in the delivery network, to be the best practice. Many commercial ADN companies have acquired and integrated these functions and present such features as part of a defense in depth strategy often cited by security professionals.


Ranked set sampling uses a two-phase sampling design that identifies sets of field locations, utilizes inexpensive measurements to rank locations within each set, and then selects one location from each set for sampling. In ranked set sampling, m sets (each of size r) of field locations are identified using simple random sampling. The locations are ranked independently within each set using professional judgment or inexpensive, fast, or surrogate measurements.


In statistics, the conditional probability table (CPT) is defined for a set of discrete and mutually dependent random variables to display conditional probabilities of a single variable with respect to the others (i.e., the probability of each possible value of one variable if we know the values taken on by the other variables). For example, assume there are three random variables x 1 , x 2 , x 3 {\displaystyle x_{1},x_{2},x_{3}} where each has K {\displaystyle K} states. Then, the conditional probability table of x 1 {\displaystyle x_{1}} provides the conditional probability values P ( x 1 = a k ∣ x 2 , x 3 ) {\displaystyle P(x_{1}=a_{k}\mid x_{2},x_{3})} – where the vertical bar | {\displaystyle |} means “given the values of” – for each of the K possible values a k {\displaystyle a_{k}} of the variable x 1 {\displaystyle x_{1}} and for each possible combination of values of x 2 , x 3 . {\displaystyle x_{2},\,x_{3}.}


In order to get a grasp on the motivations which inspired the development of the idea of coordinative definitions, it is important to understand the doctrine of formalism as it is conceived in the philosophy of mathematics. For the formalists, mathematics, and particularly geometry, is divided into two parts: the pure and the applied. The first part consists in an uninterpreted axiomatic system, or syntactic calculus, in which terms such as point, straight line and between (the so-called primitive terms) have their meanings assigned to them implicitly by the axioms in which they appear. On the basis of deductive rules eternally specified in advance, pure geometry provides a set of theorems derived in a purely logical manner from the axioms.


In order to design a form or document, the writer should understand and evaluate the different constraints in the rhetorical situation; this is called functional analysis. One of the biggest components in analyzing a form or document is to determine the communicative purpose of the form or document. Leo Lentz and Henk Pander Maat, at the University of Utrecht, break down communicative purpose into four elements: intended communicative effect: the intended effect should fall into one of three categories; "a cognitive change in the mental state of the reader, who learns something or forms a particular attitude, a change in the reader's behavior, such as handling a machine or buying a product, or a change in the social reality as a result of the collective behavior of readers, such as the sale of a product". topic: this is based on the reader's needs, since the reader is the one expected to act on the information. target group: this should be a specific group described either by demographic variables or communicative predispositions. organizational goal: this is the change that should occur in every individual reader.After analyzing the communicative purpose, the technical communicator can design a form or document that will match the requirements and meet expectations for it.


When programming in machine code, assembly language, and certain other programming languages, programmers work with the low-level digital structure of the data registers. These registers operate on voltages, where zero volts represents Boolean 0, and a reference voltage (often +5 V, +3.3 V, +1.8 V) represents Boolean 1. Such languages support both numeric operations and logical operations.


In natural resources management and environmental policy more generally, demand management refers to policies to control consumer demand for environmentally sensitive or harmful goods such as water and energy. Within manufacturing firms the term is used to describe the activities of demand forecasting, planning, and order fulfillment. In the environmental context demand management is increasingly taken seriously to reduce the economy's throughput of scarce resources for which market pricing does not reflect true costs. Examples include metering of municipal water, and carbon taxes on gasoline.


In mathematics, a modular invariant of a group is an invariant of a finite group acting on a vector space of positive characteristic (usually dividing the order of the group). The study of modular invariants was originated in about 1914 by Dickson (2004).


Testing and the overall quality process remain problematic for several key reasons. Traditional testing processes are too slow.


However, there are other number systems that are not accurately described by these axioms; in particular, the theory defined in the same way for integers instead of real numbers is undecidable, even for existential sentences (Diophantine equations) by Matiyasevich's theorem.The existential theory of the reals is the fragment of the first-order theory consisting of sentences in which all the quantifiers are existential and they appear before any of the other symbols. That is, it is the set of all true sentences of the form where F ( X 1 , … X n ) {\displaystyle F(X_{1},\dots X_{n})} is a quantifier-free formula involving equalities and inequalities of real polynomials. The decision problem for the existential theory of the reals is the algorithmic problem of testing whether a given sentence belongs to this theory; equivalently, for strings that pass the basic syntactical checks (they use the correct symbols with the correct syntax, and have no unquantified variables) it is the problem of testing whether the sentence is a true statement about the real numbers.


In the Standard Model of particle physics, the Cabibbo–Kobayashi–Maskawa matrix, CKM matrix, quark mixing matrix, or KM matrix is a unitary matrix which contains information on the strength of the flavour-changing weak interaction. Technically, it specifies the mismatch of quantum states of quarks when they propagate freely and when they take part in the weak interactions. It is important in the understanding of CP violation. This matrix was introduced for three generations of quarks by Makoto Kobayashi and Toshihide Maskawa, adding one generation to the matrix previously introduced by Nicola Cabibbo. This matrix is also an extension of the GIM mechanism, which only includes two of the three current families of quarks.


In mathematics, the coclass of a finite p-group of order pn is n − c, where c is the class.


In the context of sensor net, public-key based access control (PKC) may be a good solution in the future to cover some issues in wireless access control. For sensor net, the danger from attackers includes; impersonation which grants access to malicious users, replay attack where the adversary captures sensitive information by replaying it, interleaving which selectively combines messages from previous sessions, reflection where an adversary sends an identical message to the originator similar to impersonation, forced delay which blocks communication message to be sent at a later time, and chosen-text attack where the attacker tries to extract the keys to access the sensor. The solution to this may be public key-based cryptography as a study done by Haodong Wang shows that PKC-based protocol presented is better than the traditional symmetric key in regards to memory usage, message complexity, and security resilience.


In mathematics, a matrix norm is a vector norm in a vector space whose elements (vectors) are matrices (of given dimensions).


In the context of centralized linear-quadratic control, with additive uncertainty in the equation of evolution but no uncertainty about coefficient values in that equation, the optimal solution for the control variables taking into account the uncertainty is the same as the solution ignoring uncertainty. This property, which gives a zero expected value of including uncertainty, is called certainty equivalence.


]_{f}} or  ] o ∈  ] f {\displaystyle \! ]_{o}\in \! ]_{f}} .


Category has the value noun phrase whereas the value of agreement is indicated by another feature structure with the features number and person being singular and third. This particular notation is called attribute value matrix (AVM). The matrix has two columns, one for the feature names and the other for the values.


The CARP can be solved with combinatorial optimization including convex hulls. The large-scale capacitated arc routing problem (LSCARP) is a variant of the capacitated arc routing problem that applies to hundreds of edges and nodes to realistically simulate and model large complex environments. == References ==


In order to reduce the reliance on legal professionals and the amount of time needed, efforts have been made to create a system to automatically classify legal text and queries. Adequate translation of both would allow accurate information retrieval without the high cost of human classification. These automatic systems generally employ Natural Language Processing (NLP) techniques that are adapted to the legal domain, and also require the creation of a legal ontology.


In mathematics, specifically in abstract algebra, power associativity is a property of a binary operation that is a weak form of associativity.


The user can direct dial from their handset if the network they are roaming in supports CAMEL (Customized Applications for Mobile networks Enhanced Logic). This allows real time billing by the home operator without having to dial the customer back. The advantage is that it is more natural and works seamlessly. The disadvantage is that not all networks support CAMEL so the list of countries where a prepaid customer can use their phone abroad is smaller than for postpaid mobile phones.


In operating systems architecture a reference monitor concept defines a set of design requirements on a reference validation mechanism, which enforces an access control policy over subjects' (e.g., processes and users) ability to perform operations (e.g., read and write) on objects (e.g., files and sockets) on a system. The properties of a reference monitor are captured by the acronym NEAT, which means: The reference validation mechanism must be Non-bypassable, so that an attacker cannot bypass the mechanism and violate the security policy. The reference validation mechanism must be Evaluable, i.e., amenable to analysis and tests, the completeness of which can be assured (verifiable). Without this property, the mechanism might be flawed in such a way that the security policy is not enforced.


In software engineering, a test case is a specification of the inputs, execution conditions, testing procedure, and expected results that define a single test to be executed to achieve a particular software testing objective, such as to exercise a particular program path or to verify compliance with a specific requirement. Test cases underlie testing that is methodical rather than haphazard. A battery of test cases can be built to produce the desired coverage of the software being tested. Formally defined test cases allow the same tests to be run repeatedly against successive versions of the software, allowing for effective and consistent regression testing.


Therefore, r = 1 2 {\displaystyle r={\frac {1}{2}}} , so b = b 1 / 2 {\displaystyle {\sqrt {b}}=b^{1/2}} . The definition of exponentiation can be extended to allow any real or complex exponent. Exponentiation by integer exponents can also be defined for a wide variety of algebraic structures, including matrices. Exponentiation is used extensively in many fields, including economics, biology, chemistry, physics, and computer science, with applications such as compound interest, population growth, chemical reaction kinetics, wave behavior, and public-key cryptography.


In the first pass, the forward–backward algorithm computes a set of forward probabilities which provide, for all t ∈ { 1 , … , T } {\displaystyle t\in \{1,\dots ,T\}} , the probability of ending up in any particular state given the first t {\displaystyle t} observations in the sequence, i.e. P ( X t | o 1: t ) {\displaystyle P(X_{t}\ |\ o_{1:t})} . In the second pass, the algorithm computes a set of backward probabilities which provide the probability of observing the remaining observations given any starting point t {\displaystyle t} , i.e. P ( o t + 1: T | X t ) {\displaystyle P(o_{t+1:T}\ |\ X_{t})} . These two sets of probability distributions can then be combined to obtain the distribution over states at any specific point in time given the entire observation sequence: P ( X t | o 1: T ) = P ( X t | o 1: t , o t + 1: T ) ∝ P ( o t + 1: T | X t ) P ( X t | o 1: t ) {\displaystyle P(X_{t}\ |\ o_{1:T})=P(X_{t}\ |\ o_{1:t},o_{t+1:T})\propto P(o_{t+1:T}\ |\ X_{t})P(X_{t}|o_{1:t})} The last step follows from an application of the Bayes' rule and the conditional independence of o t + 1: T {\displaystyle o_{t+1:T}} and o 1: t {\displaystyle o_{1:t}} given X t {\displaystyle X_{t}} . As outlined above, the algorithm involves three steps: computing forward probabilities computing backward probabilities computing smoothed values.The forward and backward steps may also be called "forward message pass" and "backward message pass" - these terms are due to the message-passing used in general belief propagation approaches.


{\displaystyle \Omega .} Define u ( h , k ) = f ( a + h , b + k ) − f ( a + h , b ) , v ( h , k ) = f ( a + h , b + k ) − f ( a , b + k ) , w ( h , k ) = f ( a + h , b + k ) − f ( a + h , b ) − f ( a , b + k ) + f ( a , b ) . {\displaystyle {\begin{aligned}u\left(h,\,k\right)&=f\left(a+h,\,b+k\right)-f\left(a+h,\,b\right),\\v\left(h,\,k\right)&=f\left(a+h,\,b+k\right)-f\left(a,\,b+k\right),\\w\left(h,\,k\right)&=f\left(a+h,\,b+k\right)-f\left(a+h,\,b\right)-f\left(a,\,b+k\right)+f\left(a,\,b\right).\end{aligned}}} These functions are defined for | h | , | k | < ε {\displaystyle \left|h\right|,\,\left|k\right|<\varepsilon } , where ε > 0 {\displaystyle \varepsilon >0} and  ×  {\displaystyle \left\times \left} is contained in Ω .


In systems engineering, the system usability scale (SUS) is a simple, ten-item attitude Likert scale giving a global view of subjective assessments of usability. It was developed by John Brooke at Digital Equipment Corporation in the UK in 1986 as a tool to be used in usability engineering of electronic office systems. The usability of a system, as defined by the ISO standard ISO 9241 Part 11, can be measured only by taking into account the context of use of the system—i.e., who is using the system, what they are using it for, and the environment in which they are using it. Furthermore, measurements of usability have several different aspects: effectiveness (can users successfully achieve their objectives) efficiency (how much effort and resource is expended in achieving those objectives) satisfaction (was the experience satisfactory)Measures of effectiveness and efficiency are also context specific.


Different websites and systems have different algorithms, but one approach, used by Amazon (company) for its online store, is to indicate to a user: "customers who bought x also bought y" (affinity analysis, collaborative filtering). This example is oriented around online purchasing behaviour, but an algorithm could also be programmed to provide suggestions based on other factors (e.g., searching, viewing, etc.).Discoverability is typically referred to in connection with search engines. A highly "discoverable" piece of content would appear at the top, or near the top of a user's search results.


The latter are referred to as vector magnetographs. These measurements are made by exploiting the Zeeman effect or, less frequently, the Hanle effect.The first magnetograph was constructed by George Ellery Hale in 1908. == References ==


This is called the Harvard architecture after the Harvard Mark I computer. Modern von Neumann computers display some traits of the Harvard architecture in their designs, such as in CPU caches.


In mathematics, for positive integers k and s, a vectorial addition chain is a sequence V of k-dimensional vectors of nonnegative integers vi for −k + 1 ≤ i ≤ s together with a sequence w, such that v−k+1 =  v−k+2 =  ⋮ ⋮ v0 = vi =vj+vr for all 1≤i≤s with -k+1≤j, r≤i-1 vs =  w = (w1,...ws), wi=(j,r).For example, a vectorial addition chain for  is V=(,,,,,,,,,,,) w=((-2,-1),(1,1),(2,2),(-2,3),(4,4),(1,5),(0,6),(7,7),(0,8))Vectorial addition chains are well suited to perform multi-exponentiation: Input: Elements x0,...,xk-1 of an abelian group G and a vectorial addition chain of dimension k computing  Output:The element x0n0...xk-1nr-1for i =-k+1 to 0 do yi → xi+k-1 for i = 1 to s do yi →yj×yr return ys


In science and in engineering, the Celsius scale and the Kelvin scale are often used in combination in close contexts, e.g. "a measured value was 0.01023 °C with an uncertainty of 70 μK". This practice is permissible because the magnitude of the degree Celsius is equal to that of the kelvin. Notwithstanding the official endorsement provided by decision no. 3 of Resolution 3 of the 13th CGPM, which stated "a temperature interval may also be expressed in degrees Celsius", the practice of simultaneously using both °C and K remains widespread throughout the scientific world as the use of SI-prefixed forms of the degree Celsius (such as "μ°C" or "microdegrees Celsius") to express a temperature interval has not been well adopted.


In number theory, primes in arithmetic progression are any sequence of at least three prime numbers that are consecutive terms in an arithmetic progression. An example is the sequence of primes (3, 7, 11), which is given by a n = 3 + 4 n {\displaystyle a_{n}=3+4n} for 0 ≤ n ≤ 2 {\displaystyle 0\leq n\leq 2} . According to the Green–Tao theorem, there exist arbitrarily long sequences of primes in arithmetic progression. Sometimes the phrase may also be used about primes which belong to an arithmetic progression which also contains composite numbers.


A CCS (centacall-second) is often used to describe 100 call-seconds, so 3600 call-seconds = 36 CCS = 1 call-hour. In a communication network, a trunk (link) can carry numerous concurrent calls by means of multiplexing. Hence a particular number of call-seconds can be carried in infinitely many ways as calls are established and cleared over time.


In mathematical logic, a formal theory is a set of sentences within a formal language. A sentence is a well-formed formula with no free variables. A sentence that is a member of a theory is one of its theorems, and the theory is the set of its theorems. Usually a theory is understood to be closed under the relation of logical consequence.


In statistics, the t-statistic is the ratio of the departure of the estimated value of a parameter from its hypothesized value to its standard error. It is used in hypothesis testing via Student's t-test. The t-statistic is used in a t-test to determine whether to support or reject the null hypothesis.


In proof theory, the Dialectica interpretation is a proof interpretation of intuitionistic logic (Heyting arithmetic) into a finite type extension of primitive recursive arithmetic, the so-called System T. It was developed by Kurt Gödel to provide a consistency proof of arithmetic. The name of the interpretation comes from the journal Dialectica, where Gödel's paper was published in a 1958 special issue dedicated to Paul Bernays on his 70th birthday.


The two measures are complementary in sense that if one knows the mid-range and the range, one can find the sample maximum and minimum values. The mid-range is rarely used in practical statistical analysis, as it lacks efficiency as an estimator for most distributions of interest, because it ignores all intermediate points, and lacks robustness, as outliers change it significantly. Indeed, for many distributions it is one of the least efficient and least robust statistics. However, it finds some use in special cases: it is the maximally efficient estimator for the center of a uniform distribution, trimmed mid-ranges address robustness, and as an L-estimator, it is simple to understand and compute.


In sociology, a social system is the patterned network of relationships constituting a coherent whole that exist between individuals, groups, and institutions. It is the formal structure of role and status that can form in a small, stable group. An individual may belong to multiple social systems at once; examples of social systems include nuclear family units, communities, cities, nations, college campuses, religions, corporations, and industries. The organization and definition of groups within a social system depend on various shared properties such as location, socioeconomic status, race, religion, societal function, or other distinguishable features.


In mathematics, a product of rings or direct product of rings is a ring that is formed by the Cartesian product of the underlying sets of several rings (possibly an infinity), equipped with componentwise operations. It is a direct product in the category of rings. Since direct products are defined up to an isomorphism, one says colloquially that a ring is the product of some rings if it is isomorphic to the direct product of these rings. For example, the Chinese remainder theorem may be stated as: if m and n are coprime integers, the quotient ring Z / m n Z {\displaystyle \mathbb {Z} /mn\mathbb {Z} } is the product of Z / m Z {\displaystyle \mathbb {Z} /m\mathbb {Z} } and Z / n Z . {\displaystyle \mathbb {Z} /n\mathbb {Z} .}


In numerical analysis, finite-difference methods (FDM) are a class of numerical techniques for solving differential equations by approximating derivatives with finite differences. Both the spatial domain and time interval (if applicable) are discretized, or broken into a finite number of steps, and the value of the solution at these discrete points is approximated by solving algebraic equations containing finite differences and values from nearby points. Finite difference methods convert ordinary differential equations (ODE) or partial differential equations (PDE), which may be nonlinear, into a system of linear equations that can be solved by matrix algebra techniques. Modern computers can perform these linear algebra computations efficiently which, along with their relative ease of implementation, has led to the widespread use of FDM in modern numerical analysis. Today, FDM are one of the most common approaches to the numerical solution of PDE, along with finite element methods.


In that work: "A viewpoint can be thought of as a combination of the idea of an “actor”, “knowledge source”, “role” or “agent” in the development process and the idea of a “view” or “perspective” which an actor maintains." An important idea in this paper was to distinguish "a representation style, the scheme and notation by which the viewpoint expresses what it can see" and "a specification, the statements expressed in the viewpoint's style describing particular domains". Subsequent work, such as IEEE 1471, preserved this distinction by utilizing two separate terms: viewpoint and view, respectively.


337). We have R+ = R if, and only if, R itself is transitive. Conversely, transitive reduction adduces a minimal relation S from a given relation R such that they have the same closure, that is, S+ = R+; however, many different S with this property may exist. Both transitive closure and transitive reduction are also used in the closely related area of graph theory.


In some cases, particularly with noun and adjective phrases, it is not always clear which dependents are to be classed as complements, and which as adjuncts. Although in principle the head-directionality parameter concerns the order of heads and complements only, considerations of head-initiality and head-finality sometimes take account of the position of the head in the phrase as a whole, including adjuncts. The structure of the various types of phrase is analyzed below in relation to specific languages, with a focus on the ordering of head and complement. In some cases (such as English and Japanese) this ordering is found to be the same in practically all types of phrase, whereas in others (such as German and Gbe) the pattern is less consistent.


In mathematics, the category of topological spaces, often denoted Top, is the category whose objects are topological spaces and whose morphisms are continuous maps. This is a category because the composition of two continuous maps is again continuous, and the identity function is continuous. The study of Top and of properties of topological spaces using the techniques of category theory is known as categorical topology. N.B. Some authors use the name Top for the categories with topological manifolds, with compactly generated spaces as objects and continuous maps as morphisms or with the category of compactly generated weak Hausdorff spaces.


Examples of this are the iAPX 432 (a project originally named the Intel 8800), the Intel 960, Intel 860 and the Intel/Hewlett-Packard Itanium architecture. However, the continuous refinement of x86 microarchitectures, circuitry and semiconductor manufacturing would make it hard to replace x86 in many segments. AMD's 64-bit extension of x86 (which Intel eventually responded to with a compatible design) and the scalability of x86 chips in the form of modern multi-core CPUs, is underlining x86 as an example of how continuous refinement of established industry standards can resist the competition from completely new architectures.


The information integration of heterogeneous data sources in traditional database is intricate, which requires the redesign of the database table such as changing the structure and/or addition of new data. In the case of semantic query, SPARQL query reflects the relationships between entities in a way that aligned with human's understanding of the domain, so the semantic intention of the query can be seen on the query itself. Unlike SPARQL, SQL query, which reflects the specific structure of the database and derived from matching the relevant primary and foreign keys of tables, loses the semantics of the query by missing the relationships between entities.


In speech, common combinations of conjugation and auxiliary verbs are contracted in a fairly regular manner. There are occasional others, such as -aranai → -annai as in wakaranai (分からない, don't understand) → wakannai (分かんない) and tsumaranai (つまらない, boring) → tsumannai (つまんない) – these are considered quite casual and are more common among the younger generation.Contractions differ by dialect, but behave similarly to the standard ones given above. For example, in the Kansai dialect, -te shimau (〜てしまう) → -temau (〜てまう).


All direct neighbors of s are visited in the first step, which form the next frontier. After each layer-traversal, the "next frontier" is switched to the frontier and new vertices will be stored in the new next frontier. The following pseudo-code outlines the idea of it, in which the data structures for the frontier and next frontier are called FS and NS respectively. 1 define bfs_sequential(graph(V,E), source s): 2 for all v in V do 3 d = -1; 4 d = 0; level = 1; FS = {}; NS = {}; 5 push(s, FS); 6 while FS !empty do 7 for u in FS do 8 for each neighbour v of u do 9 if d = -1 then 10 push(v, NS); 11 d = level; 12 FS = NS, NS = {}, level = level + 1;


In statistics and signal processing, the method of empirical orthogonal function (EOF) analysis is a decomposition of a signal or data set in terms of orthogonal basis functions which are determined from the data. The term is also interchangeable with the geographically weighted Principal components analysis in geophysics.The i th basis function is chosen to be orthogonal to the basis functions from the first through i − 1, and to minimize the residual variance. That is, the basis functions are chosen to be different from each other, and to account for as much variance as possible. The method of EOF analysis is similar in spirit to harmonic analysis, but harmonic analysis typically uses predetermined orthogonal functions, for example, sine and cosine functions at fixed frequencies.


A strategic minority could overpower an honest majority. This problem can be minimized through education or ballot design to encourage uninformed voters to give more-extreme rankings. A different path to minimize this problem is to use median scores instead of total scores, as median scores are less amenable to exaggeration, as in majority judgment.


{\displaystyle V^{-}.} We denote with δ ( V + ) {\displaystyle \delta (V^{+})} the set of edges that connect the two sets. We can then rewrite the Hamiltonian as H  = − ∑ i j ∈ E ( V + ) J i j − ∑ i j ∈ E ( V − ) J i j + ∑ i j ∈ δ ( V + ) J i j = − ∑ i j ∈ E ( G ) J i j + 2 ∑ i j ∈ δ ( V + ) J i j = C + 2 ∑ i j ∈ δ ( V + ) J i j {\displaystyle {\begin{aligned}H&=-\sum _{ij\in E(V^{+})}J_{ij}-\sum _{ij\in E(V^{-})}J_{ij}+\sum _{ij\in \delta (V^{+})}J_{ij}\\&=-\sum _{ij\in E(G)}J_{ij}+2\sum _{ij\in \delta (V^{+})}J_{ij}\\&=C+2\sum _{ij\in \delta (V^{+})}J_{ij}\end{aligned}}} Minimizing this energy is equivalent to the min-cut problem or by setting the graph weights as w i j = − J i j , {\displaystyle w_{ij}=-J_{ij},} the max-cut problem.


CHANGE-LABEL: It works exactly the same as CHANGE-EDGE.As a summary, we conclude that having n 1 {\displaystyle n_{1}} calls to CREATE_NODE and n 2 {\displaystyle n_{2}} calls to CHANGE_EDGE will result in the creation of 2 ⋅ n 1 + n 2 {\displaystyle 2\cdot n_{1}+n_{2}} tables. Since each table has size O ( d ) {\displaystyle O(d)} without taking into account the recursive calls, then filling in a table requires O ( d 2 ) {\displaystyle O(d^{2})} where the additional d factor comes from updating the inedges at other nodes. Therefore the amount of work required to complete a sequence of operations is bounded by the number of tables created multiplied by O ( d 2 ) {\displaystyle O(d^{2})} . Each access operation can be done in O ( L o g ( d ) ) {\displaystyle O(Log(d))} and there are m {\displaystyle m} edge and label operations, thus it requires m ⋅ O ( L o g ( d ) ) {\displaystyle m\cdot O(Log(d))} . We conclude that There exists a data structure that can complete any n {\displaystyle n} sequence of CREATE-NODE, CHANGE-EDGE and CHANGE-LABEL in O ( n ⋅ d 2 ) + m ⋅ O ( L o g ( d ) ) {\displaystyle O(n\cdot d^{2})+m\cdot O(Log(d))} .


In mathematics, an algebraic matroid is a matroid, a combinatorial structure, that expresses an abstraction of the relation of algebraic independence.


In order of net exports in 2011, 2009 and 2006 in thousand bbl/d and thousand m3/d: Source: US Energy Information Administration 1 peak production already passed in this state 2 Canadian statistics are complicated by the fact it is both an importer and exporter of crude oil, and refines large amounts of oil for the U.S. market. It is the leading source of U.S. imports of oil and products, averaging 2,500,000 bbl/d (400,000 m3/d) in August 2007. Total world production/consumption (as of 2005) is approximately 84 million barrels per day (13,400,000 m3/d).


The probability that at least one of the events will occur is equal to one. For example, there are theoretically only two possibilities for flipping a coin. Flipping a head and flipping a tail are collectively exhaustive events, and there is a probability of one of flipping either a head or a tail.


In modern poetry, Formalist poets may be considered as the opposite of writers of free verse. These are only labels, and rarely sum up matters satisfactorily. 'Formalism' in poetry represents an attachment to poetry that recognises and uses schemes of rhyme and rhythm to create poetic effects and to innovate. To distinguish it from archaic poetry the term 'neo-formalist' is sometimes used. See for example: The Formalist, a literary magazine (now defunct) for formalist poetry New Formalism, a movement within the poetry of the United States.


In mathematics, the Muller–Schupp theorem states that a finitely generated group G has context-free word problem if and only if G is virtually free. The theorem was proved by David Muller and Paul Schupp in 1983.


In most dynamically-typed languages, the list of methods on an object can be altered at runtime. This requires late binding.


Formally, a relation R over a set X can be seen as a set of ordered pairs (x, y) of members of X. The relation R holds between x and y if (x, y) is a member of R. For example, the relation "is less than" on the natural numbers is an infinite set Rless of pairs of natural numbers that contains both (1,3) and (3,4), but neither (3,1) nor (4,4). The relation "is a nontrivial divisor of" on the set of one-digit natural numbers is sufficiently small to be shown here: Rdiv = { (2,4), (2,6), (2,8), (3,6), (3,9), (4,8) }; for example 2 is a nontrivial divisor of 8, but not vice versa, hence (2,8) ∈ Rdiv, but (8,2) ∉ Rdiv. If R is a relation that holds for x and y one often writes xRy.


In the abstract setting of oriented matroids, Bland's rule cycles on some examples. A restricted class of oriented matroids on which Bland's rule avoids cycling has been termed "Bland oriented matroids" by Jack Edmonds. Another pivoting rule, the criss-cross algorithm, avoids cycles on all oriented-matroid linear-programs.


In mathematical logic, Gödel's β function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. The β function is used, in particular, in showing that the class of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions. The β function was introduced without the name in the proof of the first of Gödel's incompleteness theorems (Gödel 1931). The β function lemma given below is an essential step of that proof. Gödel gave the β function its name in (Gödel 1934).


Such implausible equilibria might arise also in games with complete information, but they may be eliminated by applying subgame perfect Nash equilibrium. However, Bayesian games often contain non-singleton information sets and since subgames must contain complete information sets, sometimes there is only one subgame—the entire game—and so every Nash equilibrium is trivially subgame perfect. Even if a game does have more than one subgame, the inability of subgame perfection to cut through information sets can result in implausible equilibria not being eliminated. To summarize: in this variant of the gift game, there are two SPEs: either the sender always gives and the receiver always accepts, or the sender always does not give and the receiver always rejects. From these, only the first one is a PBE; the other is not a PBE since it cannot be supported by any belief-system.


In effect, work stealing distributes the scheduling work over idle processors, and as long as all processors have work to do, no scheduling overhead occurs.Work stealing contrasts with work sharing, another popular scheduling approach for dynamic multithreading, where each work item is scheduled onto a processor when it is spawned. Compared to this approach, work stealing reduces the amount of process migration between processors, because no such migration occurs when all processors have work to do.The idea of work stealing goes back to the implementation of the Multilisp programming language and work on parallel functional programming languages in the 1980s. It is employed in the scheduler for the Cilk programming language, the Java fork/join framework, the .NET Task Parallel Library, and the Rust Tokio runtime.


In morphometrics, landmark point or shortly landmark is a point in a shape object in which correspondences between and within the populations of the object are preserved. In other disciplines, landmarks may be known as vertices, anchor points, control points, sites, profile points, 'sampling' points, nodes, markers, fiducial markers, etc. Landmarks can be defined either manually by experts or automatically by a computer program. There are three basic types of landmarks: anatomical landmarks, mathematical landmarks or pseudo-landmarks.


In mathematics, an analytic proof is a proof of a theorem in analysis that only makes use of methods from analysis, and which does not predominantly make use of algebraic or geometrical methods. The term was first used by Bernard Bolzano, who first provided a non-analytic proof of his intermediate value theorem and then, several years later provided a proof of the theorem that was free from intuitions concerning lines crossing each other at a point, and so he felt happy calling it analytic (Bolzano 1817). Bolzano's philosophical work encouraged a more abstract reading of when a demonstration could be regarded as analytic, where a proof is analytic if it does not go beyond its subject matter (Sebastik 2007). In proof theory, an analytic proof has come to mean a proof whose structure is simple in a special way, due to conditions on the kind of inferences that ensure none of them go beyond what is contained in the assumptions and what is demonstrated.


In the field of relational database design, normalization is a systematic way of ensuring that a database structure is suitable for general-purpose querying and free of certain undesirable characteristics—insertion, update, and deletion anomalies that could lead to loss of data integrity. A standard piece of database design guidance is that the designer should create a fully normalized design; selective denormalization can subsequently be performed, but only for performance reasons. The trade-off is storage space vs performance.


Borrow 1 from the thousands place for a ten in the hundreds place, minus 7 from the row below, the difference 3 is added to the 2 on top to form 5. The 7 on the bottom is subtracted, shown by the space. Borrow 1 from the hundreds place, which leaves 4.


In mathematics, the relaxation of a (mixed) integer linear program is the problem that arises by removing the integrality constraint of each variable. For example, in a 0–1 integer program, all constraints are of the form x i ∈ { 0 , 1 } {\displaystyle x_{i}\in \{0,1\}} .The relaxation of the original integer program instead uses a collection of linear constraints 0 ≤ x i ≤ 1. {\displaystyle 0\leq x_{i}\leq 1.} The resulting relaxation is a linear program, hence the name. This relaxation technique transforms an NP-hard optimization problem (integer programming) into a related problem that is solvable in polynomial time (linear programming); the solution to the relaxed linear program can be used to gain information about the solution to the original integer program.


In object-oriented programming, behavioral subtyping is the principle that subclasses should satisfy the expectations of clients accessing subclass objects through references of superclass type, not just as regards syntactic safety (such as the absence of "method-not-found" errors) but also as regards behavioral correctness. Specifically, properties that clients can prove using the specification of an object's presumed type should hold even though the object is actually a member of a subtype of that type. For example, consider a type Stack and a type Queue, which both have a put method to add an element and a get method to remove one.


In project management, resource leveling is defined by A Guide to the Project Management Body of Knowledge (PMBOK Guide) as "A technique in which start and finish dates are adjusted based on resource limitation with the goal of balancing demand for resources with the available supply." Resource leveling problem could be formulated as an optimization problem. The problem could be solved by different optimization algorithms such as exact algorithms or meta-heuristic methods.When performing project planning activities, the manager will attempt to schedule certain tasks simultaneously. When more resources such as machines or people are needed than are available, or perhaps a specific person is needed in both tasks, the tasks will have to be rescheduled concurrently or even sequentially to manage the constraint.


In order to determine how judges weigh the different factors, 103 written judgements of commonplace cases were used to establish a database comprising 94 relevant factors for percentage split determination. : 273 The factors relevant for a percentage split determination are: Past contributions of a husband relative to those of a wife The husband's future needs relative to those of the wife The wealth of the marriageThe factors relevant for a determination of past contributions are The relative direct and indirect contributions of both parties The length of the marriage The relative contributions of both parties to the homemaking roleThe hierarchy provides a structure that is used to decompose the task of predicting an outcome into 35 subtasks. Outputs of tasks further down the hierarchy are used as inputs into sub-tasks higher up the hierarchy. Each sub-task is treated as a separate and smaller data mining exercise.


In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a " 2 × 3 {\displaystyle 2\times 3} matrix", or a matrix of dimension 2 × 3 {\displaystyle 2\times 3} . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra.


In rank selection, the selection probability does not depend directly on the fitness, but on the fitness rank of an individual within the population. This puts large fitness differences into perspective; moreover, the exact fitness values themselves do not have to be available, but only a sorting of the individuals according to quality. Linear ranking, which goes back to Baker, is often used.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 2357, 12357, 23457, and 123457 are the patterns related to Braille pattern dots-1234, since the two additional dots of kantenji patterns 01234, 12347, and 012347 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


However, a separation oracle can be implemented using n-1 applications of the minimum cut procedure. The maximum independent set problem. It can be approximated by an LP with a constraint for every odd-length cycle.