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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
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
equation Exponential dispersion model Exponential distribution Exponential error Exponential factorial Exponential family Exponential field Ordered exponential
List_of_exponential_topics
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 rule of thumb technique for smoothing time series data using the exponential window function
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
Probability distribution
versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special
Gamma_distribution
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
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
Arithmetic operation
integer Mathematics portal Double exponential function – Exponential function of an exponential function Exponential decay – Decrease in value at a rate
Exponentiation
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
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
Statistical hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Chi-squared_test
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
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
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
Function of the observed sample results
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
P-value
Statistical methods for comparing samples
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Two-proportion_Z-test
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
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
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
Fourth standardized moment in statistics
Student's t-distribution, Rayleigh distribution, Laplace distribution, exponential distribution, Poisson distribution and the logistic distribution. Such
Kurtosis
Regression analysis
also outside this scope. Other examples of nonlinear functions include exponential functions, logarithmic functions, trigonometric functions, power functions
Nonlinear_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
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
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
Statistical measure of association
matter, so φc may be used with nominal data types or higher (notably, ordered or numerical). Cramér's V varies from 0 (corresponding to no association
Cramér's_V
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
Statistical measure of variability
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Median_absolute_deviation
Method of plotting numeric data
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Violin_plot
In mathematics, a quantitative measure of the shape of a set of points
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Moment_(mathematics)
Interpretation of probability
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Bayesian_probability
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
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 sampling technique
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Latin_hypercube_sampling
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
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 hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
F-test
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
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 quality control
condition. Variants such as the cumulative sum (CUSUM) chart and the exponentially weighted moving average charts (EWMA chart) are used to improve sensitivity
Statistical_process_control
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
Type of scatter plot
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Volcano_plot_(statistics)
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)
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
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
Experiment methodology
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
A/B_testing
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
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)
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
Distribution of an uncertain quantity
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Prior_probability
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
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
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
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)
Statistical interpretation with many tests
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Multiple_comparisons_problem
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
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
Type of mathematical expression
variable is substituted for an exponential function applied to the first variable, for example P(x, ex), may be called an exponential polynomial. A rational fraction
Polynomial
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
Statistics concept
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Polynomial_regression
How many standard deviations apart from the mean an observed datum is
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Standard_score
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 property
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Standard_error
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
Function related to statistics and probability theory
in particular since most common probability distributions—notably the exponential family—are only logarithmically concave, and concavity of the objective
Likelihood_function
Conditional probability used in Bayesian statistics
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Posterior_probability
Statistical measure of how far values spread from their average
dx-\mu ^{2},} where the integral is an improper Riemann integral. The exponential distribution with parameter λ > 0 {\displaystyle \lambda >0} is a
Variance
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)
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
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
Male
Arthurian
, a son of Lot; traitor to Arthur.
Boy/Male
Hindu
Orderly
Boy/Male
English Arthurian Legend
Brave.
Boy/Male
African, Indian, Sanskrit
Clear Spoken Person; Ordered
Girl/Female
English, Peruvian
Plaster; Powdered
Girl/Female
Greek
Murdered Agamemnon.
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
Girl/Female
African, Arabic, Muslim
Well-ordered; Well-arranged
Boy/Male
Hindu, Indian, Telugu
Bordered; Friendly Element
Boy/Male
Tamil
Mitanshu | மீதாஂஷà¯Â
Bordered, Friendly element
Mitanshu | மீதாஂஷà¯Â
Boy/Male
Tamil
Orderly
Boy/Male
Indian
Ordered, Pasted, Appointed
Boy/Male
Muslim
Ordered, Pasted, Appointed
Girl/Female
Indian
Well-arranged, Well-ordered
Boy/Male
Arabic, Australian, Muslim
Ordered; Appointed
Boy/Male
Indian
Responsibility; Ordered
Boy/Male
American, British, Christian, English
Brave; Brave Counselor
Girl/Female
Muslim
Well-arranged, Well-ordered
Girl/Female
Shakespearean
The Tragedy of Macbeth' Lady Macduff, wife to Macduff, murdered on Macbeth's orders.
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’.
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
Biblical
sweat; swelling
Boy/Male
Muslim
Rare, Precious
Girl/Female
American, British, English, Irish
Brave; Alert; A Phonetic Form of the Initials Kc; Similar to the Irish Name Casey; Vigorous; Watchful
Girl/Female
Danish, German
Power of the Wolf; Power of the Home
Boy/Male
Hindu, Indian
Blessing of God
Boy/Male
Hindu, Indian
King of Sunlight
Boy/Male
French Teutonic American Shakespearean English Welsh
Intelligent.
Boy/Male
Indian, Sanskrit
Bearer of the Goddess Shri
Surname or Lastname
English and Scottish
English and Scottish : variant spelling of Banks 1.
Girl/Female
Arabic, Muslim
This was the Name of a Narrator of Hadith; Daughter of Ali Al-bazzaz
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
a.
Having three prominent longitudinal angles; as, a three-cornered stem.
n.
To admit to holy orders; to ordain; to receive into the ranks of the ministry.
n.
One who gives orders.
n.
A noncommissioned officer or soldier who attends a superior officer to carry his orders, or to render other service.
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 puts in order, arranges, methodizes, or regulates.
a.
Covered or adorned with osiers; as, osiered banks.
imp. & p. p.
of Order
v. i.
To give orders; to issue commands.
a.
Observant of order, authority, or rule; hence, obedient; quiet; peaceable; not unruly; as, orderly children; an orderly community.
a.
Well-ordered; orderly; regular; methodical.
a.
Performed in good or established order; well-regulated.
adv.
According to due order; regularly; methodically; duly.
a.
Being on duty; keeping order; conveying orders.
a.
Having three corners, or angles; as, a three-cornered hat.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.
n.
To give an order to; to command; as, to order troops to advance.
a.
Conformed to order; in order; regular; as, an orderly course or plan.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.
n.
An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia.