In order to explain the verifier-based definition of NP, consider the subset sum problem: Assume that we are given some integers, {−7, −3, −2, 5, 8}, and we wish to know whether some of these integers sum up to zero. Here the answer is "yes", since the integers {−3, −2, 5} corresponds to the sum (−3) + (−2) + 5 = 0. To answer whether some of the integers add to zero we can create an algorithm that obtains all the possible subsets. As the number of integers that we feed into the algorithm becomes larger, both the number of subsets and the computation time grows exponentially.


In the following, let M be a G-module.


In statistics and in machine learning, a linear predictor function is a linear function (linear combination) of a set of coefficients and explanatory variables (independent variables), whose value is used to predict the outcome of a dependent variable. This sort of function usually comes in linear regression, where the coefficients are called regression coefficients. However, they also occur in various types of linear classifiers (e.g. logistic regression, perceptrons, support vector machines, and linear discriminant analysis), as well as in various other models, such as principal component analysis and factor analysis. In many of these models, the coefficients are referred to as "weights".


In sociolinguistics, a register is a variety of language used for a particular purpose or particular communicative situation. For example, when speaking officially or in a public setting, an English speaker may be more likely to follow prescriptive norms for formal usage than in a casual setting, for example, by pronouncing words ending in -ing with a velar nasal instead of an alveolar nasal (e.g., walking rather than walkin'), choosing words that are considered more "formal" (such as father vs. dad or child vs. kid), and refraining from using words considered nonstandard, such as ain't and y'all. As with other types of language variation, there tends to be a spectrum of registers rather than a discrete set of obviously distinct varieties—numerous registers can be identified, with no clear boundaries between them. Discourse categorization is a complex problem, and even according to the general definition of register given above (language variation defined by use rather than user), there are cases where other kinds of language variation, such as regional or age dialect, overlap.


According to Paul A. Sabatier, the model has "outlived its usefulness" and should be replaced. The model's issues have led to a paradoxical situation in which current research and updated versions of the model continue to rely on the framework created by Anderson. But the very concept of the stages model has been discredited, which attacks the cycle's status as a heuristic.Due to these problems, alternative and newer versions of the model have aimed to create a more comprehensive view of the policy cycle.


748 If random vector X is elliptically distributed, then so is DX for any matrix D with full row rank. Thus any linear combination of the components of X is elliptical (though not necessarily with the same elliptical distribution), and any subset of X is elliptical. : p. 748


In mathematics, an antimatroid is a formal system that describes processes in which a set is built up by including elements one at a time, and in which an element, once available for inclusion, remains available until it is included. Antimatroids are commonly axiomatized in two equivalent ways, either as a set system modeling the possible states of such a process, or as a formal language modeling the different sequences in which elements may be included. Dilworth (1940) was the first to study antimatroids, using yet another axiomatization based on lattice theory, and they have been frequently rediscovered in other contexts.The axioms defining antimatroids as set systems are very similar to those of matroids, but whereas matroids are defined by an exchange axiom, antimatroids are defined instead by an anti-exchange axiom, from which their name derives. Antimatroids can be viewed as a special case of greedoids and of semimodular lattices, and as a generalization of partial orders and of distributive lattices. Antimatroids are equivalent, by complementation, to convex geometries, a combinatorial abstraction of convex sets in geometry. Antimatroids have been applied to model precedence constraints in scheduling problems, potential event sequences in simulations, task planning in artificial intelligence, and the states of knowledge of human learners.


Angles CBD and FBA are both right angles; therefore angle ABD equals angle FBC, since both are the sum of a right angle and angle ABC. Since AB is equal to FB, BD is equal to BC and angle ABD equals angle FBC, triangle ABD must be congruent to triangle FBC. Since A-K-L is a straight line, parallel to BD, then rectangle BDLK has twice the area of triangle ABD because they share the base BD and have the same altitude BK, i.e., a line normal to their common base, connecting the parallel lines BD and AL. (lemma 2) Since C is collinear with A and G, and this line is parallel to FB, then square BAGF must be twice in area to triangle FBC.


In mathematics, the Gauss circle problem is the problem of determining how many integer lattice points there are in a circle centered at the origin and with radius r {\displaystyle r} . This number is approximated by the area of the circle, so the real problem is to accurately bound the error term describing how the number of points differs from the area. The first progress on a solution was made by Carl Friedrich Gauss, hence its name.


In recreational mathematics, a polyform is a plane figure or solid compound constructed by joining together identical basic polygons. The basic polygon is often (but not necessarily) a convex plane-filling polygon, such as a square or a triangle. More specific names have been given to polyforms resulting from specific basic polygons, as detailed in the table below. For example, a square basic polygon results in the well-known polyominoes.


In spite of its apparently paradoxical nature, the phenomenon is real, and can be explained as a consequence of the general mathematical properties of social networks. The mathematics behind this are directly related to the arithmetic-geometric mean inequality and the Cauchy–Schwarz inequality.Formally, Feld assumes that a social network is represented by an undirected graph G = (V, E), where the set V of vertices corresponds to the people in the social network, and the set E of edges corresponds to the friendship relation between pairs of people. That is, he assumes that friendship is a symmetric relation: if x is a friend of y, then y is a friend of x. The friendship between x and y is therefore modeled by the edge {x, y}, and the number of friends an individual has corresponds to a vertex's degree. The average number of friends of a person in the social network is therefore given by the average of the degrees of the vertices in the graph.


This is one example where some upper bound helps in proving lower bounds; the construction of a circuit given by Baur and Strassen implies a lower bound for more general polynomials. The lack of ability to prove lower bounds brings us to consider simpler models of computation. Some examples are: monotone circuits (in which all the field elements are nonnegative real numbers), constant depth circuits, and multilinear circuits (in which every gate computes a multilinear polynomial). These restricted models have been studied extensively and some understanding and results were obtained.


In quantum information theory, the no low-energy trivial state (NLTS) conjecture is a precursor to a quantum PCP theorem (qPCP) and posits the existence of families of Hamiltonians with all low-energy states of non-trivial complexity. An NLTS proof would be a consequence of one aspect of qPCP problems – the inability to certify an approximation of local Hamiltonians via NP completeness. In other words, an NLTS proof would be one consequence of the QMA complexity of qPCP problems. On a high level, if proved, NLTS would be one property of the non-Newtonian complexity of quantum computation.


In terms of Metrics that the QA & UX Manager work with, this task mainly is about collecting and analyze data an about game and gamer activity in relation to a particular game. In terms of the communication characterized parts of the work the QA & UX Manager do, this is often done in relation with meetings with the development team and where the QA & UX Manager pass on his or her knowledge and data to the development team. == References ==


In order to qualify for protection, a work must be an expression with a degree of originality, and it must be in a fixed medium, such as written down on paper or recorded digitally. The idea itself is not protected. That is, a copy of someone else's original idea is not infringing unless it copies that person's unique, tangible expression of the idea. Some of these limitations, especially regarding what qualifies as original, are embodied only in case law (judicial precedent), rather than in statutes.


In statistics, a generalized linear model (GLM) is a flexible generalization of ordinary linear regression. The GLM generalizes linear regression by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value. Generalized linear models were formulated by John Nelder and Robert Wedderburn as a way of unifying various other statistical models, including linear regression, logistic regression and Poisson regression.


In number theory, Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula c q ( n ) = ∑ 1 ≤ a ≤ q ( a , q ) = 1 e 2 π i a q n , {\displaystyle c_{q}(n)=\sum _{1\leq a\leq q \atop (a,q)=1}e^{2\pi i{\tfrac {a}{q}}n},} where (a, q) = 1 means that a only takes on values coprime to q. Srinivasa Ramanujan mentioned the sums in a 1918 paper. In addition to the expansions discussed in this article, Ramanujan's sums are used in the proof of Vinogradov's theorem that every sufficiently large odd number is the sum of three primes.


In the example above, the algorithm was guided by the conditional expectation of a random variable F {\displaystyle F} . In some cases, instead of an exact conditional expectation, an upper bound (or sometimes a lower bound) on some conditional expectation is used instead. This is called a pessimistic estimator.


In model theory, definable sets are important objects of study. For instance, in N {\displaystyle \mathbb {N} } the formula ∀ u ∀ v ( ∃ w ( x × w = u × v ) → ( ∃ w ( x × w = u ) ∨ ∃ w ( x × w = v ) ) ) ∧ x ≠ 0 ∧ x ≠ 1 {\displaystyle \forall u\forall v(\exists w(x\times w=u\times v)\rightarrow (\exists w(x\times w=u)\lor \exists w(x\times w=v)))\land x\neq 0\land x\neq 1} defines the subset of prime numbers, while the formula ∃ y ( 2 × y = x ) {\displaystyle \exists y(2\times y=x)} defines the subset of even numbers. In a similar way, formulas with n free variables define subsets of M n {\displaystyle {\mathcal {M}}^{n}} . For example, in a field, the formula y = x × x {\displaystyle y=x\times x} defines the curve of all ( x , y ) {\displaystyle (x,y)} such that y = x 2 {\displaystyle y=x^{2}} .


The U.S. Securities and Exchange Commission issued a statement in 1984 with the goal of reminding companies that securities fraud also applies to "statements that can reasonably be expected to reach investors and the trading markets".Several companies have been accused in court of using knowingly false announcements to gain market advantage. In 1969, the United States Justice Department accused IBM of doing this in the case United States v. IBM.


This generalized definition implies that the above-mentioned geometric entities are a special kind of vectors, as they are elements of a special kind of vector space called Euclidean space. This particular article is about vectors strictly defined as arrows in Euclidean space. When it becomes necessary to distinguish these special vectors from vectors as defined in pure mathematics, they are sometimes referred to as geometric, spatial, or Euclidean vectors.


Then, the current non-integer solution is no longer feasible to the relaxation. This process is repeated until an optimal integer solution is found.


Its worst-case roundoff errors grow asymptotically as at most O(ε log n), where ε is the machine precision (assuming a fixed condition number, as discussed below). In comparison, the naive technique of accumulating the sum in sequence (adding each xi one at a time for i = 1, ..., n) has roundoff errors that grow at worst as O(εn). Kahan summation has a worst-case error of roughly O(ε), independent of n, but requires several times more arithmetic operations. If the roundoff errors are random, and in particular have random signs, then they form a random walk and the error growth is reduced to an average of O ( ε log  n ) {\displaystyle O(\varepsilon {\sqrt {\log n}})} for pairwise summation.A very similar recursive structure of summation is found in many fast Fourier transform (FFT) algorithms, and is responsible for the same slow roundoff accumulation of those FFTs.


In the 1980s, the revolution of the personal computer and the popularity of computer bulletin board systems (BBSes) (accessed via modem) created an influx of tech-savvy users. These BBSes became popular for computer hackers and others interested in the technology, and served as a medium for previously scattered independent phone phreaks to share their discoveries and experiments. This not only led to unprecedented collaboration between phone phreaks, but also spread the notion of phreaking to others who took it upon themselves to study, experiment with, or exploit the telephone system. This was also at a time when the telephone company was a popular subject of discussion in the US, as the monopoly of AT&T Corporation was forced into divestiture.


In telecommunication, a line code is a pattern of voltage, current, or photons used to represent digital data transmitted down a communication channel or written to a storage medium. This repertoire of signals is usually called a constrained code in data storage systems. Some signals are more prone to error than others as the physics of the communication channel or storage medium constrains the repertoire of signals that can be used reliably.Common line encodings are unipolar, polar, bipolar, and Manchester code.


There are differing views as to exactly what phonemes are and how a given language should be analyzed in phonemic (or phonematic) terms. However, a phoneme is generally regarded as an abstraction of a set (or equivalence class) of speech sounds (phones) that are perceived as equivalent to each other in a given language. For example, the English k sounds in the words kill and skill are not identical (as described below), but they are distributional variants of a single phoneme /k/.


In numerical optimization, the nonlinear conjugate gradient method generalizes the conjugate gradient method to nonlinear optimization. For a quadratic function f ( x ) {\displaystyle \displaystyle f(x)} f ( x ) = ‖ A x − b ‖ 2 , {\displaystyle \displaystyle f(x)=\|Ax-b\|^{2},} the minimum of f {\displaystyle f} is obtained when the gradient is 0: ∇ x f = 2 A T ( A x − b ) = 0 {\displaystyle \nabla _{x}f=2A^{T}(Ax-b)=0} .Whereas linear conjugate gradient seeks a solution to the linear equation A T A x = A T b {\displaystyle \displaystyle A^{T}Ax=A^{T}b} , the nonlinear conjugate gradient method is generally used to find the local minimum of a nonlinear function using its gradient ∇ x f {\displaystyle \nabla _{x}f} alone. It works when the function is approximately quadratic near the minimum, which is the case when the function is twice differentiable at the minimum and the second derivative is non-singular there. Given a function f ( x ) {\displaystyle \displaystyle f(x)} of N {\displaystyle N} variables to minimize, its gradient ∇ x f {\displaystyle \nabla _{x}f} indicates the direction of maximum increase.


In probability theory, Gauss's inequality (or the Gauss inequality) gives an upper bound on the probability that a unimodal random variable lies more than any given distance from its mode. Let X be a unimodal random variable with mode m, and let τ 2 be the expected value of (X − m)2. (τ 2 can also be expressed as (μ − m)2 + σ 2, where μ and σ are the mean and standard deviation of X.) Then for any positive value of k, Pr ( | X − m | > k ) ≤ { ( 2 τ 3 k ) 2 if k ≥ 2 τ 3 1 − k τ 3 if 0 ≤ k ≤ 2 τ 3 . {\displaystyle \Pr(|X-m|>k)\leq {\begin{cases}\left({\frac {2\tau }{3k}}\right)^{2}&{\text{if }}k\geq {\frac {2\tau }{\sqrt {3}}}\\1-{\frac {k}{\tau {\sqrt {3}}}}&{\text{if }}0\leq k\leq {\frac {2\tau }{\sqrt {3}}}.\end{cases}}} The theorem was first proved by Carl Friedrich Gauss in 1823.


Sometimes the stress of the 0 is made different from a letter o in some way, although many fonts do not do this.High-quality typesetting generally prefers text figures in body text: they integrate better with lowercase letters and small capitals, unlike runs of lining figures. Lining figures are called for in all-capitals settings (hence the alternative name titling figures), and may work better in tables and spreadsheets. Although many conventional typefaces have both types of numerals in full, early digital fonts only had one or the other (with the exception of those used by professional printers).


For ν = 1 {\displaystyle \nu =1} the Student's t distribution t ν {\displaystyle t_{\nu }} becomes the standard Cauchy distribution, whereas for ν → ∞ {\displaystyle \nu \rightarrow \infty } it becomes the standard normal distribution N ( 0 , 1 ) {\displaystyle N(0,1)} . The Student's t-distribution plays a role in a number of widely used statistical analyses, including Student's t-test for assessing the statistical significance of the difference between two sample means, the construction of confidence intervals for the difference between two population means, and in linear regression analysis. In the form of the location-scale t-distribution l s t ( μ , τ 2 , ν ) {\displaystyle lst(\mu ,\tau ^{2},\nu )} it generalizes the normal distribution and also arises in the Bayesian analysis of data from a normal family as a compound distribution when marginalizing over the variance parameter.


An incomplete Cholesky factorization is given by a sparse lower triangular matrix K that is in some sense close to L. The corresponding preconditioner is KK*. One popular way to find such a matrix K is to use the algorithm for finding the exact Cholesky decomposition in which K has the same sparsity pattern as A (any entry of K is set to zero if the corresponding entry in A is also zero). This gives an incomplete Cholesky factorization which is as sparse as the matrix A.


In the 1990s, specialized computers were released where two computers that each had their own memory controller could be networked at such a low level that the software run could use the memory, or CPU of either computer as if they were one unit. With AMD's release of the Opteron, and Intel's corresponding CPU, systems that share more than one memory controller in a single system have become common in applications that require the power of more than one common desktop. For these systems schemes like non-uniform memory architecture are used.Channels are the highest-level structure at the local memory controller level. Modern computers can have two, three or even more channels.


In mathematics, logic and computer science, a formal language (a set of finite sequences of symbols taken from a fixed alphabet) is called recursive if it is a recursive subset of the set of all possible finite sequences over the alphabet of the language. Equivalently, a formal language is recursive if there exists a Turing machine that, when given a finite sequence of symbols as input, always halts and accepts it if it belongs to the language and halts and rejects it otherwise. In Theoretical computer science, such always-halting Turing machines are called total Turing machines or algorithms (Sipser 1997).


In order to understand the public's opinion on youth marketing, one must be able to understand the experiences that each generation has been exposed to while growing up. Generation Y is very similar to the baby boomer generation especially at different points in life. So it is essential to see what experiences each generation has experienced while growing up. But different formative experiences affect each person of Generation Y. For example, the events that made the biggest impression on members of Generation Y who graduated from school in 2000 were Columbine, the war in Kosovo, and Princess Diana's death.


The written test is usually done at a computerized learning center and results are available immediately. The oral and practical exams include questions about common rigging practices. The practical test consists of inspecting and repacking 20 reserves, along with hand sewing and a simple machine-sewn patch on a canopy.


In the Russian Federation, a state secret (Государственная тайна) is information protected by the state on its military, foreign policy, economic, intelligence, counterintelligence, operational and investigative and other activities, dissemination of which could harm state security.


In probability and statistics, the Hellinger distance (closely related to, although different from, the Bhattacharyya distance) is used to quantify the similarity between two probability distributions. It is a type of f-divergence. The Hellinger distance is defined in terms of the Hellinger integral, which was introduced by Ernst Hellinger in 1909.It is sometimes called the Jeffreys distance.


In mathematics, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions. Optimization problems can be divided into two categories, depending on whether the variables are continuous or discrete: An optimization problem with discrete variables is known as a discrete optimization, in which an object such as an integer, permutation or graph must be found from a countable set. A problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found. They can include constrained problems and multimodal problems.


This scheme, a type of virtual memory, allows in-memory data not currently in use to be moved to secondary storage and back in a way which is transparent to applications, to increase overall memory capacity. On some systems, a request for virtual storage may allocate a block of virtual addresses for which no page frames have been assigned, and the system will only assign and initialize page frames when page faults occur. On some systems a guard page may be used, either for error detection or to automatically grow data structures. On some systems, the page fault mechanism is also used for executable space protection such as W^X.


295). Skolem's paradox is that every countable axiomatisation of set theory in first-order logic, if it is consistent, has a model that is countable. This appears contradictory because it is possible to prove, from those same axioms, a sentence that intuitively says (or that precisely says in the standard model of the theory) that there exist sets that are not countable.


In practice, bitstreams are not used directly to encode bytestreams; a communication channel may use a signalling method that does not directly translate to bits (for instance, by transmitting signals of multiple frequencies) and typically also encodes other information such as framing and error correction together with its data.


In recent years, neural networks have generated a great deal of interest by outperforming traditional methods on longstanding problems across many fields. Machine learning, and by extension neural networks, have been used in many facets of MRI — for instance, speeding up image reconstruction, or improving reconstruction quality when working with a lack of data. Neural networks have also been used in motion artifact correction thanks to their ability to learn visual information from data, as well as infer underlying, latent representations in data.


In the United States, the director of the Cybersecurity and Infrastructure Security Agency (CISA), Jen Easterly, described the exploit as "one of the most serious I've seen in my entire career, if not the most serious", explaining that hundreds of millions of devices were affected and advising vendors to prioritize software updates. Civilian agencies contracted by the United States government had until 24 December 2021 to patch vulnerabilities. On 4 January, the Federal Trade Commission (FTC) stated its intent to pursue companies that fail to take reasonable steps to update used Log4j software.


decoding, determining the probability of a given label sequence Y {\displaystyle Y} given X {\displaystyle X} . inference, determining the most likely label sequence Y {\displaystyle Y} given X {\displaystyle X} .The conditional dependency of each Y i {\displaystyle Y_{i}} on X {\displaystyle X} is defined through a fixed set of feature functions of the form f ( i , Y i − 1 , Y i , X ) {\displaystyle f(i,Y_{i-1},Y_{i},X)} , which can be thought of as measurements on the input sequence that partially determine the likelihood of each possible value for Y i {\displaystyle Y_{i}} . The model assigns each feature a numerical weight and combines them to determine the probability of a certain value for Y i {\displaystyle Y_{i}} .


In recent years, as the general population has become more e-mail savvy, the lines have blurred somewhat between face-to-face and e-mail communication. E-mail is now thought of as a verbal tool, with its capacity to enable immediate feedback, leverage natural language, and embed emotion via acronyms and emoticons. However, there is a downside of e-mail: volume overload. Emails often have large unnecessary quantities of information which is non-job essential and/or spam.


Moreover, this factorization is unique up to the order of the factors. Although integer factorization is a sort of inverse to multiplication, it is much more difficult algorithmically, a fact which is exploited in the RSA cryptosystem to implement public-key cryptography. Polynomial factorization has also been studied for centuries.


In mathematics, the theory of Latin squares is an active research area with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Problems posed here appeared in, for instance, the Loops (Prague) conferences and the Milehigh (Denver) conferences.


In the distributed memory model, the usual approach is to partition the vertex set V {\displaystyle V} of the graph into p {\displaystyle p} sets V 0 , … , V p − 1 {\displaystyle V_{0},\dots ,V_{p-1}} . Here, p {\displaystyle p} is the amount of available processing elements (PE). The vertex set partitions are then distributed to the PEs with matching index, additionally to the corresponding edges. Every PE has its own subgraph representation, where edges with an endpoint in another partition require special attention.


In most EQA schemes, laboratories receive scores for their results. The most popular score is the Z-score, also called standard deviation index (SDI). The score is given per analyte and per test item.


(I3) If A {\displaystyle A} and B {\displaystyle B} are two independent sets (i.e., each set is independent) and A {\displaystyle A} has more elements than B {\displaystyle B} , then there exists x ∈ A ∖ B {\displaystyle x\in A\backslash B} such that B ∪ { x } {\displaystyle B\cup \{x\}} is in I {\displaystyle {\mathcal {I}}} . This is sometimes called the augmentation property or the independent set exchange property.The first two properties define a combinatorial structure known as an independence system (or abstract simplicial complex). Actually, assuming (I2), property (I1) is equivalent to the fact that at least one subset of E {\displaystyle E} is independent, i.e., I ≠ ∅ {\displaystyle {\mathcal {I}}\neq \emptyset } .


The emergence of affordable consumer telephony devices with advanced features such as last number redial and preprogrammed numbers paralleled phone industry deregulation and the Breakup of the Bell System in the early 1980s. While Speed dial technology had been invented nearly a decade earlier by Bell Labs, it did not become a consumer product until deregulation. Previously, connecting non-AT&T handsets was generally prohibited and most phones were leased devices (similar to residential broadband routers).


The main cabinet of the minicomputer was the 6000 CPU, housing the computer's main Z80A microprocessor and nine expansion slots (none populated by default); the 6000 CPU-1, with a second Z80A processor seven expansion slots and a floppy disk drive; and the 6000 CPU-2, which has two such disk drives and a third Z80A processor. Each cabinet houses 64 KB of RAM with parity. Optional was a video board, additional disk controllers, a mass-storage controller board for hard disks and tape drives (the latter making use of the board's integrated parallel interface), a dual-channel RS-232 serial interface board, and a serial communication interface board with support for asynchronous, synchronous, and bit-oriented communications protocols.


In order to avoid this problem, additional framing bits are added to either end of every byte, typically one bit on either side known as the "start and stop bits". This guarantees at least one 1-to-0 transition for every byte, more than enough to keep the clocks locked. However, these bits also expand every 8 bits of data (one byte) to 10 bits, an overhead of 20%.


In mathematics and theoretical computer science, analysis of Boolean functions is the study of real-valued functions on { 0 , 1 } n {\displaystyle \{0,1\}^{n}} or { − 1 , 1 } n {\displaystyle \{-1,1\}^{n}} (such functions are sometimes known as pseudo-Boolean functions) from a spectral perspective. The functions studied are often, but not always, Boolean-valued, making them Boolean functions. The area has found many applications in combinatorics, social choice theory, random graphs, and theoretical computer science, especially in hardness of approximation, property testing, and PAC learning.


In some system distributions, sudo has largely supplanted the default use of a distinct superuser login for administrative tasks, most notably in some Linux distributions as well as Apple's macOS. This allows for more secure logging of admin commands and prevents some exploits.


In case of any failure, the destination switches onto the alternative path/route. This architecture is simple for implementation and results fast restoration. Its major drawback is the wastage of bandwidth, since no traffic travels through the redundant path.


In politics, rankings focus on the comparison of economic, social, environmental and governance performance of countries. In relation to credit standing, the ranking of a security refers to where that particular security would stand in a wind up of the issuing company, i.e., its seniority in the company's capital structure. For instance, capital notes are subordinated securities; they would rank behind senior debt in a wind up. In other words, the holders of senior debt would be paid out before subordinated debt holders received any funds.


In order to accurately measure longitude, the precise time of a sextant sighting (down to the second, if possible) must be recorded. Each second of error is equivalent to 15 seconds of longitude error, which at the equator is a position error of .25 of a nautical mile, about the accuracy limit of manual celestial navigation. The spring-driven marine chronometer is a precision timepiece used aboard ship to provide accurate time for celestial observations. A chronometer differs from a spring-driven watch principally in that it contains a variable lever device to maintain even pressure on the mainspring, and a special balance designed to compensate for temperature variations.A spring-driven chronometer is set approximately to Greenwich mean time (GMT) and is not reset until the instrument is overhauled and cleaned, usually at three-year intervals.


Furthermore, they may develop undesirable emergent goals that may be hard to detect before the system is in deployment, where it faces new situations and data distributions.Today, these problems affect existing commercial systems such as language models, robots, autonomous vehicles, and social media recommendation engines. Some AI researchers argue that more capable future systems will be more severely affected since these problems partially result from the systems being highly capable.Many leading AI scientists such as Geoffrey Hinton and Stuart Russell argue that AI is approaching superhuman capabilities and could endanger human civilization if misaligned.AI alignment is a subfield of AI safety, the study of how to build safe AI systems. Other subfields of AI safety include robustness, monitoring, and capability control. Research challenges in alignment include instilling complex values in AI, developing honest AI, scalable oversight, auditing and interpreting AI models, and preventing emergent AI behaviors like power-seeking. Alignment research has connections to interpretability research, (adversarial) robustness, anomaly detection, calibrated uncertainty, formal verification, preference learning, safety-critical engineering, game theory, algorithmic fairness, and the social sciences, among others.


The meaning of a sentence is conveyed if the truth conditions for the sentence are understood. Additionally, there are many sentences that are understood although their truth condition is uncertain. One popular argument for this view is that some sentences are necessarily true — that is, they are true whatever happens to obtain. All such sentences have the same truth conditions, but arguably do not thereby have the same meaning. Likewise, the sets {x: x is alive} and {x: x is alive and x is not a rock} are identical — they have precisely the same members — but presumably the sentences "Nixon is alive" and "Nixon is alive and is not a rock" have different meanings.


The Rage 128 used an 8 kB buffer to store texels that were used by the 3D engine. In order to improve performance even more, ATI engineers also incorporated an 8 KB pixel cache used to write pixels back to the frame buffer. 8 million transistors, 0.25 micrometer fabrication 3D Feature Set Hardware support for vertex arrays, fog and fog table support Alpha blending, vertex and Z-based fog, video textures, texture lighting Single clock bilinear and trilinear texture filtering and texture compositing Perspective-correct mip-mapped texturing with chroma-key support Vertex and Z-based reflections, shadows, spotlights, 1.00 biasing Hidden surface removal using 16, 24, or 32-bit Z-buffering Gouraud and specular shaded polygons Line and edge anti-aliasing, bump mapping, 8-bit stencil buffer 250 MHz RAMDAC, AGP 2×


An example is Google's PageRank algorithm. The principal eigenvector of a modified adjacency matrix of the World Wide Web graph gives the page ranks as its components.


In parallel computing, the Geometric Arithmetic Parallel Processor (GAPP), invented by Polish mathematician Włodzimierz Holsztyński in 1981, was patented by Martin Marietta and is now owned by Silicon Optix, Inc. The GAPP's network topology is a mesh-connected array of single-bit SIMD processing elements (PEs), where each PE can communicate with its neighbor to the north, east, south, and west. Each cell has its own memory. The space of addresses is the same for all cells. The data travels from the cell memories to the cell registers, and in the opposite direction, in parallel.


In mathematics, Lazard's universal ring is a ring introduced by Michel Lazard in Lazard (1955) over which the universal commutative one-dimensional formal group law is defined. There is a universal commutative one-dimensional formal group law over a universal commutative ring defined as follows. We let F ( x , y ) {\displaystyle F(x,y)} be x + y + ∑ i , j c i , j x i y j {\displaystyle x+y+\sum _{i,j}c_{i,j}x^{i}y^{j}} for indeterminates c i , j {\displaystyle c_{i,j}} , and we define the universal ring R to be the commutative ring generated by the elements c i , j {\displaystyle c_{i,j}} , with the relations that are forced by the associativity and commutativity laws for formal group laws.


In physics and geometry, there are two closely related vector spaces, usually three-dimensional but in general of any finite dimension. Position space (also real space or coordinate space) is the set of all position vectors r in Euclidean space, and has dimensions of length; a position vector defines a point in space. (If the position vector of a point particle varies with time, it will trace out a path, the trajectory of a particle.) Momentum space is the set of all momentum vectors p a physical system can have; the momentum vector of a particle corresponds to its motion, with units of −1.


The triples result in the graph shown in the given figure. One of the advantages of using Uniform Resource Identifiers (URIs) is that they can be dereferenced using the HTTP protocol. According to the so-called Linked Open Data principles, such a dereferenced URI should result in a document that offers further data about the given URI.


For an input x {\displaystyle \mathbf {x} } from source X {\displaystyle X} , only the syndrome given by s = H x {\displaystyle \mathbf {s} =\mathbf {H} \mathbf {x} } is transmitted, which is 3 bits. With received y {\displaystyle \mathbf {y} } and s {\displaystyle \mathbf {s} } , suppose there are two inputs x 1 {\displaystyle \mathbf {x_{1}} } and x 2 {\displaystyle \mathbf {x_{2}} } with same syndrome s {\displaystyle \mathbf {s} } . That means H x 1 = H x 2 {\displaystyle \mathbf {H} \mathbf {x_{1}} =\mathbf {H} \mathbf {x_{2}} } , which is H ( x 1 − x 2 ) = 0 {\displaystyle \mathbf {H} (\mathbf {x_{1}} -\mathbf {x_{2}} )=0} .


In mathematical logic, an uninterpreted function or function symbol is one that has no other property than its name and n-ary form. Function symbols are used, together with constants and variables, to form terms. The theory of uninterpreted functions is also sometimes called the free theory, because it is freely generated, and thus a free object, or the empty theory, being the theory having an empty set of sentences (in analogy to an initial algebra). Theories with a non-empty set of equations are known as equational theories. The satisfiability problem for free theories is solved by syntactic unification; algorithms for the latter are used by interpreters for various computer languages, such as Prolog. Syntactic unification is also used in algorithms for the satisfiability problem for certain other equational theories, see Unification (computer science).


)^{2}}}=\prod \limits _{k=1}^{n}{\frac {n+k}{k}}{\text{ for all }}n\geq 0.} They are called central since they show up exactly in the middle of the even-numbered rows in Pascal's triangle. The first few central binomial coefficients starting at n = 0 are: 1, 2, 6, 20, 70, 252, 924, 3432, 12870, 48620, ...; (sequence A000984 in the OEIS)


It is called the Wooley integer semigroup and members of this semigroup are called Wooley integers. Similarly, the set of integers in W is itself a multiplicative semigroup. It is called the wild integer semigroup and members of this semigroup are called wild numbers.


In natural languages, an indicative conditional is a conditional sentence such as "If Leona is at home, she isn't in Paris", whose grammatical form restricts it to discussing what could be true. Indicatives are typically defined in opposition to counterfactual conditionals, which have extra grammatical marking which allows them to discuss eventualities which are no longer possible. Indicatives are a major topic of research in philosophy of language, philosophical logic, and linguistics. Open questions include which logical operation indicatives denote, how such denotations could be composed from their grammatical form, and the implications of those denotations for areas including metaphysics, psychology of reasoning, and philosophy of mathematics.


In statistics, a weighted median of a sample is the 50% weighted percentile. It was first proposed by F. Y. Edgeworth in 1888. Like the median, it is useful as an estimator of central tendency, robust against outliers. It allows for non-uniform statistical weights related to, e.g., varying precision measurements in the sample.


{\displaystyle \mathbf {\lambda } _{j}=-\mathbf {J} ^{-1}\left.} After each iteration, the unconstrained particle positions are updated using x ^ i ( t + Δ t ) ← x ^ i ( t + Δ t ) + ∑ k = 1 n λ k ∂ σ k ∂ x i ( Δ t ) 2 m i − 1 . {\displaystyle {\hat {\mathbf {x} }}_{i}(t+\Delta t)\leftarrow {\hat {\mathbf {x} }}_{i}(t+\Delta t)+\sum _{k=1}^{n}\lambda _{k}{\frac {\partial \sigma _{k}}{\partial \mathbf {x} _{i}}}\left(\Delta t\right)^{2}m_{i}^{-1}.}


Mcgee and Prusak (1993) noted that core competencies are not what an organization owns, but rather what it knows.Bartlett (1999) indicates that empowerment is not possible in an autocratic organization, that networks cannot be sustained in fixed hierarchical structure, and that learning is not possible in an environment constrained by rigid policies and procedures. Davenport (1997) used an information ecology approach, in which he explored the use and abuse of information in the context of infighting, resource hoarding, and political battles as well as appropriate management in such a context. Simard (2000) states that knowledge is inextricably linked to organizational mandates. Some providers strive for objectivity, others selectively disseminate information and knowledge, while still others use information to further their agenda. Users must understand that information is not innocent, and that all information is not created equal.


A fractional weighted version of the conjecture, posed by Jack Edmonds and Rick Giles, was refuted by Alexander Schrijver.The Lucchesi–Younger theorem states that the minimum size of a dijoin, in any given directed graph, equals the maximum number of disjoint dicuts that can be found in the graph. The minimum weight dijoin in a weighted graph can be found in polynomial time, and is a special case of the submodular flow problem.In planar graphs, dijoins and feedback arc sets are dual concepts. The dual graph of a directed graph, embedded in the plane, is a graph with a vertex for each face of the given graph, and a dual edge between two dual vertices when the corresponding two faces are separated by an edge.


In the case where V = W {\displaystyle V=W} , a linear map is called a linear endomorphism. Sometimes the term linear operator refers to this case, but the term "linear operator" can have different meanings for different conventions: for example, it can be used to emphasize that V {\displaystyle V} and W {\displaystyle W} are real vector spaces (not necessarily with V = W {\displaystyle V=W} ), or it can be used to emphasize that V {\displaystyle V} is a function space, which is a common convention in functional analysis. Sometimes the term linear function has the same meaning as linear map, while in analysis it does not. A linear map from V to W always maps the origin of V to the origin of W. Moreover, it maps linear subspaces in V onto linear subspaces in W (possibly of a lower dimension); for example, it maps a plane through the origin in V to either a plane through the origin in W, a line through the origin in W, or just the origin in W. Linear maps can often be represented as matrices, and simple examples include rotation and reflection linear transformations. In the language of category theory, linear maps are the morphisms of vector spaces.


The primary achievement of ludics is the discovery of a relationship between two natural, but distinct notions of type, or proposition. The first view, which might be termed the proof-theoretic or Gentzen-style interpretation of propositions, says that the meaning of a proposition arises from its introduction and elimination rules. Focalization refines this viewpoint by distinguishing between positive propositions, whose meaning arises from their introduction rules, and negative propositions, whose meaning arises from their elimination rules.


In solvent extraction, a distribution ratio is often quoted as a measure of how well-extracted a species is. The distribution ratio (Kd) is equal to the concentration of a solute in the organic phase divided by its concentration in the aqueous phase. Depending on the system, the distribution ratio can be a function of temperature, the concentration of chemical species in the system, and a large number of other parameters. Note that D is related to the ΔG of the extraction process.


In standard gematria (mispar hechrechi), each letter is given a numerical value between 1 and 400, as shown in the following table. In mispar gadol, the five final letters are given their own values, ranging from 500 to 900. It is possible that this well-known cipher was used to conceal other more hidden ciphers in Jewish texts. For instance, a scribe may discuss a sum using the 'standard gematria' cipher, but may intend the sum to be checked with a different secret cipher. A mathematical formula for finding a letter's corresponding number in mispar gadol is: f ( x ) = 10 ⌊ x − 1 9 ⌋ × ( ( x − 1 mod 9 ) + 1 ) , {\displaystyle f(x)=10^{\left\lfloor {\frac {x-1}{9}}\right\rfloor }\times ((x-1\mod 9)+1),} where x is the position of the letter in the language letters index (regular order of letters), and the floor and modulo functions are used.


In software engineering, test design is the activity of deriving and specifying test cases from test conditions to test software.


In some cases, a page fault may indicate a software bug, which can be prevented by using memory protection as one of key benefits of an MMU: an operating system can use it to protect against errant programs by disallowing access to memory that a particular program should not have access to. Typically, an operating system assigns each program its own virtual address space.An paged MMU also mitigates the problem of external fragmentation of memory. After blocks of memory have been allocated and freed, the free memory may become fragmented (discontinuous) so that the largest contiguous block of free memory may be much smaller than the total amount.


In the case of equality constraints, this theorem is proved with the calculus of variations and Lagrange multipliers. The constraints can be written as ∫ − ∞ ∞ f j ( x ) p ( x ) d x = a j {\displaystyle \int _{-\infty }^{\infty }f_{j}(x)p(x)dx=a_{j}} We consider the functional J ( p ) = ∫ − ∞ ∞ p ( x ) ln  p ( x ) d x − η 0 ( ∫ − ∞ ∞ p ( x ) d x − 1 ) − ∑ j = 1 n λ j ( ∫ − ∞ ∞ f j ( x ) p ( x ) d x − a j ) {\displaystyle J(p)=\int _{-\infty }^{\infty }p(x)\ln {p(x)}dx-\eta _{0}\left(\int _{-\infty }^{\infty }p(x)dx-1\right)-\sum _{j=1}^{n}\lambda _{j}\left(\int _{-\infty }^{\infty }f_{j}(x)p(x)dx-a_{j}\right)} where η 0 {\displaystyle \eta _{0}} and λ j , j ≥ 1 {\displaystyle \lambda _{j},j\geq 1} are the Lagrange multipliers. The zeroth constraint ensures the second axiom of probability.


Optimizing the FSSE results in a compromise between fairness (especially avoiding scheduling starvation) and achieving high spectral efficiency. If the cost of each user is known, in terms of consumed resources per transferred information bit, the FSSE measure may be redefined to reflect proportional fairness. In a proportional fair system, this "proportionally fair shared spectrum efficiency" (or "fairly shared radio resource cost") is maximized. This policy is less fair since "expensive" users are given lower throughput than others, but still scheduling starvation is avoided.


All the preferences cast by voters are awarded the points associated with their rank position. Then, all the points for each option are tallied and the one with the most points is the winner. Where a few winners (W) are instead required following the count, the W highest-ranked options are selected. Positional voting is not only a means of identifying a single winner but also a method for converting sets of individual preferences (ranked ballots) into one collective and fully rank-ordered set. It is possible and legitimate for options to be tied in this resultant set; even in first place.


The circuit will not function when the path delay exceeds the clock cycle delay so modifying the circuit to remove the timing failure (and eliminate the critical path) is an important part of the logic design engineer's task. Critical path also defines the maximum delay in all the multiple register-to-register paths, and it must not be greater than the clock cycle time. After meeting the timing closure, one way to improve the circuit performance is to insert a register in between the combinational path of the critical path.


In the field of calculus of variations in mathematics, the method of Lagrange multipliers on Banach spaces can be used to solve certain infinite-dimensional constrained optimization problems. The method is a generalization of the classical method of Lagrange multipliers as used to find extrema of a function of finitely many variables.


In natural language processing, Latent Dirichlet Allocation (LDA) is a Bayesian network (and, therefore, a generative statistical model) that explains a set of observations through unobserved groups, and each group explains why some parts of the data are similar. The LDA is an example of a Bayesian topic model. In this, observations (e.g., words) are collected into documents, and each word's presence is attributable to one of the document's topics. Each document will contain a small number of topics.


On mechanical Dutch typewriters, there is a key that produces 'ij' (in a single letterspace, located directly to the right of the L). However, this is not the case on modern computer keyboards. In many word puzzles, such as Lingo, ij fills one square, but in others, such as Scrabble, ij fills two squares.


The examples within the position paper are just "examples" of current carrier practices for illustration purposes, but do not reflect any official Oftel regulation. The main networks often agree to unlock handsets for a charge, either at the end of a contract or, for prepaid handsets, after several months. Some Blackberry handsets supplied by Vodafone (e.g., Storm) are examples of a UK carrier not offering unlocking codes.


A set of acronyms are commonly used: PMDr (premotor dorsal, rostral), PMDc, PMVr, PMVc. Some researchers use a different terminology. Field 7 or F7 denotes PMDr; F2 = PMDc; F5=PMVr; F4=PMVc.


The set of values of η for which the function f X ( x ; η ) {\displaystyle f_{X}(x;\eta )} is integrable is called the natural parameter space. It can be shown that the natural parameter space is always convex. A(η) is called the log-partition function because it is the logarithm of a normalization factor, without which f X ( x ; θ ) {\displaystyle f_{X}(x;\theta )} would not be a probability distribution: A ( η ) = log  ( ∫ X h ( x ) exp  ( η ( θ ) ⋅ T ( x ) ) d x ) {\displaystyle A(\eta )=\log \left(\int _{X}h(x)\,\exp(\eta (\theta )\cdot T(x))\,\mathrm {d} x\right)} The function A is important in its own right, because the mean, variance and other moments of the sufficient statistic T(x) can be derived simply by differentiating A(η). For example, because log(x) is one of the components of the sufficient statistic of the gamma distribution, E   {\displaystyle \operatorname {\mathcal {E}} } can be easily determined for this distribution using A(η). Technically, this is true because K ( u ∣ η ) = A ( η + u ) − A ( η ) , {\displaystyle K\left(u\mid \eta \right)=A(\eta +u)-A(\eta )\,,} is the cumulant generating function of the sufficient statistic.


In statistics, ranking is the data transformation in which numerical or ordinal values are replaced by their rank when the data are sorted. For example, the numerical data 3.4, 5.1, 2.6, 7.3 are observed, the ranks of these data items would be 2, 3, 1 and 4 respectively. For example, the ordinal data hot, cold, warm would be replaced by 3, 1, 2.


In mathematics, real trees (also called R {\displaystyle \mathbb {R} } -trees) are a class of metric spaces generalising simplicial trees. They arise naturally in many mathematical contexts, in particular geometric group theory and probability theory. They are also the simplest examples of Gromov hyperbolic spaces.


In some cases, storefronts and aggregates have intervened to stop review bombs and delete the negative reviews. In February 2019, Rotten Tomatoes announced that it would no longer accept user reviews for a film until after its official release.In 2017, Valve added review histograms to Steam user review scores to show how these change over time; according to Valve's Alden Kroll, this can help a potential purchaser of a game recognize a short term review bomb that is not indicative of the game itself, compared to a game that has a long tail of bad reviews. Kroll said they did not want to silence the ability of users to leave reviews but recognized they needed to highlight phenomena like review bombs to aid customers. In March 2019, Valve stated that it would employ a new system to detect spikes of negative "off-topic" reviews on games: if it is determined that they were the result of a review bomb campaign, the time period will be flagged, and all reviews made during that period (whether negative or positive) will be excluded from the user rating displayed for a game.


In mathematics, the Bareiss algorithm, named after Erwin Bareiss, is an algorithm to calculate the determinant or the echelon form of a matrix with integer entries using only integer arithmetic; any divisions that are performed are guaranteed to be exact (there is no remainder). The method can also be used to compute the determinant of matrices with (approximated) real entries, avoiding the introduction of any round-off errors beyond those already present in the input.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 35678, 135678, 345678, and 1345678 are the patterns related to Braille pattern dots-23456, since the two additional dots of kantenji patterns 023456, 234567, and 0234567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


This JNI interface pointer can be stored, but remains valid only in the current thread. Other threads must first call AttachCurrentThread() to attach themselves to the VM and obtain a JNI interface pointer. Once attached, a native thread works like a regular Java thread running within a native method.


In probability theory, Foster's theorem, named after Gordon Foster, is used to draw conclusions about the positive recurrence of Markov chains with countable state spaces. It uses the fact that positive recurrent Markov chains exhibit a notion of "Lyapunov stability" in terms of returning to any state while starting from it within a finite time interval.


In networking, packets are the key foundation for scheduling. There are many different types of packet travelling around network core every day, and they are treated totally different. For example, voice and video packets have higher priority than normal packets. In order to manage and distribute packet effectively, network devices also use input queue to determine which packet will be transmitted first.


In the counter-counter mode, the Cascaded Cipher uses full-strength AES-128 in counter mode to generate a secure key stream and supplies this key-stream to a reduced round Serpent also operating in counter mode to encrypt each plaintext block. To increase performance, each inner key stream block is reused several times to encrypt multiple blocks.


In theory some measures of guarantee that an obtained solution solves the original problem with reasonable accuracy. Typically in applications only the first stage optimal solution x ∗ {\displaystyle x^{*}} has a practical value since almost always a "true" realization of the random data will be different from the set of constructed (generated) scenarios. Suppose ξ {\displaystyle \xi } contains d {\displaystyle d} independent random components, each of which has three possible realizations (for example, future realizations of each random parameters are classified as low, medium and high), then the total number of scenarios is K = 3 d {\displaystyle K=3^{d}} . Such exponential growth of the number of scenarios makes model development using expert opinion very difficult even for reasonable size d {\displaystyle d} . The situation becomes even worse if some random components of ξ {\displaystyle \xi } have continuous distributions.


Through her attempts to solve Fermat's Last Theorem, Germain developed a result now known as Germain's Theorem which states that if p is an odd prime and 2p + 1 is also prime, then p must divide x, y, or z. Otherwise, x n + y n ≠ z n {\textstyle x^{n}+y^{n}\neq z^{n}} . This case where p does not divide x, y, or z is called the first case. Sophie Germain’s work was the most progress achieved on Fermat’s last theorem at that time.


Next, set the first vector v1=u1. Then, we set u2=v2-proju1v2. This process is repeated to for k vectors, with the final vector being uk= vk-Σ(j=1)(k-1)projukvk.


Even if they are not words, morphemes can prime for complete words that include them. An example of this would be that the morpheme 'psych' can prime for the word 'psychology'. In support with further detail, when an individual processes a word sometimes that word can be affected when the prior word is linked semantically.


In pseudocode, the general algorithm for building decision trees is: Check for the above base cases. For each attribute a, find the normalized information gain ratio from splitting on a. Let a_best be the attribute with the highest normalized information gain. Create a decision node that splits on a_best. Recurse on the sublists obtained by splitting on a_best, and add those nodes as children of node.


The edges forming the silhouette are extruded away from the light to construct the faces of the shadow volume. This volume must extend over the range of the entire visible scene; often the dimensions of the shadow volume are extended to infinity to accomplish this (see optimization below.) To form a closed volume, the front and back end of this extrusion must be covered.


That is, given the neighbors N i {\displaystyle N_{i}} of X i , X i {\displaystyle X_{i},X_{i}} is independent of all other X j {\displaystyle X_{j}} (Markov property). The main difference with a hidden Markov model is that neighborhood is not defined in 1 dimension but within a network, i.e. X i {\displaystyle X_{i}} is allowed to have more than the two neighbors that it would have in a Markov chain.


In mathematics, especially order theory, a prefix ordered set generalizes the intuitive concept of a tree by introducing the possibility of continuous progress and continuous branching. Natural prefix orders often occur when considering dynamical systems as a set of functions from time (a totally-ordered set) to some phase space. In this case, the elements of the set are usually referred to as executions of the system. The name prefix order stems from the prefix order on words, which is a special kind of substring relation and, because of its discrete character, a tree.


A transition takes place to the next state as a result of a binary input 1 or 0 and the encoder's present output state. The encoding procedure is as follows. In general, the encoder outputs + level for a binary 1 input and a − level for a binary 0 input.


In network science, a biased random walk on a graph is a time path process in which an evolving variable jumps from its current state to one of various potential new states; unlike in a pure random walk, the probabilities of the potential new states are unequal. Biased random walks on a graph provide an approach for the structural analysis of undirected graphs in order to extract their symmetries when the network is too complex or when it is not large enough to be analyzed by statistical methods. The concept of biased random walks on a graph has attracted the attention of many researchers and data companies over the past decade especially in the transportation and social networks.


In marketing, discriminant analysis was once often used to determine the factors which distinguish different types of customers and/or products on the basis of surveys or other forms of collected data. Logistic regression or other methods are now more commonly used. The use of discriminant analysis in marketing can be described by the following steps: Formulate the problem and gather data—Identify the salient attributes consumers use to evaluate products in this category—Use quantitative marketing research techniques (such as surveys) to collect data from a sample of potential customers concerning their ratings of all the product attributes. The data collection stage is usually done by marketing research professionals.


In the Oxford Advanced Learner's Dictionary, the word alphabet is defined as "a set of letters or symbols in a fixed order used for writing a language". The YES "alphabet" is a list of Chinese character strokes in the order of "㇐ ㇕ ㇅ ㇎ ㇡ ㇋ ㇊ ㇍ ㇈ ㇆ ㇇ ㇌ 飞 ㇀ ㇑ ㇗ ㇞ ㇉ ㄣ ㇙ ㇄ ㇟ ㇚ ㇓ ㇜ ㇛ ㇢ ㇔ ㇏ ㇂". This stroke alphabet is built on the basis of Unicode CJK Strokes and the Standard of Chinese Character Bending Strokes of the GB13000.1 Character Set. There are totally 30 strokes, sorted by the standard basic strokes order of “heng (橫, 横, 一), ti (提, ㇀), shu (豎, 竖, 丨), pie (撇, 丿), dian (點, 点, 丶), na (捺, ㇏)” and the bending points order of “zhe (折), wan (彎, 弯) and gou (鉤, 钩)”.


In this context, "numeric" means that the computer treats sequences of bits as binary numbers (base two numbers) and executes arithmetic operations like add, subtract, multiply, or divide. "Logical" refers to the Boolean logical operations of disjunction, conjunction, and negation between two sequences of bits, in which each bit in one sequence is simply compared to its counterpart in the other sequence. Programmers therefore have the option of working in and applying the rules of either numeric algebra or Boolean algebra as needed. A core differentiating feature between these families of operations is the existence of the carry operation in the first but not the second.


Phonetically palatalized consonants may vary in their exact realization. Some languages add semivowels before or after the palatalized consonant (onglides or offglides). In such cases, the vowel (especially a non-front vowel) following a palatalized consonant typically has a palatal onglide.


In natural language processing a w-shingling is a set of unique shingles (therefore n-grams) each of which is composed of contiguous subsequences of tokens within a document, which can then be used to ascertain the similarity between documents. The symbol w denotes the quantity of tokens in each shingle selected, or solved for. The document, "a rose is a rose is a rose" can therefore be maximally tokenized as follows: (a,rose,is,a,rose,is,a,rose)The set of all contiguous sequences of 4 tokens (Thus 4=n, thus 4-grams) is { (a,rose,is,a), (rose,is,a,rose), (is,a,rose,is), (a,rose,is,a), (rose,is,a,rose) } Which can then be reduced, or maximally shingled in this particular instance to { (a,rose,is,a), (rose,is,a,rose), (is,a,rose,is) }.


In number theory, octic reciprocity is a reciprocity law relating the residues of 8th powers modulo primes, analogous to the law of quadratic reciprocity, cubic reciprocity, and quartic reciprocity. There is a rational reciprocity law for 8th powers, due to Williams. Define the symbol ( x p ) k {\displaystyle \left({\frac {x}{p}}\right)_{k}} to be +1 if x is a k-th power modulo the prime p and -1 otherwise. Let p and q be distinct primes congruent to 1 modulo 8, such that ( p q ) 4 = ( q p ) 4 = + 1.


In mathematics, a set is countable if either it is finite or it can be made in one to one correspondence with the set of natural numbers. Equivalently, a set is countable if there exists an injective function from it into the natural numbers; this means that each element in the set may be associated to a unique natural number, or that the elements of the set can be counted one at a time, although the counting may never finish due to an infinite number of elements. In more technical terms, assuming the axiom of countable choice, a set is countable if its cardinality (the number of elements of the set) is not greater than that of the natural numbers. A countable set that is not finite is said to be countably infinite. The concept is attributed to Georg Cantor, who proved the existence of uncountable sets, that is, sets that are not countable; for example the set of the real numbers.


For each cell C {\displaystyle C} , we let W ( C ) {\displaystyle W(C)} be the sum of all W ( k ) {\displaystyle W(k)} , where the sum is taken over all sampled k {\displaystyle k} in the cell C {\displaystyle C} . For each cell C {\displaystyle C} , we let T ( C ) {\displaystyle T(C)} be the auxiliary value for cell C {\displaystyle C} , which is commonly called the "benchmark target" for cell C {\displaystyle C} . Next, we compute a benchmark factor F ( C ) = T ( C ) / W ( C ) {\displaystyle F(C)=T(C)/W(C)} .


One of the most widely used transmission system technologies in the Internet and the Public switched telephone network (PSTN) is synchronous optical networking (SONET). Also, transmission system is the medium through which data is transmitted from one point to another. Examples of common transmission systems people use everyday are: the internet, mobile networks, cordless cables, etc.


In mathematics, a set B of vectors in a vector space V is called a basis (PL: bases) if every element of V may be written in a unique way as a finite linear combination of elements of B. The coefficients of this linear combination are referred to as components or coordinates of the vector with respect to B. The elements of a basis are called basis vectors. Equivalently, a set B is a basis if its elements are linearly independent and every element of V is a linear combination of elements of B. In other words, a basis is a linearly independent spanning set. A vector space can have several bases; however all the bases have the same number of elements, called the dimension of the vector space. This article deals mainly with finite-dimensional vector spaces. However, many of the principles are also valid for infinite-dimensional vector spaces.


In statistics, family-wise error rate (FWER) is the probability of making one or more false discoveries, or type I errors when performing multiple hypotheses tests.


These two conditions are sufficient to ensure that all faces are alike and all vertices are alike. Note, however, that this definition does not work for abstract polytopes. A regular polytope can be represented by a Schläfli symbol of the form {a, b, c, ..., y, z}, with regular facets as {a, b, c, ..., y}, and regular vertex figures as {b, c, ..., y, z}.


In practice, loop variants are often taken to be non-negative integers, or even required to be so, but the requirement that every loop have an integer variant removes the expressive power of unbounded iteration from a programming language. Unless such a (formally verified) language allows a transfinite proof of termination for some other equally powerful construct such as a recursive function call, it is no longer capable of full μ-recursion, but only primitive recursion. Ackermann's function is the canonical example of a recursive function that cannot be computed in a loop with an integer variant. In terms of their computational complexity, however, functions that are not primitive recursive lie far beyond the realm of what is usually considered tractable.


In statistics, binomial regression is a regression analysis technique in which the response (often referred to as Y) has a binomial distribution: it is the number of successes in a series of n {\displaystyle n} independent Bernoulli trials, where each trial has probability of success p {\displaystyle p} . In binomial regression, the probability of a success is related to explanatory variables: the corresponding concept in ordinary regression is to relate the mean value of the unobserved response to explanatory variables. Binomial regression is closely related to binary regression: a binary regression can be considered a binomial regression with n = 1 {\displaystyle n=1} , or a regression on ungrouped binary data, while a binomial regression can be considered a regression on grouped binary data (see comparison). Binomial regression models are essentially the same as binary choice models, one type of discrete choice model: the primary difference is in the theoretical motivation (see comparison). In machine learning, binomial regression is considered a special case of probabilistic classification, and thus a generalization of binary classification.


Linnaeus made the same distinction between plantains and bananas when first naming two "species" of Musa. Members of the "plantain subgroup" of banana cultivars, most important as food in West Africa and Latin America, correspond to the Chiquita description, having long pointed fruit. They are described by Ploetz et al. as "true" plantains, distinct from other cooking bananas.


In recent years the long-standing use of term "disorder" to discuss entropy has met with some criticism. Critics of the terminology state that entropy is not a measure of 'disorder' or 'chaos', but rather a measure of energy's diffusion or dispersal to more microstates. Shannon's use of the term 'entropy' in information theory refers to the most compressed, or least dispersed, amount of code needed to encompass the content of a signal.


The induced action of G {\displaystyle G} on the symplectic manifold ( T ∗ N , d τ ) {\displaystyle (T^{*}N,\mathrm {d} \tau )} , given by g ⋅ η := ( T π ( η ) g − 1 ) ∗ η {\displaystyle g\cdot \eta :=(T_{\pi (\eta )}g^{-1})^{*}\eta } for g ∈ G , η ∈ T ∗ N {\displaystyle g\in G,\eta \in T^{*}N} is Hamiltonian with momentum map − ι ρ ( ξ ) τ {\displaystyle -\iota _{\rho (\xi )}\tau } for all ξ ∈ g {\displaystyle \xi \in {\mathfrak {g}}} . Here ι ρ ( ξ ) τ {\displaystyle \iota _{\rho (\xi )}\tau } denotes the contraction of the vector field ρ ( ξ ) {\displaystyle \rho (\xi )} , the infinitesimal action of ξ {\displaystyle \xi } , with the 1-form τ {\displaystyle \tau } . The facts mentioned below may be used to generate more examples of momentum maps.


In mathematics, specifically in elementary arithmetic and elementary algebra, given an equation between two fractions or rational expressions, one can cross-multiply to simplify the equation or determine the value of a variable. The method is also occasionally known as the "cross your heart" method because lines resembling a heart outline can be drawn to remember which things to multiply together. Given an equation like a b = c d , {\displaystyle {\frac {a}{b}}={\frac {c}{d}},} where b and d are not zero, one can cross-multiply to get a d = b c or a = b c d . {\displaystyle ad=bc\quad {\text{or}}\quad a={\frac {bc}{d}}.} In Euclidean geometry the same calculation can be achieved by considering the ratios as those of similar triangles.


. . , n 2 {\displaystyle 1,2,...,n^{2}} , the magic square is said to be 'normal'.


The size of a graph is | E | {\displaystyle |E|} , its number of edges. The degree or valency of a vertex is the number of edges that are incident to it, where a loop is counted twice. The degree of a graph is the maximum of the degrees of its vertices.


In some scenarios, an argument by example may be valid if it leads from a singular premise to an existential conclusion (i.e. proving that a claim is true for at least one case, instead of for all cases). For example: Socrates is wise. Therefore, someone is wise.


Successful runs might also write a result on magnetic tape or generate some data cards to be used in a later computation. The turnaround time for a single job often spanned entire days.


In semiotics, the commutation test is used to analyze a signifying system. The test identifies signifiers as well as their signifieds, value and significance.


In set theory a serial relation is a homogeneous relation expressing the connection of an element of a sequence to the following element. The successor function used by Peano to define natural numbers is the prototype for a serial relation. Bertrand Russell used serial relations in The Principles of Mathematics (1903) as he explored the foundations of order theory and its applications.


The algorithm takes time bounded by a polynomial in n {\displaystyle n} , the dimension of K {\displaystyle K} and 1 / ε {\displaystyle 1/\varepsilon } . The algorithm combines two ideas: By using a Markov chain Monte Carlo (MCMC) method, it is possible to generate points that are nearly uniformly randomly distributed within a given convex body. The basic scheme of the algorithm is a nearly uniform sampling from within K {\displaystyle K} by placing a grid consisting of n {\displaystyle n} -dimensional cubes and doing a random walk over these cubes.


However, this set of nodes is optimal for interpolation over C M n  {\displaystyle C_{M}^{n}} the set of n times differentiable functions whose n-th derivatives are bounded in absolute values by a constant M as shown by N. S. Hoang. Using a computer, one can approximate the values of the minimal Lebesgue constants, here for the canonical interval: There are uncountable infinitely many sets of nodes in  that minimize, for fixed n > 1, the Lebesgue constant. Though if we assume that we always take −1 and 1 as nodes for interpolation (which is called a canonical node configuration), then such a set is unique and zero-symmetric.


900 MHz (902–928 MHz, allocated in 1993) 1.9 GHz (1920–1930 MHz, developed in 1993 and allocated in October 2005, especially with DECT 6.0) 2.4 GHz (2400–2500 MHz, allocated in 1998) 5.8 GHz (5725–5875 MHz, allocated in 2003 due to crowding on the 2.4 GHz band)Over-crowding of earlier frequency allocations led users to discontinue using telephone equipment that operated on those frequencies, leaving those bands relatively clear. Radio hobbyists monitor usage of the older equipment with telephone activity in the US AM broadcast band, some 27 MHz frequencies and most older 43-50 MHz frequencies. 1.7 MHz cordless phones were the earliest models available at retailers, and are generally identifiable by their large metal telescoping antennas.


In the multiset {a, a, a, b, b, b}, a and b both have multiplicity 3.These objects are all different when viewed as multisets, although they are the same set, since they all consist of the same elements. As with sets, and in contrast to tuples, the order in which elements are listed does not matter in discriminating multisets, so {a, a, b} and {a, b, a} denote the same multiset. To distinguish between sets and multisets, a notation that incorporates square brackets is sometimes used: the multiset {a, a, b} can be denoted by .The cardinality of a multiset is the sum of the multiplicities of all its elements.


In mathematical analysis, idempotent analysis is the study of idempotent semirings, such as the tropical semiring. The lack of an additive inverse in the semiring is compensated somewhat by the idempotent rule A ⊕ A = A {\displaystyle A\oplus A=A} . == References ==


In quantum information theory, the conditional entropy is generalized to the conditional quantum entropy. The latter can take negative values, unlike its classical counterpart.


About the year 1900 I found this out".Sheila Ostrander and Lynn Schroeder, authors of the paranormal, visited Czechoslovakia in 1968, where they happened upon a cardboard pyramid manufactured commercially by Drbal. They met Drbal, and dedicated a chapter of their popular 1970 book Psychic Discoveries Behind the Iron Curtain to pyramid power. This book introduced both the concept of pyramid power and the story about Antoine Bovis to the English-speaking world.


In the United States, the Federal Communications Commission requires all interconnected VoIP service providers to comply with requirements comparable to those for traditional telecommunications service providers. VoIP operators in the US are required to support local number portability; make service accessible to people with disabilities; pay regulatory fees, universal service contributions, and other mandated payments; and enable law enforcement authorities to conduct surveillance pursuant to the Communications Assistance for Law Enforcement Act (CALEA). Operators of Interconnected VoIP (fully connected to the PSTN) are mandated to provide Enhanced 911 service without special request, provide for customer location updates, clearly disclose any limitations on their E-911 functionality to their consumers, obtain affirmative acknowledgements of these disclosures from all consumers, and may not allow their customers to opt-out of 911 service. VoIP operators also receive the benefit of certain US telecommunications regulations, including an entitlement to interconnection and exchange of traffic with incumbent local exchange carriers via wholesale carriers.


In telephone systems where calls from distant automated exchanges arrive for manual subscribers or non-dialable points, there often would be a ringdown operator (reachable from the distant operator console by dialling NPA+181) who would manually ring the desired subscriber on a party line or toll station. On some systems, this function was carried out by the inward operator (NPA+121). In both cases, this is a telephone operator at the destination who provides assistance solely to other operators on inbound toll calls; the ringdown operator nominally cannot be dialed directly by the subscriber.


In mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by Hugo Steinhaus for the analysis of comparison sort algorithms. These numbers give the worst-case number of comparisons used by both binary insertion sort and merge sort. However, there are other algorithms that use fewer comparisons.


In modern field of computational intelligence, the social learning theory is adopted to develop a new computer optimization algorithm, the social learning algorithm. Emulating the observational learning and reinforcement behaviors, a virtual society deployed in the algorithm seeks the strongest behavioral patterns with the best outcome. This corresponds to searching for the best solution in solving optimization problems. Compared with other bio-inspired global optimization algorithms that mimic natural evolution or animal behaviors, the social learning algorithm has its prominent advantages.


When the feature works properly, it is nearly transparent to the user, appearing as a single long text message. Previously, due to incompatibilities between providers and lack of support in some phone models, there was not widespread use of this feature.In the late 2000s to early 2010s, this feature was adopted more widely. Not only do many handsets support this feature, but support for the feature also exists amongst SMS gateway providers. The way concatenation works in GSM and UMTS networks is specified in SMS Point to Point specification, 3GPP TS 23.040.On networks which do not support Concatenated SMS (neither the standard scheme nor the simplified one), the message is delivered as individual SMS text messages rather than one concatenated message.


{\displaystyle 1,1,2,4,10,32,122,544,2770,15872,101042.} (sequence A001250 in the OEIS).The number of antichains in a fence is a Fibonacci number; the distributive lattice with this many elements, generated from a fence via Birkhoff's representation theorem, has as its graph the Fibonacci cube.A partially ordered set is series-parallel if and only if it does not have four elements forming a fence.Several authors have also investigated the number of order-preserving maps from fences to themselves, or to fences of other sizes.An up-down poset Q(a,b) is a generalization of a zigzag poset in which there are a downward orientations for every upward one and b total elements.


In mathematics, zero dynamics is known as the concept of evaluating the effect of zero on systems.


Both of these tie in to notions of size. Importantly, injection existence between any two sets provides a preorder. A power class does not inject into its underlying set and the latter does not map onto the former.


In the following code sample, two optimizations can be applied. Although the calculation x = y + z and x * x is loop-invariant, precautions must be taken before moving the code outside the loop. It is possible that the loop condition is false (for example, if n holds a negative value), and in such case, the loop body should not be executed at all. One way of guaranteeing correct behaviour is using a conditional branch outside of the loop.


In queueing theory, a discipline within the mathematical theory of probability, a BCMP network is a class of queueing network for which a product-form equilibrium distribution exists. It is named after the authors of the paper where the network was first described: Baskett, Chandy, Muntz, and Palacios. The theorem is a significant extension to a Jackson network allowing virtually arbitrary customer routing and service time distributions, subject to particular service disciplines.The paper is well known, and the theorem was described in 1990 as "one of the seminal achievements in queueing theory in the last 20 years" by J. Michael Harrison and Ruth J. Williams.


{\displaystyle T\geqslant |S|-\varepsilon N\geqslant (1-R)N-\varepsilon N=(1-R-\varepsilon )N.} Finally, we have Δ ( C ∗ ( m 1 ) , C ∗ ( m 2 ) ) ⩾ H q − 1 ( 1 2 − ε ) ⋅ 2 k ⋅ T ⩾ H q − 1 ( 1 2 − ε ) ⋅ 2 k ⋅ ( 1 − R − ε ) ⋅ N . {\displaystyle \Delta (C^{*}(m_{1}),C^{*}(m_{2}))\geqslant H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right)\cdot 2k\cdot T\geqslant H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right)\cdot 2k\cdot (1-R-\varepsilon )\cdot N.} This is true for any arbitrary m 1 ≠ m 2 {\displaystyle m_{1}\neq m_{2}} . So C ∗ {\displaystyle C^{*}} has the relative distance at least ( 1 − R − ε ) H q − 1 ( 1 2 − ε ) , {\displaystyle (1-R-\varepsilon )H_{q}^{-1}\left({\tfrac {1}{2}}-\varepsilon \right),} which completes the proof.


In the following, n {\displaystyle n} denotes the number of people in the initial circle, and k {\displaystyle k} denotes the count for each step, that is, k − 1 {\displaystyle k-1} people are skipped and the k {\displaystyle k} -th is executed. The people in the circle are numbered from 1 {\displaystyle 1} to n {\displaystyle n} , the starting position being 1 {\displaystyle 1} and the counting being inclusive.


However it is not the smallest such graph: it is known that there is a universal graph for n-vertex trees, with only n vertices and O(n log n) edges, and that this is optimal. A construction based on the planar separator theorem can be used to show that n-vertex planar graphs have universal graphs with O(n3/2) edges, and that bounded-degree planar graphs have universal graphs with O(n log n) edges.


Inversion of control has been widely used by application development frameworks since the rise of GUI environments and continues to be used both in GUI environments and in web server application frameworks. Inversion of control makes the framework extensible by the methods defined by the application programmer.Event-driven programming is often implemented using IoC so that the custom code need only be concerned with the handling of events, while the event loop and dispatch of events/messages is handled by the framework or the runtime environment. In web server application frameworks, dispatch is usually called routing, and handlers may be called endpoints. The phrase "inversion of control" has separately also come to be used in the community of Java programmers to refer specifically to the patterns of injecting objects' dependencies that occur with "IoC containers" in Java frameworks such as the Spring framework. In this different sense, "inversion of control" refers to granting the framework control over the implementations of dependencies that are used by application objects rather than to the original meaning of granting the framework control flow (control over the time of execution of application code e.g. callbacks).


To illustrate this, consider the following statements: P {\displaystyle P}: Sam ate an orange for lunch Q {\displaystyle Q}: Sam ate a fruit for lunchThen, to say, "Sam ate an orange for lunch" implies "Sam ate a fruit for lunch" ( P → Q {\displaystyle P\to Q} ). Logically, if Sam did not eat a fruit for lunch, then Sam also cannot have eaten an orange for lunch (by contraposition). However, merely saying that Sam did not eat an orange for lunch provides no information on whether or not Sam ate a fruit (of any kind) for lunch.


In the context of spoken languages, a phone is an unanalyzed sound of a language. A phone is a speech segment that possesses distinct physical or perceptual properties and serves as the basic unit of phonetic speech analysis. Phones are generally either vowels or consonants. A phonetic transcription (based on phones) is enclosed within square brackets (), rather than the slashes (/ /) of a phonemic transcription, (based on phonemes).


In some cases, the importance of the raters (experts) might not be the same as each other. In this case, the Weighted Kendall's W should be used. Suppose that object i {\displaystyle i} is given the rank r i j {\displaystyle r_{ij}} by judge number j {\displaystyle j} , where there are in total n {\displaystyle n} objects and m {\displaystyle m} judges. Also, the weight of judge j {\displaystyle j} is shown by ϑ j {\displaystyle \vartheta _{j}} (in real-world situation, the importance of each rater can be different).


An outstanding rationale for email authentication is the ability to automate email filtering at receiving servers. That way, spoofed messages can be rejected before they arrive to a user's Inbox. While protocols strive to devise ways to reliably block distrusted mail, security indicators can tag unauthenticated messages that still reach the Inbox. A 2018 study shows that security indicators can lower the click-through ratio by more than ten points, 48.9% to 37.2% of the users who open spoofed messages.


In set theory, an infinite set is a set that is not a finite set. Infinite sets may be countable or uncountable.


In second-order intuitionistic logic, the second-order polymorphic lambda calculus (F2) was discovered by Girard (1972) and independently by Reynolds (1974). Girard proved the Representation Theorem: that in second-order intuitionistic predicate logic (P2), functions from the natural numbers to the natural numbers that can be proved total, form a projection from P2 into F2. Reynolds proved the Abstraction Theorem: that every term in F2 satisfies a logical relation, which can be embedded into the logical relations P2. Reynolds proved that a Girard projection followed by a Reynolds embedding form the identity, i.e., the Girard-Reynolds Isomorphism.


In telecommunication, a convolutional code is a type of error-correcting code that generates parity symbols via the sliding application of a boolean polynomial function to a data stream. The sliding application represents the 'convolution' of the encoder over the data, which gives rise to the term 'convolutional coding'. The sliding nature of the convolutional codes facilitates trellis decoding using a time-invariant trellis. Time invariant trellis decoding allows convolutional codes to be maximum-likelihood soft-decision decoded with reasonable complexity.


{\textstyle \bigcup _{n\in \mathbb {N} }A_{n}\in N.} Briefly, a sigma-ideal must contain the empty set and contain subsets and countable unions of its elements.


The algorithms then adjust the weights, instead of adjusting the values associated with the individual state-action pairs. Methods based on ideas from nonparametric statistics (which can be seen to construct their own features) have been explored. Value iteration can also be used as a starting point, giving rise to the Q-learning algorithm and its many variants. Including Deep Q-learning methods when a neural network is used to represent Q, with various applications in stochastic search problems.The problem with using action-values is that they may need highly precise estimates of the competing action values that can be hard to obtain when the returns are noisy, though this problem is mitigated to some extent by temporal difference methods. Using the so-called compatible function approximation method compromises generality and efficiency.


This can be visualized as a checkerboard pattern in a matrix. Therefore, each processing unit can only have outgoing edges to PEs in the same row and column. This bounds the amount of communication partners for each PE to p r + p c − 1 {\displaystyle p_{r}+p_{c}-1} out of p = p r × p c {\displaystyle p=p_{r}\times p_{c}} possible ones.


In most Unix and Unix-like operating systems, the ps program (short for "process status") displays the currently-running processes. A related Unix utility named top provides a real-time view of the running processes.


Examples include 1ESS switch. A machine with three replications of each element is termed triple modular redundant (TMR). The voting circuit can determine which replication is in error when a two-to-one vote is observed.


In the above procedure, the algorithm checks whether the middle element ( m {\displaystyle m} ) is equal to the target ( T {\displaystyle T} ) in every iteration. Some implementations leave out this check during each iteration. The algorithm would perform this check only when one element is left (when L = R {\displaystyle L=R} ).


Beaumont created a list of over 150 personally significant books and collected replicas from bookstores. The books were treated, burned, displayed, and arranged in over thirty feet of floor to ceiling shelving. Through the metaphor of fire and the social horror of book burning, the project grieves the irretrievable loss of species (DNA) contained in the rainforest, as irretrievable as the loss of the ancient body of knowledge contained at the Library of Alexandria—both sources of encyclopedic information.


The information asymmetry problem occurs in a scenario where one of the two people has more or less information than the other. In the context of public administration, bureaucrats have an information advantage over the government and ministers as the former work at the ground level and have more knowledge about the dynamic and changing situation. Due to this government may frame policies that are not based on complete information and therefore problems in the implementation of public policies may occur.


In mathematics, physics, and engineering, a Euclidean vector or simply a vector (sometimes called a geometric vector or spatial vector) is a geometric object that has magnitude (or length) and direction. Vectors can be added to other vectors according to vector algebra. A Euclidean vector is frequently represented by a directed line segment, or graphically as an arrow connecting an initial point A with a terminal point B, and denoted by A B → {\displaystyle {\overrightarrow {AB}}} . A vector is what is needed to "carry" the point A to the point B; the Latin word vector means "carrier".


These are implemented in part because of the difficulty in ensuring that different terminals transmit at exactly the times required. Handsets that are moving will need to constantly adjust their timings to ensure their transmission is received at precisely the right time, because as they move further from the base station, their signal will take longer to arrive. This also means that the major TDMA systems have hard limits on cell sizes in terms of range, though in practice the power levels required to receive and transmit over distances greater than the supported range would be mostly impractical anyway.


In order to provide access to relevant data to users ChemXSeer provides new features that are not available in traditional search engines or digital libraries. Chemical Entity Search: A tool capable of identifying Chemical formulae and chemical names, and extracting and disambiguating them from general terms within documents. Those disambiguated terms are used for performing searches.


This is determined to a great degree by the stage of the call setup procedure at which a call is counted as connected. In modern communications systems, such as cellular (mobile) networks, the call setup procedure maybe very complex and the point at which a call is considered successfully connected may be defined in a number of ways, thus influencing the way the call setup success rate is calculated. If a call is connected successfully but the dialled number is busy, the call is counted as successful.


Though multiple systems have been postulated, few have reported results. One system, “SMILE,” which attempted to automatically extract classifications from case texts, resulted in an f-measure (which is a calculation of both recall rate and precision) of under 0.3 (compared to perfect f-measure of 1.0). This is probably much lower than an acceptable rate for general usage.Despite the limited results, many theorists predict that the evolution of such systems will eventually replace manual classification systems.


In India, an idea was mooted in 2003 to create a National Do Not Call Registry, and finally got implemented in 2014. Since then the government is taking various measures to curb the menace that includes termination of the violators telecom resources. As of now there is no regulation for telecallers to classify an abandoned call or allowed percentage as yet, but it will come sooner or later.


In the following compilation, M is the length of the longest pattern, m their total length, n the length of the searchable text, o the number of occurrences.


In mycology, the terms teleomorph, anamorph, and holomorph apply to portions of the life cycles of fungi in the phyla Ascomycota and Basidiomycota: Teleomorph: the sexual reproductive stage (morph), typically a fruiting body. Anamorph: an asexual reproductive stage (morph), often mold-like. When a single fungus produces multiple morphologically distinct anamorphs, these are called synanamorphs. Holomorph: the whole fungus, including anamorphs and teleomorph.


In order to recommend the most appropriate users to provide answers in a social network, we need to find approaches to detect users' authority in a social network. In the field of information retrieval, there has been a trend of research investigating ways to detect users' authority effectively and accurately in a social network. Cha et al. investigate possible metrics for determining authority users on popular social network Twitter. They propose the following three simple network-based metrics and discuss their usefulness in determining a user's influence.


Given iterates x 1 , x 2 , . .


With virtual memory, a contiguous range of virtual addresses can be mapped to several non-contiguous blocks of physical memory; this non-contiguous allocation is one of the benefits of paging.However, paged mapping causes another problem, internal fragmentation. This occurs when a program requests a block of memory that does not cleanly map into a page, for instance, if a program requests a 1 KB buffer to perform file work. In this case, the request results in an entire page being set aside even though only 1 KB of the page will ever be used; if pages are larger than 1 KB, the remainder of the page is wasted. If many small allocations of this sort are made, memory can be used up even though much of it remains empty.In some early microprocessor designs, memory management was performed by a separate integrated circuit such as the VLSI Technology VI475 (1986), the Motorola 68851 (1984) used with the Motorola 68020 CPU in the Macintosh II, or the Z8010 and Z8015 (1985) used with the Zilog Z8000 family of processors. Later microprocessors (such as the Motorola 68030 and the Zilog Z280) placed the MMU together with the CPU on the same integrated circuit, as did the Intel 80286 and later x86 microprocessors.


In probability theory, Kolmogorov equations, including Kolmogorov forward equations and Kolmogorov backward equations, characterize continuous-time Markov processes. In particular, they describe how the probability that a continuous-time Markov process is in a certain state changes over time.


These are normally used with vowels, but may occur with consonants. For example, in the Athabaskan language Hupa, voiceless velar fricatives distinguish three degrees of labialization, transcribed either /x/, /x̹/, /xʷ/ or /x/, /x̜ʷ/, /xʷ/. The extensions to the IPA has two additional symbols for degrees of rounding: Spread  and open-rounded  (as in English).


At the software level, portability of measurement description is the key attribute that distinguishes a synthetic instrument from the more commonly found instrumentation software—software that is limited to hardware scripting and data flow processing. Not all measurement related software systems inherently provide for the abstract, portable synthesis of measurements. Even if they do have such provisions, they may not typically be applied that way by users, especially if the system encourages non-abstracted access to hardware.


In recent years, there has been a surge in large data sets available on human movements. These data sets are usually obtained from cell phone or GPS data, with varying degrees of accuracy. For example, cell phone data is usually recorded whenever a call or a text message has been made or received by the user, and contains the location of the tower that the phone has connected to as well as the time stamp. In urban areas, user and the telecommunication tower might be only a few hundred meters away from each other, while in rural areas this distance might well be in region of a few kilometers.


For polynomials, the standard basis thus consists of the monomials and is commonly called monomial basis. For matrices M m × n {\displaystyle {\mathcal {M}}_{m\times n}} , the standard basis consists of the m×n-matrices with exactly one non-zero entry, which is 1. For example, the standard basis for 2×2 matrices is formed by the 4 matrices e 11 = ( 1 0 0 0 ) , e 12 = ( 0 1 0 0 ) , e 21 = ( 0 0 1 0 ) , e 22 = ( 0 0 0 1 ) . {\displaystyle \mathbf {e} _{11}={\begin{pmatrix}1&0\\0&0\end{pmatrix}},\quad \mathbf {e} _{12}={\begin{pmatrix}0&1\\0&0\end{pmatrix}},\quad \mathbf {e} _{21}={\begin{pmatrix}0&0\\1&0\end{pmatrix}},\quad \mathbf {e} _{22}={\begin{pmatrix}0&0\\0&1\end{pmatrix}}.}