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Generalisation of the exponential integral to non-commutative algebras
The ordered exponential, also called the path-ordered exponential, is a mathematical operation defined in non-commutative algebras, equivalent to the
Ordered_exponential
Ordered field with a function generalizing the exponential function
mathematics, an ordered exponential field is an ordered field together with a function which generalises the idea of exponential functions on the ordered field
Ordered_exponential_field
Probability distribution
In probability theory and statistics, the exponential distribution or negative exponential distribution is the probability distribution of the distance
Exponential_distribution
equation Exponential dispersion model Exponential distribution Exponential error Exponential factorial Exponential family Exponential field Ordered exponential
List_of_exponential_topics
Mathematical field
{\displaystyle \mathbb {T} ^{LE}} of logarithmic-exponential transseries is a non-Archimedean ordered differential field which extends comparability of
Transseries
Mathematical field with an extra operation
In mathematics, an exponential field is a field with a further unary operation that is a homomorphism from the field's additive group to its multiplicative
Exponential_field
Procedure of ordering a product operators
This is the case of the Wilson loop, which is defined as a path-ordered exponential to guarantee that the Wilson loop encodes the holonomy of the gauge
Path-ordering
Algebraic object with an ordered structure
squares forms a fan. Linearly ordered group – Group with translationally invariant total order Ordered exponential field – Ordered field with a function generalizing
Ordered_field
Generates a forecast of future values of a time series
Exponential smoothing or exponential moving average (EMA) is a technique for smoothing time series data using the exponential window function. Whereas
Exponential_smoothing
Method of statistical physics
a_{k}(t)\partial a_{j}(t)}}G(s,t){\dot {A}}_{i})} . We have used the time-ordered exponential G ( s , t ) = T − exp ( ∫ s t d u i L ( 1 − P ( u ) ) ) {\displaystyle
Mori–Zwanzig_formalism
Family of probability distributions related to the normal distribution
In probability and statistics, an exponential family is a parametric set of probability distributions of a certain form, specified below. This special
Exponential_family
Algebraic structure with addition, multiplication, and division
1007/BF00327219, MR 1554154, S2CID 121442989 Kuhlmann, Salma (2000), Ordered exponential fields, Fields Institute Monographs, vol. 12, American Mathematical
Field_(mathematics)
Estimate of time taken for running an algorithm
an exponential. In this sense, problems that have sub-exponential time algorithms are somewhat more tractable than those that only have exponential algorithms
Time_complexity
Type of mathematical equation
relation is not satisfied, the general solution is provided by the ordered exponential instead [citation needed]. x ( t ) = OE [ A ] ( t ) c = T { e ∫
Matrix_differential_equation
Integral using products instead of sums
establish a path-ordering while integrating. A typical result is the ordered exponential. The Magnus expansion provides one technique for computing the Volterra
Product_integral
Expansion of the time evolution operator
Neumann series above and which includes the time ordered products; it is the path-ordered exponential: U ( t , t 0 ) = ∑ n = 0 ∞ U n ( t , t 0 ) = ∑ n
Dyson_series
Partial quantifier elimination for ordered fields with exponentials
Wilkie about the theory of ordered fields with an exponential function, or equivalently about the geometric nature of exponential varieties. In terms of model
Wilkie's_theorem
Type of statistical measure over subsets of a dataset
the weights in the exponential moving average which follows. An exponential moving average (EMA), also known as an exponentially weighted moving average
Moving_average
Topological quantum field theory
integral and P exp {\displaystyle {\mathcal {P}}\exp } is the path-ordered exponential. Consider a link L in M, which is a collection of ℓ disjoint loops
Chern–Simons_theory
(without the exponential function) is decidable. The ordered real field R {\displaystyle \mathbb {R} } is a structure over the language of ordered rings L
Tarski's exponential function problem
Tarski's_exponential_function_problem
Theory of quantum gauge fields on a lattice
SU(3) elements along a path (i.e. the ordered multiplication of their matrices) approximates a path-ordered exponential (geometric integral), from which Wilson
Lattice_gauge_theory
View of quantum mechanics
exponentials need to be replaced by the unitary propagator for the evolution generated by H0,S(t), or more explicitly with a time-ordered exponential
Interaction_picture
Concept in non-equilibrium physics
operator U ( t 2 , t 1 ) {\displaystyle U(t_{2},t_{1})} is the time-ordered exponential of an integral, U ( t 2 , t 1 ) = T ( e − i ∫ t 1 t 2 H ( t ′ ) d
Keldysh_formalism
Algorithmic search method
An exponential tree is a type of search tree where the number of children of its nodes decreases doubly-exponentially with increasing depth. Values are
Exponential_tree
Matrix representing the effect of scattering on a physical system
to quantum field theory, the S-matrix may be calculated as a time-ordered exponential of the integrated Hamiltonian in the interaction picture; it may
S-matrix
Class of statistical models
overdispersed exponential family (or exponential family with dispersion) is a generalization of an exponential family and the exponential dispersion model
Generalized_linear_model
Number representing a continuous quantity
and even without knowing it. For example, the standard series of the exponential function e x = ∑ n = 0 ∞ x n n ! {\displaystyle e^{x}=\sum _{n=0}^{\infty
Real_number
Change of state over time, especially in physics
operators on a Hilbert space. The propagators can be expressed as time-ordered exponentials of the integrated Hamiltonian. The asymptotic properties of time
Time_evolution
Group with translationally invariant total order
In mathematics, specifically abstract algebra, a linearly ordered or totally ordered group is a group G equipped with a total order "≤" that is translation-invariant
Linearly_ordered_group
Finite ordered list of elements
In mathematics, a tuple is a finite sequence (or ordered list) of numbers. More generally, it is a sequence of mathematical objects, called the elements
Tuple
Unproven computational hardness assumption
In computational complexity theory, the exponential time hypothesis or ETH is an unproven computational hardness assumption that was formulated by Impagliazzo
Exponential_time_hypothesis
continuous Bernoulli distribution is a one-parameter exponential family obtained from exponential tilting of the continuous uniform distribution. It provides
List of probability distributions
List_of_probability_distributions
Generalization of the real numbers
axioms for the real exponential field exp satisfies all the Ressayre axioms for the real exponential field The surreals with exponential is an elementary
Surreal_number
Arithmetic operation
integer Mathematics portal Double exponential function – Exponential function of an exponential function Exponential decay – Decrease in value at a rate
Exponentiation
Probability distribution
versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special
Gamma_distribution
Intrinsic geometric structures in mathematics
solution of this differential equation is often expressed as a path-ordered exponential; see for example Nelson (1969). A similar argument applies to the
Riemannian connection on a surface
Riemannian_connection_on_a_surface
Algorithm for searching sorted, infinite lists
In computer science, an exponential search (also called doubling search or galloping search or Struzik search) is an algorithm, created by Jon Bentley
Exponential_search
Data structure for Boolean functions
getting a graph whose number of nodes would be linear (in n) at best and exponential at worst (e.g., a ripple carry adder). Consider the Boolean function
Binary_decision_diagram
Formula in Lie group theory
Lie groups, the exponential map is a map from the Lie algebra g of a Lie group G into G. In case G is a matrix Lie group, the exponential map reduces to
Derivative of the exponential map
Derivative_of_the_exponential_map
Orbitrap Ordal Demokan Order and disorder (physics) Order operator Ordered exponential Orders of magnitude (charge) Orders of magnitude (density) Orders
Index_of_physics_articles_(O)
2D conformal field theories
) {\displaystyle V_{\alpha }(z)=V_{\alpha ,\alpha }(z)} . Normal-ordered exponentials of the free boson are affine primary fields. In particular, the field
Massless free scalar bosons in two dimensions
Massless_free_scalar_bosons_in_two_dimensions
Formulations of quantum mechanics
exponentials need to be replaced by the unitary propagator for the evolution generated by H0,s(t), or more explicitly with a time-ordered exponential
Dynamical_pictures
Statistical principle
whose domain does not vary with the parameter being estimated, only in exponential families is there a sufficient statistic whose dimension remains bounded
Sufficient_statistic
Empirical law on the variance of species in a habitat
are more precise and should be used. Morisita's overlap index Natural exponential family Scaling pattern of occupancy Spatial ecology Taylor, L. R. (1961)
Taylor's_law
Well-quasi-ordering of finite trees
states that the set of finite trees over a well-quasi-ordered set of labels is itself well-quasi-ordered under homeomorphic embedding. A finitary application
Kruskal's_tree_theorem
Type of infinite structure
completeness results for expansions of the ordered field of real numbers by restricted Pfaffian functions and the exponential function" (PDF). Journal of the American
O-minimal_theory
Approximation method in statistics
from an exponential family with identity as its natural sufficient statistics and mild-conditions are satisfied (e.g. for normal, exponential, Poisson
Least_squares
Triangular array of the binomial coefficients
of Pascal's triangle in terms of the matrix exponential can be given: Pascal's triangle is the exponential of the matrix which has the sequence 1, 2, 3
Pascal's_triangle
Indicator in technical analysis
* (n - 1) + newdata) / n, which is equivalent to the aforementioned exponential smoothing. So new data is simply divided by n, or multiplied by α and
Relative_strength_index
Probability of survival beyond any specified time
example, a curve representing the exponential distribution overlays the distribution of AC failure times; the exponential distribution approximates the distribution
Survival_function
Number with a real and an imaginary part
formula could be used to reduce any trigonometric identity to much simpler exponential identities. The idea of a complex number as a point in the complex plane
Complex_number
Measure of statistical dispersion
calculate the IQR, the data set is divided into quartiles, or four rank-ordered even parts via linear interpolation. These quartiles are denoted by Q1
Interquartile_range
Statistical modeling method
be meaningfully ordered; when modeling ordinal data, e.g. ratings on a scale from 0 to 5, where the different outcomes can be ordered but where the quantity
Linear_regression
Number of orderings allowing ties
the ordered Bell numbers causes their ordinary generating function to diverge; instead the exponential generating function is used. For the ordered Bell
Ordered_Bell_number
Statistic which divides a data set into 100 parts and analyzes it as a percentage
always be a member of the original ordered list. The 100th percentile is defined to be the largest value in the ordered list. This method is also called
Percentile
Mathematical relation making a non-equal comparison
solutions exist, describing them. The complexity of this algorithm is doubly exponential in the number of variables. It is an active research domain to design
Inequality_(mathematics)
Optimization method
iteration t is C(n,t) -- the number of subsets of size t. This grows exponentially with n. It is possible to reduce the problem to a different problem
Lexicographic max-min optimization
Lexicographic_max-min_optimization
Regression analysis
also outside this scope. Other examples of nonlinear functions include exponential functions, logarithmic functions, trigonometric functions, power functions
Nonlinear_regression
Data visualization
median of this ordered data set is 70°F. The first quartile value (Q1 or 25th percentile) is the number that marks one quarter of the ordered data set. In
Box_plot
Statistics concept
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Polynomial_regression
Complex-valued function
_{i}|\lambda _{i}(X)|} is the trace-class norm. One definition uses the exponential trace formula. For finite-dimensional matrices, we have det ( I + A )
Fredholm_determinant
Distinction between nominal, ordinal, interval and ratio variables
four levels are not exhaustive and proposed seven instead: Names Grades (ordered labels like beginner, intermediate, advanced) Ranks (orders with 1 being
Level_of_measurement
Probabilistic problem-solving algorithm
to a degree of freedom. Monte Carlo methods provide a way out of this exponential increase in computation time. As long as the function in question is
Monte_Carlo_method
Distributed version control system
showed exponential work to merge certain conflicts. Although not resolved completely in the subsequent versions of Darcs, the frequency of exponential merges
Darcs
Unit of information
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Data
Apparent lack of pattern or predictability in events
Probability distribution Bernoulli distribution Binomial distribution Exponential distribution Normal distribution Pareto distribution Poisson distribution
Randomness
Problem in computer science
{\displaystyle m=O(n)} m = ( 1 + ε ) n {\displaystyle m=(1+\varepsilon )n} In the exponential label case, each item that is inserted can be given a label that is the
List-labeling_problem
Type of Monte Carlo algorithms for signal processing and statistical inference
recognition Auxiliary particle filter Cost Reference particle filter Exponential Natural Particle Filter Feynman-Kac and mean-field particle methodologies
Particle_filter
MR 1975381. S2CID 118338851. Zbl 1088.06001. Exponential law for spaces. at the nLab Tim Campion. "Exponential law w.r.t. compact-open topology". Vladimir
Core-compact_space
Generalization of the one-dimensional normal distribution to higher dimensions
interior of an ellipse and the chi-squared distribution simplifies to an exponential distribution with mean equal to two (rate equal to half). The complementary
Multivariate normal distribution
Multivariate_normal_distribution
Unsolved problem in computer science
that solves the task and runs in polynomial time (as opposed to, say, exponential time), meaning the task completion time is bounded above by a polynomial
P_versus_NP_problem
Type of chart
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Bar_chart
Measure of the shape of a function
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Moment_(mathematics)
Measure of distance between two proportions
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Cohen's_h
Mathematical function of two positive real arguments
means. The arithmetic–geometric mean is used in fast algorithms for exponential, trigonometric functions, and other special functions, as well as some
Arithmetic–geometric_mean
Method of plotting numeric data
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Violin_plot
Mathematical function for the probability a given outcome occurs in an experiment
For example, suppose we want to generate a random variable having an exponential distribution with parameter λ {\displaystyle \lambda } — that is, with
Probability_distribution
Study of collection and analysis of data
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Statistics
Theorem in statistics
, however, it turns out to be sub-optimal. Since the exponential distribution is an exponential family, it is known that its sufficient statistic X ¯
Lehmann–Scheffé_theorem
Type of transfinite numbers
points of an exponential map. Consequently, they are not reachable from 0 via a finite series of applications of the chosen exponential map and of "weaker"
Epsilon_number
an ordered set, though that is an ambiguous term that many authors reserve for partially ordered sets or totally ordered sets. The term pre-ordered set
Hierarchy_(mathematics)
Joint-stock holding company
status as a secondary website to the older XNXX by 2009, experiencing exponential growth over the 2010s. The site offered nearly 13,000 videos in 2008
WGCZ_Holding
Nonparametric measure of rank correlation
a moving window. Instead, the Hermite series based estimator uses an exponential weighting scheme to track time-varying Spearman's rank correlation from
Spearman's rank correlation coefficient
Spearman's_rank_correlation_coefficient
Processes that maintain quality at a constant level
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Quality_control
Study of health and disease within a population
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Epidemiology
In mathematics, invertible homomorphism
{\displaystyle x,y\in \mathbb {R} ^{+},} so it is a group homomorphism. The exponential function exp : R → R + {\displaystyle \exp :\mathbb {R} \to \mathbb {R}
Isomorphism
Relative measure of dispersion expressed as the ratio of standard deviation to the mean
these fields, the exponential distribution is often more important than the normal distribution. The standard deviation of an exponential distribution is
Coefficient_of_variation
Unbiased statistical estimator minimizing variance
an exponential family with sufficient statistic T = log ( 1 + e − X ) {\displaystyle T=\log(1+e^{-X})} . In fact this is a full rank exponential family
Minimum-variance unbiased estimator
Minimum-variance_unbiased_estimator
Search algorithm finding the position of a target value within a sorted array
search problems in computational geometry and in numerous other fields. Exponential search extends binary search to unbounded lists. The binary search tree
Binary_search
Classified Episodes
"The Secret of Code No. 571E1115" 19 May 2006 (2006-05-19) Spreading exponentially, a deadly virus threatens the city's extinction. 416 "Red Rose Killer"
List of CID episodes: 1998–2009
List_of_CID_episodes:_1998–2009
Category whose objects are finite sets and whose morphisms are functions
B, the categorical sum is given by the disjoint union A + B, and the exponential object BA is given by the set of all functions with domain A and codomain
FinSet
Statistical model for a binary dependent variable
by some value of the predictor. base e {\displaystyle e} denotes the exponential function. The odds of the dependent variable equaling a case (given some
Logistic_regression
Statistical property
of heteroscedasticity or the distribution is a member of the linear exponential family and the conditional expectation function is correctly specified)
Homoscedasticity and heteroscedasticity
Homoscedasticity_and_heteroscedasticity
Statistical hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Chi-squared_test
Relationship between items in a set
themselves are totally ordered. For example, materials are totally preordered by hardness, while degrees of hardness are totally ordered. If two items are
Ranking
Statistical sampling technique
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Latin_hypercube_sampling
Concept in statistics
particular, VGLMs allow for response variables outside the classical exponential family and for more than one parameter. Each parameter (not necessarily
Vector generalized linear model
Vector_generalized_linear_model
Statistical test comparing two probability distributions
statistic and for the critical values for the normal distribution and the exponential distribution have been published, and later publications also include
Kolmogorov–Smirnov_test
Number of occurrences in an experiment or study
the absolute frequencies of all events at or below a certain point in an ordered list of events. These frequencies are often depicted graphically or in
Frequency_(statistics)
be infinitely repeated and which has a well-defined set of outcomes. exponential family event A subset of the sample space of a procedure or experiment
Glossary of probability and statistics
Glossary_of_probability_and_statistics
ORDERED EXPONENTIAL
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ORDERED EXPONENTIAL