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Epiphenomenalism is a position in the philosophy of mind on the mind–body problem. It holds that subjective mental events are completely dependent for their existence on corresponding physical and biochemical events within the human body, but do not themselves influence physical events. According to epiphenomenalism, t... | Wikipedia/Epiphenomenalism |
Action theory or theory of action is an area in philosophy concerned with theories about the processes causing willful human bodily movements of a more or less complex kind. This area of thought involves epistemology, ethics, metaphysics, jurisprudence, and philosophy of mind, and has attracted the strong interest of p... | Wikipedia/Action_theory_(philosophy) |
Libertarianism is one of the main philosophical positions related to the problems of free will and determinism which are part of the larger domain of metaphysics. In particular, libertarianism is an incompatibilist position which argues that free will is logically incompatible with a deterministic universe. Libertarian... | Wikipedia/Libertarianism_(metaphysics) |
In the field of artificial intelligence, an inference engine is a software component of an intelligent system that applies logical rules to the knowledge base to deduce new information. The first inference engines were components of expert systems. The typical expert system consisted of a knowledge base and an inferenc... | Wikipedia/Inference_engine |
In the philosophy of mind, functionalism is the thesis that each and every mental state (for example, the state of having a belief, of having a desire, or of being in pain) is constituted solely by its functional role, which means its causal relation to other mental states, sensory inputs, and behavioral outputs. Funct... | Wikipedia/Functionalism_(philosophy_of_mind) |
A theory of art is intended to contrast with a definition of art. Traditionally, definitions are composed of necessary and sufficient conditions, and a single counterexample overthrows such a definition. Theorizing about art, on the other hand, is analogous to a theory of a natural phenomenon like gravity. In fact, the... | Wikipedia/Institutional_theory_of_art |
An immediate inference is an inference which can be made from only one statement or proposition. For instance, from the statement "All toads are green", the immediate inference can be made that "no toads are not green" or "no toads are non-green" (Obverse). There are a number of immediate inferences which can validly b... | Wikipedia/Immediate_inference |
Inference is a live album by pianist Marilyn Crispell and saxophonist Tim Berne which was recorded during the Toronto Jazz Festival in 1992 and released on the Music & Arts label.
== Reception ==
The AllMusic review by Scott Yanow said "This set has plenty of stimulating and unpredictable interplay by the two giants... | Wikipedia/Inference_(album) |
In the general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of matter within it.
The equations were published by Albert Einstein in 1915 in the form of a tensor equation which related the local spacetime curvature (expr... | Wikipedia/Einstein_equation |
In physics, specifically field theory and particle physics, the Proca action describes a massive spin-1 field of mass m in Minkowski spacetime. The corresponding equation is a relativistic wave equation called the Proca equation. The Proca action and equation are named after Romanian physicist Alexandru Proca.
The Proc... | Wikipedia/Proca_equation |
An operator is a function over a space of physical states onto another space of states. The simplest example of the utility of operators is the study of symmetry (which makes the concept of a group useful in this context). Because of this, they are useful tools in classical mechanics. Operators are even more important ... | Wikipedia/Operator_(quantum_mechanics) |
The Bethe–Salpeter equation (BSE, named after Hans Bethe and Edwin Salpeter) is an integral equation, the solution of which describes the structure of a relativistic two-body (particles) bound state in a covariant formalism quantum field theory (QFT). The equation was first published in 1950 at the end of a paper by Y... | Wikipedia/Bethe–Salpeter_equation |
In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form
d
V
=
ρ
... | Wikipedia/Differential_volume_element |
Maxwell's equations, or Maxwell–Heaviside equations, are a set of coupled partial differential equations that, together with the Lorentz force law, form the foundation of classical electromagnetism, classical optics, electric and magnetic circuits.
The equations provide a mathematical model for electric, optical, and ... | Wikipedia/Maxwell_equation |
In physics, the Hamilton–Jacobi equation, named after William Rowan Hamilton and Carl Gustav Jacob Jacobi, is an alternative formulation of classical mechanics, equivalent to other formulations such as Newton's laws of motion, Lagrangian mechanics and Hamiltonian mechanics.
The Hamilton–Jacobi equation is a formulation... | Wikipedia/Hamilton's_principal_function |
Fuzzy Sets and Systems is a peer-reviewed international scientific journal published by Elsevier on behalf of the International Fuzzy Systems Association (IFSA) and was founded in 1978. The editors-in-chief (as of 2010) are Bernard De Baets of the Department of Data Analysis and Mathematical Modelling (at Ghent Univers... | Wikipedia/Fuzzy_Sets_and_Systems |
In mathematics and mathematical biology, the Mackey–Glass equations, named after Michael Mackey and Leon Glass, refer to a family of delay differential equations whose behaviour manages to mimic both healthy and pathological behaviour in certain biological contexts, controlled by the equation's parameters. Originally, ... | Wikipedia/Mackey–Glass_equations |
In the theory of dynamical systems, the exponential map can be used as the evolution function of the discrete nonlinear dynamical system.
== Family ==
The family of exponential functions is called the exponential family.
== Forms ==
There are many forms of these maps, many of which are equivalent under a coordinate... | Wikipedia/Exponential_map_(discrete_dynamical_systems) |
Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
Originally founded in 1842 in Berlin, it expanded internationally in the 1960s, and through mergers in th... | Wikipedia/Springer_Science+Business_Media_Dordrecht |
The Biham–Middleton–Levine traffic model is a self-organizing cellular automaton traffic flow model. It consists of a number of cars represented by points on a lattice with a random starting position, where each car may be one of two types: those that only move downwards (shown as blue in this article), and those that ... | Wikipedia/BML_traffic_model |
In cryptography, encryption (more specifically, encoding) is the process of transforming information in a way that, ideally, only authorized parties can decode. This process converts the original representation of the information, known as plaintext, into an alternative form known as ciphertext. Despite its goal, encr... | Wikipedia/Encryption_algorithms |
The Kuramoto model (or Kuramoto–Daido model), first proposed by Yoshiki Kuramoto (蔵本 由紀, Kuramoto Yoshiki), is a mathematical model used in describing synchronization. More specifically, it is a model for the behavior of a large set of coupled oscillators. Its formulation was motivated by the behavior of systems of che... | Wikipedia/Kuramoto_model |
In physics, the Landau–Hopf theory of turbulence, named for Lev Landau and Eberhard Hopf, was until the mid-1970s, the accepted theory of how a fluid flow becomes turbulent. It states that as a fluid flows faster, it develops more Fourier modes. At first, a few modes dominate, but under stronger conditions, it forces ... | Wikipedia/Landau-Hopf_theory_of_turbulence |
The New York Academy of Sciences (NYAS), originally founded as the Lyceum of Natural History in January 1817, is a nonprofit professional society based in New York City, with more than 20,000 members from 100 countries. It is the fourth-oldest scientific society in the United States.
The academy hosts programs and pu... | Wikipedia/New_York_Academy_of_Sciences |
The physics of a bouncing ball concerns the physical behaviour of bouncing balls, particularly its motion before, during, and after impact against the surface of another body. Several aspects of a bouncing ball's behaviour serve as an introduction to mechanics in high school or undergraduate level physics courses. Howe... | Wikipedia/Bouncing_ball_dynamics |
A population model is a type of mathematical model that is applied to the study of population dynamics.
== Rationale ==
Models allow a better understanding of how complex interactions and processes work. Modeling of dynamic interactions in nature can provide a manageable way of understanding how numbers change over ... | Wikipedia/Population_model |
The Rabinovich–Fabrikant equations are a set of three coupled ordinary differential equations exhibiting chaotic behaviour for certain values of the parameters. They are named after Mikhail Rabinovich and Anatoly Fabrikant, who described them in 1979.
== System description ==
The equations are:
... | Wikipedia/Rabinovich–Fabrikant_equations |
Chaos: Making a New Science is a debut non-fiction book by James Gleick that initially introduced the principles and early development of the chaos theory to the public. It was a finalist for the National Book Award and the Pulitzer Prize in 1987, and was shortlisted for the Science Book Prize in 1989. The book was pub... | Wikipedia/Chaos:_Making_a_New_Science |
The Duffing equation (or Duffing oscillator), named after Georg Duffing (1861–1944), is a non-linear second-order differential equation used to model certain damped and driven oscillators. The equation is given by
x
¨
... | Wikipedia/Duffing_equation |
A number of different Markov models of DNA sequence evolution have been proposed. These substitution models differ in terms of the parameters used to describe the rates at which one nucleotide replaces another during evolution. These models are frequently used in molecular phylogenetic analyses. In particular, they ar... | Wikipedia/Evolutionary_model |
In mathematics, the Gauss map (also known as Gaussian map or mouse map), is a nonlinear iterated map of the reals into a real interval given by the Gaussian function:
x
n
+
1
=
exp
(
... | Wikipedia/Gauss_iterated_map |
Society for Industrial and Applied Mathematics (SIAM) is a professional society dedicated to applied mathematics, computational science, and data science through research, publications, and community. SIAM is the world's largest scientific society devoted to applied mathematics, and roughly two-thirds of its membership... | Wikipedia/SIAM_Journal_on_Applied_Dynamical_Systems |
In mathematics, specifically in the study of dynamical systems, an orbit is a collection of points related by the evolution function of the dynamical system. It can be understood as the subset of phase space covered by the trajectory of the dynamical system under a particular set of initial conditions, as the system ev... | Wikipedia/Orbit_(dynamics) |
A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support variable-length output. The values returned by a hash function are called hash values, hash codes, (hash/message) digests, or simply hashes. The values are usually used... | Wikipedia/Hash_functions |
In systems theory, a linear system is a mathematical model of a system based on the use of a linear operator.
Linear systems typically exhibit features and properties that are much simpler than the nonlinear case.
As a mathematical abstraction or idealization, linear systems find important applications in automatic con... | Wikipedia/Linear_theory |
Cardiotocography (CTG) is a technique used to monitor the fetal heartbeat and uterine contractions during pregnancy and labour. The machine used to perform the monitoring is called a cardiotocograph.
Fetal heart sounds were described as early as 350 years ago and approximately 200 years ago mechanical stethoscopes, suc... | Wikipedia/Cardiotocography |
Passive dynamics refers to the dynamical behavior of actuators, robots, or organisms when not drawing energy from a supply (e.g., batteries, fuel, ATP). Depending on the application, considering or altering the passive dynamics of a powered system can have drastic effects on performance, particularly energy economy, s... | Wikipedia/Passive_dynamics |
In lab experiments that study chaos theory, approaches designed to control chaos are based on certain observed system behaviors. Any chaotic attractor contains an infinite number of unstable, periodic orbits. Chaotic dynamics, then, consists of a motion where the system state moves in the neighborhood of one of these o... | Wikipedia/Control_of_chaos |
In mathematics, iterated function systems (IFSs) are a method of constructing fractals; the resulting fractals are often self-similar. IFS fractals are more related to set theory than fractal geometry. They were introduced in 1981.
IFS fractals, as they are normally called, can be of any number of dimensions, but are c... | Wikipedia/Iterated_function_system |
The dyadic transformation (also known as the dyadic map, bit shift map, 2x mod 1 map, Bernoulli map, doubling map or sawtooth map) is the mapping (i.e., recurrence relation)
T
:
[
0
,
1
)
→
[
0
,
1
... | Wikipedia/Dyadic_transformation |
Chaos theory is a mathematical theory describing erratic behavior in certain nonlinear dynamical systems.
Chaos Theory may also refer to:
== Film and television ==
Chaos Theory (film), a 2008 comedy-drama
"Chaos Theory", an episode of ER (season 9)
"Chaos Theory", an episode of CSI: Crime Scene Investigation (season... | Wikipedia/Chaos_theory_(disambiguation) |
In mathematics, an interval exchange transformation is a kind of dynamical system that generalises circle rotation. The phase space consists of the unit interval, and the transformation acts by cutting the interval into several subintervals, and then permuting these subintervals. They arise naturally in the study of ... | Wikipedia/Interval_exchange_transformation |
A neuron (American English), neurone (British English), or nerve cell, is an excitable cell that fires electric signals called action potentials across a neural network in the nervous system. They are located in the nervous system and help to receive and conduct impulses. Neurons communicate with other cells via synaps... | Wikipedia/Neuron |
In statistical mechanics, universality is the observation that there are properties for a large class of systems that are independent of the dynamical details of the system. Systems display universality in a scaling limit, when a large number of interacting parts come together. The modern meaning of the term was introd... | Wikipedia/Universality_(dynamical_systems) |
In the theory of dynamical systems, the shadowing lemma is a lemma describing the behaviour of pseudo-orbits near a hyperbolic invariant set. Informally, the theory states that every pseudo-orbit (which one can think of as a numerically computed trajectory with rounding errors on every step) stays uniformly close to so... | Wikipedia/Shadowing_lemma |
Stein's lemma, named in honor of Charles Stein, is a theorem of probability theory that is of interest primarily because of its applications to statistical inference — in particular, to James–Stein estimation and empirical Bayes methods — and its applications to portfolio choice theory. The theorem gives a formula for ... | Wikipedia/Stein's_lemma |
A random r-regular graph is a graph selected from
G
n
,
r
{\displaystyle {\mathcal {G}}_{n,r}}
, which denotes the probability space of all r-regul... | Wikipedia/Random_regular_graph |
The Hann function is named after the Austrian meteorologist Julius von Hann. It is a window function used to perform Hann smoothing or hanning. The function, with length
L
{\displaystyle L}
and amplitude
1
/
L
... | Wikipedia/Hann_function |
In statistics, the Khmaladze transformation is a mathematical tool used in constructing convenient goodness of fit tests for hypothetical distribution functions. More precisely, suppose
X
1
,
…
,
X
... | Wikipedia/Khmaladze_transformation |
In combinatorial mathematics and probability theory, the Schrödinger method, named after the Austrian physicist Erwin Schrödinger, is used to solve some problems of distribution and occupancy.
Suppose
X
1
,
…
,
... | Wikipedia/Schrödinger_method |
In statistics, the Anscombe transform, named after Francis Anscombe, is a variance-stabilizing transformation that transforms a random variable with a Poisson distribution into one with an approximately standard Gaussian distribution. The Anscombe transform is widely used in photon-limited imaging (astronomy, X-ray) wh... | Wikipedia/Anscombe_transform |
In probability theory and statistics, the factorial moment generating function (FMGF) of the probability distribution of a real-valued random variable X is defined as
M
X
(
t
)
=
E
... | Wikipedia/Factorial_moment_generating_function |
A hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or hidden) Markov process (referred to as
X
{\displaystyle X}
). An HMM requires that there be an observable process
Y
{\displaystyle Y}
... | Wikipedia/Poisson_hidden_Markov_model |
The Bayes factor is a ratio of two competing statistical models represented by their evidence, and is used to quantify the support for one model over the other. The models in question can have a common set of parameters, such as a null hypothesis and an alternative, but this is not necessary; for instance, it could als... | Wikipedia/Bayesian_model_comparison |
In probability theory, a degenerate distribution on a measure space
(
E
,
A
,
μ
)
{\displaystyle (E,{\mathcal {A}},\mu )}
is a probability distribution whose support is a null set with... | Wikipedia/Degenerate_distribution |
In information theory, the entropy power inequality (EPI) is a result that relates to so-called "entropy power" of random variables. It shows that the entropy power of suitably well-behaved random variables is a superadditive function. The entropy power inequality was proved in 1948 by Claude Shannon in his seminal pap... | Wikipedia/Entropy_power_inequality |
Jump diffusion is a stochastic process that involves jumps and diffusion. It has important applications in magnetic reconnection, coronal mass ejections, condensed matter physics, and pattern theory and computational vision.
== In physics ==
In crystals, atomic diffusion typically consists of jumps between vacant lat... | Wikipedia/Jump-diffusion_model |
The leftover hash lemma is a lemma in cryptography first stated by Russell Impagliazzo, Leonid Levin, and Michael Luby.
Given a secret key X that has n uniform random bits, of which an adversary was able to learn the values of some t < n bits of that key, the leftover hash lemma states that it is possible to produce a ... | Wikipedia/Leftover_hash_lemma |
The Box–Muller transform, by George Edward Pelham Box and Mervin Edgar Muller, is a random number sampling method for generating pairs of independent, standard, normally distributed (zero expectation, unit variance) random numbers, given a source of uniformly distributed random numbers. The method was first mentioned e... | Wikipedia/Box–Muller_transform |
In queueing theory, a discipline within the mathematical theory of probability, an M/M/1 queue represents the queue length in a system having a single server, where arrivals are determined by a Poisson process and job service times have an exponential distribution. The model name is written in Kendall's notation. The m... | Wikipedia/M/M/1_model |
In probability theory, two sequences of probability measures are said to be contiguous if asymptotically they share the same support. Thus the notion of contiguity extends the concept of absolute continuity to the sequences of measures.
The concept was originally introduced by Le Cam (1960) as part of his foundational ... | Wikipedia/Contiguity_(probability_theory) |
The Barabási–Albert (BA) model is an algorithm for generating random scale-free networks using a preferential attachment mechanism. Several natural and human-made systems, including the Internet, the World Wide Web, citation networks, and some social networks are thought to be approximately scale-free and certainly con... | Wikipedia/BA_model |
The Sethi model was developed by Suresh P. Sethi and describes the process of how sales evolve over time in response to advertising. The model assumes that the rate of change in sales depend on three effects: response to advertising that acts positively on the unsold portion of the market, the loss due to forgetting or... | Wikipedia/Sethi_model |
The Kirkwood superposition approximation was introduced in 1935 by John G. Kirkwood as a means of representing a discrete probability distribution. The Kirkwood approximation for a discrete probability density function
P
(
x
1
... | Wikipedia/Kirkwood_approximation |
In probability theory, Kolmogorov equations characterize continuous-time Markov processes. In particular, they describe how the probability of a continuous-time Markov process in a certain state changes over time. There are four distinct equations: the Kolmogorov forward equation for continuous processes, now understo... | Wikipedia/Kolmogorov_backward_equation |
In mathematics, the base flow of a random dynamical system is the dynamical system defined on the "noise" probability space that describes how to "fast forward" or "rewind" the noise when one wishes to change the time at which one "starts" the random dynamical system.
== Definition ==
In the definition of a random dy... | Wikipedia/Base_flow_(random_dynamical_systems) |
In mathematics — specifically, in large deviations theory — a rate function is a function used to quantify the probabilities of rare events. Such functions are used to formulate large deviation principles. A large deviation principle quantifies the asymptotic probability of rare events for a sequence of probabilities.
... | Wikipedia/Rate_function |
A random function – of either one variable (a random process), or two or more variables
(a random field) – is called Gaussian if every finite-dimensional distribution is a multivariate normal distribution. Gaussian random fields on the sphere are useful (for example) when analysing
the anomalies in the cosmic microwav... | Wikipedia/Large_deviations_of_Gaussian_random_functions |
In mathematics — specifically, in measure theory — Malliavin's absolute continuity lemma is a result due to the French mathematician Paul Malliavin that plays a foundational rôle in the regularity (smoothness) theorems of the Malliavin calculus. Malliavin's lemma gives a sufficient condition for a finite Borel measure... | Wikipedia/Malliavin's_absolute_continuity_lemma |
The Watts–Strogatz model is a random graph generation model that produces graphs with small-world properties, including short average path lengths and high clustering. It was proposed by Duncan J. Watts and Steven Strogatz in their article published in 1998 in the Nature scientific journal. The model also became known ... | Wikipedia/Watts_and_Strogatz_model |
In probability theory, if a large number of events are all independent of one another and each has probability less than 1, then there is a positive (possibly small) probability that none of the events will occur. The Lovász local lemma allows a slight relaxation of the independence condition: As long as the events are... | Wikipedia/Lovász_local_lemma |
For statistics in probability theory, the Boolean-Poisson model or simply Boolean model for a random subset of the plane (or higher dimensions, analogously) is one of the simplest and most tractable models in stochastic geometry. Take a Poisson point process of rate
λ
{\display... | Wikipedia/Boolean_model_(probability_theory) |
In statistics and statistical physics, the Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from which direct sampling is difficult. New samples are added to the sequence in two steps: first a new sample is proposed base... | Wikipedia/Metropolis_algorithm |
In probability theory and statistics, the cumulants κn of a probability distribution are a set of quantities that provide an alternative to the moments of the distribution. Any two probability distributions whose moments are identical will have identical cumulants as well, and vice versa.
The first cumulant is the mea... | Wikipedia/Logmoment_generating_function |
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by ... | Wikipedia/Probabilistic_algorithm |
In queueing theory, a discipline within the mathematical theory of probability, the M/M/c queue (or Erlang–C model: 495 ) is a multi-server queueing model. In Kendall's notation it describes a system where arrivals form a single queue and are governed by a Poisson process, there are c servers, and job service times are... | Wikipedia/M/M/c_model |
A Markov logic network (MLN) is a probabilistic logic which applies the ideas of a Markov network to first-order logic, defining probability distributions on possible worlds on any given domain.
== History ==
In 2002, Ben Taskar, Pieter Abbeel and Daphne Koller introduced relational Markov networks as templates to sp... | Wikipedia/Markov_logic_network |
In probability theory and statistics, the covariance function describes how much two random variables change together (their covariance) with varying spatial or temporal separation. For a random field or stochastic process Z(x) on a domain D, a covariance function C(x, y) gives the covariance of the values of the rando... | Wikipedia/Covariance_function |
In statistics, the algebra of random variables provides rules for the symbolic manipulation of random variables, while avoiding delving too deeply into the mathematically sophisticated ideas of probability theory. Its symbolism allows the treatment of sums, products, ratios and general functions of random variables, as... | Wikipedia/Algebra_of_random_variables |
In probability theory, Bernstein inequalities give bounds on the probability that the sum of random variables deviates from its mean. In the simplest case, let X1, ..., Xn be independent Bernoulli random variables taking values +1 and −1 with probability 1/2 (this distribution is also known as the Rademacher distributi... | Wikipedia/Bernstein_inequalities_(probability_theory) |
In theoretical computer science, the algorithmic Lovász local lemma gives an algorithmic way of constructing objects that obey a system of constraints with limited dependence.
Given a finite set of bad events {A1, ..., An} in a probability space with limited dependence amongst the Ais and with specific bounds on their ... | Wikipedia/Algorithmic_Lovász_local_lemma |
Recurrence period density entropy (RPDE) is a method, in the fields of dynamical systems, stochastic processes, and time series analysis, for determining the periodicity, or repetitiveness of a signal.
== Overview ==
Recurrence period density entropy is useful for characterising the extent to which a time series repe... | Wikipedia/Recurrence_period_density_entropy |
In mathematics, specifically in the theory of Markovian stochastic processes in probability theory, the Chapman–Kolmogorov equation (CKE) is an identity relating the joint probability distributions of different sets of coordinates on a stochastic process. The equation was derived independently by both the British mat... | Wikipedia/Chapman–Kolmogorov_equation |
In probability theory, a conditional event algebra (CEA) is an alternative to a standard, Boolean algebra of possible events (a set of possible events related to one another by the familiar operations and, or, and not) that contains not just ordinary events but also conditional events that have the form "if A, then B".... | Wikipedia/Goodman–Nguyen–van_Fraassen_algebra |
In mathematics, Weingarten functions are rational functions indexed by partitions of integers that can be used to calculate integrals of products of matrix coefficients over classical groups. They were first studied by Weingarten (1978) who found their asymptotic behavior, and named by Collins (2003), who evaluated the... | Wikipedia/Weingarten_function |
In probability theory, Wald's equation, Wald's identity or Wald's lemma is an important identity that simplifies the calculation of the expected value of the sum of a random number of random quantities. In its simplest form, it relates the expectation of a sum of randomly many finite-mean, independent and identically d... | Wikipedia/Wald's_equation |
Inverse transform sampling (also known as inversion sampling, the inverse probability integral transform, the inverse transformation method, or the Smirnov transform) is a basic method for pseudo-random number sampling, i.e., for generating sample numbers at random from any probability distribution given its cumulative... | Wikipedia/Inverse_transform_sampling_method |
In mathematics, Varadhan's lemma is a result from the large deviations theory named after S. R. Srinivasa Varadhan. The result gives information on the asymptotic distribution of a statistic φ(Zε) of a family of random variables Zε as ε becomes small in terms of a rate function for the variables.
== Statement of the... | Wikipedia/Varadhan's_lemma |
In probability theory, a product-form solution is a particularly efficient form of solution for determining some metric of a system with distinct sub-components, where the metric for the collection of components can be written as a product of the metric across the different components. Using capital Pi notation a produ... | Wikipedia/Product-form_solution |
In probability theory, it is possible to approximate the moments of a function f of a random variable X using Taylor expansions, provided that f is sufficiently differentiable and that the moments of X are finite.
A simulation-based alternative to this approximation is the application of Monte Carlo simulations.
==... | Wikipedia/Taylor_expansions_for_the_moments_of_functions_of_random_variables |
In the domain of physics and probability, a Markov random field (MRF), Markov network or undirected graphical model is a set of random variables having a Markov property described by an undirected graph. In other words, a random field is said to be a Markov random field if it satisfies Markov properties. The concept or... | Wikipedia/Markov_network |
In mathematics — specifically, in large deviations theory — the contraction principle is a theorem that states how a large deviation principle on one space "pushes forward" (via the pushforward of a probability measure) to a large deviation principle on another space via a continuous function.
== Statement ==
Let X a... | Wikipedia/Contraction_principle_(large_deviations_theory) |
In the mathematical theory of random dynamical systems, an absorbing set is a subset of the phase space that exhibits a capturing property. It acts like a gravitational center, with the property that all trajectories of the system eventually enter and remain within that set.
Absorbing sets ultimately contain the trans... | Wikipedia/Absorbing_set_(random_dynamical_systems) |
In mathematics, the second moment method is a technique used in probability theory and analysis to show that a random variable has positive probability of being positive. More generally, the "moment method" consists of bounding the probability that a random variable fluctuates far from its mean, by using its moments.
T... | Wikipedia/Second_moment_method |
The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function
f
(
x
)
=
e
−
x
2
... | Wikipedia/Integration_of_the_normal_density_function |
The Beverton–Holt model is a classic discrete-time population model which gives the expected number n t+1 (or density) of individuals in generation t + 1 as a function of the number of individuals in the previous generation,
n
t
+
1
... | Wikipedia/Beverton–Holt_model |
In queueing theory, a discipline within the mathematical theory of probability, Buzen's algorithm (or convolution algorithm) is an algorithm for calculating the normalization constant G(N) in the Gordon–Newell theorem. This method was first proposed by Jeffrey P. Buzen in his 1971 PhD dissertation and subsequently pub... | Wikipedia/Buzen's_algorithm |
Word error rate (WER) is a common metric of the performance of a speech recognition or machine translation system. The WER metric typically ranges from 0 to 1, where 0 indicates that the compared pieces of text are exactly identical, and 1 (or larger) indicates that they are completely different with no similarity. Thi... | Wikipedia/Word_error_rate |
Calligraphy (from Ancient Greek καλλιγραφία (kalligraphía) 'beautiful writing') is a visual art related to writing. It is the design and execution of lettering with a pen, ink brush, or other writing instruments.: 17 Contemporary calligraphic practice can be defined as "the art of giving form to signs in an expressiv... | Wikipedia/Calligraphic |
In mathematics, an additive set function is a function
μ
\mu
mapping sets to numbers, with the property that its value on a union of two disjoint sets equals the sum of its values on these sets, namely,
μ
(
A
∪
B
)
=
μ
... | Wikipedia/Sigma-additive_set_function |
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