In telecommunications, asynchronous communication is transmission of data, generally without the use of an external clock signal, where data can be transmitted intermittently rather than in a steady stream. Any timing required to recover data from the communication symbols is encoded within the symbols. The most significant aspect of asynchronous communications is that data is not transmitted at regular intervals, thus making possible variable bit rate, and that the transmitter and receiver clock generators do not have to be exactly synchronized all the time. In asynchronous transmission, data is sent one byte at a time and each byte is preceded by start and stop bits.


In the first of their famous series of papers on graph minors, Neil Robertson and Paul Seymour (1983) define a path-decomposition of a graph G to be a sequence of subsets Xi of vertices of G, with two properties: For each edge of G, there exists an i such that both endpoints of the edge belong to subset Xi, and For every three indices i ≤ j ≤ k, X i ∩ X k ⊆ X j . {\displaystyle X_{i}\cap X_{k}\subseteq X_{j}.} The second of these two properties is equivalent to requiring that the subsets containing any particular vertex form a contiguous subsequence of the whole sequence. In the language of the later papers in Robertson and Seymour's graph minor series, a path-decomposition is a tree decomposition (X,T) in which the underlying tree T of the decomposition is a path graph. The width of a path-decomposition is defined in the same way as for tree-decompositions, as maxi |Xi| − 1, and the pathwidth of G is the minimum width of any path-decomposition of G. The subtraction of one from the size of Xi in this definition makes little difference in most applications of pathwidth, but is used to make the pathwidth of a path graph be equal to one.


In some cases, one may wish to compute the location of a corner with subpixel accuracy. To achieve an approximate solution, the Förstner algorithm solves for the point closest to all the tangent lines of the corner in a given window and is a least-square solution. The algorithm relies on the fact that for an ideal corner, tangent lines cross at a single point. The equation of a tangent line T x ′ ( x ) {\displaystyle T_{\mathbf {x} '}(\mathbf {x} )} at pixel x ′ {\displaystyle \mathbf {x} '} is given by: T x ′ ( x ) = ∇ I ( x ′ ) ⊤ ( x − x ′ ) = 0 {\displaystyle T_{\mathbf {x'} }(\mathbf {x} )=\nabla I(\mathbf {x'} )^{\top }(\mathbf {x} -\mathbf {x'} )=0} where ∇ I ( x ′ ) =  ⊤ {\displaystyle \nabla I(\mathbf {x'} )={\begin{bmatrix}I_{\mathbf {x} }&I_{\mathbf {y} }\end{bmatrix}}^{\top }} is the gradient vector of the image I {\displaystyle I} at x ′ {\displaystyle \mathbf {x'} } .


In principle, a sufficiently aggressive optimizing compiler could destroy the effectiveness of Kahan summation: for example, if the compiler simplified expressions according to the associativity rules of real arithmetic, it might "simplify" the second step in the sequence t = sum + y; c = (t - sum) - y;to c = ((sum + y) - sum) - y;and then to c = 0;thus eliminating the error compensation. In practice, many compilers do not use associativity rules (which are only approximate in floating-point arithmetic) in simplifications, unless explicitly directed to do so by compiler options enabling "unsafe" optimizations, although the Intel C++ Compiler is one example that allows associativity-based transformations by default. The original K&R C version of the C programming language allowed the compiler to re-order floating-point expressions according to real-arithmetic associativity rules, but the subsequent ANSI C standard prohibited re-ordering in order to make C better suited for numerical applications (and more similar to Fortran, which also prohibits re-ordering), although in practice compiler options can re-enable re-ordering, as mentioned above. A portable way to inhibit such optimizations locally is to break one of the lines in the original formulation into two statements, and make two of the intermediate products volatile: function KahanSum(input) var sum = 0.0 var c = 0.0 for i = 1 to input.length do var y = input - c volatile var t = sum + y volatile var z = t - sum c = z - y sum = t next i return sum


Those object types in turn reference the primitive object types defined in the GML standard. Some other markup languages for geography use schema constructs, but GML builds on the existing XML schema model instead of creating a new schema language. Application schemas are normally designed using ISO 19103 (Geographic information – Conceptual schema language) conformant UML, and then the GML Application created by following the rules given in Annex E of ISO 19136.


To assure that no single particle could trigger the counters he spread them out in a horizontal plane. In this configuration, the frequency of coincidences was greater than that calculated on the basis of the individual rates and the resolving time of the coincidence circuit. Rossi concluded that:... once in a while the recording equipment is struck by very extensive showers of particles, which cause coincidences between counters, even placed at large distances from one another.


In single-linkage or nearest-neighbor clustering, the oldest form of agglomerative hierarchical clustering, the dissimilarity between clusters is measured as the minimum distance between any two points from the two clusters. With this dissimilarity, d ( A ∪ B , C ) = min ( d ( A , C ) , d ( B , C ) ) , {\displaystyle d(A\cup B,C)=\min(d(A,C),d(B,C)),} meeting as an equality rather than an inequality the requirement of reducibility. (Single-linkage also obeys a Lance–Williams formula, but with a negative coefficient from which it is more difficult to prove reducibility.)


One can use this isomorphism to construct a lot of non-commutative endomorphism rings. For example: End  ( Z × Z ) ≅ M 2 ( Z ) {\displaystyle \operatorname {End} (\mathbb {Z} \times \mathbb {Z} )\cong M_{2}(\mathbb {Z} )} , since End  ( Z ) ≅ Z {\displaystyle \operatorname {End} (\mathbb {Z} )\cong \mathbb {Z} } . Also, when R = K {\displaystyle R=K} is a field, there is a canonical isomorphism End  ( K ) ≅ K {\displaystyle \operatorname {End} (K)\cong K} , so End  ( K n ) ≅ M n ( K ) {\displaystyle \operatorname {End} (K^{n})\cong M_{n}(K)} , that is, the endomorphism ring of a K {\displaystyle K} -vector space is identified with the ring of n-by-n matrices with entries in K {\displaystyle K} . More generally, the endomorphism algebra of the free module M = R n {\displaystyle M=R^{n}} is naturally n {\displaystyle n} -by- n {\displaystyle n} matrices with entries in the ring R {\displaystyle R} .As a particular example of the last point, for any ring R with unity, End(RR) = R, where the elements of R act on R by left multiplication. In general, endomorphism rings can be defined for the objects of any preadditive category.


In physics, the term clusters denotes small, polyatomic particles. As a rule of thumb, any particle made of between 3×100 and 3×107 atoms is considered a cluster. The term can also refer to the organization of protons and neutrons within an atomic nucleus, e.g. the alpha particle (also known as "α-cluster"), consisting of two protons and two neutrons (as in a helium nucleus).


In mathematics, a derivation is a function on an algebra which generalizes certain features of the derivative operator. Specifically, given an algebra A over a ring or a field K, a K-derivation is a K-linear map D: A → A that satisfies Leibniz's law: D ( a b ) = a D ( b ) + D ( a ) b . {\displaystyle D(ab)=aD(b)+D(a)b.} More generally, if M is an A-bimodule, a K-linear map D: A → M that satisfies the Leibniz law is also called a derivation.


Equivalently, a divisor a of b is a unitary divisor if and only if every prime factor of a has the same multiplicity in a as it has in b. The sum-of-unitary-divisors function is denoted by the lowercase Greek letter sigma thus: σ*(n). The sum of the k-th powers of the unitary divisors is denoted by σ*k(n): σ k ∗ ( n ) = ∑ d ∣ n gcd ( d , n / d ) = 1 d k . {\displaystyle \sigma _{k}^{*}(n)=\sum _{d\,\mid \,n \atop \gcd(d,\,n/d)=1}\!\!d^{k}.} If the proper unitary divisors of a given number add up to that number, then that number is called a unitary perfect number. The concept of a unitary divisor originates from R. Vaidyanathaswamy (1931)  who used the term block divisor.


It was initially optimized for the Pentium 4 processor and managed to immediately boost the performance of a supercomputer based on that CPU from 1.5 TFLOPS to 2 TFLOPS. As of 2005, the library was available at no cost for noncommercial use. A later open source version was released under the terms of the BSD license.


But if there is both a right identity and a left identity, then they must be equal, resulting in a single two-sided identity. To see this, note that if l is a left identity and r is a right identity, then l = l ∗ r = r. In particular, there can never be more than one two-sided identity: if there were two, say e and f, then e ∗ f would have to be equal to both e and f. It is also quite possible for (S, ∗) to have no identity element, such as the case of even integers under the multiplication operation. Another common example is the cross product of vectors, where the absence of an identity element is related to the fact that the direction of any nonzero cross product is always orthogonal to any element multiplied. That is, it is not possible to obtain a non-zero vector in the same direction as the original. Yet another example of structure without identity element involves the additive semigroup of positive natural numbers.


Once all the multiples of each discovered prime have been marked as composites, the remaining unmarked numbers are primes. The earliest known reference to the sieve (Ancient Greek: κόσκινον Ἐρατοσθένους, kóskinon Eratosthénous) is in Nicomachus of Gerasa's Introduction to Arithmetic, an early 2nd cent. CE book which attributes it to Eratosthenes of Cyrene, a 3rd cent. BCE Greek mathematician, though describing the sieving by odd numbers instead of by primes.One of a number of prime number sieves, it is one of the most efficient ways to find all of the smaller primes. It may be used to find primes in arithmetic progressions.


In mathematics, computer science and network science, network theory is a part of graph theory. It defines networks as graphs where the nodes or edges possess attributes. Network theory analyses these networks over the symmetric relations or asymmetric relations between their (discrete) components.


+ error term {\displaystyle y_{t}=a+w_{0}x_{t}+w_{1}x_{t-1}+w_{2}x_{t-2}+...+{\text{error term}}} or the form y t = a + w 0 x t + w 1 x t − 1 + w 2 x t − 2 + . . .


For type sum, the identity object is the void type, which stores no information and it is impossible to address an inhabitant. The concept of monoidal category does not presume that values of such aggregate types can be taken apart; on the contrary, it provides a framework that unifies classical and quantum information theory.In category theory, monoidal categories can be used to define the concept of a monoid object and an associated action on the objects of the category. They are also used in the definition of an enriched category.


In some cases these functions are not defined on the whole of ℝ3. For example, the trilinears of X365 which is the 365th entry in the Encyclopedia of Triangle Centers, are a1/2: b1/2: c1/2 so a, b, c cannot be negative. Furthermore, in order to represent the sides of a triangle they must satisfy the triangle inequality. So, in practice, every function's domain is restricted to the region of ℝ3 where a ≤ b + c, b ≤ c + a, and c ≤ a + b. This region T is the domain of all triangles, and it is the default domain for all triangle-based functions.


In GIS, the RMSD is one measure used to assess the accuracy of spatial analysis and remote sensing. In hydrogeology, RMSD and NRMSD are used to evaluate the calibration of a groundwater model. In imaging science, the RMSD is part of the peak signal-to-noise ratio, a measure used to assess how well a method to reconstruct an image performs relative to the original image.


In planning and problem solving, or more formally one-person games, the search space is seen as a directed graph with states as nodes, and transitions as edges. States can have properties, and such a property P is hereditary if for each state S that has P, each state that can be reached from S also has P. The subset of all states that have P plus the subset of all states that have ~P form a partition of the set of states called a hereditary partition. This notion can trivially be extended to more discriminating partitions by instead of properties, considering aspects of states and their domains. If states have an aspect A, with di ⊂ D a partition of the domain D of A, then the subsets of states for which A ∈ di form a hereditary partition of the total set of states iff ∀i, from any state where A ∈ di only other states where A ∈ di can be reached.


In relational algebra, if R ⊆ X × Y {\displaystyle R\subseteq X\times Y} and S ⊆ Y × Z {\displaystyle S\subseteq Y\times Z} are relations, then the composite relation S R ⊆ X × Z {\displaystyle SR\subseteq X\times Z} is defined so that x S R z {\displaystyle x\,SR\,z} if and only if there is a y ∈ Y {\displaystyle y\in Y} such that x R y {\displaystyle x\,R\,y} and y S z {\displaystyle y\,S\,z} . This definition is a generalisation of the definition of functional composition. The defining properties of an equivalence relation R {\displaystyle R} on a set X {\displaystyle X} can then be reformulated as follows: id ⊆ R {\displaystyle \operatorname {id} \subseteq R} .


Additional methods for improving the algorithm's efficiency were developed in the 20th century. The Euclidean algorithm has many theoretical and practical applications. It is used for reducing fractions to their simplest form and for performing division in modular arithmetic.


In telephony, a message-waiting indicator (MWI) is a Telcordia Technologies (formerly Bellcore) term for an FSK-based telephone calling feature that illuminates an LED on selected telephones to notify a telephone user of waiting voicemail messages on most North American public telephone networks and PBXs. As described in Telcordia Generic Requirements document GR-283-CORE, a Message_Waiting_Indicator (MWI) is a mechanism that informs the subscriber about the status of recorded messages. The subscriber may subscribe to a notification feature that makes use of the status of this MWI.


With the keyboard and display modules strapped to the operator's forearms, text could be entered by bringing the wrists together and typing. The same technology was used by IBM researchers to create the half-keyboard "belt computer. Also in 1994, Mik Lamming and Mike Flynn at Xerox EuroPARC demonstrated the Forget-Me-Not, a wearable device that would record interactions with people and devices and store this information in a database for later query.


In mathematical optimization, linear-fractional programming (LFP) is a generalization of linear programming (LP). Whereas the objective function in a linear program is a linear function, the objective function in a linear-fractional program is a ratio of two linear functions. A linear program can be regarded as a special case of a linear-fractional program in which the denominator is the constant function 1. Formally, a linear-fractional program is defined as the problem of maximizing (or minimizing) a ratio of affine functions over a polyhedron, maximize c T x + α d T x + β subject to A x ≤ b , {\displaystyle {\begin{aligned}{\text{maximize}}\quad &{\frac {\mathbf {c} ^{T}\mathbf {x} +\alpha }{\mathbf {d} ^{T}\mathbf {x} +\beta }}\\{\text{subject to}}\quad &A\mathbf {x} \leq \mathbf {b} ,\end{aligned}}} where x ∈ R n {\displaystyle \mathbf {x} \in \mathbb {R} ^{n}} represents the vector of variables to be determined, c , d ∈ R n {\displaystyle \mathbf {c} ,\mathbf {d} \in \mathbb {R} ^{n}} and b ∈ R m {\displaystyle \mathbf {b} \in \mathbb {R} ^{m}} are vectors of (known) coefficients, A ∈ R m × n {\displaystyle A\in \mathbb {R} ^{m\times n}} is a (known) matrix of coefficients and α , β ∈ R {\displaystyle \alpha ,\beta \in \mathbb {R} } are constants. The constraints have to restrict the feasible region to { x | d T x + β > 0 } {\displaystyle \{\mathbf {x} |\mathbf {d} ^{T}\mathbf {x} +\beta >0\}} , i.e. the region on which the denominator is positive. Alternatively, the denominator of the objective function has to be strictly negative in the entire feasible region.


The utility function has the linear form: u ( x 1 , x 2 ) = x 1 + x 2 . {\displaystyle u(x_{1},x_{2})=x_{1}+x_{2}.} The utility function is only weakly convex, and indeed the demand is not unique: when p 1 = p 2 {\displaystyle p_{1}=p_{2}} , the consumer may divide his income in arbitrary ratios between product types 1 and 2 and get the same utility.


In programming, several notations denote hexadecimal numbers, usually involving a prefix. The prefix 0x is used in C, which would denote this value as 0x60CB. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digits.


In the Unified Modeling Language (UML), an Element is an abstract class with no superclass. It is used as the superclass or base class, as known by object oriented programmers, for all the metaclasses in the UML infrastructure library. All other elements in the UML inherit, directly or indirectly from Element. An Element has a derived composition association to itself to support the general capability for elements to own other elements. As such, it has no additional attributes as part of its specification.


In mathematics, a sparsely totient number is a certain kind of natural number. A natural number, n, is sparsely totient if for all m > n, φ ( m ) > φ ( n ) {\displaystyle \varphi (m)>\varphi (n)} where φ {\displaystyle \varphi } is Euler's totient function. The first few sparsely totient numbers are: 2, 6, 12, 18, 30, 42, 60, 66, 90, 120, 126, 150, 210, 240, 270, 330, 420, 462, 510, 630, 660, 690, 840, 870, 1050, 1260, 1320, 1470, 1680, 1890, 2310, 2730, 2940, 3150, 3570, 3990, 4620, 4830, 5460, 5610, 5670, 6090, 6930, 7140, 7350, 8190, 9240, 9660, 9870, ... (sequence A036913 in the OEIS). The concept was introduced by David Masser and Peter Man-Kit Shiu in 1986. As they showed, every primorial is sparsely totient.


In some cases, the phenomenon under study may have important spatial or temporal structure that must be considered during analysis, such as time series or image-based data. In 2005, Tibshirani and colleagues introduced the fused lasso to extend the use of lasso to this type of data. The fused lasso objective function is min β { 1 N ∑ i = 1 N ( y i − x i t β ) 2 } subject to ∑ j = 1 p | β j | ≤ t 1 and ∑ j = 2 p | β j − β j − 1 | ≤ t 2 . {\displaystyle {\begin{aligned}&\min _{\beta }\left\{{\frac {1}{N}}\sum _{i=1}^{N}\left(y_{i}-x_{i}^{t}\beta \right)^{2}\right\}\\&{\text{ subject to }}\sum _{j=1}^{p}|\beta _{j}|\leq t_{1}{\text{ and }}\sum _{j=2}^{p}|\beta _{j}-\beta _{j-1}|\leq t_{2}.\end{aligned}}} The first constraint is the lasso constraint, while the second directly penalizes large changes with respect to the temporal or spatial structure, which forces the coefficients to vary smoothly to reflect the system's underlying logic.


All these principles limit the set of possible correlations in non-trivial ways. Moreover, they are all device-independent: this means that they can be falsified under the assumption that we can decide if two or more events are space-like separated. The drawback of the device-independent approach is that, even when taken together, all the afore-mentioned physical principles do not suffice to single out the set of quantum correlations. In other words: all such reconstructions are partial.


By quadratic reciprocity and the restriction of the vertices to primes congruent to 1 mod 4, this is a symmetric relation, so it defines an undirected graph, which turns out to be isomorphic to the Rado graph.Another construction of the Rado graph shows that it is an infinite circulant graph, with the integers as its vertices and with an edge between each two integers whose distance (the absolute value of their difference) belongs to a particular set S {\displaystyle S} . To construct the Rado graph in this way, S {\displaystyle S} may be chosen randomly, or by choosing the indicator function of S {\displaystyle S} to be the concatenation of all finite binary sequences.The Rado graph can also be constructed as the block intersection graph of an infinite block design in which the number of points and the size of each block are countably infinite. It can also be constructed as the Fraïssé limit of the class of finite graphs.


z ∈ I ∗ {\displaystyle z\in I^{*}} if and only if there exists a c ∈ R {\displaystyle c\in R} , where c {\displaystyle c} is not contained in any minimal prime ideal of R {\displaystyle R} , such that c z p e ∈ I  {\displaystyle cz^{p^{e}}\in I^{}} for all e ≫ 0 {\displaystyle e\gg 0} . If R {\displaystyle R} is reduced, then one can instead consider all e > 0 {\displaystyle e>0} .Here I  {\displaystyle I^{}} is used to denote the ideal of R {\displaystyle R} generated by the p e {\displaystyle p^{e}} 'th powers of elements of I {\displaystyle I} , called the e {\displaystyle e} th Frobenius power of I {\displaystyle I} . An ideal is called tightly closed if I = I ∗ {\displaystyle I=I^{*}} .


In mathematics, specifically group theory, finite groups of prime power order p n {\displaystyle p^{n}} , for a fixed prime number p {\displaystyle p} and varying integer exponents n ≥ 0 {\displaystyle n\geq 0} , are briefly called finite p-groups. The p-group generation algorithm by M. F. Newman and E. A. O'Brien is a recursive process for constructing the descendant tree of an assigned finite p-group which is taken as the root of the tree.


This signal would feed into the sound-card audio-input of the PC, and Banpaia would decode the ESN/MDN pair from this signal and display it on the screen. The hacker could then copy that data into the Oki 900 phone and reboot it, after which the phone network could not distinguish the Oki from the original phone whose signal had been received. This gave the cloner, through the Oki phone, the ability to use the mobile-phone service of the legitimate subscriber whose phone was cloned – just as if that phone had been physically stolen, except that the subscriber retained his or her phone, unaware that the phone had been cloned—at least until that subscriber received his or her next bill.


For every input position, the parser generates a state set. Each state is a tuple (X → α • β, i), consisting of the production currently being matched (X → α β) the current position in that production (visually represented by the dot •) the position i in the input at which the matching of this production began: the origin position(Earley's original algorithm included a look-ahead in the state; later research showed this to have little practical effect on the parsing efficiency, and it has subsequently been dropped from most implementations.) A state is finished when its current position is the last position of the right side of the production, that is, when there is no symbol to the right of the dot • in the visual representation of the state.


In operations research, the makespan of a project is the length of time that elapses from the start of work to the end. This type of multi-mode resource constrained project scheduling problem (MRCPSP) seeks to create the shortest logical project schedule, by efficiently using project resources, adding the lowest number of additional resources as possible to achieve the minimum makespan. The term commonly appears in the context of scheduling.


{\displaystyle (A-\mu I)^{-1}.} The closer the approximation μ {\displaystyle \mu } to the eigenvalue is chosen, the faster the algorithm converges; however, incorrect choice of μ {\displaystyle \mu } can lead to slow convergence or to the convergence to an eigenvector other than the one desired. In practice, the method is used when a good approximation for the eigenvalue is known, and hence one needs only few (quite often just one) iterations.


In the data transformation stage, a series of rules or functions are applied to the extracted data in order to prepare it for loading into the end target. An important function of transformation is data cleansing, which aims to pass only "proper" data to the target. The challenge when different systems interact is in the relevant systems' interfacing and communicating.


(See, for example, the Fermi–Pasta–Ulam–Tsingou experiment of 1953.) Assumption of the ergodic hypothesis allows proof that certain types of perpetual motion machines of the second kind are impossible. Systems that are ergodic are said to have the property of ergodicity; a broad range of systems in geometry, physics, and probability are ergodic. Ergodic systems are studied in ergodic theory.


In the 1980s, a tiny CPU that executed FORTH was fabricated into a DRAM chip to improve PUSH and POP. FORTH is a stack-oriented programming language and this improved its efficiency. The transputer also had large on chip memory given that it was made in the early 1980s making it essentially a processor-in-memory. Notable PIM projects include the Berkeley IRAM project (IRAM) at the University of California, Berkeley project and the University of Notre Dame PIM effort.


For example, Rd2xBd6. Concise reversible algebraic notation is similar to reversible algebraic notation, but omits the file or rank if it is not needed to disambiguate the move. For example, Rd2xB6.


In modular construction, modules are a bundle of redundant project components that are produced en masse prior to installation.Building components are often arranged into modules in the industrialization of construction. In industrial design, modularity refers to an engineering technique that builds larger systems by combining smaller subsystems. In manufacturing, modularity typically refers to modular design, either as the use of exchangeable parts or options in the fabrication of an object or the design and manufacture of modular components. In organizational design, Richard L. Daft and Arie Y. Lewin (1993) identified a paradigm called "modular organization" that had as its ground the need for flexible learning organizations in constant change and the need to solve their problems through coordinated self-organizing processes. This modular organization is characterized by decentralized decision-making, flatter hierarchies, self-organization of units.


In the Microsoft family of operating systems, Windows Vista and later versions have support for both MSI and MSI-X. Support was added in the Longhorn development cycle around 2004. MSI is not supported in earlier versions like Windows XP or Windows Server 2003.Solaris Express 6/05 released in 2005 added support for MSI an MSI-X as part of their new device driver interface (DDI) interrupt framework.FreeBSD 6.3 and 7.0 released in 2008 added support for MSI and MSI-X.OpenBSD 5.0 released in 2011 added support for MSI. 6.0 added support for MSI-X.Linux gained support for MSI and MSI-X around 2003.


Portuguese and Spanish also have unique forms for 1st, 2nd and 3rd person reflexive when they follow the preposition com/con ('with'). That holds true for both singular and plural pronouns for Portuguese, but only for singular in Spanish.


In metadata, Annotea is an RDF standard sponsored by the W3C to enhance document-based collaboration via shared document metadata based on tags, bookmarks, and other annotations. In this case document metadata includes: Keywords Comments Notes Explanations Errors CorrectionsIn general, Annotea associates text strings to a web document or selected parts of a web document without actually needing to modify the original document. Users that access any web documents can also load the metadata associated with it from a selected annotation server (or groups of servers) and see a peer group's comments on the document. Similarly shared metadata tags can be attached to web documents to help in future retrieval.


Tikhonov (Tychonoff) fixed-point theorem: Let V be a locally convex topological vector space. For any nonempty compact convex set X in V, any continuous function f: X → X has a fixed point. Browder fixed-point theorem: Let K be a nonempty closed bounded convex set in a uniformly convex Banach space.


In set theory, a set is called hereditarily countable if it is a countable set of hereditarily countable sets.


In non-PAE modes of 32-bit x86 processors, the usable RAM may be limited to less than 4 GB. Limits on memory and address space vary by platform and operating system. Limits on physical memory for 32-bit platforms also depend on the presence and use of Physical Address Extension (PAE), which allows 32-bit systems to use more than 4 GB of physical memory. PAE and 64-bit systems may be able to address up to the full address space of the x86 processor.


In mathematics, the hyperoperation sequence is an infinite sequence of arithmetic operations (called hyperoperations in this context) that starts with a unary operation (the successor function with n = 0). The sequence continues with the binary operations of addition (n = 1), multiplication (n = 2), and exponentiation (n = 3). After that, the sequence proceeds with further binary operations extending beyond exponentiation, using right-associativity. For the operations beyond exponentiation, the nth member of this sequence is named by Reuben Goodstein after the Greek prefix of n suffixed with -ation (such as tetration (n = 4), pentation (n = 5), hexation (n = 6), etc.) and can be written as using n − 2 arrows in Knuth's up-arrow notation. Each hyperoperation may be understood recursively in terms of the previous one by: a  b = a  ( a  ( a  ( ⋯  ( a  ( a  a ) ) ⋯ ) ) ) ⏟ b copies of a , n ≥ 2 {\displaystyle ab=\underbrace {a(a(a(\cdots (a(aa))\cdots )))} _{\displaystyle b{\mbox{ copies of }}a},\quad n\geq 2} It may also be defined according to the recursion rule part of the definition, as in Knuth's up-arrow version of the Ackermann function: a  b = a  ( a  ( b − 1 ) ) , n ≥ 1 {\displaystyle ab=a\left(a\left(b-1\right)\right),\quad n\geq 1} This can be used to easily show numbers much larger than those which scientific notation can, such as Skewes's number and googolplexplex (e.g. 50  50 {\displaystyle 5050} is much larger than Skewes's number and googolplexplex), but there are some numbers which even they cannot easily show, such as Graham's number and TREE(3).This recursion rule is common to many variants of hyperoperations.


In network theory, link analysis is a data-analysis technique used to evaluate relationships (Tap link) between nodes. Relationships may be identified among various types of nodes (100k), including organizations, people and transactions. Link analysis has been used for investigation of criminal activity (fraud , counterterrorism, and intelligence), computer security analysis, search engine optimization, market research, medical research, and art.


The Opteron CPU directly supports up to an 8-way configuration, which can be found in mid-level servers. Enterprise-level servers use additional (and expensive) routing chips to support more than 8 CPUs per box. In a variety of computing benchmarks, the Opteron architecture has demonstrated better multi-processor scaling than the Intel Xeon which didn't have a point to point system until QPI and integrated memory controllers with the Nehalem design.


Equipped with the λ-calculus and "general" recursion, Kleene with help of Church and J. Barkley Rosser produced proofs (1933, 1935) to show that the two calculi are equivalent. Church subsequently modified his methods to include use of Herbrand–Gödel recursion and then proved (1936) that the Entscheidungsproblem is unsolvable: there is no algorithm that can determine whether a well formed formula has a beta normal form.Many years later in a letter to Davis (c. 1965), Gödel said that "he was, at the time of these  lectures, not at all convinced that his concept of recursion comprised all possible recursions".


Another popular strategy for avoiding linguistic controversy is dependency grammar parsing. Most modern parsers are at least partly statistical; that is, they rely on a corpus of training data which has already been annotated (parsed by hand).


Some machines that support parity or ECC allow checking to be enabled or disabled in the BIOS, permitting cheaper non-parity RAM to be used. If parity RAM is used the chipset will usually use it to implement error correction, rather than halting the machine on a single-bit parity error. However, as discussed in the article on ECC memory, errors, while not everyday events, are not negligibly infrequent. Even in the absence of manufacturing defects, naturally occurring radiation causes random errors; tests on Google's many servers found that memory errors were not rare events, and that the incidence of memory errors and the range of error rates across different DIMMs were much higher than previously reported.


In probability theory and statistics, a sequence of independent Bernoulli trials with probability 1/2 of success on each trial is metaphorically called a fair coin. One for which the probability is not 1/2 is called a biased or unfair coin. In theoretical studies, the assumption that a coin is fair is often made by referring to an ideal coin. John Edmund Kerrich performed experiments in coin flipping and found that a coin made from a wooden disk about the size of a crown and coated on one side with lead landed heads (wooden side up) 679 times out of 1000.


In neural networking or heuristic algorithms (computer terms generally used to describe 'learning' computers or 'AI simulations'), a black box is used to describe the constantly changing section of the program environment which cannot easily be tested by the programmers. This is also called a white box in the context that the program code can be seen, but the code is so complex that it is functionally equivalent to a black box. In physics, a black box is a system whose internal structure is unknown, or need not be considered for a particular purpose. In cryptography to capture the notion of knowledge obtained by an algorithm through the execution of a cryptographic protocol such as a zero-knowledge proof protocol. If the output of an algorithm when interacting with the protocol matches that of a simulator given some inputs, it only needs to know the inputs.


In number theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be partitioned into two subsets S1 and S2 such that the sum of the numbers in S1 equals the sum of the numbers in S2. Although the partition problem is NP-complete, there is a pseudo-polynomial time dynamic programming solution, and there are heuristics that solve the problem in many instances, either optimally or approximately. For this reason, it has been called "the easiest hard problem".There is an optimization version of the partition problem, which is to partition the multiset S into two subsets S1, S2 such that the difference between the sum of elements in S1 and the sum of elements in S2 is minimized. The optimization version is NP-hard, but can be solved efficiently in practice.The partition problem is a special case of two related problems: In the subset sum problem, the goal is to find a subset of S whose sum is a certain target number T given as input (the partition problem is the special case in which T is half the sum of S).


A branch may have one incoming control flow and two or more outgoing control flows. When the condition is fulfilled, a branch activates exactly only one of the outgoing control flows and deactivates the others. The counterpart of a branch is a merge.


The service will then prompt the user to enter the dialed number of the party to be called. The disadvantage of this method of roaming is that the user will not be able to dial numbers directly from the handset. The advantage is that it works in almost all locations around the world since USSD is ubiquitous and free.


In the first half of the 20th century, telecommunication services developed progressively from completely manual setup of calls by operators called by subscribers, to automatic systems that could connect subscribers of the same local exchange through the use of telephone dials installed in each telephone. In the 1940s, the Bell System in the United States and Canada developed methods and technologies, called direct distance dialing and first implemented in 1951, that enabled telephone subscriber to dial long-distance telephone calls themselves without calling an operator. In the United Kingdom, a similar technology called subscriber trunk dialling (STD) was ready by 1958, when Queen Elizabeth II, who was in Bristol, publicised STD by dialling Edinburgh, the farthest distance a call could be directly dialled in the UK, on 5 December 1958. The STD system was completed in 1979.The technology was extended when, from 8 March 1963, subscribers in London were able to directly dial Paris using international direct dialling.


In the field of mathematical optimization, Lagrangian relaxation is a relaxation method which approximates a difficult problem of constrained optimization by a simpler problem. A solution to the relaxed problem is an approximate solution to the original problem, and provides useful information. The method penalizes violations of inequality constraints using a Lagrange multiplier, which imposes a cost on violations. These added costs are used instead of the strict inequality constraints in the optimization. In practice, this relaxed problem can often be solved more easily than the original problem. The problem of maximizing the Lagrangian function of the dual variables (the Lagrangian multipliers) is the Lagrangian dual problem.


{\displaystyle E=E=\alpha +\beta x_{i}+E=\alpha +\beta x_{i}.} The line of best fit for the bivariate dataset takes the form y = α + βx and is called the regression line. α and β correspond to the intercept and slope, respectively.In an experiment, the variable manipulated by an experimenter is something that is proven to work, called an independent variable.


In mathematics, the Samuelson–Berkowitz algorithm efficiently computes the characteristic polynomial of an n × n {\displaystyle n\times n} matrix whose entries may be elements of any unital commutative ring. Unlike the Faddeev–LeVerrier algorithm, it performs no divisions, so may be applied to a wider range of algebraic structures.


In the absence of parentheses, the parallel operator is defined as taking precedence over addition or subtraction, similar to multiplication.


In mathematics, the prime signature of a number is the multiset of (nonzero) exponents of its prime factorization. The prime signature of a number having prime factorization p 1 m 1 p 2 m 2 … p n m n {\displaystyle p_{1}^{m_{1}}p_{2}^{m_{2}}\dots p_{n}^{m_{n}}} is the multiset { m 1 , m 2 , … , m n } {\displaystyle \left\{m_{1},m_{2},\dots ,m_{n}\right\}} . For example, all prime numbers have a prime signature of {1}, the squares of primes have a prime signature of {2}, the products of 2 distinct primes have a prime signature of {1, 1} and the products of a square of a prime and a different prime (e.g. 12, 18, 20, ...) have a prime signature of {2, 1}.


For example, individuals in a population can be assigned to compartments with labels – for example, S, I, or R, (Susceptible, Infectious, or Recovered) and they progress between compartments. The order of the labels usually shows the flow patterns between the compartments; for instance, SIR means each individual is originally susceptible then changes to infectious and finally gets recovered and remained recovered (immune) forever. On the other hand, public health may apply some interventions such as vaccination or contact tracing to reduce the spread of an epidemic disease.


In statistics, a sum of squares due to lack of fit, or more tersely a lack-of-fit sum of squares, is one of the components of a partition of the sum of squares of residuals in an analysis of variance, used in the numerator in an F-test of the null hypothesis that says that a proposed model fits well. The other component is the pure-error sum of squares. The pure-error sum of squares is the sum of squared deviations of each value of the dependent variable from the average value over all observations sharing its independent variable value(s). These are errors that could never be avoided by any predictive equation that assigned a predicted value for the dependent variable as a function of the value(s) of the independent variable(s). The remainder of the residual sum of squares is attributed to lack of fit of the model since it would be mathematically possible to eliminate these errors entirely.


In multitasking computer operating systems, a daemon ( or ) is a computer program that runs as a background process, rather than being under the direct control of an interactive user. Traditionally, the process names of a daemon end with the letter d, for clarification that the process is in fact a daemon, and for differentiation between a daemon and a normal computer program. For example, syslogd is a daemon that implements system logging facility, and sshd is a daemon that serves incoming SSH connections. In a Unix environment, the parent process of a daemon is often, but not always, the init process.


The distinction arises because it is conventional to talk not about estimating fixed effects but rather about predicting random effects, but the two terms are otherwise equivalent. (This is a bit strange since the random effects have already been "realized"; they already exist. The use of the term "prediction" may be because in the field of animal breeding in which Henderson worked, the random effects were usually genetic merit, which could be used to predict the quality of offspring (Robinson page 28)).


Complementary configuration occurs when multiple information sources supply different information about the same features. This strategy is used for fusing information at raw data level within decision-making algorithms.


Effectiveness in using a system for controlling a continuous industrial process would generally be measured in very different terms to, say, effectiveness in using a text editor. Thus, it can be difficult, if not impossible, to answer the question "is system A more usable than system B", because the measures of effectiveness and efficiency may be very different. However, it can be argued that given a sufficiently high-level definition of subjective assessments of usability, comparisons can be made between systems.


In numerical linear algebra, the Bartels–Stewart algorithm is used to numerically solve the Sylvester matrix equation A X − X B = C {\displaystyle AX-XB=C} . Developed by R.H. Bartels and G.W.


There is specific verbal morphology—a particular form of the verb indicates passive voice.The problem arises with non-European languages. Many constructions in these languages share at least one property with the canonical European passive, but not all. While it seems justified to call these constructions passive when comparing them to European languages' passive constructions, as a whole the passives of the world's languages do not share a single common feature.


In muscle physiology, physiological cross-sectional area (PCSA) is the area of the cross section of a muscle perpendicular to its fibers, generally at its largest point. It is typically used to describe the contraction properties of pennate muscles. It is not the same as the anatomical cross-sectional area (ACSA), which is the area of the crossection of a muscle perpendicular to its longitudinal axis. In a non-pennate muscle the fibers are parallel to the longitudinal axis, and therefore PCSA and ACSA coincide.


In telecommunications, 8b/10b is a line code that maps 8-bit words to 10-bit symbols to achieve DC balance and bounded disparity, and at the same time provide enough state changes to allow reasonable clock recovery. This means that the difference between the counts of ones and zeros in a string of at least 20 bits is no more than two, and that there are not more than five ones or zeros in a row. This helps to reduce the demand for the lower bandwidth limit of the channel necessary to transfer the signal.An 8b/10b code can be implemented in various ways with focus on different performance parameters.


They are infinite in number. They constitute the comparatively rare instances where the strict converse of Fermat's Little Theorem does not hold. This fact precludes the use of that theorem as an absolute test of primality.The Carmichael numbers form the subset K1 of the Knödel numbers.


In this case, rather than simply counting through elements of the population and selecting every kth unit, we allocate each element a space along a number line according to its selection probability. We then generate a random start from a uniform distribution between 0 and 1, and move along the number line in steps of 1. Example: We have a population of 5 units (A to E).


In relational databases, the information schema (information_schema) is an ANSI-standard set of read-only views that provide information about all of the tables, views, columns, and procedures in a database. It can be used as a source of the information that some databases make available through non-standard commands, such as: the SHOW command of MySQL the DESCRIBE command of Oracle's SQL*Plus the \d command in psql (PostgreSQL's default command-line program). => SELECT count(table_name) FROM information_schema.tables; count ------- 99 (1 row) => SELECT column_name, data_type, column_default, is_nullable FROM information_schema.columns WHERE table_name='alpha'; column_name | data_type | column_default | is_nullable -------------+-----------+----------------+------------- foo | integer | | YES bar | character | | YES (2 rows) => SELECT * FROM information_schema.information_schema_catalog_name; catalog_name -------------- johnd (1 row)


In software, semantic technology encodes meanings separately from data and content files, and separately from application code. This enables machines as well as people to understand, share and reason with them at execution time. With semantic technologies, adding, changing and implementing new relationships or interconnecting programs in a different way can be just as simple as changing the external model that these programs share. With traditional information technology, on the other hand, meanings and relationships must be predefined and "hard wired" into data formats and the application program code at design time.


In the European Union the classifications for vehicle types are defined by: Commission Directive 2001/116/EC of 20 December 2001, adapting to technical progress Council Directive 70/156/EEC on the approximation of the laws of the Member States relating to the type-approval of motor vehicles and their trailers Directive 2002/24/EC of the European Parliament and of the Council of 18 March 2002 relating to the type-approval of two or three wheeled motor vehicles and repealing Council Directive 92/61/EECEuropean Community, is based on the Community's WVTA (whole vehicle type-approval) system. Under this system, manufacturers can obtain certification for a vehicle type in one Member State if it meets the EC technical requirements and then market it EU-wide with no need for further tests. Total technical harmonization already has been achieved in three vehicle categories (passenger cars, motorcycles, and tractors) and soon will extend to other vehicle categories (coaches and utility vehicles). It is essential that European car manufacturers be ensured access to as large a market as possible. While the Community type-approval system allows manufacturers to benefit fully from internal market opportunities, worldwide technical harmonization in the context of the United Nations Economic Commission for Europe (UNECE) offers a market beyond European borders.


In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by dom  ( f ) {\displaystyle \operatorname {dom} (f)} or dom  f {\displaystyle \operatorname {dom} f} , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be".More precisely, given a function f: X → Y {\displaystyle f\colon X\to Y} , the domain of f is X. In modern mathematical language, the domain is part of the definition of a function rather than a property of it. In the special case that X and Y are both subsets of R {\displaystyle \mathbb {R} } , the function f can be graphed in the Cartesian coordinate system.


In mathematics, the classification of finite simple groups states that every finite simple group is cyclic, or alternating, or in one of 16 families of groups of Lie type, or one of 26 sporadic groups. The list below gives all finite simple groups, together with their order, the size of the Schur multiplier, the size of the outer automorphism group, usually some small representations, and lists of all duplicates.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 567, 1567, 4567, and 14567 are the patterns related to Braille pattern dots-345, since the two additional dots of kantenji patterns 0345, 3457, and 03457 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


As blacks integrate to white communities they are perpetuating a system in which blacks are inferior to whites. Blacks would continue to function in an environment of being second class citizens, he believes, never reaching equity to white citizens. Carmichael therefore uses the concept of black nationalism to promote an equality that would begin to dismantle institutional racism.


In mathematics and computer science, a random tree is a tree or arborescence that is formed by a stochastic process. Types of random trees include: Uniform spanning tree, a spanning tree of a given graph in which each different tree is equally likely to be selected Random minimal spanning tree, spanning trees of a graph formed by choosing random edge weights and using the minimum spanning tree for those weights Random binary tree, binary trees with a given number of nodes, formed by inserting the nodes in a random order or by selecting all possible trees uniformly at random Random recursive tree, increasingly labelled trees, which can be generated using a simple stochastic growth rule. Treap or randomized binary search tree, a data structure that uses random choices to simulate a random binary tree for non-random update sequences Rapidly exploring random tree, a fractal space-filling pattern used as a data structure for searching high-dimensional spaces Brownian tree, a fractal tree structure created by diffusion-limited aggregation processes Random forest, a machine-learning classifier based on choosing random subsets of variables for each tree and using the most frequent tree output as the overall classification Branching process, a model of a population in which each individual has a random number of children


In mathematics, an operation is a function which takes zero or more input values (also called "operands" or "arguments") to a well-defined output value. The number of operands is the arity of the operation. The most commonly studied operations are binary operations (i.e., operations of arity 2), such as addition and multiplication, and unary operations (i.e., operations of arity 1), such as additive inverse and multiplicative inverse. An operation of arity zero, or nullary operation, is a constant.


In the following, we state two equivalent forms of the theorem, and show their equivalence. Later, we prove the theorem. This is done in the following steps: Reducing the theorem to sentences (formulas with no free variables) in prenex form, i.e. with all quantifiers (∀ and ∃) at the beginning.


In the following, let X {\displaystyle X} be a topological space, G , H {\displaystyle G,H} topological groups and a group homomorphism ϕ: H → G {\displaystyle \phi \colon H\to G} .


In 1972, Jurjen Battjes, commissioned by the Dutch Technical Advisory Committee for Flood Defences, summarised the available research and provided a solid theoretical foundation. This work led to an improved version of Hunt's Formula, which explicitly included parameters for the angle of incidence of the waves, the effect of a berm, and the slope's roughness. However, the available experimental data on roughness and the berm were insufficient to establish a definitive formula.


The inequality is a limiting case of Sobolev imbedding and can be stated as the following theorem: Let Ω {\displaystyle \Omega } be a bounded domain in R n {\displaystyle \mathbb {R} ^{n}} satisfying the cone condition. Let m p = n {\displaystyle mp=n} and p > 1 {\displaystyle p>1} . Set A ( t ) = exp  ( t n / ( n − m ) ) − 1.


One of the biggest problems with this form of scientific fraud is that "university investigations into research misconduct are often inadequate, opaque and poorly conducted. They challenge the idea that institutions can police themselves on research integrity. "Sometimes intentional fabrication can be difficult to distinguish from unintentional academic incompetence or malpractice.


As a result of being relatively close to the femtocell, the mobile phone (user equipment) expends significantly less power for communication with it, thus increasing battery life. They may also get better voice quality (via HD voice) depending on a number of factors such as operator/network support, customer contract/price plan, phone and operating system support. Some carriers may also offer more attractive tariffs, for example discounted calls from home.


Shortly after Neo visits the Oracle, Morpheus is captured by agents who plan to hack into his mind. Because Morpheus, as a hovercraft captain, possesses access codes to the Zion mainframe computer, the surviving members of the ship's crew are about to unplug Morpheus from the Matrix, without reconnecting his mind and body, a process that will kill him. Neo and Trinity, however, reenter the Matrix to make a daring and successful rescue of Morpheus. Neo saves Trinity from a helicopter crash, confirming Morpheus' belief that Neo is indeed the One. Neo is eventually killed by Agent Smith shortly after the rescue, but revived as the One and returned to the Nebuchadnezzar before the Machines' Sentinels can destroy the ship.


In mathematics, topology (from the Greek words τόπος, 'place, location', and λόγος, 'study') is concerned with the properties of a geometric object that are preserved under continuous deformations, such as stretching, twisting, crumpling and bending, but not tearing or gluing. A topological space is a set endowed with a structure, called a topology, which allows defining continuous deformation of subspaces, and, more generally, all kinds of continuity. Euclidean spaces, and, more generally, metric spaces are examples of a topological space, as any distance or metric defines a topology. The deformations that are considered in topology are homeomorphisms and homotopies.


In puzzle games, scores are usually gained by solving the puzzles quickly. Higher scores can be gained by performing combos of puzzle solving. There is often a time bonus which can add extra points. The level number is often a multiplier on the points, so higher scores are possible on harder levels.


In quantum information theory, superdense coding (also referred to as dense coding) is a quantum communication protocol to communicate a number of classical bits of information by only transmitting a smaller number of qubits, under the assumption of sender and receiver pre-sharing an entangled resource. In its simplest form, the protocol involves two parties, often referred to as Alice and Bob in this context, which share a pair of maximally entangled qubits, and allows Alice to transmit two bits (i.e., one of 00, 01, 10 or 11) to Bob by sending only one qubit. This protocol was first proposed by Charles H. Bennett and Stephen Wiesner in 1970 (though not published by them until 1992) and experimentally actualized in 1996 by Klaus Mattle, Harald Weinfurter, Paul G. Kwiat and Anton Zeilinger using entangled photon pairs. Superdense coding can be thought of as the opposite of quantum teleportation, in which one transfers one qubit from Alice to Bob by communicating two classical bits, as long as Alice and Bob have a pre-shared Bell pair.The transmission of two bits via a single qubit is made possible by the fact that Alice can choose among four quantum gate operations to perform on her share of the entangled state.


Manchester Ship Canal at Latchford, Stockton Heath and Lower Walton in Warrington, and also slightly further west at Moore. Near the eastern end of the canal in Salford, the Barton Road Swing Bridge is adjacent to the Barton Swing Aqueduct – a 234-foot, 800-ton trough holding some 800 tons of water (retained by gates at either end) swings so that it is at right angles to the Bridgewater Canal to allow ships to pass up the Ship Canal. Myton Swing Bridge - road bridge in Kingston upon Hull Oulton Broad swing bridge – rail Reedham Swing Bridge (52.55887°N 1.57237°E / 52.55887; 1.57237) – rail Ross Bridge, Penzance Sandwich Toll Bridge (rebuilt 1892) Selby swing bridge – rail Somerleyton swing bridge Trowse Bridge at Norwich.


{\displaystyle X.} Remark.


The goal is for the referee to find an algorithm such that if the statement is true, there is a way for Alice to win with probability greater than 3/4, and if the statement is false, there is a way for Bob to win with probability greater than 3/4. This probability is equal to 1-ε.In the language of complexity theory, a promise problem L = ( L yes , L no ) {\displaystyle L=(L_{\text{yes}},L_{\text{no}})} has a classical refereed game (classical RG) if there exists a referee described by polynomial time randomized computation, such that 1. for each x ∈ L yes {\displaystyle x\in L_{\text{yes}}} , there is a strategy for Alice to win with probability ≥ 3/4, and2. for each x ∈ L no {\displaystyle x\in L_{\text{no}}} , there is a strategy for Bob to win with probability ≥ 3/4.It is known that RG = EXP.


It should not be confused with the dot product (projection product). If two vectors have the same direction or have the exact opposite direction from each other (that is, they are not linearly independent), or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths.


P(if A, then B) is normally interpreted not as an ordinary probability—not, specifically, as P(A′ ∨ B)—but as the conditional probability of B given A, P(B | A) = P(A ∧ B) / P(A). This raises a question: what about a probability like P(if A, then B, and if C, then D)? For this, there is no standard answer. What would be needed, for consistency, is a treatment of if-then as a binary operation, →, such that for conditional events A → B and C → D, P(A → B) = P(B | A), P(C → D) = P(D | C), and P((A → B) ∧ (C → D)) is well-defined and reasonable. This treatment is what conditional event algebras try to provide.


In real social networks individuals exhibit a tendency to re-connect with past contacts (ex. family, friends, co-workers, etc.) rather than strangers. In 1970, Mark Granovetter examined this behaviour in the social networks of a group of workers and identified tie strength, a characteristic of social ties describing the frequency of contact between two individuals. From this comes the idea of strong and weak ties, where an individual's strong ties are those she has come into frequent contact with. Link-centric preferential attachment aims to explain the mechanism behind strong and weak ties as a stochastic reinforcement process for old ties in agent-based modeling where nodes have long-term memory.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 378, 1378, 3478, and 13478 are the patterns related to Braille pattern dots-236, since the two additional dots of kantenji patterns 0236, 2367, and 02367 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


In optimal transport, a branch of mathematics, polar factorization of vector fields is a basic result due to Brenier (1987), with antecedents of Knott-Smith (1984) and Rachev (1985), that generalizes many existing results among which are the polar decomposition of real matrices, and the rearrangement of real-valued functions.


It is trained by repeatedly exposing it to examples of the problem and learning the significance (weights) of the input nodes. : 196 The neural network used by Split_up is said to generalise well if the output of the network is correct (or nearly correct) for examples not seen during training, which classifies it as an intelligent system. : 274


However, most prepaid phones now offer roaming using one of the following methods: The prepaid mobile phone user dials a "trigger" number from the foreign location using a USSD message which is not charged for while roaming. Upon receipt of the USSD, the customer's operator will then return the call. When the service calls back, the user is being charged for the cost of the service from the credit available in the home network.


In part because the Shannon capacity is difficult to compute, researchers have looked for other graph invariants that are easy to compute and that provide bounds on the Shannon capacity.


In set theory, XY is the notation representing the set of all functions from Y to X. As "2" can be defined as {0,1} (see, for example, von Neumann ordinals), 2S (i.e., {0,1}S) is the set of all functions from S to {0,1}. As shown above, 2S and the power set of S, P(S), are considered identical set-theoretically. This equivalence can be applied to the example above, in which S = {x, y, z}, to get the isomorphism with the binary representations of numbers from 0 to 2n − 1, with n being the number of elements in the set S or |S| = n. First, the enumerated set { (x, 1), (y, 2), (z, 3) } is defined in which the number in each ordered pair represents the position of the paired element of S in a sequence of binary digits such as {x, y} = 011(2); x of S is located at the first from the right of this sequence and y is at the second from the right, and 1 in the sequence means the element of S corresponding to the position of it in the sequence exists in the subset of S for the sequence while 0 means it does not. For the whole power set of S, we get: Such a injective mapping from P(S) to integers is arbitrary, so this representation of all the subsets of S is not unique, but the sort order of the enumerated set does not change its cardinality.


In 1976, refinanced by the Canada Development Corporation, it returned to operation as AES Data, and went on to successfully market its brand of word processors worldwide until its demise in the mid-1980s. Its first office product, the AES-90, combined for the first time a CRT-screen, a floppy-disk and a microprocessor, that is, the very same winning combination that would be used by IBM for its PC seven years later. The AES-90 software was able to handle French and English typing from the start, displaying and printing the texts side-by-side, a Canadian government requirement.


In the following, expose ( v ) {\displaystyle {\text{expose}}(v)} extracts the left child l {\displaystyle l} , key k {\displaystyle k} , and right child r {\displaystyle r} of node v {\displaystyle v} into a tuple ( l , k , r ) {\displaystyle (l,k,r)} . Node ( l , k , r ) {\displaystyle {\text{Node}}(l,k,r)} creates a node with left child l {\displaystyle l} , key k {\displaystyle k} and right child r {\displaystyle r} . " s 1 | | s 2 {\displaystyle s_{1}||s_{2}} " means that two statements s 1 {\displaystyle s_{1}} and s 2 {\displaystyle s_{2}} can run in parallel.


In set theory language here, speak of a function class when f ⊂ A × C {\displaystyle f\subset A\times C} and provenly ∀ ( a ∈ A ) . ∃ ! ( c ∈ C ) . ⟨ a , c ⟩ ∈ f {\displaystyle \forall (a\in A).\,\exists !


Nevertheless, the machine was air cooled, and would have been the fastest such machine on the market. The machine ran an early version of the Mach kernel for multi-processor support. The compilers were designed to keep the processors as full as possible by reducing the number of branch delay slots, and did a particularly good job of it.


In mathematical logic and automated theorem proving, resolution is a rule of inference leading to a refutation complete theorem-proving technique for sentences in propositional logic and first-order logic. For propositional logic, systematically applying the resolution rule acts as a decision procedure for formula unsatisfiability, solving the (complement of the) Boolean satisfiability problem. For first-order logic, resolution can be used as the basis for a semi-algorithm for the unsatisfiability problem of first-order logic, providing a more practical method than one following from Gödel's completeness theorem. The resolution rule can be traced back to Davis and Putnam (1960); however, their algorithm required trying all ground instances of the given formula. This source of combinatorial explosion was eliminated in 1965 by John Alan Robinson's syntactical unification algorithm, which allowed one to instantiate the formula during the proof "on demand" just as far as needed to keep refutation completeness.The clause produced by a resolution rule is sometimes called a resolvent.


In numerical analysis, pairwise summation, also called cascade summation, is a technique to sum a sequence of finite-precision floating-point numbers that substantially reduces the accumulated round-off error compared to naively accumulating the sum in sequence. Although there are other techniques such as Kahan summation that typically have even smaller round-off errors, pairwise summation is nearly as good (differing only by a logarithmic factor) while having much lower computational cost—it can be implemented so as to have nearly the same cost (and exactly the same number of arithmetic operations) as naive summation. In particular, pairwise summation of a sequence of n numbers xn works by recursively breaking the sequence into two halves, summing each half, and adding the two sums: a divide and conquer algorithm.


In real analysis, a branch of mathematics, a modulus of convergence is a function that tells how quickly a convergent sequence converges. These moduli are often employed in the study of computable analysis and constructive mathematics. If a sequence of real numbers x i {\displaystyle x_{i}} converges to a real number x {\displaystyle x} , then by definition, for every real ε > 0 {\displaystyle \varepsilon >0} there is a natural number N {\displaystyle N} such that if i > N {\displaystyle i>N} then | x − x i | < ε {\displaystyle \left|x-x_{i}\right|<\varepsilon } . A modulus of convergence is essentially a function that, given ε {\displaystyle \varepsilon } , returns a corresponding value of N {\displaystyle N} .


Example: Slow memory diagram depicts a slow consistency example. The first process writes 1 to the memory location X and then it writes 1 to the memory location Y. The second process reads 1 from Y and it then reads 0 from X even though X was written before Y. Hutto, Phillip W., and Mustaque Ahamad (1990) illustrate that by appropriate programming, slow memory (consistency) can be expressive and efficient. They mention that slow memory has two valuable properties; locality and supporting reduction from atomic memory. They propose two algorithms to present the expressiveness of slow memory.


Mersenne primes were studied in antiquity because of their close connection to perfect numbers: the Euclid–Euler theorem asserts a one-to-one correspondence between even perfect numbers and Mersenne primes. Many of the largest known primes are Mersenne primes because Mersenne numbers are easier to check for primality. As of 2023, 51 Mersenne primes are known.


In the early 1970s, a noted nuclear scientist Isadore Perlman undertook the analysis of numerous Cypriot ceramics sent to him by the Swedish archaeologist, Einar Gherstad, when he pioneered high-precision methods of neutron activation analysis at the Lawrence Berkeley Laboratory in the US. Neutron activation analysis helps to determine the origin of ancient pottery and other artifacts through the analysis of the clay from which they were made. He was helped in the project by another noted scientist Frank Asaro.Second millennium BC pottery from Cyprus was one of the first archaeological projects that Perlman and Asaro undertook. The project of the origin of the then assumed Second Millennium Palestinian Bichrome Ware was undertaken as part of the PhD thesis of Michal Artzy.


In statistics, a hidden Markov random field is a generalization of a hidden Markov model. Instead of having an underlying Markov chain, hidden Markov random fields have an underlying Markov random field. Suppose that we observe a random variable Y i {\displaystyle Y_{i}} , where i ∈ S {\displaystyle i\in S} . Hidden Markov random fields assume that the probabilistic nature of Y i {\displaystyle Y_{i}} is determined by the unobservable Markov random field X i {\displaystyle X_{i}} , i ∈ S {\displaystyle i\in S} .


In mathematics, the fundamental theorem of arithmetic, also called the unique factorization theorem and prime factorization theorem, states that every integer greater than 1 can be represented uniquely as a product of prime numbers, up to the order of the factors. For example, 1200 = 2 4 ⋅ 3 1 ⋅ 5 2 = ( 2 ⋅ 2 ⋅ 2 ⋅ 2 ) ⋅ 3 ⋅ ( 5 ⋅ 5 ) = 5 ⋅ 2 ⋅ 5 ⋅ 2 ⋅ 3 ⋅ 2 ⋅ 2 = … {\displaystyle 1200=2^{4}\cdot 3^{1}\cdot 5^{2}=(2\cdot 2\cdot 2\cdot 2)\cdot 3\cdot (5\cdot 5)=5\cdot 2\cdot 5\cdot 2\cdot 3\cdot 2\cdot 2=\ldots } The theorem says two things about this example: first, that 1200 can be represented as a product of primes, and second, that no matter how this is done, there will always be exactly four 2s, one 3, two 5s, and no other primes in the product. The requirement that the factors be prime is necessary: factorizations containing composite numbers may not be unique (for example, 12 = 2 ⋅ 6 = 3 ⋅ 4 {\displaystyle 12=2\cdot 6=3\cdot 4} ).


In order to further eliminate irrelevant links and search results, DeepPeep uses the HIerarchical Form Identification (HIFI) framework that classifies links and search results based on the website's structure and content. Unlike other forms of classification which solely relies on the web form labels for organization, HIFI utilizes both the structure and content of the web form for classification. Utilizing these two classifiers, HIFI organizes the web forms in a hierarchical fashion which ranks the a web form's relevance to the target keyword.


In mathematics, specifically in abstract algebra, a torsion-free abelian group is an abelian group which has no non-trivial torsion elements; that is, a group in which the group operation is commutative and the identity element is the only element with finite order. While finitely generated abelian groups are completely classified, not much is known about infinitely generated abelian groups, even in the torsion-free countable case.


Lexical recognition is of particular value in the field of computer speech recognition, since the ability to build and search a network of semantically connected ideas would greatly increase the effectiveness of speech-recognition software. Statistical models can be used to segment and align recorded speech to words or phones. Applications include automatic lip-synch timing for cartoon animation, follow-the-bouncing-ball video sub-titling, and linguistic research. Automatic segmentation and alignment software is commercially available.


In the context of complex networks, attack tolerance is the network's robustness meaning the ability to maintain the overall connectivity and diameter of the network as nodes are removed. Several graph metrics have been proposed to predicate network robustness. Algebraic connectivity is a graph metric that shows the best graph robustness among them.


In physics, a vector typically arises as the outcome of a measurement or series of measurements, and is represented as a list (or tuple) of numbers such as ( v 1 , v 2 , v 3 ) . {\displaystyle (v_{1},v_{2},v_{3}).} The numbers in the list depend on the choice of coordinate system. For instance, if the vector represents position with respect to an observer (position vector), then the coordinate system may be obtained from a system of rigid rods, or reference axes, along which the components v1, v2, and v3 are measured.


We illustrate using the simple case of a one-dimensional parameter, but an analogous derivation holds more generally. In the one-dimensional case, we have p ( x ) = g ( η ) h ( x ) e η T ( x ) . {\displaystyle p(x)=g(\eta )h(x)e^{\eta T(x)}.}


Every variable Xi in the sequence is associated with a Bernoulli trial or experiment. They all have the same Bernoulli distribution. Much of what can be said about the Bernoulli process can also be generalized to more than two outcomes (such as the process for a six-sided die); this generalization is known as the Bernoulli scheme. The problem of determining the process, given only a limited sample of Bernoulli trials, may be called the problem of checking whether a coin is fair.


In telecommunication and data storage, Manchester code (also known as phase encoding, or PE) is a line code in which the encoding of each data bit is either low then high, or high then low, for equal time. It is a self-clocking signal with no DC component. Consequently, electrical connections using a Manchester code are easily galvanically isolated.


Others have attacked the problem from the database end, by defining an object-oriented data model for the database, and defining a database programming language that allows full programming capabilities as well as traditional query facilities. Object databases suffered because of a lack of standardization: although standards were defined by ODMG, they were never implemented well enough to ensure interoperability between products. Nevertheless, object databases have been used successfully in many applications: usually specialized applications such as engineering databases or molecular biology databases rather than mainstream commercial data processing. However, object database ideas were picked up by the relational vendors and influenced extensions made to these products and indeed to the SQL language. An alternative to translating between objects and relational databases is to use an object–relational mapping (ORM) library.


Other related phrasings include cumulative knowledge, collective knowledge or pooled knowledge. Distributed knowledge is the union of all the knowledge of individuals in a community of agents. Distributed knowledge differs from the concept of Wisdom of the crowd, in that the latter is concerned with opinions, not knowledge.


In mathematics, the Munn semigroup is the inverse semigroup of isomorphisms between principal ideals of a semilattice (a commutative semigroup of idempotents). Munn semigroups are named for the Scottish mathematician Walter Douglas Munn (1929–2008).


In petroleum and natural gas extraction, a Christmas tree, or "tree", is an assembly of valves, casing spools, and fittings used to regulate the flow of pipes in an oil well, gas well, water injection well, water disposal well, gas injection well, condensate well, and other types of well.


A tone reproduction curve is applied to the electronic image prior to printing, so that the reflectance of the print closely approximates a proportionality to the luminance intent implied by the electronic image. It is easier to demonstrate the need for a TRC using halftoned printing methods such as inkjet, or xerographic technologies. However, the need also applies to continuous-tone methods such as photographic paper printing.


In programming, several notations denote hexadecimal numbers, usually involving a prefix. The prefix 0x is used in C, which would denote this value as 0x7613. Hexadecimal is used in the transfer encoding Base16, in which each byte of the plaintext is broken into two 4-bit values and represented by two hexadecimal digits.


In some programming languages, const is a type qualifier (a keyword applied to a data type) that indicates that the data is read-only. While this can be used to declare constants, const in the C family of languages differs from similar constructs in other languages in being part of the type, and thus has complicated behavior when combined with pointers, references, composite data types, and type-checking. In other languages, the data is not in a single memory location, but copied at compile time on each use. Languages which use it include C, C++, D, JavaScript, Julia, and Rust.


In text databases, a document collection defined by a document by term D matrix (of size m×n, where m is the number of documents and n is the number of terms), the number of clusters can roughly be estimated by the formula m n t {\displaystyle {\tfrac {mn}{t}}} where t is the number of non-zero entries in D. Note that in D each row and each column must contain at least one non-zero element.


That is (after rewriting the expression with parentheses and in infix notation if necessary), rearranging the parentheses in such an expression will not change its value. Consider the following equations: Even though the parentheses were rearranged on each line, the values of the expressions were not altered. Since this holds true when performing addition and multiplication on any real numbers, it can be said that "addition and multiplication of real numbers are associative operations".


For if every even number greater than 4 is the sum of two odd primes, adding 3 to each even number greater than 4 will produce the odd numbers greater than 7 (and 7 itself is equal to 2+2+3). In 2013, Harald Helfgott released a proof of Goldbach's weak conjecture. As of 2018, the proof is widely accepted in the mathematics community, but it has not yet been published in a peer-reviewed journal.


That a given psychological attribute is a continuous quantity is a logically coherent and empirically testable hypothesis. Appearing in the next issue of the same journal were important papers by Dana Scott (1964), who proposed a hierarchy of cancellation conditions for the indirect testing of the solvability and Archimedean axioms, and David Krantz (1964) who connected the Luce & Tukey work to that of Hölder (1901). Work soon focused on extending the theory of conjoint measurement to involve more than just two attributes.


In mathematics a p-group G {\displaystyle G} is called power closed if for every section H {\displaystyle H} of G {\displaystyle G} the product of p k {\displaystyle p^{k}} powers is again a p k {\displaystyle p^{k}} th power. Regular p-groups are an example of power closed groups. On the other hand, powerful p-groups, for which the product of p k {\displaystyle p^{k}} powers is again a p k {\displaystyle p^{k}} th power are not power closed, as this property does not hold for all sections of powerful p-groups. The power closed 2-groups of exponent at least eight are described in (Mann 2005, Th. 16).


In mathematics, a simple group is a nontrivial group whose only normal subgroups are the trivial group and the group itself. A group that is not simple can be broken into two smaller groups, namely a nontrivial normal subgroup and the corresponding quotient group. This process can be repeated, and for finite groups one eventually arrives at uniquely determined simple groups, by the Jordan–Hölder theorem. The complete classification of finite simple groups, completed in 2004, is a major milestone in the history of mathematics.


Two nonsingular quadratic forms over F2 are isomorphic if and only if they have the same dimension and the same Arf invariant. This fact was essentially known to Leonard Dickson (1901), even for any finite field of characteristic 2, and Arf proved it for an arbitrary perfect field. The Arf invariant is particularly applied in geometric topology, where it is primarily used to define an invariant of (4k + 2)-dimensional manifolds (singly even-dimensional manifolds: surfaces (2-manifolds), 6-manifolds, 10-manifolds, etc.) with certain additional structure called a framing, and thus the Arf–Kervaire invariant and the Arf invariant of a knot. The Arf invariant is analogous to the signature of a manifold, which is defined for 4k-dimensional manifolds (doubly even-dimensional); this 4-fold periodicity corresponds to the 4-fold periodicity of L-theory. The Arf invariant can also be defined more generally for certain 2k-dimensional manifolds.


A tighter bound, was conjectured by Hirschman and Everett, proven in 1975 by W. Beckner and in the same year interpreted as a generalized quantum mechanical uncertainty principle by Białynicki-Birula and Mycielski. The equality holds in the case of Gaussian distributions. Note, however, that the above entropic uncertainty function is distinctly different from the quantum Von Neumann entropy represented in phase space.


In mid to late 2009 a tool named Detect and Eliminate Computer Acquired Forensics (DECAF) was announced by an uninvolved group of programmers. The tool would reportedly protect computers against COFEE and render the tool ineffective. It alleged that it would provide real-time monitoring of COFEE signatures on USB devices and in running applications and that when a COFEE signature is detected, DECAF would perform numerous user-defined processes. These included COFEE log clearing, ejecting USB devices, and contamination or spoofing of MAC addresses. On December 18, 2009, the DECAF creators announced that the tool was a hoax and part of "a stunt to raise awareness for security and the need for better forensic tools".


In modern multitasking environment, an application process usually has in its address space (or spaces) chunks of memory of following types: Machine code, including: program's own code (historically known as code segment or text segment); shared libraries. Data, including: initialized data (data segment); uninitialized (but allocated) variables; run-time stack; heap; shared memory and memory mapped files.Some parts of address space may be not mapped at all. Some systems have a "split" memory architecture where machine code, constants, and data are in different locations, and may have different address sizes. For example, PIC18 microcontrollers have a 21-bit program counter to address machine code and constants in Flash memory, and 12-bit address registers to address data in SRAM.


In the case of two thieves  and t colours, a fair split would require at most t cuts. If, however, only t − 1 cuts are available, Hungarian mathematician Gábor Simonyi shows that the two thieves can achieve an almost fair division in the following sense. If the necklace is arranged so that no t-split is possible, then for any two subsets D1 and D2 of { 1, 2, ..., t }, not both empty, such that D 1 ∩ D 2 = ∅ {\displaystyle D_{1}\cap D_{2}=\varnothing } , a (t − 1)-split exists such that: If colour i ∈ D 1 {\displaystyle i\in D_{1}} , then partition 1 has more beads of colour i than partition 2; If colour i ∈ D 2 {\displaystyle i\in D_{2}} , then partition 2 has more beads of colour i than partition 1; If colour i is in neither partition, both partitions have equally many beads of colour i.This means that if the thieves have preferences in the form of two "preference" sets D1 and D2, not both empty, there exists a (t − 1)-split so that thief 1 gets more beads of types in his preference set D1 than thief 2; thief 2 gets more beads of types in her preference set D2 than thief 1; and the rest are equal.


In predicate logic, what is described in layman's terms as "something" can more specifically be regarded as existential quantification, that is, the predication of a property or relation to at least one member of the domain. It is a type of quantifier, a logical constant which is interpreted as "there exists," "there is at least one," or "for some." It expresses that a propositional function can be satisfied by at least one member of a domain of discourse. In other terms, it is the predication of a property or relation to at least one member of the domain. It asserts that a predicate within the scope of an existential quantifier is true of at least one value of a predicate variable.


In the Japanese kantenji braille, the standard 8-dot Braille patterns 358, 1358, 3458, and 13458 are the patterns related to Braille pattern dots-246, since the two additional dots of kantenji patterns 0246, 2467, and 02467 are placed above the base 6-dot cell, instead of below, as in standard 8-dot braille.


These scenarios will cause issues in the program running by providing false data. To prevent this, one method is that the entire data-structure can be kept under critical section so that only one operation is handled at a time. Another method is locking the node in use under critical section, so that other operations do not use the same node. Using critical section, thus, ensures that the code provides expected outputs.


In mathematics, a Euclidean group is the group of (Euclidean) isometries of a Euclidean space E n {\displaystyle \mathbb {E} ^{n}} ; that is, the transformations of that space that preserve the Euclidean distance between any two points (also called Euclidean transformations). The group depends only on the dimension n of the space, and is commonly denoted E(n) or ISO(n). The Euclidean group E(n) comprises all translations, rotations, and reflections of E n {\displaystyle \mathbb {E} ^{n}} ; and arbitrary finite combinations of them. The Euclidean group can be seen as the symmetry group of the space itself, and contains the group of symmetries of any figure (subset) of that space.


Alessandro Volta began investigating pneumatic chemistry in 1776 and argued that there were different types of inflammable air based on experiments on marsh gases. Pneumatic chemists credited with discovering chemical elements include Joseph Priestley, Henry Cavendish, Joseph Black, Daniel Rutherford, and Carl Scheele. Other individuals who investigated gases during this period include Robert Boyle, Stephen Hales, William Brownrigg, Antoine Lavoisier, Joseph Louis Gay-Lussac, and John Dalton.


The language they defined was known as CycL. After CycL, a number of ontology languages have been developed. Most are declarative languages, and are either frame languages, or are based on first-order logic.


In the following identities, δ {\displaystyle \delta } is a derivation of a differential ring R . {\displaystyle R. }: 76 If r ∈ R {\displaystyle r\in R} and c {\displaystyle c} is a constant in R {\displaystyle R} (that is, δ c = 0 {\displaystyle \delta c=0} ), then If r ∈ R {\displaystyle r\in R} and u {\displaystyle u} is a unit in R , {\displaystyle R,} then If n {\displaystyle n} is a nonnegative integer and r ∈ R {\displaystyle r\in R} then If u 1 , … , u n {\displaystyle u_{1},\ldots ,u_{n}} are units in R , {\displaystyle R,} and n 1 , … , n n {\displaystyle n_{1},\ldots ,n_{n}} are integers, one has the logarithmic derivative identity:


Monoidal categories can be seen as a generalization of these and other examples. Every (small) monoidal category may also be viewed as a "categorification" of an underlying monoid, namely the monoid whose elements are the isomorphism classes of the category's objects and whose binary operation is given by the category's tensor product. A rather different application, of which monoidal categories can be considered an abstraction, is that of a system of data types closed under a type constructor that takes two types and builds an aggregate type; the types are the objects and ⊗ {\displaystyle \otimes } is the aggregate constructor.


A probability function, P {\displaystyle P} , which assigns each event in the event space a probability, which is a number between 0 and 1.In order to provide a sensible model of probability, these elements must satisfy a number of axioms, detailed in this article. In the example of the throw of a standard die, we would take the sample space to be { 1 , 2 , 3 , 4 , 5 , 6 } {\displaystyle \{1,2,3,4,5,6\}} . For the event space, we could simply use the set of all subsets of the sample space, which would then contain simple events such as { 5 } {\displaystyle \{5\}} ("the die lands on 5"), as well as complex events such as { 2 , 4 , 6 } {\displaystyle \{2,4,6\}} ("the die lands on an even number").


In the Java virtual machine, internal type signatures are used to identify methods and classes at the level of the virtual machine code. Example: The method String String.substring(int, int) is represented in bytecode as Ljava/lang/String.substring(II)Ljava/lang/String;. The signature of the main method looks like this: And in the disassembled bytecode, it takes the form of Lsome/package/Main/main:([Ljava/lang/String;)V The method signature for the main() method contains three modifiers: public indicates that the main() method can be called by any object. static indicates that the main() method is a class method. void indicates that the main() method has no return value.


Algorithms are needed for efficient computation of the statistics (e.g., mean and variance) of the modal parameters from the posterior distribution. Unlike non-Bayesian methods, the algorithms are often implicit and iterative. E.g., optimization algorithms may be involved in the determination of most probable value, which may not converge for poor quality data.


In the example graph shown, the algorithm is initially called with R = Ø, P = {1,2,3,4,5,6}, and X = Ø. The pivot u should be chosen as one of the degree-three vertices, to minimize the number of recursive calls; for instance, suppose that u is chosen to be vertex 2. Then there are three remaining vertices in P \ N(u): vertices 2, 4, and 6. The iteration of the inner loop of the algorithm for v = 2 makes a recursive call to the algorithm with R = {2}, P = {1,3,5}, and X = Ø. Within this recursive call, one of 1 or 5 will be chosen as a pivot, and there will be two second-level recursive calls, one for vertex 3 and the other for whichever vertex was not chosen as pivot. These two calls will eventually report the two cliques {1,2,5} and {2,3}.


In mobile-telephone technology, the UniPro protocol stack follows the architecture of the classical OSI Reference Model. In UniPro, the OSI Physical Layer is split into two sublayers: Layer 1 (the actual physical layer) and Layer 1.5 (the PHY Adapter layer) which abstracts from differences between alternative Layer 1 technologies. The actual physical layer is a separate specification as the various PHY options are reused in other MIPI Alliance specifications. The UniPro specification itself covers Layers 1.5, 2, 3, 4 and the DME (Device Management Entity).


In the field of multivariate statistics, kernel principal component analysis (kernel PCA) is an extension of principal component analysis (PCA) using techniques of kernel methods. Using a kernel, the originally linear operations of PCA are performed in a reproducing kernel Hilbert space.


Although much attention is focused on WCDMA, the concept is applicable to all standards, including GSM, CDMA2000, TD-SCDMA, WiMAX and LTE solutions. The use of femtocells allows network coverage in places where the signal to the main network cells might be too weak. Furthermore, femtocells lower contention on the main network cells, by forming a connection from the end user, through an internet connection, to the operator's private network infrastructure elsewhere.


In mathematics, gradient descent (also often called steepest descent) is a first-order iterative optimization algorithm for finding a local minimum of a differentiable function. The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the direction of steepest descent. Conversely, stepping in the direction of the gradient will lead to a local maximum of that function; the procedure is then known as gradient ascent. It is particularly useful in machine learning for minimizing the cost or loss function.


In mathematics, the class of L-matrices are those matrices whose off-diagonal entries are less than or equal to zero and whose diagonal entries are positive; that is, an L-matrix L satisfies L = ( ℓ i j ) ; ℓ i i > 0 ; ℓ i j ≤ 0 , i ≠ j . {\displaystyle L=(\ell _{ij});\quad \ell _{ii}>0;\quad \ell _{ij}\leq 0,\quad i\neq j.}


In mathematics, the affine hull or affine span of a set S in Euclidean space Rn is the smallest affine set containing S, or equivalently, the intersection of all affine sets containing S. Here, an affine set may be defined as the translation of a vector subspace. The affine hull aff(S) of S is the set of all affine combinations of elements of S, that is, aff  ( S ) = { ∑ i = 1 k α i x i | k > 0 , x i ∈ S , α i ∈ R , ∑ i = 1 k α i = 1 } . {\displaystyle \operatorname {aff} (S)=\left\{\sum _{i=1}^{k}\alpha _{i}x_{i}\,{\Bigg |}\,k>0,\,x_{i}\in S,\,\alpha _{i}\in \mathbb {R} ,\,\sum _{i=1}^{k}\alpha _{i}=1\right\}.}


In programming language theory, semantics is the rigorous mathematical study of the meaning of programming languages. Semantics assigns computational meaning to valid strings in a programming language syntax. It is closely related to, and often crosses over with, the semantics of mathematical proofs. Semantics describes the processes a computer follows when executing a program in that specific language. This can be shown by describing the relationship between the input and output of a program, or an explanation of how the program will be executed on a certain platform, hence creating a model of computation.


In most practical contexts, a programming language involves a computer; consequently, programming languages are usually defined and studied this way. Programming languages differ from natural languages in that natural languages are only used for interaction between people, while programming languages also allow humans to communicate instructions to machines. The domain of the language is also worth consideration. Markup languages like XML, HTML, or troff, which define structured data, are not usually considered programming languages.


Vectors play an important role in physics: the velocity and acceleration of a moving object and the forces acting on it can all be described with vectors. Many other physical quantities can be usefully thought of as vectors. Although most of them do not represent distances (except, for example, position or displacement), their magnitude and direction can still be represented by the length and direction of an arrow. The mathematical representation of a physical vector depends on the coordinate system used to describe it. Other vector-like objects that describe physical quantities and transform in a similar way under changes of the coordinate system include pseudovectors and tensors.


In recreational number theory, a primeval number is a natural number n for which the number of prime numbers which can be obtained by permuting some or all of its digits (in base 10) is larger than the number of primes obtainable in the same way for any smaller natural number. Primeval numbers were first described by Mike Keith. The first few primeval numbers are 1, 2, 13, 37, 107, 113, 137, 1013, 1037, 1079, 1237, 1367, 1379, 10079, 10123, 10136, 10139, 10237, 10279, 10367, 10379, 12379, 13679, ... (sequence A072857 in the OEIS)The number of primes that can be obtained from the primeval numbers is 0, 1, 3, 4, 5, 7, 11, 14, 19, 21, 26, 29, 31, 33, 35, 41, 53, 55, 60, 64, 89, 96, 106, ... (sequence A076497 in the OEIS)The largest number of primes that can be obtained from a primeval number with n digits is 1, 4, 11, 31, 106, 402, 1953, 10542, 64905, 362451, 2970505, ... (sequence A076730 in the OEIS)The smallest n-digit number to achieve this number of primes is 2, 37, 137, 1379, 13679, 123479, 1234679, 12345679, 102345679


In standard logic, propositions are considered to be either true or false. In contradistinction, subjective logic assumes that humans cannot determine with absolute certainty whether a proposition about the real world is absolutely true or false. In subjective logic the posteriori probability estimates of binary events can be represented by beta distributions.


The design freedom of the time was very important because designers were very constrained by the cost of electronics, and only starting to explore how a computer could best be organized. Some of the basic features introduced during this period included index registers (on the Ferranti Mark 1), a return address saving instruction (UNIVAC I), immediate operands (IBM 704), and detecting invalid operations (IBM 650). By the end of the 1950s, commercial builders had developed factory-constructed, truck-deliverable computers.


Limit theory helps in operational usage. For instance, in KBE derivation of a populated design (geometrical objects, etc., similar concerns apply in shape theory), equivalence assumptions allow convergence where potentially large, and perhaps even computationally indeterminate, solution sets are handled deftly. Yet, in a chain of computation, downstream events may very well find some types of results from earlier resolutions of ramification as problematic for their own algorithms.


If the measure ρ is reducible with μ the associated reducer, then if f is square integrable for μ, and if g is square integrable for ρ and is orthogonal with P0 = 1 one has equivalence: f ( x ) = ∫ I g ( t ) − g ( x ) t − x ρ ( t ) d t ⇔ g ( x ) = ( x − c 1 ) f ( x ) − T μ ( f ( x ) ) = φ ( x ) μ ( x ) ρ ( x ) f ( x ) − T ρ ( μ ( x ) ρ ( x ) f ( x ) ) {\displaystyle f(x)=\int _{I}{\frac {g(t)-g(x)}{t-x}}\rho (t)dt\Leftrightarrow g(x)=(x-c_{1})f(x)-T_{\mu }(f(x))={\frac {\varphi (x)\mu (x)}{\rho (x)}}f(x)-T_{\rho }\left({\frac {\mu (x)}{\rho (x)}}f(x)\right)} c1 indicates the moment of order 1 of ρ and Tρ the operator g ( x ) ↦ ∫ I g ( t ) − g ( x ) t − x ρ ( t ) d t . {\displaystyle g(x)\mapsto \int _{I}{\frac {g(t)-g(x)}{t-x}}\rho (t)\,dt.}