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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
Mathematical field
{\displaystyle \mathbb {T} ^{LE}} of logarithmic-exponential transseries is a non-Archimedean ordered differential field which extends comparability of
Transseries
equation Exponential dispersion model Exponential distribution Exponential error Exponential factorial Exponential family Exponential field Ordered exponential
List_of_exponential_topics
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
(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
Arithmetic operation
integer Mathematics portal Double exponential function – Exponential function of an exponential function Exponential decay – Decrease in value at a rate
Exponentiation
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Type of chart
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Bar_chart
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
Statistical model for count data
Multinomial logistic regression Mixed logit Probit Multinomial probit Ordered logit Ordered probit Poisson Multilevel model Fixed effects Random effects Linear
Poisson_regression
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
Statistical hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
F-test
Estimator for quality of a statistical model
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Akaike_information_criterion
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
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
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)
Number of values in the final calculation of a statistic that are free to vary
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Degrees of freedom (statistics)
Degrees_of_freedom_(statistics)
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
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
Experiment methodology
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
A/B_testing
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
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
Regression analysis
also outside this scope. Other examples of nonlinear functions include exponential functions, logarithmic functions, trigonometric functions, power functions
Nonlinear_regression
Statistical property quantifying how much a collection of data is spread out
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Statistical_dispersion
Concept in inferential statistics
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Statistical_significance
Interpretation of probability
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Bayesian_probability
Nonparametric test of the null hypothesis
study with a sample of ten hares and ten tortoises, the total number of ordered pairs is ten times ten or 100 pairs of hares and tortoises. Suppose the
Mann–Whitney_U_test
Test of normality in frequentist statistics
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Shapiro–Wilk_test
Unit of information
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Data
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
Statistical hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Chi-squared_test
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)
Numerical measure of a statistical relationship between variables
polychoric correlation coefficient measures the association between two ordered-categorical variables. It's technically defined as the estimate of the
Correlation_coefficient
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
Statistical property
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Standard_error
Statistical matching technique
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Propensity_score_matching
Type of scatter plot
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Volcano_plot_(statistics)
Model for generating observable data in probability and statistics
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Generative_model
Statistical sampling technique
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Latin_hypercube_sampling
Kth smallest value in a statistical sample
{\displaystyle X_{1},X_{2},..,X_{n}} a random sample of size n from an exponential distribution with parameter λ, the order statistics X(i) for i = 1,2
Order_statistic
Statistical measure of the magnitude of a phenomenon
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Effect_size
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
Method of plotting numeric data
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Violin_plot
Apparent lack of pattern or predictability in events
Probability distribution Bernoulli distribution Binomial distribution Exponential distribution Normal distribution Pareto distribution Poisson distribution
Randomness
Statistical relationship
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Correlation
Measure of the asymmetry of random variables
skewness of 0 A half-normal distribution has a skewness just below 1 An exponential distribution has a skewness of 2 A lognormal distribution can have a
Skewness
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
Mathematical relation assigning a probability event to a cost
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Loss_function
Covariance and correlation
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Cross-correlation
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
Sequence of data points over time
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Time_series
Statistical method for handling multiple comparisons
"Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data". Annals of Statistics. 34 (6): 2980–3018. arXiv:math/0602311. Bibcode:2006math
False_discovery_rate
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
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)
N-th root of the product of n numbers
logarithms, and then returning the result to linear scale by using the exponential function exp {\displaystyle \exp } , a 1 a 2 ⋯ a n t n = exp ( ln
Geometric_mean
Statistical hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Student's_t-test
Non-parametric method for testing whether samples originate from the same distribution
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Kruskal–Wallis_test
Fundamental theorem in probability theory and statistics
more rapidly than t 2 / n {\textstyle t^{2}/n} . By the limit of the exponential function ( e x = lim n → ∞ ( 1 + x n ) n {\textstyle e^{x}=\lim _{n\to
Central_limit_theorem
Metric for fit of statistical models
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Goodness_of_fit
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
Girl/Female
Greek
Murdered Agamemnon.
Boy/Male
Hindu
Orderly
Boy/Male
Tamil
Orderly
Girl/Female
Shakespearean
The Tragedy of Macbeth' Lady Macduff, wife to Macduff, murdered on Macbeth's orders.
Boy/Male
Indian
Ordered, Pasted, Appointed
Boy/Male
Tamil
Mitanshu | மீதாஂஷà¯Â
Bordered, Friendly element
Mitanshu | மீதாஂஷà¯Â
Boy/Male
African, Indian, Sanskrit
Clear Spoken Person; Ordered
Boy/Male
American, British, Christian, English
Brave; Brave Counselor
Boy/Male
Hindu, Indian, Telugu
Bordered; Friendly Element
Surname or Lastname
English (Lancashire)
English (Lancashire) : habitational name from a place in Lancashire, called Ormerod, from the Old Norse personal name Ormr (see Orme 1) or Ormarr (a compound of orm ‘serpent’ + herr ‘army’) + Old English rod ‘clearing’.
Girl/Female
Muslim
Well-arranged, Well-ordered
Boy/Male
Muslim
Ordered, Pasted, Appointed
Girl/Female
English, Peruvian
Plaster; Powdered
Male
English
Old English Arthurian legend name of a Knight of the Round Table who was the illegitimate son and traitor of King Arthur, possibly MORDRED means "sea counsel." He was brother (or half-brother) to Agravain, Gaheris, Gareth, and Gawain, and noted for having crowned himself and married Guinevere while Arthur was waging war on Emperor Lucius of Rome. He was killed by Arthur at the Battle of Camlann.Â
Boy/Male
Arabic, Australian, Muslim
Ordered; Appointed
Boy/Male
Indian
Responsibility; Ordered
Boy/Male
English Arthurian Legend
Brave.
Girl/Female
Indian
Well-arranged, Well-ordered
Male
Arthurian
, a son of Lot; traitor to Arthur.
Girl/Female
African, Arabic, Muslim
Well-ordered; Well-arranged
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
Boy/Male
Hindu
King of poor
Boy/Male
Arabic
Caution; Care
Girl/Female
American, British, Christian, English, French, German, Latin
Pure; Pet Form of Various Names Containing the Element Gin; Abbreviation of Virginia; Virgin; Maiden
Girl/Female
French American English Latin
Flower.
Surname or Lastname
English
English : unexplained. Possibly a variant of Stelling.
Boy/Male
Indian, Mythological
One whose Fame is World Wide
Surname or Lastname
English
English : variant of Pinnock.
Boy/Male
Arabic, Muslim
A Person who Collects Wood; Name of a Sahabi who Participated in the Battle of Badr; He was the Messenger of the Holy Prophet (Peace be Upon Him) to the Ruler of Egypt
Boy/Male
American, British, English
Dwells at the Ash Tree Grove
Boy/Male
Muslim/Islamic
Name of a Prophet
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
n.
One who puts in order, arranges, methodizes, or regulates.
imp. & p. p.
of Order
a.
Well-ordered; orderly; regular; methodical.
n.
To admit to holy orders; to ordain; to receive into the ranks of the ministry.
n.
To give an order to; to command; as, to order troops to advance.
adv.
According to due order; regularly; methodically; duly.
a.
Conformed to order; in order; regular; as, an orderly course or plan.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.
a.
Having three prominent longitudinal angles; as, a three-cornered stem.
n.
A noncommissioned officer or soldier who attends a superior officer to carry his orders, or to render other service.
n.
An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia.
a.
Covered or adorned with osiers; as, osiered banks.
v. i.
To give orders; to issue commands.
a.
Being on duty; keeping order; conveying orders.
a.
Performed in good or established order; well-regulated.
n.
An ecclesiastical grade or rank, as of deacon, priest, or bishop; the office of the Christian ministry; -- often used in the plural; as, to take orders, or to take holy orders, that is, to enter some grade of the ministry.
n.
One who gives orders.
a.
Having three corners, or angles; as, a three-cornered hat.
a.
Observant of order, authority, or rule; hence, obedient; quiet; peaceable; not unruly; as, orderly children; an orderly community.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.