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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 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
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
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 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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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
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
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
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
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
(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
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
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
Type of chart
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Bar_chart
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
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 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
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
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)
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
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
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
Regression analysis
also outside this scope. Other examples of nonlinear functions include exponential functions, logarithmic functions, trigonometric functions, power functions
Nonlinear_regression
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
Statistical matching technique
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Propensity_score_matching
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
Range to estimate an unknown parameter
exponent of the power law distribution Confidence interval for mean of the exponential distribution Confidence interval for mean of the Poisson distribution
Confidence_interval
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
Apparent lack of pattern or predictability in events
Probability distribution Bernoulli distribution Binomial distribution Exponential distribution Normal distribution Pareto distribution Poisson distribution
Randomness
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
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
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 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
Measure of a system's order
point), or in the ordered phase (i.e. below the critical point). At high temperatures, the correlation decays to zero exponentially with the distance
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Experiment methodology
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
A/B_testing
Extension of linear logic
self-dual modality allowing exchange, but still linear, and the usual exponentials (? and !) of linear logic, allowing nonlinear structural rules to be
Noncommutative_logic
Statistical hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Chi-squared_test
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
Method of plotting numeric data
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Violin_plot
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
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
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
Statistical property
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Standard_error
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
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
Simultaneous observation and analysis of more than one outcome variable
It rotates the axes of variation to give a new set of orthogonal axes, ordered so that they summarize decreasing proportions of the variation. Factor
Multivariate_statistics
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
Condition in which the value of a measurement or observation is only partially known
{\displaystyle L=\prod _{i}\lambda (u_{i})^{\delta _{i}}S(u_{i}).} For the exponential distribution, this becomes even simpler, because the hazard rate, λ {\displaystyle
Censoring_(statistics)
Quantity that indexes a parametrized family of probability distributions
distributions, the Poisson distributions, the binomial distributions, and the exponential family of distributions. For example, the family of normal distributions
Statistical_parameter
Statistical measure of variability
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Median_absolute_deviation
Statistical hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
F-test
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
Idea that small causes can have large effects
conditions if points arbitrarily close together separate over time at an exponential rate. The definition is not topological, but essentially metrical. Lorenz
Butterfly_effect
Linear regression model with a single explanatory variable
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Simple_linear_regression
Statistics concept
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Polynomial_regression
Class of statistical survival models
{\displaystyle x} , it is typically assumed that the hazard responds exponentially; each unit increase in x {\displaystyle x} results in proportional scaling
Proportional_hazards_model
Statistical sampling technique
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Latin_hypercube_sampling
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
Statistic measuring inter-rater agreement for categorical items
depending on the categories. It is especially useful when categories are ordered, because larger disagreements can be weighed more heavily. Recall that
Cohen's_kappa
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
Method of statistical sampling
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Stratified_randomization
Used to count, measure, and label
an algebraic function and the exponential of an algebraic function. This gives another countable ring: the exponential periods. The number e as well as
Number
Statistical model validation technique
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Cross-validation_(statistics)
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
Presence/absence of symmetry or correlation in a many-particle system
| x − x ′ | {\displaystyle |x-x'|} increases. Typically, it decays exponentially to zero at large distances, and the system is considered to be disordered
Order_and_disorder
Series of questions for gathering information
value or order. Ordinal-polytomous, where the respondent has more than two ordered options (Bounded)Continuous, where the respondent is presented with a continuous
Questionnaire
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
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
clustering Equivalence relation Exact cover Knuth's Algorithm X Dancing Links Exponential formula Faà di Bruno's formula Feshbach–Fano partitioning Foliation Frequency
List_of_partition_topics
Type of average of a collection of numbers
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Arithmetic_mean
Normality test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Jarque–Bera_test
Association of one output to each input
also allowed. An elementary function is the same, with logarithms and exponential functions allowed. A function f : X → Y , {\displaystyle f:X\to Y,} with
Function_(mathematics)
Statistical test that compares goodness of fit
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Likelihood-ratio_test
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
Boy/Male
Hindu
Orderly
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’.
Male
Arthurian
, a son of Lot; traitor to Arthur.
Boy/Male
Indian
Responsibility; Ordered
Girl/Female
Shakespearean
The Tragedy of Macbeth' Lady Macduff, wife to Macduff, murdered on Macbeth's orders.
Girl/Female
Greek
Murdered Agamemnon.
Boy/Male
Muslim
Ordered, Pasted, Appointed
Boy/Male
American, British, Christian, English
Brave; Brave Counselor
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
Indian
Ordered, Pasted, Appointed
Girl/Female
Indian
Well-arranged, Well-ordered
Boy/Male
Tamil
Orderly
Boy/Male
Hindu, Indian, Telugu
Bordered; Friendly Element
Boy/Male
African, Indian, Sanskrit
Clear Spoken Person; Ordered
Boy/Male
English Arthurian Legend
Brave.
Boy/Male
Arabic, Australian, Muslim
Ordered; Appointed
Boy/Male
Tamil
Mitanshu | மீதாஂஷà¯Â
Bordered, Friendly element
Mitanshu | மீதாஂஷà¯Â
Girl/Female
Muslim
Well-arranged, Well-ordered
Girl/Female
African, Arabic, Muslim
Well-ordered; Well-arranged
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
Girl/Female
Indian, Malayalam
Patience
Boy/Male
British, English, French, German, Hebrew, Latin
Helper
Female
Egyptian
, a priestess of Amen Ra.
Boy/Male
Hindu, Indian, Sanskrit
An Ascetic
Boy/Male
Hindu, Indian
Honour; Pride
Surname or Lastname
English (mainly Bristol and Gwent)
English (mainly Bristol and Gwent) : of uncertain origin, apparently a habitational name from some lost or unidentified place deriving its name from Old English seolfor ‘silver’ + þorn ‘thorn bush’.
Boy/Male
Armenian, Australian
Protector; Shepherd
Girl/Female
Muslim/Islamic
Excursion spot
Boy/Male
Indian, Punjabi, Sikh
Blissful Peace
Surname or Lastname
English
English : variant spelling of Thwaites.
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
a.
Well-ordered; orderly; regular; methodical.
imp. & p. p.
of Order
a.
Conformed to order; in order; regular; as, an orderly course or plan.
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.
a.
Covered or adorned with osiers; as, osiered banks.
a.
Performed in good or established order; well-regulated.
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.
n.
A noncommissioned officer or soldier who attends a superior officer to carry his orders, or to render other service.
a.
Having three corners, or angles; as, a three-cornered hat.
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.
Being on duty; keeping order; conveying orders.
adv.
According to due order; regularly; methodically; duly.
a.
Having three prominent longitudinal angles; as, a three-cornered stem.
n.
One who gives orders.
v. i.
To give orders; to issue commands.
n.
An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia.
n.
Right arrangement; a normal, correct, or fit condition; as, the house is in order; the machinery is out of order.