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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
Unproven computational hardness assumption
In computational complexity theory, the exponential time hypothesis (ETH) states that satisfiability of 3-CNF Boolean formulas (3-SAT) cannot be solved
Exponential_time_hypothesis
equation Exponential dispersion model Exponential distribution Exponential error Exponential factorial Exponential family Exponential field Ordered exponential
List_of_exponential_topics
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
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
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
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
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
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
Mathematical field with an extra operation
required. Considering the ordered field R {\displaystyle \mathbb {R} } equipped with this function gives the ordered real exponential field, denoted R exp
Exponential_field
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
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)
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
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
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
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
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
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
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
The log of the S-matrix in scattering
concretely defined and computed by the Dyson series, which expands a time-ordered exponential.The scattering generator is concretely defined and computed by the
Scattering_generator
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
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
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
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
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
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
Arithmetic operation
system. Mathematics portal Double exponential function – Exponential function of an exponential function Exponential decay – Decrease in value at a rate
Exponentiation
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
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
Generalization of the real numbers
In mathematics, the surreal number system is a totally ordered proper class containing not only the real numbers but also infinite and infinitesimal numbers
Surreal_number
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
Probability distribution
versatile two-parameter family of continuous probability distributions. The exponential distribution, Erlang distribution, and chi-squared distribution are special
Gamma_distribution
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
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
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
Regression analysis
also outside this scope. Other examples of nonlinear functions include exponential functions, logarithmic functions, trigonometric functions, power functions
Nonlinear_regression
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)
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
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
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
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
Unit of information
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Data
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
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
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
Search algorithm used in sorted arrays
search problems in computational geometry and in numerous other fields. Exponential search extends binary search to unbounded lists. The binary search tree
Binary_search
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
President of Brazil from 2019 to 2023
crisis while the number of Brazilians infected by the virus climbed exponentially by mid-2020. Bolsonaro claimed that COVID-19 was no deadlier than "the
Jair_Bolsonaro
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
Set of vectors used to define coordinates
all are with given high probability pairwise almost orthogonal, grows exponentially with dimension. More precisely, consider equidistribution in n-dimensional
Basis_(linear_algebra)
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
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
Probability distribution
generalized normal distribution, also known as the Subbotin distribution, exponential power distribution or the generalized error distribution, is a parametric
Generalized normal distribution
Generalized_normal_distribution
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 variation in statistics
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Standard_deviation
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
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
Statistics concept
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Errors_and_residuals
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
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
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
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
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
Mathematical operation modeling parallel resistors
that the Hermitian semi-definite matrices form a commutative partially ordered semigroup under the parallel sum operation. […] [6] Mitra, Sujit Kumar;
Parallel_(operator)
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
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
Apparent lack of pattern or predictability in events
Probability distribution Bernoulli distribution Binomial distribution Exponential distribution Normal distribution Pareto distribution Poisson distribution
Randomness
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)
Statistical hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Student's_t-test
Statistical hypothesis test
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Chi-squared_test
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 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
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
Experiment methodology
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
A/B_testing
Statistical model for a binary dependent variable
coefficient multiplied by some value of the predictor. base e denotes the exponential function. The odds of the dependent variable equaling a case (given some
Logistic_regression
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
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
Photographic image processing tecnhique
regression AVHRR iterative estimation MSS, TM DOS with exponential scattering model TM DOS with exponential scattering model, downwelling atmospheric radiance
Atmospheric_correction
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
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
Associative algebra used in combinatorics
incidence algebra, and computed using exponential generating functions. Consider the poset D of positive integers ordered by divisibility, denoted by a | b
Incidence_algebra
Statistical phenomenon
shape Parametric family Likelihood (monotone) Location–scale family Exponential family Completeness Sufficiency Statistical functional Bootstrap U V
Regression_toward_the_mean
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
Supply chain management method
Subsequently, with these platforms continually expanding, China has experienced exponential economic growth, leading to increased disposable income for its citizens
Drop_shipping
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
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
Fourth standardized moment in statistics
Student's t-distribution, Rayleigh distribution, Laplace distribution, exponential distribution, Poisson distribution and the logistic distribution. Such
Kurtosis
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
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
Statistical property
models. One-parameter exponential families have monotone likelihood-functions. In particular, the one-dimensional exponential family of probability density
Monotone_likelihood_ratio
Infinite sum
squaring method for the matrix exponential revisited. SIAM review, 51(4), 747-764. How and How Not to Compute the Exponential of a Matrix Nicolas Bourbaki
Series_(mathematics)
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ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
Girl/Female
Muslim
Well-arranged, Well-ordered
Girl/Female
Greek
Murdered Agamemnon.
Girl/Female
Shakespearean
The Tragedy of Macbeth' Lady Macduff, wife to Macduff, murdered on Macbeth's orders.
Girl/Female
English, Peruvian
Plaster; Powdered
Girl/Female
African, Arabic, Muslim
Well-ordered; Well-arranged
Boy/Male
Hindu
Orderly
Boy/Male
Hindu, Indian, Telugu
Bordered; Friendly Element
Boy/Male
Indian
Ordered, Pasted, Appointed
Male
Arthurian
, a son of Lot; traitor to Arthur.
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
African, Indian, Sanskrit
Clear Spoken Person; Ordered
Boy/Male
Indian
Responsibility; Ordered
Boy/Male
Tamil
Mitanshu | மீதாஂஷà¯Â
Bordered, Friendly element
Mitanshu | மீதாஂஷà¯Â
Girl/Female
Indian
Well-arranged, Well-ordered
Boy/Male
Tamil
Orderly
Boy/Male
Muslim
Ordered, Pasted, Appointed
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’.
Boy/Male
Arabic, Australian, Muslim
Ordered; Appointed
Boy/Male
English Arthurian Legend
Brave.
Boy/Male
American, British, Christian, English
Brave; Brave Counselor
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
ORDERED EXPONENTIAL
a.
Being on duty; keeping order; conveying orders.
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.
One who gives orders.
adv.
According to due order; regularly; methodically; duly.
n.
To give an order for; to secure by an order; as, to order a carriage; to order groceries.
n.
One who puts in order, arranges, methodizes, or regulates.
a.
Covered or adorned with osiers; as, osiered banks.
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.
v. i.
To give orders; to issue commands.
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.
An assemblage of genera having certain important characters in common; as, the Carnivora and Insectivora are orders of Mammalia.
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.
A noncommissioned officer or soldier who attends a superior officer to carry his orders, or to render other service.
n.
To admit to holy orders; to ordain; to receive into the ranks of the ministry.
imp. & p. p.
of Order
a.
Having three corners, or angles; as, a three-cornered hat.
a.
Well-ordered; orderly; regular; methodical.
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