In mathematics, a De Morgan algebra (named after Augustus De Morgan, a British mathematician and logician) is a structure A = (A, ∨, ∧, 0, 1, ¬) such that: (A, ∨, ∧, 0, 1) is a bounded distributive lattice, and ¬ is a De Morgan involution: ¬(x ∧ y) = ¬x ∨ ¬y and ¬¬x = x. (i.e. an involution that additionally satisfies De Morgan's laws)In a De Morgan algebra, the laws ¬x ∨ x = 1 (law of the excluded middle), and ¬x ∧ x = 0 (law of noncontradiction)do not always hold. In the presence of the De Morgan laws, either law implies the other, and an algebra which satisfies them becomes a Boolean algebra. Remark: It follows that ¬(x ∨ y) = ¬x ∧ ¬y, ¬1 = 0 and ¬0 = 1 (e.g. ¬1 = ¬1 ∨ 0 = ¬1 ∨ ¬¬0 = ¬(1 ∧ ¬0) = ¬¬0 = 0).


This says that the least significant n bits of k plus the remaining bits of k are equivalent to k modulo 2n−1. This equivalence can be used repeatedly until at most n bits remain. In this way, the remainder after dividing k by the Mersenne number 2n−1 is computed without using division.


In radio or wireless telephony, Private Line is a term trademarked by Motorola to describe an implementation of a Continuous Tone-Coded Squelch System (CTCSS), a method of using low-frequency subaudible tones to share a single radio channel among multiple users. Each user group would use a different low frequency tone. Motorola's trade name, especially the abbreviation PL, has become a genericized trademark for the method.


In mathematics the discrete least squares meshless (DLSM) method is a meshless method based on the least squares concept. The method is based on the minimization of a least squares functional, defined as the weighted summation of the squared residual of the governing differential equation and its boundary conditions at nodal points used to discretize the domain and its boundaries.


In the following figure, the minimization problem on the left side of the equation is illustrated. One seeks to vary x such that the vertical distance between the convex and concave curves at x is as small as possible. The position of the vertical line in the figure is the (approximate) optimum. The next figure illustrates the maximization problem on the right hand side of the above equation.


By varying the weighting parameter b, one can trace out the entire contract curve: If b = 1 the problem is the same as the previous problem, and it identifies an efficient point at one edge of the lens formed by the indifference curves of the initial endowment; if b = 0 all the weight is on person 2's utility instead of person 1's, and so the optimization identifies the efficient point on the other edge of the lens. As b varies smoothly between these two extremes, all the in-between points on the contract curve are traced out. Note that the above optimizations are not ones that the two people would actually engage in, either explicitly or implicitly. Instead, these optimizations are simply a way for the economist to identify points on the contract curve.


In the early 1980s, 1G was introduced as voice-only communication via "brick phones". Later in 1991, the development of 2G introduced Short Message Service (SMS) and Multimedia Messaging Service (MMS) capabilities, allowing picture messages to be sent and received between phones. In 1998, 3G was introduced to provide faster data-transmission speeds to support video calling and internet access. 4G was released in 2008 to support more demanding services such as gaming services, HD mobile TV, video conferencing, and 3D TV. 5G technology was initially released in 2019, but is still only available in certain areas.


In number theory, a Wilson prime is a prime number p {\displaystyle p} such that p 2 {\displaystyle p^{2}} divides ( p − 1 ) ! + 1 {\displaystyle (p-1)!+1} , where " ! {\displaystyle !} " denotes the factorial function; compare this with Wilson's theorem, which states that every prime p {\displaystyle p} divides ( p − 1 ) !


Then either the inner or outer circle participants – or the front or back line of desks – moves to the next space. Following a brief settling-in period, the host starts the second round of meetings. In Round Robin speed networking, a participant would meet an average of 10 contacts during an hour-long event.


Inverses are commonly used in groups—where every element is invertible, and rings—where invertible elements are also called units. They are also commonly used for operations that are not defined for all possible operands, such as inverse matrices and inverse functions.


Planes are further subdivided into Unicode blocks, which, unlike planes, do not have a fixed size. The 327 blocks defined in Unicode 15.0 cover 26% of the possible code point space, and range in size from a minimum of 16 code points (sixteen blocks) to a maximum of 65,536 code points (Supplementary Private Use Area-A and -B, which constitute the entirety of planes 15 and 16). For future usage, ranges of characters have been tentatively mapped out for most known current and ancient writing systems.


With an attentive and planned assessment, a homeowner can spot many problems that cause energy losses and make decisions about possible energy efficiency upgrades. During a home energy audit it is important to have a checklist of areas that were inspected as well as problems identified. Once the audit is completed, a plan for suggested actions needs to be developed.


In 1990, he asked "Is There a Double Smoothly Undulating Integer? ", and he computed "All Known Replicating Fibonacci Digits Less than One Billion". With his colleague John R. Hendricks, he was the first to compute the smallest perfect (nasik) magic tesseract. The "Pickover sequence" dealing with e and pi was named after him, as was the "Cliff random number generator" and the Pickover attractor, sometimes also referred to as the Clifford Attractor.


In probability theory and in particular in information theory, total correlation (Watanabe 1960) is one of several generalizations of the mutual information. It is also known as the multivariate constraint (Garner 1962) or multiinformation (Studený & Vejnarová 1999). It quantifies the redundancy or dependency among a set of n random variables.


Most proofs of soundness are trivial. For example, in an axiomatic system, proof of soundness amounts to verifying the validity of the axioms and that the rules of inference preserve validity (or the weaker property, truth). If the system allows Hilbert-style deduction, it requires only verifying the validity of the axioms and one rule of inference, namely modus ponens. (and sometimes substitution) Soundness properties come in two main varieties: weak and strong soundness, of which the former is a restricted form of the latter.


In statistical hypothesis testing, a result has statistical significance when a result at least as "extreme" would be very infrequent if the null hypothesis were true. More precisely, a study's defined significance level, denoted by α {\displaystyle \alpha } , is the probability of the study rejecting the null hypothesis, given that the null hypothesis is true; and the p-value of a result, p {\displaystyle p} , is the probability of obtaining a result at least as extreme, given that the null hypothesis is true. The result is statistically significant, by the standards of the study, when p ≤ α {\displaystyle p\leq \alpha } . The significance level for a study is chosen before data collection, and is typically set to 5% or much lower—depending on the field of study.In any experiment or observation that involves drawing a sample from a population, there is always the possibility that an observed effect would have occurred due to sampling error alone.


Here "simple" indicates that the underlying type theory is the theory of simple types, also called the simple theory of types. Leon Chwistek and Frank P. Ramsey proposed this as a simplification of the complicated and clumsy ramified theory of types specified in the Principia Mathematica by Alfred North Whitehead and Bertrand Russell. Simple types is sometimes also meant to exclude polymorphic and dependent types.


As many of these computers will give reduced privileges to ordinary users, it is possible that much of this has been done by network administrators. To some extent, this may be offset by better connectivity to home machines and increasing performance of home computers, especially those with GPUs, which have also benefited other volunteer computing projects such as Folding@Home. The spread of mobile computing devices provides another large resource for volunteer computing. For example, in 2012, Piotr Luszczek (a former doctoral student of Jack Dongarra) presented results showing that an iPad 2 matched the historical performance of a Cray-2 (the fastest computer in the world in 1985) on an embedded LINPACK benchmark.


A fuzzbox (or "fuzz box”) alters an audio signal until it is nearly a square wave and adds complex overtones by way of a frequency multiplier.A fuzz bass sound can be created by turning up the volume of a tube amp or transistor amp to the point that preamplifier tube (or transistor preamp) clipping" occurs. In practice, when a bass amp is "cranked" to its maximum volume, the fuzz tone will also include some power amplifier clipping. While some musicians seek out the additional "grit" provided by power amp clipping, audio engineers and bass technicians recommend avoiding power amp clipping, as it can blow speakers.


In contrast, the basis signals used to construct the signal subspace are identified empirically, and may for example be chirps, or particular characteristic shapes of transients after particular triggering events, rather than pure sinusoids. The Wiener filter grades smoothly between linear components that are dominated by signal, and linear components that are dominated by noise. The noise components are filtered out, but not quite completely; the signal components are retained, but not quite completely; and there is a transition zone which is partly accepted. In contrast, the signal subspace approach represents a sharp cut-off: an orthogonal component either lies within the signal subspace, in which case it is 100% accepted, or orthogonal to it, in which case it is 100% rejected. This reduction in dimensionality, abstracting the signal into a much shorter vector, can be a particularly desired feature of the method.In the simplest case signal subspace methods assume white noise, but extensions of the approach to colored noise removal and the evaluation of the subspace-based speech enhancement for robust speech recognition have also been reported.


These handicap ratings where a player receives points can be denoted with an "R" in front, where the "R" indicates the player is receiving points. It is also possible to have a handicap system where the player owes point due to being higher-skilled, in which case the same two-number system is also used. These owed handicaps are denoted with an "O" in front that is short for "owed".


It has been proved useful in recognizing targets (i.e. battle tanks) in infrared images of real scenes after training with synthetic images, since real images of those targets are scarce. Due to the limitation of the training set, how realistic the synthetic images are matters a lot when it comes to recognize the real scenes test set. The overall CNN networks structure contains 7 convolution layers, 3 max pooling layers and a Softmax layer as output.


The geometric mean of two numbers, a {\displaystyle a} and b {\displaystyle b} , is the length of one side of a square whose area is equal to the area of a rectangle with sides of lengths a {\displaystyle a} and b {\displaystyle b} . Similarly, the geometric mean of three numbers, a {\displaystyle a} , b {\displaystyle b} , and c {\displaystyle c} , is the length of one edge of a cube whose volume is the same as that of a cuboid with sides whose lengths are equal to the three given numbers. The geometric mean is one of the three classical Pythagorean means, together with the arithmetic mean and the harmonic mean. For all positive data sets containing at least one pair of unequal values, the harmonic mean is always the least of the three means, while the arithmetic mean is always the greatest of the three and the geometric mean is always in between (see Inequality of arithmetic and geometric means.)


In mathematics, graphs are useful in geometry and certain parts of topology such as knot theory. Algebraic graph theory has close links with group theory. Algebraic graph theory has been applied to many areas including dynamic systems and complexity.


This could be simply presented in small cards or stories – the developers estimate the time needed for the implementation of each card. Thus the work organization changes into self-pulling system – each morning during a stand-up meeting, each member of the team reviews what has been done yesterday, what is to be done today and tomorrow, and prompts for any inputs needed from colleagues or the customer. This requires transparency of the process, which is also beneficial for team communication. The myth underlying this principle is haste makes waste. However, lean implementation has shown that it is a good practice to deliver fast in order to see and analyze the output as early as possible.


In mathematics, the bicyclic semigroup is an algebraic object important for the structure theory of semigroups. Although it is in fact a monoid, it is usually referred to as simply a semigroup. It is perhaps most easily understood as the syntactic monoid describing the Dyck language of balanced pairs of parentheses. Thus, it finds common applications in combinatorics, such as describing binary trees and associative algebras.


During the second quarter of 2004, it launched new low-power Geode NX processors based on the K7 Thoroughbred architecture with speeds of fanless processors 667 MHz and 1 GHz, and 1.4 GHz processor with fan, of TDP 25 W. This technology is used in a variety of embedded systems (Casino slot machines and customer kiosks for instance), several UMPC designs in Asia markets, as well as the OLPC XO-1 computer, an inexpensive laptop computer intended to be distributed to children in developing countries around the world. The Geode LX processor was announced in 2005 and is said will continue to be available through 2015.AMD has also introduced 64-bit processors into its embedded product line starting with the AMD Opteron processor. Leveraging the high throughput enabled through HyperTransport and the Direct Connect Architecture these server-class processors have been targeted at high-end telecom and storage applications.


In mathematics, a vertex cycle cover (commonly called simply cycle cover) of a graph G is a set of cycles which are subgraphs of G and contain all vertices of G. If the cycles of the cover have no vertices in common, the cover is called vertex-disjoint or sometimes simply disjoint cycle cover. This is sometimes known as exact vertex cycle cover. In this case the set of the cycles constitutes a spanning subgraph of G. A disjoint cycle cover of an undirected graph (if it exists) can be found in polynomial time by transforming the problem into a problem of finding a perfect matching in a larger graph.If the cycles of the cover have no edges in common, the cover is called edge-disjoint or simply disjoint cycle cover.


In China, the Telecommunications Regulations of the People's Republic of China (promulgated on 25 September 2000), stipulated the Ministry of Industry and Information Technology (MIIT) as the government department regulating all telecommunications related activities, including electronic commerce. On the same day, the Administrative Measures on Internet Information Services were released, the first administrative regulations to address profit-generating activities conducted through the Internet, and lay the foundation for future regulations governing e-commerce in China. On 28 August 2004, the eleventh session of the tenth NPC Standing Committee adopted an Electronic Signature Law, which regulates data message, electronic signature authentication and legal liability issues. It is considered the first law in China's e-commerce legislation. It was a milestone in the course of improving China's electronic commerce legislation, and also marks the entering of China's rapid development stage for electronic commerce legislation.


Thus, in contrast to many Monte Carlo primality tests (randomized algorithms that can return a false positive), the primality testing algorithm based on Proth's theorem is a Las Vegas algorithm, always returning the correct answer but with a running time that varies randomly. Note that if a is chosen to be a quadratic nonresidue as described above, the runtime is constant, safe for the time spent on finding such a quadratic nonresidue. Finding such a value is very fast compared to the actual test.


In certain physics applications such as in the computation of bands in a periodic volume, it is often a case that the elements of a matrix will be very complicated functions of frequency and wavenumber, and the matrix will be non-singular (I.e., it has the inverse matrix.) for most combinations of frequency and wavenumber, but will also be singular (I.e., it does not have the inverse matrix.) for certain specific combinations.


In the late 1990s and early 2000s, the market shifted for buyers, but since 2003 and 2004, it has been a strong seller's market, with net-back as the best estimation for prices.. Research from Global Energy Monitor in 2019 warned that up to US$1.3 trillion in new LNG export and import infrastructure currently under development is at significant risk of becoming stranded, as global gas risks becoming oversupplied, particularly if the United States and Canada play a larger role.The current surge in unconventional oil and gas in the U.S. has resulted in lower gas prices in the U.S. This has led to discussions in Asia' oil linked gas markets to import gas based on Henry Hub index.


The concept of notational associativity described here is related to, but different from, the mathematical associativity. An operation that is mathematically associative, by definition requires no notational associativity. (For example, addition has the associative property, therefore it does not have to be either left associative or right associative.) An operation that is not mathematically associative, however, must be notationally left-, right-, or non-associative. (For example, subtraction does not have the associative property, therefore it must have notational associativity.)


In mathematics, a rotation map is a function that represents an undirected edge-labeled graph, where each vertex enumerates its outgoing neighbors. Rotation maps were first introduced by Reingold, Vadhan and Wigderson (“Entropy waves, the zig-zag graph product, and new constant-degree expanders”, 2002) in order to conveniently define the zig-zag product and prove its properties. Given a vertex v {\displaystyle v} and an edge label i {\displaystyle i} , the rotation map returns the i {\displaystyle i} 'th neighbor of v {\displaystyle v} and the edge label that would lead back to v {\displaystyle v} .


In the Japanese kantenji braille, the standard 8-dot Braille patterns 2678, 12678, 24678, and 124678 are the patterns related to Braille pattern dots-1356, since the two additional dots of kantenji patterns 01356, 13567, and 013567 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


The names of architectural styles (as well as their adaptations) varied between countries. Many homes combined the elements of several different styles and are not easily distinguishable as one particular style or another.


Those that remain are often used only in niche markets or as parts of other systems; of the designs from these traditional vendors, only SPARC and POWER have any significant remaining market.The ARM architecture is illustrative of the adaptations made by RISC vendors to respond to changing competitive circumstances, being first introduced to deliver higher performance in desktop computers such as the Acorn Archimedes, but also being introduced in embedded applications such as laser printer raster image processing. ARM, in partnership with Apple, developed a low-power design and then specialized in that market, which at the time was a niche. With the rise in mobile computing, especially after the introduction of the iPhone, ARM became the most widely used high-end CPU design in the market.Competition between RISC and conventional CISC approaches was also the subject of theoretical analysis in the early 1980s, leading, for example, to the iron law of processor performance.


So we take a sample of the k {\displaystyle k} , get a sampling weight W(k) for all sampled k {\displaystyle k} , and then sum up W ( k ) ⋅ Y ( k ) {\displaystyle W(k)\cdot Y(k)} for all sampled k {\displaystyle k} . One property usually common to the weights W ( k ) {\displaystyle W(k)} described here is that if we sum them over all sampled k {\displaystyle k} , then this sum is an estimate of the total number of units k {\displaystyle k} in the population (for example, the total employment, or the total number of items). Because we have a sample, this estimate of the total number of units in the population will differ from the true population total.


In the client-to-gateway implementation, one or more servers are protected behind an Accepting SDP Host such that the Accepting SDP Host acts as a gateway between the clients and the protected servers. This implementation can be used inside an enterprise network to mitigate common lateral movement attacks such as server scanning, OS and application vulnerability exploits, password cracking, man-in-the-middle, Pass-the-Hash (PtH), and others. Alternatively, it can be implemented on the Internet to isolate protected servers from unauthorized users and mitigate attacks such as denial of service, OS and application vulnerability exploits, password cracking, man-in-the-middle, and others.


In mathematics, in the field of group theory, a group is said to be strictly simple if it has no proper nontrivial ascendant subgroups. That is, G {\displaystyle G} is a strictly simple group if the only ascendant subgroups of G {\displaystyle G} are { e } {\displaystyle \{e\}} (the trivial subgroup), and G {\displaystyle G} itself (the whole group). In the finite case, a group is strictly simple if and only if it is simple. However, in the infinite case, strictly simple is a stronger property than simple.


If we assume that a function f: R n → R {\displaystyle f\colon {\textbf {R}}^{n}\to {\textbf {R}}} is differentiable (or even analytic) in each variable separately, it is not true that f {\displaystyle f} will necessarily be continuous. A counterexample in two dimensions is given by f ( x , y ) = x y x 2 + y 2 . {\displaystyle f(x,y)={\frac {xy}{x^{2}+y^{2}}}.} If in addition we define f ( 0 , 0 ) = 0 {\displaystyle f(0,0)=0} , this function has well-defined partial derivatives in x {\displaystyle x} and y {\displaystyle y} at the origin, but it is not continuous at origin. (Indeed, the limits along the lines x = y {\displaystyle x=y} and x = − y {\displaystyle x=-y} are not equal, so there is no way to extend the definition of f {\displaystyle f} to include the origin and have the function be continuous there.)


In order candidate for P after the current one c. valid (P, c): check whether candidate c is a solution for P. output (P, c): use the solution c of P as appropriate to the application.The next procedure must also tell when there are no more candidates for the instance P, after the current one c. A convenient way to do that is to return a "null candidate", some conventional data value Λ that is distinct from any real candidate. Likewise the first procedure should return Λ if there are no candidates at all for the instance P. The brute-force method is then expressed by the algorithm c ← first(P) while c ≠ Λ do if valid(P,c) then output(P, c) c ← next(P, c) end while For example, when looking for the divisors of an integer n, the instance data P is the number n. The call first(n) should return the integer 1 if n ≥ 1, or Λ otherwise; the call next(n,c) should return c + 1 if c < n, and Λ otherwise; and valid(n,c) should return true if and only if c is a divisor of n. (In fact, if we choose Λ to be n + 1, the tests n ≥ 1 and c < n are unnecessary. )The brute-force search algorithm above will call output for every candidate that is a solution to the given instance P. The algorithm is easily modified to stop after finding the first solution, or a specified number of solutions; or after testing a specified number of candidates, or after spending a given amount of CPU time.


As a result, the variance for the estimator in GAN is usually much larger than that in Wasserstein GAN. See also Figure 3 of.The problem with D J S {\displaystyle D_{JS}} is much more severe in actual machine learning situations. Consider training a GAN to generate ImageNet, a collection of photos of size 256-by-256.


In real mode or V86 mode, the size of a segment can range from 1 byte up to 65,536 bytes (using 16-bit offsets). The 16-bit segment selector in the segment register is interpreted as the most significant 16 bits of a linear 20-bit address, called a segment address, of which the remaining four least significant bits are all zeros. The segment address is always added to a 16-bit offset in the instruction to yield a linear address, which is the same as physical address in this mode. For instance, the segmented address 06EFh:1234h (here the suffix "h" means hexadecimal) has a segment selector of 06EFh, representing a segment address of 06EF0h, to which the offset is added, yielding the linear address 06EF0h + 1234h = 08124h.


In spite of its known drawbacks, one of the most widely used methods for community detection is modularity maximization. Modularity is a benefit function that measures the quality of a particular division of a network into communities. The modularity maximization method detects communities by searching over possible divisions of a network for one or more that have particularly high modularity. Since exhaustive search over all possible divisions is usually intractable, practical algorithms are based on approximate optimization methods such as greedy algorithms, simulated annealing, or spectral optimization, with different approaches offering different balances between speed and accuracy. A popular modularity maximization approach is the Louvain method, which iteratively optimizes local communities until global modularity can no longer be improved given perturbations to the current community state. An algorithm that utilizes the RenEEL scheme, which is an example of the Extremal Ensemble Learning (EEL) paradigm, is currently the best modularity maximizing algorithm.The usefulness of modularity optimization is questionable, as it has been shown that modularity optimization often fails to detect clusters smaller than some scale, depending on the size of the network (resolution limit); on the other hand the landscape of modularity values is characterized by a huge degeneracy of partitions with high modularity, close to the absolute maximum, which may be very different from each other.


If N − 1 and M − 1 are coprime, on the other hand, the only two fixed points are the upper-left and lower-right corners of the matrix. The number of cycles of any length k>1 is given by (Cate & Twigg, 1977): 1 k ∑ d | k μ ( k / d ) gcd ( N d − 1 , M N − 1 ) , {\displaystyle {\frac {1}{k}}\sum _{d|k}\mu (k/d)\gcd(N^{d}-1,MN-1),} where μ is the Möbius function and the sum is over the divisors d of k. Furthermore, the cycle containing a=1 (i.e. the second element of the first row of the matrix) is always a cycle of maximum length L, and the lengths k of all other cycles must be divisors of L (Cate & Twigg, 1977). For a given cycle C, every element x ∈ C {\displaystyle x\in C} has the same greatest common divisor d = gcd ( x , M N − 1 ) {\displaystyle d=\gcd(x,MN-1)} .


In network routing, VCG mechanisms are a family of payment schemes based on the added value concept. The basic idea of a VCG mechanism in network routing is to pay the owner of each link or node (depending on the network model) that is part of the solution, its declared cost plus its added value. In many routing problems, this mechanism is not only strategyproof, but also the minimum among all strategyproof mechanisms. In the case of network flows, unicast or multicast, a minimum cost flow (MCF) in graph G is calculated based on the declared costs dk of each of the links and payment is calculated as follows: Each link (or node) e k {\displaystyle \scriptstyle e_{k}} in the MCF is paid p k = d k + M C F ( G − e k ) − M C F ( G ) {\displaystyle p_{k}=d_{k}+MCF(G-e_{k})-MCF(G)} ,where MCF(G) indicates the cost of the minimum cost flow in graph G and G − ek indicates graph G without the link ek.


In software development, Linus's law is the assertion that "given enough eyeballs, all bugs are shallow". The law was formulated by Eric S. Raymond in his essay and book The Cathedral and the Bazaar (1999), and was named in honor of Linus Torvalds.A more formal statement is: "Given a large enough beta-tester and co-developer base, almost every problem will be characterized quickly and the fix obvious to someone." Presenting the code to multiple developers with the purpose of reaching consensus about its acceptance is a simple form of software reviewing. Researchers and practitioners have repeatedly shown the effectiveness of reviewing processes in finding bugs and security issues.


The Cantor set is an example of an uncountable set of Lebesgue measure 0 which is not of strong measure zero.Borel's conjecture states that every strong measure zero set is countable. It is now known that this statement is independent of ZFC (the Zermelo–Fraenkel axioms of set theory, which is the standard axiom system assumed in mathematics). This means that Borel's conjecture can neither be proven nor disproven in ZFC (assuming ZFC is consistent).


In modern computer systems, files are typically accessed using names (filenames). In some operating systems, the name is associated with the file itself. In others, the file is anonymous, and is pointed to by links that have names. In the latter case, a user can identify the name of the link with the file itself, but this is a false analogue, especially where there exists more than one link to the same file.


In the bijective base-26 system one may use the Latin alphabet letters "A" to "Z" to represent the 26 digit values one to twenty-six. (A=1, B=2, C=3, ..., Z=26) With this choice of notation, the number sequence (starting from 1) begins A, B, C, ..., X, Y, Z, AA, AB, AC, ..., AX, AY, AZ, BA, BB, BC, ... Each digit position represents a power of twenty-six, so for example, the numeral ABC represents the value 1 × 262 + 2 × 261 + 3 × 260 = 731 in base 10. Many spreadsheets including Microsoft Excel use this system to assign labels to the columns of a spreadsheet, starting A, B, C, ..., Z, AA, AB, ..., AZ, BA, ..., ZZ, AAA, etc. For instance, in Excel 2013, there can be up to 16384 columns (214 in binary code), labeled from A to XFD. A variant of this system is used to name variable stars. It can be applied to any problem where a systematic naming using letters is desired, while using the shortest possible strings.


In qualitative research, there are many ways of analyzing data gathered in the field. One of the two most common methods of data analysis are thematic analysis and narrative analysis. As mentioned before, the type of analysis a researcher decides to use depends on the research question asked, the researcher's field, and the researcher's personal method of choice.


They include standard JTAG (IEEE 1149.1), cJTAG (IEEE 1149.7) and 4-bit parallel trace interfaces (mainly used for system traces), supplemented by the ARM-specific Serial Wire Debug (SWD) standard. MIPI10/20/34 debug connectors became the standard for ARM-based embedded designs. Many embedded designs in the mobile space use high-speed parallel trace ports (up to 600 megabits per second per pin).


In the Japanese kantenji braille, the standard 8-dot Braille patterns 2578, 12578, 24578, and 124578 are the patterns related to Braille pattern dots-1346, since the two additional dots of kantenji patterns 01346, 13467, and 013467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


Various broadcast relay stations can help to extend a station's area by retransmitting them on the same or another channel. What is usually called a repeater in amateur radio is called a broadcast translator (different channel) or booster (same channel) in American broadcasting, or the much broader category or rebroadcasters in Canadian broadcasting (which includes more than just the low-power broadcasting used in the U.S.) Boosters are used only within the broadcast range of the parent station, and serve the same function locally as regional and national single-frequency networks do in Europe. Distributed transmission has also undergone tests in the U.S., but to preserve stations' market share in their home media markets, these will be limited to the broadcast area of a single large station. Satellite radio, which is designed for use without a dish, also uses ground repeaters in large cities due to the many obstructions their high-rise buildings cause to the many current and potential customers that are concentrated there.


In probability theory, an interacting particle system (IPS) is a stochastic process ( X ( t ) ) t ∈ R + {\displaystyle (X(t))_{t\in \mathbb {R} ^{+}}} on some configuration space Ω = S G {\displaystyle \Omega =S^{G}} given by a site space, a countably-infinite-order graph G {\displaystyle G} and a local state space, a compact metric space S {\displaystyle S} . More precisely IPS are continuous-time Markov jump processes describing the collective behavior of stochastically interacting components. IPS are the continuous-time analogue of stochastic cellular automata. Among the main examples are the voter model, the contact process, the asymmetric simple exclusion process (ASEP), the Glauber dynamics and in particular the stochastic Ising model.


In physics, attempts have been made to explain stretched exponential behaviour as a linear superposition of simple exponential decays. This requires a nontrivial distribution of relaxation times, ρ(u), which is implicitly defined by Alternatively, a distribution is used. ρ can be computed from the series expansion: For rational values of β, ρ(u) can be calculated in terms of elementary functions. But the expression is in general too complex to be useful except for the case β = 1/2 where Figure 2 shows the same results plotted in both a linear and a log representation. The curves converge to a Dirac delta function peaked at u = 1 as β approaches 1, corresponding to the simple exponential function. The moments of the original function can be expressed as The first logarithmic moment of the distribution of simple-exponential relaxation times is where Eu is the Euler constant.


The graph density of simple graphs is defined to be the ratio of the number of edges |E| with respect to the maximum possible edges. For undirected simple graphs, the graph density is: D = | E | ( | V | 2 ) = 2 | E | | V | ( | V | − 1 ) {\displaystyle D={\frac {|E|}{\binom {|V|}{2}}}={\frac {2|E|}{|V|(|V|-1)}}} For directed, simple graphs, the maximum possible edges is twice that of undirected graphs (as there are two directions to an edge) so the density is: D = | E | 2 ( | V | 2 ) = | E | | V | ( | V | − 1 ) {\displaystyle D={\frac {|E|}{2{\binom {|V|}{2}}}}={\frac {|E|}{|V|(|V|-1)}}} where E is the number of edges and V is the number of vertices in the graph.


In number theory, the Selberg sieve is a technique for estimating the size of "sifted sets" of positive integers which satisfy a set of conditions which are expressed by congruences. It was developed by Atle Selberg in the 1940s.


Non-interpolated string literals are sometimes referred to as "raw strings", but this is distinct from "raw string" in the sense of escaping. For example, in Python, a string prefixed with r or R has no escaping or interpolation, a normal string (no prefix) has escaping but no interpolation, and a string prefixed with f or F has escaping and interpolation. For example, the following Perl code: produces the output: Nancy said Hello World to the crowd of people.


In the United States, a disclaimer must be conspicuous in the contract, such as in a different kind of print or font that makes it stand out. On the other hand, express warranty, or any affirmation of fact or promise to the buyer or description of the good, oral or written, can be negated or limited only if such disclaimers are reasonable. UCC § 2-316(1) Some jurisdictions, however, limit the ability of sellers or manufacturers to disclaim the implied warranty of merchantability or fitness, such as Massachusetts. (Massachusetts General Laws, Chapter 106: Section 2-316A).


Meiser (1993) designed a fast algorithm to determine the face of an arrangement of hyperplanes containing an input point. Another question about an arrangement in real space is to decide how many regions are simplices (the n-dimensional generalization of triangles and tetrahedra).


The first problem to address is to determine whether a given prime is Elkies or Atkin. In order to do so, we make use of modular polynomials, which come from the study of modular forms and an interpretation of elliptic curves over the complex numbers as lattices.


]_{f}} which are composed by parallel computations. The ordinary denotation of α {\displaystyle \alpha } is simply whatever denotation it would have in a non-alternative-based system. The focus denotation of a constituent is typically the set of all ordinary denotations one could get by substituting a focused constituent for another expression of the same type.


This means that when something changes, previously unexchanged information needs to be exchanged, or two programs need to interoperate in a new way, the humans must get involved. Off-line, the parties must define and communicate between them the knowledge needed to make the change, and then recode the data structures and program logic to accommodate it, and then apply these changes to the database and the application. Then, and only then, can they implement the changes.


In some programming languages an operator may be ad hoc polymorphic, that is, have definitions for more than one kind of data, (such as in Java where the + operator is used both for the addition of numbers and for the concatenation of strings). Such an operator is said to be overloaded. In languages that support operator overloading by the programmer (such as C++) but have a limited set of operators, operator overloading is often used to define customized uses for operators. In the example IF ORDER_DATE > "12/31/2011" AND ORDER_DATE < "01/01/2013" THEN CONTINUE ELSE STOP, the operators are: > (greater than), AND and < (less than).


for every two objects A and B a set Mor(A,B) of things called morphisms from A to B. If f is in Mor(A,B), we write f: A → B. for every three objects A, B and C a binary operation Mor(A,B) × Mor(B,C) → Mor(A,C) called composition of morphisms. The composition of f: A → B and g: B → C is written as g ∘ f or gf.


In the case of a simple attack, a firewall could have a simple rule added to deny all incoming traffic from the attackers, based on protocols, ports, or the originating IP addresses. More complex attacks will however be hard to block with simple rules: for example, if there is an ongoing attack on port 80 (web service), it is not possible to drop all incoming traffic on this port because doing so will prevent the server from serving legitimate traffic. Additionally, firewalls may be too deep in the network hierarchy, with routers being adversely affected before the traffic gets to the firewall. Also, many security tools still do not support IPv6 or may not be configured properly, so the firewalls often might get bypassed during the attacks.


In order to support user interaction with application directories, several files have special status.


Where a member becomes aware that irregularities have occurred in relation to a client's tax affairs he should advise the client of the consequences, and the manner of disclosure. If necessary, appropriate specialist advice should be taken. Where a client refuses to follow the advice of a member in relation to issues involving disclosure, the member should consider whether he should continue to act.


In mathematics, the spiral optimization (SPO) algorithm is a metaheuristic inspired by spiral phenomena in nature. The first SPO algorithm was proposed for two-dimensional unconstrained optimization based on two-dimensional spiral models. This was extended to n-dimensional problems by generalizing the two-dimensional spiral model to an n-dimensional spiral model. There are effective settings for the SPO algorithm: the periodic descent direction setting and the convergence setting.


In the environment of convergent network, specific services with certain network technologies will receive different regulatory treatments. The 1996 Act created distinct regulatory categories for services that are provided by different network technologies. Besides the existing regulation framework for regulating telecommunications services and cable services in another title, the 1996 Act defines a category of services, “information services,” that distinguished from “telecommunications services” and was not subject to either telephone or cable regulation. “Information services” are consisted of the offering of a capability for generating, acquiring, storing, transforming, processing, retrieving, utilizing, or making available information via telecommunications.


However, over time, the weak verbs have become the normal form of verbs in all Germanic languages, with most strong verbs being reassigned to the weak class. For example, in Old English the verb to lock (lūcan) was strong (present tense ic lūce 'I lock', past tense ic lēac 'I locked'), but has now become weak. This transition is ongoing. For example, the English verb to cleave currently exists in both a conservative strong form (past tense I clove) and an innovative weak form (past tense I cleaved).


This can happen if datasets are regional and/or demographically partitioned. For example, datasets containing images of animals vary significantly from country to country. Concept drift (same label, different features): local nodes may share the same labels but some of them correspond to different features at different local nodes.


In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions. In other words, for every natural number k, there exist arithmetic progressions of primes with k terms. The proof is an extension of Szemerédi's theorem. The problem can be traced back to investigations of Lagrange and Waring from around 1770.


In the development of social networks, there has appeared a new economic phenomenon: doing business via social networks. For example, there are many users of WeChat called wei-businessmen (Wechat businessman, a new form of e-commerce in Wechat) who sell products on WeChat. Doing business via social networks is not that easy. The identities of users in social networks are not the same as that in the real world.


In statistics and machine learning, the bias–variance tradeoff is the property of a model that the variance of the parameter estimated across samples can be reduced by increasing the bias in the estimated parameters. The bias–variance dilemma or bias–variance problem is the conflict in trying to simultaneously minimize these two sources of error that prevent supervised learning algorithms from generalizing beyond their training set: The bias error is an error from erroneous assumptions in the learning algorithm. High bias can cause an algorithm to miss the relevant relations between features and target outputs (underfitting). The variance is an error from sensitivity to small fluctuations in the training set. High variance may result from an algorithm modeling the random noise in the training data (overfitting).The bias–variance decomposition is a way of analyzing a learning algorithm's expected generalization error with respect to a particular problem as a sum of three terms, the bias, variance, and a quantity called the irreducible error, resulting from noise in the problem itself.


In statistics and probability theory, the nonparametric skew is a statistic occasionally used with random variables that take real values. It is a measure of the skewness of a random variable's distribution—that is, the distribution's tendency to "lean" to one side or the other of the mean. Its calculation does not require any knowledge of the form of the underlying distribution—hence the name nonparametric. It has some desirable properties: it is zero for any symmetric distribution; it is unaffected by a scale shift; and it reveals either left- or right-skewness equally well. In some statistical samples it has been shown to be less powerful than the usual measures of skewness in detecting departures of the population from normality.


In mathematics, a Markov information source, or simply, a Markov source, is an information source whose underlying dynamics are given by a stationary finite Markov chain.


LDA can be generalized to multiple discriminant analysis, where c becomes a categorical variable with N possible states, instead of only two. Analogously, if the class-conditional densities p ( x → ∣ c = i ) {\displaystyle p({\vec {x}}\mid c=i)} are normal with shared covariances, the sufficient statistic for P ( c ∣ x → ) {\displaystyle P(c\mid {\vec {x}})} are the values of N projections, which are the subspace spanned by the N means, affine projected by the inverse covariance matrix. These projections can be found by solving a generalized eigenvalue problem, where the numerator is the covariance matrix formed by treating the means as the samples, and the denominator is the shared covariance matrix. See “Multiclass LDA” above for details.


In the following scenario a web browser is developed using defense in depth - the browser developers receive security training the codebase is checked automatically using security analysis tools the browser is regularly audited by an internal security team ... is occasionally audited by an external security team ... is executed inside a sandbox


"Abundancy" may also be expressed as σ − 1 ( n ) {\displaystyle \sigma _{-1}(n)} where σ k {\displaystyle \sigma _{k}} denotes a divisor function with σ k ( n ) {\displaystyle \sigma _{k}(n)} equal to the sum of the k-th powers of the divisors of n. The numbers 1 through 5 are all solitary. The smallest "friendly number" is 6, forming for example, the "friendly" pair 6 and 28 with "abundancy" σ(6) / 6 = (1+2+3+6) / 6 = 2, the same as σ(28) / 28 = (1+2+4+7+14+28) / 28 = 2. The shared value 2 is an integer in this case but not in many other cases.


In mathematics and logic, ambiguity can be considered to be an instance of the logical concept of underdetermination—for example, X = Y {\displaystyle X=Y} leaves open what the value of X is—while its opposite is a self-contradiction, also called inconsistency, paradoxicalness, or oxymoron, or in mathematics an inconsistent system—such as X = 2 , X = 3 {\displaystyle X=2,X=3} , which has no solution. Logical ambiguity and self-contradiction is analogous to visual ambiguity and impossible objects, such as the Necker cube and impossible cube, or many of the drawings of M. C. Escher.


In pharmacokinetics, a compartment is a defined volume of body fluids, typically of the human body, but also those of other animals with multiple organ systems. The meaning in this area of study is different from the concept of anatomic compartments, which are bounded by fasciae, the sheath of fibrous tissue that enclose mammalian organs. Instead, the concept focuses on broad types of fluidic systems. This analysis is used in attempts to mathematically describe distribution of small molecules throughout organisms with multiple compartments.


In some languages, any gender markers have been so eroded over time (possibly through deflexion) that they are no longer recognizable. Many German nouns, for example, do not indicate their gender through either meaning or form. In such cases a noun's gender must simply be memorized, and gender can be regarded as an integral part of each noun when considered as an entry in the speaker's lexicon. (This is reflected in dictionaries, which typically indicate the gender of noun headwords where applicable.) Second-language learners are often encouraged to memorize a modifier, usually a definite article, in conjunction with each noun—for example, a learner of French may learn the word for "chair" as la chaise (meaning "the chair"); this carries the information that the noun is chaise, and that it is feminine (because la is the feminine singular form of the definite article).


Other constituents (such as oblique, genitive, and object of comparative) are called nonterms (N). The predicate is marked (P). According to Geoffrey K. Pullum (1977), the GR hierarchy directly corresponds to the accessibility hierarchy: A schematic representation of a clause in this formalism might look like:


In the first series of experiments, experts in the use of the various techniques were tasked with both the creation of the index and its use against the sample queries. Each system had its own concept about how a query should be structured, which would today be known as a query language. Much of the criticism of the first experiments focused on whether the experiments were truly testing the systems, or the user's ability to translate the query into the query language.This led to the second series of experiments, Cranfield 2, that considered the question of converting the query into the language. To do this, instead of considering the generation of the query as a black box, each step was broken down.


In politics, emergent democracy represents the rise of political structures and behaviors without central planning and by the action of many individual participants, especially when mediated by the Internet. It has been likened to the democratic system of ancient Greece in the sense that people could publicly participate as much or as little as they please, although a form of representation exists which is based on personal trust networks instead of party affiliations. More recently, American writer and researcher Clay Shirky has referred to this as "the power of organizing without organizations."


Let the set of neighbors of node u {\displaystyle u} be denoted nbr  ( u ) {\displaystyle \operatorname {nbr} (u)} . The average degree is then μ = 1 N ∑ u ∈ V | nbr  ( u ) | = 2 M N ≥ 1 {\displaystyle \mu ={\frac {1}{N}}\sum _{u\in V}|\operatorname {nbr} (u)|={\frac {2M}{N}}\geq 1} . Let the number of "friends of friends" of node u {\displaystyle u} be denoted FF  ( u ) = ∑ v ∈ nbr  ( u ) | nbr  ( v ) | {\displaystyle \operatorname {FF} (u)=\sum _{v\in \operatorname {nbr} (u)}|\operatorname {nbr} (v)|} .


In most European countries the official accident statistics contain no information on rolling cars, only Great Britain can deliver official statistical data. Regarding other sources, only a few accident databases on rollover accidents exist. Although only less than 10% of all vehicle accidents with severe injuries involve rollovers, approximately 25% of all seriously injured occupants were involved in accidents where their car rolled. These numbers are currently increasing, as rollover frequency of several new vehicle types like mini vans, SUV or MPV is a lot higher than for most conventional cars.


In mathematics, in the realm of group theory, a group is said to be capable if it occurs as the inner automorphism group of some group. These groups were first studied by Reinhold Baer, who showed that a finite abelian group is capable if and only if it is a product of cyclic groups of orders n1,...,nk where ni divides ni+1 and nk–1=nk.


In 2017, 2.3 million out of Kickstarter's 7.9 million users had donated toward more than one project.Traditionally, journalists are not involved in advertising and marketing. Crowdfunding means that journalists are attracting funders while trying to remain independent, which may pose a conflict. Therefore, being directly involved with financial aspects can call journalistic integrity and journalistic objectivity into question.


In signal processing, independent component analysis (ICA) is a computational method for separating a multivariate signal into additive subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other. ICA is a special case of blind source separation. A common example application is the "cocktail party problem" of listening in on one person's speech in a noisy room.


In proof theory, particularly the proof theory of constructive mathematics based on the Curry–Howard correspondence, one often identifies a mathematical proposition with its set of proofs (if any). A given proposition may have many proofs, of course; according to the principle of proof irrelevance, normally only the truth of the proposition matters, not which proof was used. However, the Curry–Howard correspondence can turn proofs into algorithms, and differences between algorithms are often important. So proof theorists may prefer to identify a proposition with a setoid of proofs, considering proofs equivalent if they can be converted into one another through beta conversion or the like.


In regards to the typology of neolithic adzes, initially two types were distinguished, When width exceeds thickness they were named flat adzes (Flachhacke), when thickness exceeds width shoe-last adzes (Schuhleistenkeile), or high adzes. Within the latter group a distinction is sometimes made between intermediate Flomborn adzes and the higher Hinkelstein adzes (Buttler 1938; Bakels 1987; Merkel 1999). Later, subdivisions were made on the basis of metric characteristics into two groups (Schietzel 1965), six groups (Modderman 1970, 184) and finally two groups again (Dohrn-Ihmig 1983). All typologies were based on the width-height ratio, while Modderman added the absolute dimension. The wide variation, from small to large and from flat to high adzes, certainly reflects a functional differentiation, but the various types do not appear to be of chronological significance.


These schemata are needed to link the pure category to sensed phenomenal appearances because the categories are, as Kant says, heterogeneous with sense intuition. Categories and sensed phenomena, however, do share one characteristic: time. Succession is the form of sense impressions and also of the Category of causality. Therefore, time can be said to be the schema of Categories or pure concepts of the understanding.


That is, at 16 byte intervals. Since all segments are 64 KB long, this explains how overlap can occur between segments and why any location in the linear memory address space can be accessed with many segment:offset pairs. The actual location of the beginning of a segment in the linear address space can be calculated with segment×16.


This is computable in polynomial time as the determinant of a maximal principal submatrix of the Laplacian matrix of G, an early result in algebraic graph theory known as Kirchhoff’s Matrix–Tree theorem. Likewise, the dimension of the bicycle space at T G ( − 1 , − 1 ) {\displaystyle T_{G}(-1,-1)} can be computed in polynomial time by Gaussian elimination. For planar graphs, the partition function of the Ising model, i.e., the Tutte polynomial at the hyperbola H 2 {\displaystyle H_{2}} , can be expressed as a Pfaffian and computed efficiently via the FKT algorithm. This idea was developed by Fisher, Kasteleyn, and Temperley to compute the number of dimer covers of a planar lattice model.


Full named-entity recognition is often broken down, conceptually and possibly also in implementations, as two distinct problems: detection of names, and classification of the names by the type of entity they refer to (e.g. person, organization, or location). The first phase is typically simplified to a segmentation problem: names are defined to be contiguous spans of tokens, with no nesting, so that "Bank of America" is a single name, disregarding the fact that inside this name, the substring "America" is itself a name. This segmentation problem is formally similar to chunking.


In the 1920s, Louis Mordell posed a conjecture that implied that Fermat's equation has at most a finite number of nontrivial primitive integer solutions, if the exponent n is greater than two. This conjecture was proved in 1983 by Gerd Faltings, and is now known as Faltings's theorem.


In the event of a worst-case emergency, called a "design basis accident" in NRC regulations, the containment is designed to seal off and contain a meltdown. Redundant systems are installed to prevent a meltdown, but as a matter of policy, one is assumed to occur and thus the requirement for a containment building. For design purposes, the reactor vessel's piping is assumed to be breached, causing a "LOCA" (Loss Of Coolant Accident) where the water in the reactor vessel is released to the atmosphere inside the containment and flashes into steam.


In probability theory, the zero-truncated Poisson (ZTP) distribution is a certain discrete probability distribution whose support is the set of positive integers. This distribution is also known as the conditional Poisson distribution or the positive Poisson distribution. It is the conditional probability distribution of a Poisson-distributed random variable, given that the value of the random variable is not zero. Thus it is impossible for a ZTP random variable to be zero.


{\displaystyle \chi '=\sum _{i=1}^{n}k_{i}s_{i}^{2}.} where k i {\displaystyle k_{i}} is a real positive number, typically k i = 1 ν i + 1 {\displaystyle k_{i}={\frac {1}{\nu _{i}+1}}} . In general, the probability distribution of χ' cannot be expressed analytically.


In order to overcome the volume size limit of FAT16, while at the same time allowing DOS real-mode code to handle the format, Microsoft designed a new version of the file system, FAT32, which supported an increased number of possible clusters, but could reuse most of the existing code, so that the conventional memory footprint was increased by less than 5 KB under DOS. Cluster values are represented by 32-bit numbers, of which 28 bits are used to hold the cluster number.


For example, a common attack on asymmetric RSA relies on the fact that the encryption steps rely on the value of the key bits. Every bit is processed with a square operation and then a multiplication operation if and only if the bit is equal to 1. An attacker with a clear trace can deduce the key simply by observing where the multiplication operations are performed.


In practice we have much fewer processors than the matrix elements. We can replace the matrix elements with submatrices, so that every processor processes more values. The scalar multiplication and addition become sequential matrix multiplication and addition. The width and height of the submatrices will be N = n / p {\displaystyle N=n/{\sqrt {p}}} .


In prehistoric time, quarter square multiplication involved floor function; that some sources attribute to Babylonian mathematics (2000–1600 BC). Antoine Voisin published a table of quarter squares from 1 to 1000 in 1817 as an aid in multiplication. A larger table of quarter squares from 1 to 100000 was published by Samuel Laundy in 1856, and a table from 1 to 200000 by Joseph Blater in 1888.Quarter square multipliers were used in analog computers to form an analog signal that was the product of two analog input signals. In this application, the sum and difference of two input voltages are formed using operational amplifiers.


It would be superseded by Peripheral Component Interconnect (PCI), starting at speeds of 133 MB/s (32-bit at 33 MHz in the standard configuration) Thus for a short time, a market opening occurred where video card manufacturers and motherboard chipset makers created their own proprietary implementations of local buses to provide graphics cards direct access to the processor and system memory. This avoided the limitations of the ISA bus while being less costly than a "licensed IBM MCA machine". It is important to note that at the time the cost to migrate to an MCA architecture machine from an ISA machine was substantial.


In terms of a graph-based computational procedure, SMILES is a string obtained by printing the symbol nodes encountered in a depth-first tree traversal of a chemical graph. The chemical graph is first trimmed to remove hydrogen atoms and cycles are broken to turn it into a spanning tree. Where cycles have been broken, numeric suffix labels are included to indicate the connected nodes. Parentheses are used to indicate points of branching on the tree. The resultant SMILES form depends on the choices: of the bonds chosen to break cycles, of the starting atom used for the depth-first traversal, and of the order in which branches are listed when encountered.


In the execute stage, the instruction operations are carried out. Instructions are delayed in this step until all of their operands are available, eliminating RAW hazards. Program correctness is maintained through effective address calculation to prevent hazards through memory. If one or more of the operands is not yet available then: wait for operand to become available on the CDB. When all operands are available, then: if the instruction is a load or store Compute the effective address when the base register is available, and place it in the load/store buffer If the instruction is a load then: execute as soon as the memory unit is available Else, if the instruction is a store then: wait for the value to be stored before sending it to the memory unit Else, the instruction is an arithmetic logic unit (ALU) operation then: execute the instruction at the corresponding functional unit


In the PINN framework, initial and boundary conditions are not analytically satisfied, thus they need to be included in the loss function of the network to be simultaneously learned with the differential equation (DE) unknown functions. Having competing objectives during the network's training can lead to unbalanced gradients while using gradient-based techniques, which causes PINNs to often struggle to accurately learn the underlying DE solution. This drawback is overcome by using functional interpolation techniques such as the Theory of Functional Connections (TFC)'s constrained expression, in the Deep-TFC framework, which reduces the solution search space of constrained problems to the subspace of neural network that analytically satisfies the constraints. A further improvement of PINN and functional interpolation approach is given by the Extreme Theory of Functional Connections (X-TFC) framework, where a single-layer Neural Network and the extreme learning machine training algorithm are employed. X-TFC allows to improve the accuracy and performance of regular PINNs, and its robustness and reliability are proved for stiff problems, optimal control, aerospace, and rarefied gas dynamics applications.


A more efficient version of the algorithm shortcuts these steps, instead replacing the larger of the two numbers by its remainder when divided by the smaller of the two (with this version, the algorithm stops when reaching a zero remainder). With this improvement, the algorithm never requires more steps than five times the number of digits (base 10) of the smaller integer. This was proven by Gabriel Lamé in 1844 (Lamé's Theorem), and marks the beginning of computational complexity theory.


In the context modeling complexity the next-symbol predictions, of one or more statistical models, are combined or competing to yield a prediction that is based on events recorded in the past. The algorithmic information content derived from each symbol prediction can be used to compute algorithmic information profiles with a time proportional to the length of the sequence. The process has been applied to DNA sequence analysis.


These coverings are called "caps". Depending on the method used for the shadow volume, the front end may be covered by the object itself, and the rear end may sometimes be omitted (see depth pass below).


In mathematics and computer science, graph edit distance (GED) is a measure of similarity (or dissimilarity) between two graphs. The concept of graph edit distance was first formalized mathematically by Alberto Sanfeliu and King-Sun Fu in 1983. A major application of graph edit distance is in inexact graph matching, such as error-tolerant pattern recognition in machine learning.The graph edit distance between two graphs is related to the string edit distance between strings. With the interpretation of strings as connected, directed acyclic graphs of maximum degree one, classical definitions of edit distance such as Levenshtein distance,Hamming distance and Jaro–Winkler distance may be interpreted as graph edit distances between suitably constrained graphs. Likewise, graph edit distance is also a generalization of tree edit distance between rooted trees.


In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. Expressed algebraically, for quantities a {\displaystyle a} and b {\displaystyle b} with a > b > 0 {\displaystyle a>b>0} , where the Greek letter phi ( φ {\displaystyle \varphi } or ϕ {\displaystyle \phi } ) denotes the golden ratio. The constant φ {\displaystyle \varphi } satisfies the quadratic equation φ 2 = φ + 1 {\displaystyle \varphi ^{2}=\varphi +1} and is an irrational number with a value of The golden ratio was called the extreme and mean ratio by Euclid, and the divine proportion by Luca Pacioli, and also goes by several other names.Mathematicians have studied the golden ratio's properties since antiquity. It is the ratio of a regular pentagon's diagonal to its side and thus appears in the construction of the dodecahedron and icosahedron.


In computability theory, a general recursive function is a partial function from the integers to the integers; no algorithm can exist for deciding whether an arbitrary such function is in fact total. When arrow notation is used for functions, a partial function f {\displaystyle f} from X {\displaystyle X} to Y {\displaystyle Y} is sometimes written as f: X ⇀ Y , {\displaystyle f:X\rightharpoonup Y,} f: X ↛ Y , {\displaystyle f:X\nrightarrow Y,} or f: X ↪ Y . {\displaystyle f:X\hookrightarrow Y.} However, there is no general convention, and the latter notation is more commonly used for inclusion maps or embeddings.Specifically, for a partial function f: X ⇀ Y , {\displaystyle f:X\rightharpoonup Y,} and any x ∈ X , {\displaystyle x\in X,} one has either: f ( x ) = y ∈ Y {\displaystyle f(x)=y\in Y} (it is a single element in Y), or f ( x ) {\displaystyle f(x)} is undefined.For example, if f {\displaystyle f} is the square root function restricted to the integers f: Z → N , {\displaystyle f:\mathbb {Z} \to \mathbb {N} ,} defined by: f ( n ) = m {\displaystyle f(n)=m} if, and only if, m 2 = n , {\displaystyle m^{2}=n,} m ∈ N , n ∈ Z , {\displaystyle m\in \mathbb {N} ,n\in \mathbb {Z} ,} then f ( n ) {\displaystyle f(n)} is only defined if n {\displaystyle n} is a perfect square (that is, 0 , 1 , 4 , 9 , 16 , … {\displaystyle 0,1,4,9,16,\ldots } ). So f ( 25 ) = 5 {\displaystyle f(25)=5} but f ( 26 ) {\displaystyle f(26)} is undefined.


In the ASCII version of the format, the vertices and faces are each described one to a line with the numbers separated by white space. In the binary version, the data is simply packed closely together at the endianness specified in the header and with the data types given in the property records. For the common property list... representation for polygons, the first number for that element is the number of vertices that the polygon has and the remaining numbers are the indices of those vertices in the preceding vertex list.


In phylogenetics, the metric is often used to compute a distance between two trees. The treedist program in the PHYLIP suite offers this function, as does the RAxML_standard package, the DendroPy Python library (under the name "symmetric difference metric"), and R packages TreeDist (`RobinsonFoulds()` function) and phangorn (`treedist()` function). For comparing groups of trees, the fastest implementations include HashRF and MrsRF. The Robinson–Foulds metric has also been used in quantitative comparative linguistics to compute distances between trees that represent how languages are related to each other.


In the 1980s and 1990s, a variety of SVR4 versions of Unix were available commercially for the x86 PC platform. However, the market for commercial Unix on PCs declined after Linux and BSD became widely available. In late 1994, Eric S. Raymond discontinued his PC-clone UNIX Software Buyer's Guide on USENET, stating, "The reason I am dropping this is that I run Linux now, and I no longer find the SVr4 market interesting or significant. "In 1998, a confidential memo at Microsoft stated, "Linux is on track to eventually own the x86 UNIX market", and further predicted, "I believe that Linux – moreso than NT – will be the biggest threat to SCO in the near future. "An InfoWorld article from 2001 characterized SCO UnixWare as having a "bleak outlook" due to being "trounced" in the market by Linux and Solaris, and IDC predicted that SCO would "continue to see a shrinking share of the market".


Babai and Szemerédi prove that every element of a finite group G has an SLP of length O(log2|G|) in every generating set. An efficient solution to the constructive membership problem is crucial to many group-theoretic algorithms. It can be stated in terms of SLPs as follows.


Similarly for the generator in Wasserstein GAN. For Wasserstein GAN, D W G A N {\displaystyle D_{WGAN}} has gradient 1 almost everywhere, while for GAN, ln  ( 1 − D ) {\displaystyle \ln(1-D)} has flat gradient in the middle, and steep gradient elsewhere.


In numerical analysis, one or more guard digits can be used to reduce the amount of roundoff error. For example, suppose that the final result of a long, multi-step calculation can be safely rounded off to N decimal places. That is to say, the roundoff error introduced by this final roundoff makes a negligible contribution to the overall uncertainty. However, it is quite likely that it is not safe to round off the intermediate steps in the calculation to the same number of digits.


In mathematical logic, Tarski's high school algebra problem was a question posed by Alfred Tarski. It asks whether there are identities involving addition, multiplication, and exponentiation over the positive integers that cannot be proved using eleven axioms about these operations that are taught in high-school-level mathematics. The question was solved in 1980 by Alex Wilkie, who showed that such unprovable identities do exist.


In response to some of these variants, and to other feedback, the paper "PRIMES is in P" was updated with a new formulation of the AKS algorithm and of its proof of correctness. (This version was eventually published in Annals of Mathematics.) While the basic idea remained the same, r was chosen in a new manner, and the proof of correctness was more coherently organized.


In modern positional numbers systems, such as the decimal system, the digits and their positions in the representation of an integer, for example, 45, are a shorthand notation for a polynomial in the radix or base, in this case, 4 × 101 + 5 × 100. As another example, in radix 5, a string of digits such as 132 denotes the (decimal) number 1 × 52 + 3 × 51 + 2 × 50 = 42. This representation is unique. Let b be a positive integer greater than 1.


For example, his f20 cores had 31 5-bit instructions, which fit four to a 20-bit word. RISC chips now dominate the market for 32-bit embedded systems. Smaller RISC chips are even growing common in the cost-sensitive 8-bit embedded-system market.


In summary, backtracking line search (and its modifications) is a method which is easy to implement, is applicable for very general functions, has very good theoretical guarantee (for both convergence to critical points and avoidance of saddle points) and works well in practice. Several other methods which have good theoretical guarantee, such as diminishing learning rates or standard GD with learning rate <1/L – both require the gradient of the objective function to be Lipschitz continuous, turn out to be a special case of Backtracking line search or satisfy Armijo's condition. Even though a priori one needs the cost function to be continuously differentiable to apply this method, in practice one can apply this method successfully also for functions which are continuously differentiable on a dense open subset such as f ( t ) = | t | {\displaystyle f(t)=|t|} or f ( t ) = R e L u ( t ) = max { t , 0 } {\displaystyle f(t)=ReLu(t)=\max\{t,0\}} .


In the 1960s and 1970s, Gallagher proved several results in large sieve methods in analytic number theory and simplified key ingredients used in the proof of the Bombieri–Vinogradov theorem. He also applied the large sieve to study the asymptotics of Galois groups of monic integral polynomials of bounded height, improving on results by van der Waerden.In 1971, he invented the larger sieve.


Recently, the graph partition problem has gained importance due to its application for clustering and detection of cliques in social, pathological and biological networks. For a survey on recent trends in computational methods and applications see Buluc et al. (2013). Two common examples of graph partitioning are minimum cut and maximum cut problems.


With the advent of high-speed computers, the minimization problem can be solved iteratively with adequate speed, and the communalities are calculated in the process, rather than being needed beforehand. The MinRes algorithm is particularly suited to this problem, but is hardly the only iterative means of finding a solution. If the solution factors are allowed to be correlated (as in 'oblimin' rotation, for example), then the corresponding mathematical model uses skew coordinates rather than orthogonal coordinates.


In mathematics, computer science and logic, convergence is the idea that different sequences of transformations come to a conclusion in a finite amount of time (the transformations are terminating), and that the conclusion reached is independent of the path taken to get to it (they are confluent). More formally, a preordered set of term rewriting transformations are said to be convergent if they are confluent and terminating.


{\displaystyle \left(\mathbf {P} ^{T}\mathbf {A} \mathbf {P} \right)\left(\mathbf {P} ^{T}\mathbf {x} \right)=\mathbf {P} ^{T}\mathbf {b} .} The problem of finding the best ordering is an NP-complete problem and is thus intractable, so heuristic methods are used instead.


In spectral graph theory, an eigenvalue of a graph is defined as an eigenvalue of the graph's adjacency matrix A {\displaystyle A} , or (increasingly) of the graph's Laplacian matrix due to its discrete Laplace operator, which is either D − A {\displaystyle D-A} (sometimes called the combinatorial Laplacian) or I − D − 1 / 2 A D − 1 / 2 {\displaystyle I-D^{-1/2}AD^{-1/2}} (sometimes called the normalized Laplacian), where D {\displaystyle D} is a diagonal matrix with D i i {\displaystyle D_{ii}} equal to the degree of vertex v i {\displaystyle v_{i}} , and in D − 1 / 2 {\displaystyle D^{-1/2}} , the i {\displaystyle i} th diagonal entry is 1 / deg  ( v i ) {\textstyle 1/{\sqrt {\deg(v_{i})}}} . The k {\displaystyle k} th principal eigenvector of a graph is defined as either the eigenvector corresponding to the k {\displaystyle k} th largest or k {\displaystyle k} th smallest eigenvalue of the Laplacian. The first principal eigenvector of the graph is also referred to merely as the principal eigenvector. The principal eigenvector is used to measure the centrality of its vertices.


In the digital realm, there can be any number of conventional primary colors making up an image; a channel in this case is extended to be the grayscale image based on any such conventional primary color. By extension, a channel is any grayscale image of the same dimension as and associated with the original image. Channel is a conventional term used to refer to a certain component of an image. In reality, any image format can use any algorithm internally to store images.


The case where the classical communication is replaced by quantum communication was considered in. This is known as the Fully Quantum Slepian-Wolf Theorem, since everything is sent down the quantum channel.


Some important languages used in OGC-compliant systems are described in the following. XML stands for eXtensible Markup language and is widely used for displaying and interpreting data from computers. Thus the development of a web-based GI system requires several useful XML encodings that can effectively describe two-dimensional graphics such as maps SVG and, at the same time, store and transfer simple features GML.


In statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model. The resulting fitted model can be used to summarize the data, to predict unobserved values from the same system, and to understand the mechanisms that may underlie the system. Mathematically, linear least squares is the problem of approximately solving an overdetermined system of linear equations A x = b, where b is not an element of the column space of the matrix A. The approximate solution is realized as an exact solution to A x = b', where b' is the projection of b onto the column space of A. The best approximation is then that which minimizes the sum of squared differences between the data values and their corresponding modeled values. The approach is called linear least squares since the assumed function is linear in the parameters to be estimated.


In preparation to the attack, weaknesses in the key schedule of KTANTAN that allows the 3-subset MITM attack was identified. Since only two key-bits are used each round, the diffusion of the key per round is small - the safety lies in the number of rounds. Due to this structure of the key-schedule, it was possible to find a large number of consecutive rounds, which never utilized certain key-bits. More precisely, the authors of the attack found that: Round 1 to 111 never uses the key-bits: k 32 , k 39 , k 44 , k 61 , k 66 , k 75 {\displaystyle k_{32},k_{39},k_{44},k_{61},k_{66},k_{75}} Round 131 to 254 never uses the key-bits: k 3 , k 20 , k 41 , k 47 , k 63 , k 74 {\displaystyle k_{3},k_{20},k_{41},k_{47},k_{63},k_{74}} This characteristics of the key-schedule is used for staging the 3-subset MITM attack, as we now are able to split the cipher into two blocks with independent key-bits. The parameters for the attack are thus: A 0 {\displaystyle A_{0}} = the keybits used by both blocks (which means the rest 68 bits not mentioned above) A 1 {\displaystyle A_{1}} = the keybits used only by the first block (defined by round 1-111) A 2 {\displaystyle A_{2}} = the keybits used only by the second block (defined by round 131-254)


In mathematics, the mediant of two fractions, generally made up of four positive integers a c {\displaystyle {\frac {a}{c}}\quad } and b d {\displaystyle \quad {\frac {b}{d}}\quad } is defined as a + b c + d . {\displaystyle \quad {\frac {a+b}{c+d}}.} That is to say, the numerator and denominator of the mediant are the sums of the numerators and denominators of the given fractions, respectively.


The area of a square is equal to the product of two of its sides (follows from 3).Next, each top square is related to a triangle congruent with another triangle related in turn to one of two rectangles making up the lower square. The proof is as follows: Let ACB be a right-angled triangle with right angle CAB.


In mathematical logic, formation rules are rules for describing which strings of symbols formed from the alphabet of a formal language are syntactically valid within the language. These rules only address the location and manipulation of the strings of the language. It does not describe anything else about a language, such as its semantics (i.e. what the strings mean). (See also formal grammar).


In mathematics, particularly in category theory, a morphism is a structure-preserving map from one mathematical structure to another one of the same type. The notion of morphism recurs in much of contemporary mathematics. In set theory, morphisms are functions; in linear algebra, linear transformations; in group theory, group homomorphisms; in analysis and topology, continuous functions, and so on.


In some OWL flavors like OWL1-DL, entities can be either classes or instances, but cannot be both. This limitations forbids metaclasses and metamodeling. This is not the case in the OWL1 full flavor, but this allows the model to be computationally undecidable. In OWL2, metaclasses can implemented with punning, that is a way to treat classes as if they were individuals. Other approaches have also been proposed and used to check the properties of ontologies at a meta level.


The eigenvectors corresponding to the smaller eigenvalues will tend to be very sensitive to the exact choice of training data, and it is often necessary to use regularisation as described in the next section. If classification is required, instead of dimension reduction, there are a number of alternative techniques available.


Computers usually solve square systems of linear equations using LU decomposition, and it is also a key step when inverting a matrix or computing the determinant of a matrix. The LU decomposition was introduced by the Polish astronomer Tadeusz Banachiewicz in 1938. To quote: "It appears that Gauss and Doolittle applied the method  only to symmetric equations. More recent authors, for example, Aitken, Banachiewicz, Dwyer, and Crout … have emphasized the use of the method, or variations of it, in connection with non-symmetric problems … Banachiewicz … saw the point … that the basic problem is really one of matrix factorization, or “decomposition” as he called it." It's also referred to as LR decomposition (factors into left and right triangular matrices).


In optimization, a descent direction is a vector p ∈ R n {\displaystyle \mathbf {p} \in \mathbb {R} ^{n}} that points towards a local minimum x ∗ {\displaystyle \mathbf {x} ^{*}} of an objective function f: R n → R {\displaystyle f:\mathbb {R} ^{n}\to \mathbb {R} } . Computing x ∗ {\displaystyle \mathbf {x} ^{*}} by an iterative method, such as line search defines a descent direction p k ∈ R n {\displaystyle \mathbf {p} _{k}\in \mathbb {R} ^{n}} at the k {\displaystyle k} th iterate to be any p k {\displaystyle \mathbf {p} _{k}} such that ⟨ p k , ∇ f ( x k ) ⟩ < 0 {\displaystyle \langle \mathbf {p} _{k},\nabla f(\mathbf {x} _{k})\rangle <0} , where ⟨ , ⟩ {\displaystyle \langle ,\rangle } denotes the inner product. The motivation for such an approach is that small steps along p k {\displaystyle \mathbf {p} _{k}} guarantee that f {\displaystyle \displaystyle f} is reduced, by Taylor's theorem. Using this definition, the negative of a non-zero gradient is always a descent direction, as ⟨ − ∇ f ( x k ) , ∇ f ( x k ) ⟩ = − ⟨ ∇ f ( x k ) , ∇ f ( x k ) ⟩ < 0 {\displaystyle \langle -\nabla f(\mathbf {x} _{k}),\nabla f(\mathbf {x} _{k})\rangle =-\langle \nabla f(\mathbf {x} _{k}),\nabla f(\mathbf {x} _{k})\rangle <0} .


In mathematics, an interval contractor (or contractor for short) associated to a set X {\displaystyle X} is an operator C {\displaystyle C} which associates to a hyperrectangle  {\displaystyle } in R n {\displaystyle {\mathbf {R}}^{n}} another box C (  ) {\displaystyle C()} of R n {\displaystyle {\mathbf {R}}^{n}} such that the two following properties are always satisfied: C (  ) ⊂  {\displaystyle C()\subset } (contractance property) C (  ) ∩ X =  ∩ X {\displaystyle C()\cap X=\cap X} (completeness property)A contractor associated to a constraint (such as an equation or an inequality) is a contractor associated to the set X {\displaystyle X} of all x {\displaystyle x} which satisfy the constraint. Contractors make it possible to improve the efficiency of branch-and-bound algorithms classically used in interval analysis.


In textbooks, channel length modulation in active mode usually is described using the Shichman–Hodges model, accurate only for old technology: where I D {\displaystyle I_{\text{D}}} = drain current, K n ′ {\displaystyle K'_{n}} = technology parameter sometimes called the transconductance coefficient, W, L = MOSFET width and length, V GS {\displaystyle V_{\text{GS}}} = gate-to-source voltage, V th {\displaystyle V_{\text{th}}} =threshold voltage, V DS {\displaystyle V_{\text{DS}}} = drain-to-source voltage, V DS,sat = V GS − V th {\displaystyle V_{\text{DS,sat}}=V_{\text{GS}}-V_{\text{th}}} , and λ = channel-length modulation parameter. In the classic Shichman–Hodges model, V th {\displaystyle V_{\text{th}}} is a device constant, which reflects the reality of transistors with long channels.


In mathematics, a strictly convex space is a normed vector space (X, || ||) for which the closed unit ball is a strictly convex set. Put another way, a strictly convex space is one for which, given any two distinct points x and y on the unit sphere ∂B (i.e. the boundary of the unit ball B of X), the segment joining x and y meets ∂B only at x and y. Strict convexity is somewhere between an inner product space (all inner product spaces being strictly convex) and a general normed space in terms of structure. It also guarantees the uniqueness of a best approximation to an element in X (strictly convex) out of a convex subspace Y, provided that such an approximation exists. If the normed space X is complete and satisfies the slightly stronger property of being uniformly convex (which implies strict convexity), then it is also reflexive by Milman-Pettis theorem.


For high-dimensional data, many of the existing methods fail due to the curse of dimensionality, which renders particular distance functions problematic in high-dimensional spaces. This led to new clustering algorithms for high-dimensional data that focus on subspace clustering (where only some attributes are used, and cluster models include the relevant attributes for the cluster) and correlation clustering that also looks for arbitrary rotated ("correlated") subspace clusters that can be modeled by giving a correlation of their attributes. Examples for such clustering algorithms are CLIQUE and SUBCLU.Ideas from density-based clustering methods (in particular the DBSCAN/OPTICS family of algorithms) have been adapted to subspace clustering (HiSC, hierarchical subspace clustering and DiSH) and correlation clustering (HiCO, hierarchical correlation clustering, 4C using "correlation connectivity" and ERiC exploring hierarchical density-based correlation clusters).


In most post-Soviet states DD.MM.YYYY format is used with dots as separators and with leading zeros. Some, such as Lithuania, have adopted the ISO 8601 YYYY-MM-DD format; previously a mixed standard with ISO 8601 order but dots as separators was in use.


Since this relaxation in US export restrictions, and because most personal computers connected to the Internet include US-sourced web browsers such as Firefox or Internet Explorer, almost every Internet user worldwide has potential access to quality cryptography via their browsers (e.g., via Transport Layer Security). The Mozilla Thunderbird and Microsoft Outlook E-mail client programs similarly can transmit and receive emails via TLS, and can send and receive email encrypted with S/MIME. Many Internet users do not realize that their basic application software contains such extensive cryptosystems. These browsers and email programs are so ubiquitous that even governments whose intent is to regulate civilian use of cryptography generally do not find it practical to do much to control distribution or use of cryptography of this quality, so even when such laws are in force, actual enforcement is often effectively impossible.


A suitable generalization of the first definition is: Let D {\displaystyle D} be a subset of R n . {\displaystyle \mathbb {R} ^{n}.}


It is the smallest finite non-abelian group. A common example from physics is the rotation group SO(3) in three dimensions (for example, rotating something 90 degrees along one axis and then 90 degrees along a different axis is not the same as doing them in reverse order). Both discrete groups and continuous groups may be non-abelian. Most of the interesting Lie groups are non-abelian, and these play an important role in gauge theory.


Finally, this generates two clearly different proposals: "cheap printer – expensive ink" or "expensive printer – cheap ink". Ultimately, the consumer decision depends on their reference interest rate or their time preference. From an economics viewpoint, there is a clear trade-off between cost per copy and cost of the printer.


In probability, statistics and related fields, a Poisson point process is a type of random mathematical object that consists of points randomly located on a mathematical space with the essential feature that the points occur independently of one another. The Poisson point process is often called simply the Poisson process, but it is also called a Poisson random measure, Poisson random point field or Poisson point field. This point process has convenient mathematical properties, which has led to its being frequently defined in Euclidean space and used as a mathematical model for seemingly random processes in numerous disciplines such as astronomy, biology, ecology, geology, seismology, physics, economics, image processing, and telecommunications.The process is named after French mathematician Siméon Denis Poisson despite Poisson's never having studied the process. Its name derives from the fact that if a collection of random points in some space forms a Poisson process, then the number of points in a region of finite size is a random variable with a Poisson distribution.


In the Visual Basic (classic) language, subprograms are termed functions or subs (or methods when associated with a class). Visual Basic 6 uses various terms called types to define what is being passed as a parameter. By default, an unspecified variable is registered as a variant type and can be passed as ByRef (default) or ByVal. Also, when a function or sub is declared, it is given a public, private, or friend designation, which determines whether it can be accessed outside the module or project that it was declared in.


In the United States, each wireless network controls how their MDCs will be used. As such, when wireless customers call a MDC, they're call is routed to the end user that their carrier selects.


Evaluating the cross-products: | e x e y e z − x A 0 0 0 R 0 0 | + | e x e y e z L − x A 0 0 0 R B 0 | = − x A R 0 e z + ( L − x A ) R B e z = 0 . {\displaystyle \left|{\begin{matrix}\mathbf {e} _{x}&\mathbf {e} _{y}&\mathbf {e} _{z}\\-x_{A}&0&0\\0&R_{0}&0\end{matrix}}\right|+\left|{\begin{matrix}\mathbf {e} _{x}&\mathbf {e} _{y}&\mathbf {e} _{z}\\L-x_{A}&0&0\\0&R_{B}&0\end{matrix}}\right|=-x_{A}R_{0}\,\mathbf {e} _{z}+(L-x_{A})R_{B}\,\mathbf {e} _{z}=0\,.}


ASK query Used to provide a simple True/False result for a query on a SPARQL endpoint. DESCRIBE query Used to extract an RDF graph from the SPARQL endpoint, the content of which is left to the endpoint to decide, based on what the maintainer deems as useful information.Each of these query forms takes a WHERE block to restrict the query, although, in the case of the DESCRIBE query, the WHERE is optional. SPARQL 1.1 specifies a language for updating the database with several new query forms.


In telecommunications, Continuous Tone-Coded Squelch System or CTCSS is one type of in-band signaling that is used to reduce the annoyance of listening to other users on a shared two-way radio communication channel. It is sometimes referred to as tone squelch or PL for Private Line, a trademark of Motorola. It does this by adding a low frequency audio tone to the voice. Where more than one group of users is on the same radio frequency (called co-channel users), CTCSS circuitry mutes those users who are using a different CTCSS tone or no CTCSS.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 23567, 123567, 234567, and 1234567 are the patterns related to Braille pattern dots-12345, since the two additional dots of kantenji patterns 012345, 123457, and 0123457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


Having established the necessary notions, the theorem is stated as follows. Chomsky–Schützenberger theorem. If L {\displaystyle L} is a context-free language admitting an unambiguous context-free grammar, and a k := | L ∩ Σ k | {\displaystyle a_{k}:=|L\ \cap \Sigma ^{k}|} is the number of words of length k {\displaystyle k} in L {\displaystyle L} , then G ( x ) = ∑ k = 0 ∞ a k x k {\displaystyle G(x)=\sum _{k=0}^{\infty }a_{k}x^{k}} is a power series over N {\displaystyle \mathbb {N} } that is algebraic over Q ( x ) {\displaystyle \mathbb {Q} (x)} .Proofs of this theorem are given by Kuich & Salomaa (1985), and by Panholzer (2005).


Given 2 1 × 0.100 2 − 2 0 × 0.111 2 {\displaystyle 2^{1}\times 0.100_{2}-2^{0}\times 0.111_{2}} we have to line up the binary points. This means we must add an extra digit to the first operand—a guard digit. This gives us 2 1 × 0.1000 2 − 2 1 × 0.0111 2 {\displaystyle 2^{1}\times 0.1000_{2}-2^{1}\times 0.0111_{2}} .


Examples of phonemic or distinctive features are: ,  (binary features) and  (a unary feature; also a place feature). Surface representations can be expressed as the result of rules acting on the features of the underlying representation. These rules are formulated in terms of transformations on features.


It is also possible to find a simultaneous embedding with fixed edges for any pair of a planar graph and a tree. It is an open question whether the existence of a simultaneous embedding with fixed edges for two given graphs can be tested in polynomial time. However, for three or more graphs, the problem is NP-complete. When simultaneous embeddings with fixed edges do exist, they can be found in polynomial time for pairs of outerplanar graphs, and for Biconnected graphs, i.e. pairs of graphs whose intersection is biconnected.


In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers a, b, and c satisfy the equation an + bn = cn for any integer value of n greater than 2. The cases n = 1 and n = 2 have been known since antiquity to have infinitely many solutions.The proposition was first stated as a theorem by Pierre de Fermat around 1637 in the margin of a copy of Arithmetica. Fermat added that he had a proof that was too large to fit in the margin. Although other statements claimed by Fermat without proof were subsequently proven by others and credited as theorems of Fermat (for example, Fermat's theorem on sums of two squares), Fermat's Last Theorem resisted proof, leading to doubt that Fermat ever had a correct proof.


The analyst must learn the set of joint conditional opinions ω Z | X Y {\displaystyle \omega _{Z|XY}} in order to apply the deduction operator and derive the marginal opinion ω Z ‖ X Y {\displaystyle \omega _{Z\|XY}} on the variable Z {\displaystyle Z} . The conditional opinions express a conditional relationship between the parent variables and the child variable. The deduced opinion is computed as ω Z ‖ X Y = ω Z | X Y ⊚ ω X Y {\displaystyle \omega _{Z\|XY}=\omega _{Z|XY}\circledcirc \omega _{XY}} .


In survey methodology, probability-proportional-to-size (pps) sampling is a sampling process where each element of the population (of size N) has some (independent) chance p i {\displaystyle p_{i}} to be selected to the sample when performing one draw. This p i {\displaystyle p_{i}} is proportional to some known quantity x i {\displaystyle x_{i}} so that p i = x i ∑ i = 1 N x i {\displaystyle p_{i}={\frac {x_{i}}{\sum _{i=1}^{N}x_{i}}}} . : 97 One of the cases this occurs in, as developed by Hanson and Hurwitz in 1943, is when we have several clusters of units, each with a different (known upfront) number of units, then each cluster can be selected with a probability that is proportional to the number of units inside it. : 250 So, for example, if we have 3 clusters with 10, 20 and 30 units each, then the chance of selecting the first cluster will be 1/6, the second would be 1/3, and the third cluster will be 1/2.


Expectancy is defined as the individual's subjectively held probability that a given action will lead to a given outcome. It can range from zero to one, with one representing 100% confidence in the outcome. For example, a person may entertain a given level of belief that they can make a foul shot in basketball or that an additional hour of study will improve their grade on an examination.


For each input command, a state-graph (or statetable or extended finite state automaton) is defined that provides a plan (or procedure for making a plan) for accomplishing the commanded task. The input command selects (or causes to be generated) an appropriate state-table, the execution of which generates a series of output commands to units at the next lower echelon. The library of state-tables contains a set of statesensitive procedural rules that identify all the task branching conditions and specify the corresponding state transition and output command parameters.The result of step 3 is that each organizational unit has for each input command a state-table of ordered production rules, each suitable for execution by an extended finite state automaton (FSA).


In mathematics, the arguments of the maxima (abbreviated arg max or argmax) are the points, or elements, of the domain of some function at which the function values are maximized. In contrast to global maxima, which refers to the largest outputs of a function, arg max refers to the inputs, or arguments, at which the function outputs are as large as possible.