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Instatistics,maximum likelihood estimation(MLE) is a method ofestimatingtheparametersof an assumedprobability distribution, given some observed data. This is achieved bymaximizingalikelihood functionso that, under the assumedstatistical model, theobserved datais most probable. Thepointin theparameter spacethat maximize... | https://en.wikipedia.org/wiki/Maximum_likelihood_estimation |
Inregression analysis,least squaresis aparameter estimationmethod in which the sum of the squares of theresiduals(a residual being the difference between an observed value and the fitted value provided by a model) is minimized.
The most important application is indata fitting. When the problem has substantialuncertain... | https://en.wikipedia.org/wiki/Least_squares |
Instatistics,maximum likelihood estimation(MLE) is a method ofestimatingtheparametersof an assumedprobability distribution, given some observed data. This is achieved bymaximizingalikelihood functionso that, under the assumedstatistical model, theobserved datais most probable. Thepointin theparameter spacethat maximize... | https://en.wikipedia.org/wiki/Maximum_likelihood |
I(μ,σ)=(1/σ2002/σ2){\displaystyle {\mathcal {I}}(\mu ,\sigma )={\begin{pmatrix}1/\sigma ^{2}&0\\0&2/\sigma ^{2}\end{pmatrix}}}
Inprobability theoryandstatistics, anormal distributionorGaussian distributionis a type ofcontinuous probability distributionfor areal-valuedrandom variable. The general form of itsprobability... | https://en.wikipedia.org/wiki/Gaussian_distribution |
Inmachine learning,backpropagationis agradientestimation method commonly used for training aneural networkto compute its parameter updates.
It is an efficient application of thechain ruleto neural networks. Backpropagation computes thegradientof aloss functionwith respect to theweightsof the network for a single input... | https://en.wikipedia.org/wiki/Backpropagation |
Aneural networkis a group of interconnected units calledneuronsthat send signals to one another. Neurons can be eitherbiological cellsormathematical models. While individual neurons are simple, many of them together in a network can perform complex tasks. There are two main types of neural networks.
In the context of ... | https://en.wikipedia.org/wiki/Neural_network#Limitations_of_backpropagation |
Innumerical analysis, one of the most important problems is designing efficient andstablealgorithmsfor finding theeigenvaluesof amatrix. Theseeigenvalue algorithmsmay also find eigenvectors.
Given ann×nsquare matrixAofrealorcomplexnumbers, aneigenvalueλand its associatedgeneralized eigenvectorvare a pair obeying the ... | https://en.wikipedia.org/wiki/Eigenvalue_algorithm |
InEuclidean geometry,linear separabilityis a property of two sets ofpoints. This is most easily visualized in two dimensions (theEuclidean plane) by thinking of one set of points as being colored blue and the other set of points as being colored red. These two sets arelinearly separableif there exists at least onelinei... | https://en.wikipedia.org/wiki/Linear_separability |
Theroot mean square deviation(RMSD) orroot mean square error(RMSE) is either one of two closely related and frequently used measures of the differences between true or predicted values on the one hand and observed values or anestimatoron the other.
Thedeviationis typically simply a differences ofscalars; it can also be... | https://en.wikipedia.org/wiki/Root_mean_square_deviation |
Inmathematics, areal-valued functionis calledconvexif theline segmentbetween any two distinct points on thegraph of the functionlies above or on the graph between the two points. Equivalently, a function is convex if itsepigraph(the set of points on or above the graph of the function) is aconvex set.
In simple terms, ... | https://en.wikipedia.org/wiki/Convex_function |
Inmathematics, thecomposition operator∘{\displaystyle \circ }takes twofunctions,f{\displaystyle f}andg{\displaystyle g}, and returns a new functionh(x):=(g∘f)(x)=g(f(x)){\displaystyle h(x):=(g\circ f)(x)=g(f(x))}. Thus, the functiongisappliedafter applyingftox.(g∘f){\displaystyle (g\circ f)}is pronounced "the compositi... | https://en.wikipedia.org/wiki/Composition_of_functions |
Aneural networkis a group of interconnected units calledneuronsthat send signals to one another. Neurons can be eitherbiological cellsormathematical models. While individual neurons are simple, many of them together in a network can perform complex tasks. There are two main types of neural networks.
In the context of ... | https://en.wikipedia.org/wiki/Neural_network |
Inmachine learningandpattern recognition, afeatureis an individual measurable property or characteristic of a data set.[1]Choosing informative, discriminating, and independent features is crucial to produce effectivealgorithmsforpattern recognition,classification, andregressiontasks. Features are usually numeric, but o... | https://en.wikipedia.org/wiki/Feature_space |
Aneural networkis a group of interconnected units calledneuronsthat send signals to one another. Neurons can be eitherbiological cellsormathematical models. While individual neurons are simple, many of them together in a network can perform complex tasks. There are two main types of neural networks.
In the context of ... | https://en.wikipedia.org/wiki/Neural_network#Fully_connected_networks |
Instatisticsandmachine learning, thebias–variance tradeoffdescribes the relationship between a model's complexity, the accuracy of its predictions, and how well it can make predictions on previously unseen data that were not used to train the model. In general, as we increase the number of tunable parameters in a model... | https://en.wikipedia.org/wiki/Bias%E2%80%93variance_tradeoff |
Forsupervised learningapplications inmachine learningandstatistical learning theory,generalization error[1](also known as theout-of-sample error[2]or therisk) is a measure of how accurately analgorithmis able to predict outcomes for previously unseen data. As learning algorithms are evaluated on finite samples, the eva... | https://en.wikipedia.org/wiki/Generalization_error |
Instatistics, amixture modelis aprobabilistic modelfor representing the presence ofsubpopulationswithin an overall population, without requiring that an observed data set should identify the sub-population to which an individual observation belongs. Formally a mixture model corresponds to themixture distributionthat re... | https://en.wikipedia.org/wiki/Gaussian_mixture_model |
Instatistics, anexpectation–maximization(EM)algorithmis aniterative methodto find (local)maximum likelihoodormaximum a posteriori(MAP) estimates ofparametersinstatistical models, where the model depends on unobservedlatent variables.[1]The EM iteration alternates between performing an expectation (E) step, which create... | https://en.wikipedia.org/wiki/Expectation%E2%80%93maximization_algorithm |
Minimax(sometimesMinmax,MM[1]orsaddle point[2]) is a decision rule used inartificial intelligence,decision theory,game theory,statistics, andphilosophyforminimizingthe possiblelossfor aworst case (maximum loss) scenario. When dealing with gains, it is referred to as "maximin" – to maximize the minimum gain. Originally ... | https://en.wikipedia.org/wiki/Minimax |
In astatistical-classificationproblem with two classes, adecision boundaryordecision surfaceis ahypersurfacethat partitions the underlyingvector spaceinto two sets, one for each class. The classifier will classify all the points on one side of the decision boundary as belonging to one class and all those on the other s... | https://en.wikipedia.org/wiki/Decision_boundary |
Invector calculus, thegradientof ascalar-valueddifferentiable functionf{\displaystyle f}ofseveral variablesis thevector field(orvector-valued function)∇f{\displaystyle \nabla f}whose value at a pointp{\displaystyle p}gives the direction and the rate of fastest increase. The gradient transforms like a vector under chang... | https://en.wikipedia.org/wiki/Gradient |
Inmathematics,matrix calculusis a specialized notation for doingmultivariable calculus, especially over spaces ofmatrices. It collects the variouspartial derivativesof a singlefunctionwith respect to manyvariables, and/or of amultivariate functionwith respect to a single variable, intovectorsand matrices that can be t... | https://en.wikipedia.org/wiki/Matrix_calculus |
Convex optimizationis a subfield ofmathematical optimizationthat studies the problem of minimizingconvex functionsoverconvex sets(or, equivalently, maximizingconcave functionsover convex sets). Many classes of convex optimization problems admit polynomial-time algorithms,[1]whereas mathematical optimization is in gene... | https://en.wikipedia.org/wiki/Convex_optimization |
Theposterior probabilityis a type ofconditional probabilitythat results fromupdatingtheprior probabilitywith information summarized by thelikelihoodvia an application ofBayes' rule.[1]From anepistemological perspective, the posterior probability contains everything there is to know about an uncertain proposition (such ... | https://en.wikipedia.org/wiki/Posterior_probability |
Adversarial machine learningis the study of the attacks onmachine learningalgorithms, and of the defenses against such attacks.[1]A survey from May 2020 revealed practitioners' common feeling for better protection of machine learning systems in industrial applications.[2]
Machine learning techniques are mostly designe... | https://en.wikipedia.org/wiki/Adversarial_machine_learning |
Inmathematics,subderivatives(orsubgradient) generalizes thederivativeto convex functions which are not necessarilydifferentiable. The set of subderivatives at a point is called thesubdifferentialat that point.[1]Subderivatives arise inconvex analysis, the study ofconvex functions, often in connection toconvex optimizat... | https://en.wikipedia.org/wiki/Subgradient |
Inoperator theory, a branch of mathematics, apositive-definite kernelis a generalization of apositive-definite functionor apositive-definite matrix. It was first introduced byJames Mercerin the early 20th century, in the context of solvingintegral operator equations. Since then, positive-definite functions and their va... | https://en.wikipedia.org/wiki/Positive_definite_kernel |
Inmachine learning,kernel machinesare a class of algorithms forpattern analysis, whose best known member is thesupport-vector machine(SVM). These methods involve using linear classifiers to solve nonlinear problems.[1]The general task ofpattern analysisis to find and study general types of relations (for examplecluster... | https://en.wikipedia.org/wiki/Kernel_method |
Inmachine learning, alinear classifiermakes aclassificationdecision for each object based on alinear combinationof itsfeatures. Such classifiers work well for practical problems such asdocument classification, and more generally for problems with many variables (features), reaching accuracy levels comparable to non-li... | https://en.wikipedia.org/wiki/Linear_classifier |
Linear least squares(LLS) is theleast squares approximationoflinear functionsto data.
It is a set of formulations for solving statistical problems involved inlinear regression, including variants forordinary(unweighted),weighted, andgeneralized(correlated)residuals.Numerical methods for linear least squaresinclude inve... | https://en.wikipedia.org/wiki/Normal_equation |
Word2vecis a technique innatural language processing(NLP) for obtainingvectorrepresentations of words. These vectors capture information about the meaning of the word based on the surrounding words. The word2vec algorithm estimates these representations by modeling text in a largecorpus. Once trained, such a model can ... | https://en.wikipedia.org/wiki/Word2vec |
Inmathematical optimizationanddecision theory, aloss functionorcost function(sometimes also called an error function)[1]is a function that maps aneventor values of one or more variables onto areal numberintuitively representing some "cost" associated with the event. Anoptimization problemseeks to minimize a loss functi... | https://en.wikipedia.org/wiki/Loss_function#L1_loss |
Inmathematical optimizationanddecision theory, aloss functionorcost function(sometimes also called an error function)[1]is a function that maps aneventor values of one or more variables onto areal numberintuitively representing some "cost" associated with the event. Anoptimization problemseeks to minimize a loss functi... | https://en.wikipedia.org/wiki/Loss_function#L2_loss |
Matrix completionis the task of filling in the missing entries of a partially observed matrix, which is equivalent to performing dataimputationin statistics. A wide range of datasets are naturally organized in matrix form. One example is the movie-ratings matrix, as appears in theNetflix problem: Given a ratings matrix... | https://en.wikipedia.org/wiki/Matrix_completion |
Aneural networkis a group of interconnected units calledneuronsthat send signals to one another. Neurons can be eitherbiological cellsormathematical models. While individual neurons are simple, many of them together in a network can perform complex tasks. There are two main types of neural networks.
In the context of ... | https://en.wikipedia.org/wiki/Neural_network#Training_neural_networks |
Indeep learning, amultilayer perceptron(MLP) is a name for a modernfeedforwardneural networkconsisting of fully connected neurons with nonlinearactivation functions, organized in layers, notable for being able to distinguish data that is notlinearly separable.[1]
Modern neural networks are trained usingbackpropagation... | https://en.wikipedia.org/wiki/Multilayer_perceptron |
Inmathematics, anormis afunctionfrom a real or complexvector spaceto the non-negative real numbers that behaves in certain ways like the distance from theorigin: itcommuteswith scaling, obeys a form of thetriangle inequality, and zero is only at the origin. In particular, theEuclidean distancein aEuclidean spaceis defi... | https://en.wikipedia.org/wiki/Norm_(mathematics) |
Inmathematics, thelogarithmof a number is theexponentby which another fixed value, thebase, must be raised to produce that number. For example, the logarithm of1000to base10is3, because1000is10to the3rd power:1000 = 103= 10 × 10 × 10. More generally, ifx=by, thenyis the logarithm ofxto baseb, writtenlogbx, solog101000 ... | https://en.wikipedia.org/wiki/Logarithm |
Inmathematics,sineandcosinearetrigonometric functionsof anangle. The sine and cosine of an acuteangleare defined in the context of aright triangle: for the specified angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of thetriangle(thehypotenuse), and the cosine... | https://en.wikipedia.org/wiki/Sine |
Inmathematics, theexponential functionis the uniquereal functionwhich mapszerotooneand has aderivativeeverywhere equal to its value. The exponential of a variablex{\displaystyle x}is denotedexpx{\displaystyle \exp x}orex{\displaystyle e^{x}}, with the two notations used interchangeably. It is calledexponentialbe... | https://en.wikipedia.org/wiki/Exponential_function |
Ridge regression(also known asTikhonov regularization, named forAndrey Tikhonov) is a method of estimating thecoefficientsof multiple-regression modelsin scenarios where the independent variables are highly correlated.[1]It has been used in many fields including econometrics, chemistry, and engineering.[2]It is a metho... | https://en.wikipedia.org/wiki/Ridge_regression |
Inmathematics,statistics,finance,[1]andcomputer science, particularly inmachine learningandinverse problems,regularizationis a process that converts theanswer to a problemto a simpler one. It is often used in solvingill-posed problemsor to preventoverfitting.[2]
Although regularization procedures can be divided in man... | https://en.wikipedia.org/wiki/Regularization_(machine_learning) |
Inmachine learning, a common task is the study and construction ofalgorithmsthat can learn from and make predictions ondata.[1]Such algorithms function by making data-driven predictions or decisions,[2]through building amathematical modelfrom input data. These input data used to build the model are usually divided into... | https://en.wikipedia.org/wiki/Training_set |
Inlinear algebra, aneigenvector(/ˈaɪɡən-/EYE-gən-) orcharacteristic vectoris avectorthat has itsdirectionunchanged (or reversed) by a givenlinear transformation. More precisely, an eigenvectorv{\displaystyle \mathbf {v} }of a linear transformationT{\displaystyle T}isscaled by a constant factorλ{\displaystyle \lambda }w... | https://en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors |
Nearest neighbor search(NNS), as a form ofproximity search, is theoptimization problemof finding the point in a given set that is closest (or most similar) to a given point. Closeness is typically expressed in terms of a dissimilarity function: the lesssimilarthe objects, the larger the function values.
Formally, the ... | https://en.wikipedia.org/wiki/Nearest_neighbor_search |
Instatisticsandmachine learning, thebias–variance tradeoffdescribes the relationship between a model's complexity, the accuracy of its predictions, and how well it can make predictions on previously unseen data that were not used to train the model. In general, as we increase the number of tunable parameters in a model... | https://en.wikipedia.org/wiki/Bias-variance_tradeoff |
Inmathematics, aconcave functionis one for which the function value at any convex combination of elements in the domain is greater than or equal to that convex combination of those domain elements. Equivalently, a concave function is any function for which thehypographis convex. The class of concave functions is in a s... | https://en.wikipedia.org/wiki/Concave_function |
Inmathematics,sineandcosinearetrigonometric functionsof anangle. The sine and cosine of an acuteangleare defined in the context of aright triangle: for the specified angle, its sine is the ratio of the length of the side opposite that angle to the length of the longest side of thetriangle(thehypotenuse), and the cosine... | https://en.wikipedia.org/wiki/Cosine#Properties |
Agenerative adversarial network(GAN) is a class ofmachine learningframeworks and a prominent framework for approachinggenerative artificial intelligence. The concept was initially developed byIan Goodfellowand his colleagues in June 2014.[1]In a GAN, twoneural networkscompete with each other in the form of azero-sum ga... | https://en.wikipedia.org/wiki/Generative_adversarial_network |
Discriminative models, also referred to asconditional models, are a class of models frequently used forclassification. They are typically used to solvebinary classificationproblems, i.e. assign labels, such as pass/fail, win/lose, alive/dead or healthy/sick, to existing datapoints.
Types of discriminative models inclu... | https://en.wikipedia.org/wiki/Discriminative_model |
Inprobabilityandstatistics, anexponential familyis aparametricset ofprobability distributionsof a certain form, specified below. This special form is chosen for mathematical convenience, including the enabling of the user to calculate expectations, covariances using differentiation based on some useful algebraic proper... | https://en.wikipedia.org/wiki/Exponential_family |
Γ(⌊k+1⌋,λ)⌊k⌋!,{\displaystyle {\frac {\Gamma (\lfloor k+1\rfloor ,\lambda )}{\lfloor k\rfloor !}},}ore−λ∑j=0⌊k⌋λjj!,{\displaystyle e^{-\lambda }\sum _{j=0}^{\lfloor k\rfloor }{\frac {\lambda ^{j}}{j!}},}orQ(⌊k+1⌋,λ){\displaystyle Q(\lfloor k+1\rfloor ,\lambda )}
λ[1−log(λ)]+e−λ∑k=0∞λklog(k!)k!{\displaystyle \lambda ... | https://en.wikipedia.org/wiki/Poisson_distribution |
TheCauchy distribution, named afterAugustin-Louis Cauchy, is acontinuous probability distribution. It is also known, especially amongphysicists, as theLorentz distribution(afterHendrik Lorentz),Cauchy–Lorentz distribution,Lorentz(ian) function, orBreit–Wigner distribution. The Cauchy distributionf(x;x0,γ){\displaysty... | https://en.wikipedia.org/wiki/Cauchy_distribution |
Instatistics,ordinary least squares(OLS) is a type oflinear least squaresmethod for choosing the unknownparametersin alinear regressionmodel (with fixed level-one[clarification needed]effects of alinear functionof a set ofexplanatory variables) by the principle ofleast squares: minimizing the sum of the squares of the ... | https://en.wikipedia.org/wiki/Ordinary_least_squares |
Inmathematics, thecomposition operator∘{\displaystyle \circ }takes twofunctions,f{\displaystyle f}andg{\displaystyle g}, and returns a new functionh(x):=(g∘f)(x)=g(f(x)){\displaystyle h(x):=(g\circ f)(x)=g(f(x))}. Thus, the functiongisappliedafter applyingftox.(g∘f){\displaystyle (g\circ f)}is pronounced "the compositi... | https://en.wikipedia.org/wiki/Composition_of_functions#Convexity |
Inmathematical analysis, themaximumandminimum[a]of afunctionare, respectively, the greatest and least value taken by the function. Known generically asextremum,[b]they may be defined either within a givenrange(thelocalorrelativeextrema) or on the entiredomain(theglobalorabsoluteextrema) of a function.[1][2][3]Pierre de... | https://en.wikipedia.org/wiki/Global_minimum |
Inmathematical optimizationanddecision theory, aloss functionorcost function(sometimes also called an error function)[1]is a function that maps aneventor values of one or more variables onto areal numberintuitively representing some "cost" associated with the event. Anoptimization problemseeks to minimize a loss functi... | https://en.wikipedia.org/wiki/Loss_function#Mean_squared_error |
Innumber theory, theFermat quotientof anintegerawith respect to anoddprimepis defined as[1][2][3][4]
or
This article is about the former; for the latter seep-derivation. The quotient is named afterPierre de Fermat.
If the baseaiscoprimeto the exponentpthenFermat's little theoremsays thatqp(a) will be an integer. If ... | https://en.wikipedia.org/wiki/Fermat_quotient |
Incommutative algebraandfield theory, theFrobenius endomorphism(afterFerdinand Georg Frobenius) is a specialendomorphismofcommutativeringswithprimecharacteristicp, an important class that includesfinite fields. The endomorphism maps every element to itsp-th power. In certain contexts it is anautomorphism, but this is n... | https://en.wikipedia.org/wiki/Frobenius_endomorphism |
Inmathematics, more specificallydifferential algebra, ap-derivation(forpaprime number) on aringR, is a mapping fromRtoRthat satisfies certain conditions outlined directly below. The notion of ap-derivationis related to that of aderivationin differential algebra.
Letpbe a prime number. Ap-derivationor Buium derivative ... | https://en.wikipedia.org/wiki/P-derivation |
Arepeating decimalorrecurring decimalis adecimal representationof a number whosedigitsare eventuallyperiodic(that is, after some place, the same sequence of digits is repeated forever); if this sequence consists only of zeros (that is if there is only a finite number of nonzero digits), the decimal is said to betermina... | https://en.wikipedia.org/wiki/Recurring_decimal#Fractions_with_prime_denominators |
TheRSA(Rivest–Shamir–Adleman)cryptosystemis apublic-key cryptosystem, one of the oldest widely used for secure data transmission. Theinitialism"RSA" comes from the surnames ofRon Rivest,Adi ShamirandLeonard Adleman, who publicly described the algorithm in 1977. An equivalent system was developed secretly in 1973 atGove... | https://en.wikipedia.org/wiki/RSA_(algorithm) |
Innumber theory, acongruenceis anequivalence relationon theintegers. The following sections list important or interesting prime-related congruences.
There are other prime-related congruences that provide necessary and sufficient conditions on the primality of certain subsequences of the natural numbers.
Many of thes... | https://en.wikipedia.org/wiki/Table_of_congruences |
Inmathematics, particularly in the area ofarithmetic, amodular multiplicative inverseof anintegerais an integerxsuch that the productaxiscongruentto 1 with respect to the modulusm.[1]In the standard notation ofmodular arithmeticthis congruence is written as
which is the shorthand way of writing the statement thatmdivi... | https://en.wikipedia.org/wiki/Modular_multiplicative_inverse |
Incombinatorialmathematics, theBell polynomials, named in honor ofEric Temple Bell, are used in the study of set partitions. They are related toStirlingandBell numbers. They also occur in many applications, such as inFaà di Bruno's formula.
Thepartialorincompleteexponential Bell polynomials are atriangular arrayof pol... | https://en.wikipedia.org/wiki/Bell_polynomials |
TheCatalan numbersare asequenceofnatural numbersthat occur in variouscounting problems, often involvingrecursivelydefined objects. They are named afterEugène Catalan, though they were previously discovered in the 1730s byMinggatu.
Then-th Catalan number can be expressed directly in terms of thecentral binomial coeffic... | https://en.wikipedia.org/wiki/Catalan_number |
Inmathematics, thecyclesof apermutationπof a finitesetScorrespondbijectivelyto theorbitsof the subgroup generated byπactingonS. These orbits aresubsetsofSthat can be written as{c1, ...,cn}, such that
The corresponding cycle ofπis written as (c1c2...cn); this expression is not unique sincec1can be chosen to be any elem... | https://en.wikipedia.org/wiki/Cycles_and_fixed_points |
Inmathematics, thefalling factorial(sometimes called thedescending factorial,[1]falling sequential product, orlower factorial) is defined as the polynomial(x)n=xn_=x(x−1)(x−2)⋯(x−n+1)⏞nfactors=∏k=1n(x−k+1)=∏k=0n−1(x−k).{\displaystyle {\begin{aligned}(x)_{n}=x^{\underline {n}}&=\overbrace {x(x-1)(x-2)\cdots (x-n+1)} ^{n... | https://en.wikipedia.org/wiki/Pochhammer_symbol |
Inmathematics, apolynomial sequenceis asequenceofpolynomialsindexed by the nonnegativeintegers0, 1, 2, 3, ..., in which eachindexis equal to thedegreeof the corresponding polynomial. Polynomial sequences are a topic of interest inenumerative combinatoricsandalgebraic combinatorics, as well asapplied mathematics.
Some... | https://en.wikipedia.org/wiki/Polynomial_sequence |
TheTouchard polynomials, studied byJacques Touchard(1939),[1]also called theexponential polynomialsorBell polynomials, comprise apolynomial sequenceofbinomial typedefined by
whereS(n,k)={nk}{\displaystyle S(n,k)=\left\{{n \atop k}\right\}}is aStirling number of the second kind, i.e., the number ofpartitions of a setof... | https://en.wikipedia.org/wiki/Touchard_polynomials |
Incombinatorial mathematics, aStirling permutationof orderkis apermutationof themultiset1, 1, 2, 2, ...,k,k(with two copies of each value from 1 tok) with the additional property that, for each valueiappearing in the permutation, any values between the two copies ofiare larger thani. For instance, the 15 Stirling permu... | https://en.wikipedia.org/wiki/Stirling_permutation |
Inmathematics, theLanczos approximationis a method for computing thegamma functionnumerically, published byCornelius Lanczosin 1964. It is a practical alternative to the more popularStirling's approximationfor calculating the gamma function with fixed precision.
The Lanczos approximation consists of the formula
for t... | https://en.wikipedia.org/wiki/Lanczos_approximation |
In mathematics,Spouge's approximationis a formula for computing an approximation of thegamma function. It was named after John L. Spouge, who defined the formula in a 1994 paper.[1]The formula is a modification ofStirling's approximation, and has the form
whereais an arbitrary positive integer and the coefficients are... | https://en.wikipedia.org/wiki/Spouge%27s_approximation |
Acellular networkormobile networkis atelecommunications networkwhere the link to and from end nodes iswirelessand the network is distributed over land areas calledcells, each served by at least one fixed-locationtransceiver(such as abase station). These base stations provide the cell with the network coverage which can... | https://en.wikipedia.org/wiki/Cellular_network |
Enhanced Data rates for GSM Evolution(EDGE), also known as2.75Gand under various other names, is a2Gdigitalmobile phonetechnology forpacket switcheddata transmission. It is a subset ofGeneral Packet Radio Service(GPRS) on theGSMnetwork and improves upon it offering speeds close to3Gtechnology, hence the name 2.75G. EDG... | https://en.wikipedia.org/wiki/Enhanced_Data_Rates_for_GSM_Evolution |
Call forwarding, orcall diversion, is atelephonyfeature of all telephone switching systems which redirects a telephone call to another destination, which may be, for example, amobileor anothertelephone numberwhere the desiredcalled partyis available. Call forwarding was invented by Ernest J. Bonanno.[1]
In North Ameri... | https://en.wikipedia.org/wiki/Call_forwarding#Mobile_(cell)_phones |
GSM frequency bandsor frequency ranges are thecellular frequenciesdesignated by theITUfor the operation ofGSMmobile phonesand othermobile devices.
A dual-band 900/1800 device is required to be compatible with most networks apart from deployments inITU Region2.
GSM-900 and GSM-1800 are used in most parts of the world ... | https://en.wikipedia.org/wiki/GSM_frequency_bands |
AGSM moduleis a device that allows electronic devices to communicate with each other over theGSMnetwork. GSM is a standard for digital cellular communications, which means that it provides a platform for mobile devices to communicate with each other wirelessly. The GSM module is a specialized device that enables a devi... | https://en.wikipedia.org/wiki/GSM_modem |
GSM servicesare a standard collection of applications and features available over theGlobal System for Mobile Communications(GSM) tomobile phonesubscribers all over the world. The GSM standards are defined by the3GPPcollaboration and implemented in hardware and software by equipment manufacturers andmobile phone operat... | https://en.wikipedia.org/wiki/GSM_services |
Cell Broadcast(CB) is a method of simultaneously sendingshort messagesto multiplemobile telephoneusers in a defined area. It is defined by theETSI's GSM committee and3GPPand is part of the2G,3G,4Gand5Gstandards.[1]It is also known as Short Message Service-Cell Broadcast (SMS-CB or CB SMS).[2][3]
Unlike Short Message S... | https://en.wikipedia.org/wiki/Cell_Broadcast |
Mobile phone trackingis a process for identifying the location of a mobile phone, whether stationary or moving. Localization may be affected by a number of technologies, such as themultilaterationof radio signals between (several)cell towersof thenetworkand the phone or by simply usingGNSS. To locate a mobile phone usi... | https://en.wikipedia.org/wiki/GSM_localization |
Multimedia Messaging Service(MMS) is a standard way to send messages that includemultimediacontent to and from amobile phoneover acellular network. Users and providers may refer to such a message as aPXT, apicture message, or amultimedia message.[1]The MMS standard extends the coreSMS(Short Message Service) capability,... | https://en.wikipedia.org/wiki/Multimedia_Messaging_Service |
Network Identity and Time Zone(NITZ)[1]is a mechanism for provisioning localtimeand date,time zoneanddaylight saving time(DST) offset, as well asnetwork provideridentity information, tomobile devicesvia a wireless network.[2]
NITZ has been an optional part of the officialGSMstandard since phase 2+ release 96.[3]
NITZ... | https://en.wikipedia.org/wiki/NITZ |
Wireless Application Protocol(WAP) is an obsoletetechnical standardfor accessing information over amobile cellular network. Introduced in 1999,[1]WAP allowed users with compatiblemobile devicesto browse content such as news, weather and sports scores provided bymobile network operators, specially designed for the limit... | https://en.wikipedia.org/wiki/Wireless_Application_Protocol |
GSM-R,Global System for Mobile Communications – RailwayorGSM-Railwayis an internationalwirelesscommunications standard forrailwaycommunication and applications.
A sub-system ofEuropean Rail Traffic Management System(ERTMS), it is used for communication between train and railway regulation control centers. The system i... | https://en.wikipedia.org/wiki/GSM-R |
Unstructured Supplementary Service Data(USSD), sometimes referred to as "quick codes" or "feature codes", is acommunications protocolused byGSMcellular telephonesto communicate with themobile network operator's computers. USSD can be used forWAPbrowsing, prepaid callback service, mobile-money services, location-based c... | https://en.wikipedia.org/wiki/Unstructured_Supplementary_Service_Data |
Incellulartelecommunications,handover, orhandoff, is the process of transferring an ongoing call or data session from one channel connected to thecore networkto another channel. Insatellite communicationsit is the process of transferring satellite control responsibility from oneearth stationto another without loss or i... | https://en.wikipedia.org/wiki/Handoff |
High Speed Packet Access(HSPA)[1]is an amalgamation of twomobileprotocols—High Speed Downlink Packet Access (HSDPA) and High Speed Uplink Packet Access (HSUPA)—that extends and improves the performance of existing3Gmobile telecommunication networks using theWCDMAprotocols. A further-improved3GPPstandard calledEvolved H... | https://en.wikipedia.org/wiki/High-Speed_Downlink_Packet_Access |
TheInternational Mobile Equipment Identity(IMEI)[1]is a numericidentifier, usuallyunique,[2][3]for3GPPandiDENmobile phones, as well as somesatellite phones. It is usually found printed inside the battery compartment of the phone but can also be displayed on-screen on most phones by entering theMMI Supplementary Service... | https://en.wikipedia.org/wiki/International_Mobile_Equipment_Identity |
Theinternational mobile subscriber identity(IMSI;/ˈɪmziː/) is a number that uniquely identifies every user of acellular network.[1]It is stored as a64-bitfield and is sent by the mobile device to the network. It is also used for acquiring other details of the mobile in thehome location register(HLR) or as locally copie... | https://en.wikipedia.org/wiki/International_Mobile_Subscriber_Identity |
Intelecommunications,long-term evolution(LTE) is astandardforwireless broadbandcommunication forcellularmobile devices and data terminals. It is considered to be a "transitional"4Gtechnology,[1]and is therefore also referred to as3.95Gas a step above3G.[2]
LTE is based on the2GGSM/EDGEand 3GUMTS/HSPAstandards. It impr... | https://en.wikipedia.org/wiki/LTE_(telecommunication) |
MSISDN(/ˈɛmɛsaɪɛsdiːɛn/MISS-den) is a number uniquely identifying a subscription in aGlobal System for Mobile communicationsor aUniversal Mobile Telecommunications Systemmobile network. It is the mapping of the telephone number to thesubscriber identity modulein a mobile or cellular phone. This abbreviation has several... | https://en.wikipedia.org/wiki/MSISDN |
NMT(Nordic Mobile Telephony) is an automatic cellular phone system specified byNordictelecommunications administrations (PTTs) and opened for service on 1 October 1981. NMT is based onanaloguetechnology (first generation or1G) and two variants exist: NMT-450 and NMT-900. The numbers indicate the frequency bands used. N... | https://en.wikipedia.org/wiki/Nordic_Mobile_Telephone |
ORFSstands forOutput RF Spectrum, where 'RF' stands forRadio Frequency.
The acronym ORFS is used in the context of mobile communication systems, e.g.,GSM. It stands for the relationship between (a) the frequency offset from the carrier and (b) the power, measured in a specific bandwidth and time, produced by the mobil... | https://en.wikipedia.org/wiki/ORFS |
Personal communications network(PCN) is the European digital cellular mobile telephone network. The underlying standard is known asDigital Cellular System, which defines a variant ofGSMoperating at 1.7–1.88 GHz.GSM-1800has since been adopted by other locations, not necessarily under the PCN/DCS name. The network struct... | https://en.wikipedia.org/wiki/Personal_communications_network |
TheReal-time Transport Protocol(RTP) specifies a general-purpose data format andnetwork protocolfor transmitting digital media streams onInternet Protocol(IP) networks. The details of media encoding, such as signal sampling rate, frame size and timing, are specified in anRTP payload format. The format parameters of the... | https://en.wikipedia.org/wiki/RTP_audio_video_profile |
Incomputer networkresearch,network simulationis a technique whereby a software program replicates the behavior of a real network. This is achieved by calculating the interactions between the different network entities such as routers, switches, nodes, access points, links, etc.[1]Most simulators use discrete event simu... | https://en.wikipedia.org/wiki/Network_simulation |
This is a comparison of standards of wireless networking technologies for devices such asmobile phones. A newgenerationof cellular standards has appeared approximately every tenth year since1Gsystems were introduced in 1979 and the early to mid-1980s.
Global System for Mobile Communications(GSM, around 80–85% market s... | https://en.wikipedia.org/wiki/Comparison_of_mobile_phone_standards |
GEO-Mobile Radio Interface(GEO stands forGeostationary Earth Orbit), better known asGMR, is anETSIstandard forsatellite phones. The GMR standard is derived from the3GPP-family terrestrial digital cellular standards and supports access to GSM/UMTS core networks. It is used byACeS,ICO,Inmarsat,SkyTerra,TerreStarandThuray... | https://en.wikipedia.org/wiki/GEO-Mobile_Radio_Interface |
TheSMGGSM 02.07Technical Specification (Version 7.1.0 Release 1998) calledDigital cellular telecommunications system (Phase 2+); Mobile Stations (MS) featuresdefines Mobile Station (MS) features and to classifies them according to their type and whether they are mandatory or optional. The MS features detailed in this s... | https://en.wikipedia.org/wiki/GSM_02.07 |
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