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In chaos theory, the correlation integral is the mean probability that the states at two different times are close: C ( ε ) = lim N → ∞ 1 N 2 ∑ i ≠ j i
Correlation_integral
Dimensionality measure in chaos theory
{x}}(i)=[x_{1}(i),x_{2}(i),\ldots ,x_{m}(i)],\qquad i=1,2,\ldots N} then the correlation integral C(ε) is calculated by: C ( ε ) = lim N → ∞ g N 2 {\displaystyle C(\varepsilon
Correlation_dimension
Integral expressing the amount of overlap of one function as it is shifted over another
cross-correlation: for real-valued functions, of a continuous or discrete variable, convolution f ∗ g {\displaystyle f*g} differs from cross-correlation f
Convolution
Correlation of a signal with a time-shifted copy of itself, as a function of shift
Autocorrelation, sometimes known as serial correlation in the discrete time case, measures the correlation of a signal with a delayed copy of itself.
Autocorrelation
Covariance and correlation
In signal processing, cross-correlation is a measure of similarity of two series as a function of the displacement of one relative to the other. This
Cross-correlation
The triple correlation of an ordinary function on the real line is the integral of the product of that function with two independently shifted copies of
Triple_correlation
Mathematical conjecture
mathematics, Montgomery's pair correlation conjecture is a conjecture made by Hugh Montgomery (1973) that the pair correlation between pairs of zeros of the
Montgomery's pair correlation conjecture
Montgomery's_pair_correlation_conjecture
Correlation as a function of distance
A correlation function is a function that gives the statistical correlation between random variables, contingent on the spatial or temporal distance between
Correlation_function
Pictorial representation of the behavior of subatomic particles
SF is the free action, whose correlation functions are given by Wick's theorem. The exponential of S in the path integral can be expanded in powers of
Feynman_diagram
Sequence of data points over time
measures Measures based on the correlation sum Correlation dimension Correlation integral Correlation density Correlation entropy Approximate entropy Sample
Time_series
Equation in statistical mechanics
Ornstein–Zernike (OZ) equation is an integral equation introduced by Leonard Ornstein and Frits Zernike that relates different correlation functions with each other
Ornstein–Zernike_equation
In chaos theory, the correlation sum is the estimator of the correlation integral, which reflects the mean probability that the states at two different
Correlation_sum
Framework for integrating diverse theories
Integral theory as developed by Ken Wilber is a synthetic metatheory aiming to unify a broad spectrum of Western theories and models and Eastern meditative
Integral_theory
Expectation value of time-ordered quantum operators
define other correlation functions such as one-particle irreducible correlation functions. In the path integral formulation, n-point correlation functions
Correlation function (quantum field theory)
Correlation_function_(quantum_field_theory)
Modification of approximate entropy
included in SampEn. However, since SampEn makes direct use of the correlation integrals, it is not a real measure of information but an approximation. The
Sample_entropy
of covalent ferromagnets using DFT-LSDA functionals, the exchange-correlation integral takes the place of the Stoner parameter. The density of states at
Colossal_magnetoresistance
Function describing the distribution of galaxies in the universe
astronomy, a correlation function describes the distribution of objects (often stars or galaxies) in the universe. By default, "correlation function" refers
Correlation function (astronomy)
Correlation_function_(astronomy)
Quantum version of the classical action
construction, which restores convexity. Background field method Correlation function Path integral formulation Renormalization group Spontaneous symmetry breaking
Effective_action
Formulation of quantum mechanics
action. The path integral formulation of quantum field theory represents the transition amplitude (corresponding to the classical correlation function) as
Path-integral_formulation
Interaction between electrons, often complicating physical calculations
Electronic correlation is the interaction between electrons in the electronic structure of a quantum system. The correlation energy is a measure of how
Electronic_correlation
Generating function for quantum correlation functions
functions are generating functionals for correlation functions, making them key objects of study in the path integral formalism. They are the imaginary time
Partition function (quantum field theory)
Partition_function_(quantum_field_theory)
Measure of a system's order
mechanics, the correlation function is a measure of the order in a system, as characterized by a mathematical correlation function. Correlation functions describe
Correlation function (statistical mechanics)
Correlation_function_(statistical_mechanics)
Calculus of stochastic differential equations
central concept is the Itô stochastic integral, a stochastic generalization of the Riemann–Stieltjes integral in analysis. The integrands and the integrators
Itô_calculus
Mathematical theorem
The Gaussian correlation inequality (GCI), formerly known as the Gaussian correlation conjecture (GCC), is a mathematical theorem in the fields of mathematical
Gaussian correlation inequality
Gaussian_correlation_inequality
Data mining framework
Outliers) LOCI (Local Correlation Integral) LDOF (Local Distance-Based Outlier Factor) EM-Outlier SOD (Subspace Outlier Degree) COP (Correlation Outlier Probabilities)
ELKI
Theoretical framework in physics
that are evaluated in the free theory. In the path integral formulation, the two-point correlation function can be written ⟨ Ω | T { ϕ ( x ) ϕ ( y ) }
Quantum_field_theory
Measures process correlation distance
The integral length scale measures the correlation distance of a process in terms of space or time. In essence, it looks at the overall memory of the process
Integral_length_scale
Integral used in physics
Stratonovich integral or Fisk–Stratonovich integral (developed simultaneously by Ruslan Stratonovich and Donald Fisk) is a stochastic integral, the most
Stratonovich_integral
Cryptographic attack
Correlation attacks are a class of cryptographic known-plaintext attacks for breaking stream ciphers whose keystreams are generated by combining the output
Correlation_attack
Description of particle density in statistical mechanics
In statistical mechanics, the radial distribution function, (or pair correlation function) g ( r ) {\displaystyle g(r)} in a system of particles (atoms
Radial_distribution_function
Mathematical transform that expresses a function of time as a function of frequency
In mathematics, the Fourier transform (FT) is an integral transform that takes a function as input and outputs another function that describes the extent
Fourier_transform
Generalization of the concept from statistical mechanics
then partition function can be understood to be a sum or integral over Gaussians. The correlation function C ( x j , x k ) {\displaystyle C(x_{j},x_{k})}
Partition function (mathematics)
Partition_function_(mathematics)
Method of solution to differential equations
Green's function in many-body theory Correlation function Propagator Green's identities Parametrix Volterra integral equation Resolvent formalism Keldysh
Green's_function
Function in quantum field theory showing probability amplitudes of moving particles
nonlocal correlation in these vacuum fluctuations, analogous to an EPR correlation. Indeed, the propagator is often called a two-point correlation function
Propagator
Molecular dynamics simulations augmented with quantum mechanics
Path integral molecular dynamics (PIMD) is a method of incorporating quantum mechanics into molecular dynamics simulations using Feynman path integrals. In
Path integral molecular dynamics
Path_integral_molecular_dynamics
Topological quantum field theory
3-form. In the Chern–Simons theory, the action is proportional to the integral of the Chern–Simons 3-form. In condensed-matter physics, Chern–Simons theory
Chern–Simons_theory
Equation relating transport coefficients to correlation functions
coefficient γ {\displaystyle \gamma } in terms of the integral of the equilibrium time correlation function of the time derivative of a corresponding microscopic
Green–Kubo_relations
Two-dimensional conformal field theory
theory is conformally invariant. The path integral representation of an N {\displaystyle N} -point correlation function of primary fields is ⟨ ∏ i = 1 N
Liouville_field_theory
Process in quantum mechanical theories
check that relativistic invariance is not lost. Alternatively, the Feynman integral approach is available for quantizing relativistic fields, and is manifestly
Canonical_quantization
Technique for determining size distribution of particles
the intensity or photon autocorrelation function (also known as photon correlation spectroscopy – PCS or quasi-elastic light scattering – QELS). In the
Dynamic_light_scattering
Branch of mathematical analysis
derivatives and integrals. Let f ( x ) {\displaystyle f(x)} be a function defined for x > 0 {\displaystyle x>0} . Form the definite integral from 0 to x {\displaystyle
Fractional_calculus
Connection between correlation functions and the S-matrix
S-matrix elements (the scattering amplitudes) from the time-ordered correlation functions of a quantum field theory. It is a step of the path that starts
LSZ_reduction_formula
Type of operator expectation value
operator is the Casimir effect. This concept is important for working with correlation functions in quantum field theory. In the context of spontaneous symmetry
Vacuum_expectation_value
Quantum chromodynamics on a lattice
context of the IBM Blue Gene supercomputer. After Wick rotation, the path integral for the partition function of QCD takes the form Z = ∫ D U e − S [ U ]
Lattice_QCD
Dimensionality reduction technique
In statistics, functional correlation is a dimensionality reduction technique used to quantify the correlation and dependence between two variables when
Functional_correlation
Study of collection and analysis of data
Chi-squared test Correlation Factor analysis Mann–Whitney U Mean square weighted deviation (MSWD) Pearson product-moment correlation coefficient Regression
Statistics
Sigmoid shape special function
{2}{\sqrt {\pi }}}\int _{0}^{z}e^{-t^{2}}\,dt.} The integral here is a complex contour integral which is path-independent because exp ( − t 2 ) {\displaystyle
Error_function
Evolutionary equation under renormalization group flow
equation is a differential equation describing the evolution of the n-point correlation functions under variation of the energy scale at which the theory is
Callan–Symanzik_equation
Formulation of the quantum many-body problem
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Second_quantization
High-temperature expansion in statistical mechanics
the two-particle correlations Δ ⟨ 2 ⟩ {\displaystyle \Delta \langle 2\rangle } determine doublets, while the three-particle correlations Δ ⟨ 3 ⟩ {\displaystyle
Cluster_expansion
Expression for two-point correlation functions
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Källén–Lehmann spectral representation
Källén–Lehmann_spectral_representation
Physical theory with fields invariant under the action of local "gauge" Lie groups
the theory. Technically, they reduce to the computations of certain correlation functions in the vacuum state. This involves a renormalization of the
Gauge_theory
Algorithm
stream mode shift register LFSR NLFSR T-function IV Attacks correlation attack correlation immunity stream cipher attacks v t e Cryptography General History
Symmetric-key_algorithm
Fourier analysis topics. Multiplier (Fourier analysis) Fourier shell correlation Pinsky phenomenon Generalized Fourier series Regressive discrete Fourier
List of Fourier analysis topics
List_of_Fourier_analysis_topics
Quantum state with the lowest possible energy
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Quantum_vacuum_state
Quantum states of two qubits
predicts perfect correlations. In a more refined formulation known as the Bell–CHSH inequality, it is shown that a certain correlation measure cannot exceed
Bell_state
Simplified model in condensed matter physics
Mathematically, the strength of this coupling is given by a "hopping integral", or "transfer integral", between nearby sites. The system is said to be in the tight-binding
Hubbard_model
Function in discrete mathematics
DTFT of a finite length sequence. (§ Sampling the DTFT) It is the cross correlation of the input sequence, x n {\displaystyle x_{n}} , and a complex sinusoid
Discrete_Fourier_transform
In mathematics, the correlation immunity of a Boolean function is a measure of the degree to which its outputs are uncorrelated with some subset of its
Correlation_immunity
Method of data analysis
"remarkable" correlations of the correlation matrix, by a solid line (positive correlation) or dotted line (negative correlation). A strong correlation is not
Principal_component_analysis
Generalization of the Dirac equation
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Dirac equation in curved spacetime
Dirac_equation_in_curved_spacetime
Quantum field giving rise to gluons
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Gluon_field
Energy difference between ground state and lightest excited state(s)
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Mass_gap
Statistical model
across choosers, unrestricted substitution patterns across choices, and correlation in unobserved factors over time. Mixed logit can choose any distribution
Mixed_logit
British statistician
integrals, and the distribution of the correlation coefficients. As a result, her first book was released in 1938, called Tables of the Correlation Coefficient
Florence_Nightingale_David
Mathematical concept applicable to physics
In vector calculus, flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. The word
Flux
Bound on probability of a random variable being far from its mean
X 2 {\displaystyle X_{1},X_{2}} . Let ρ {\displaystyle \rho } be the correlation coefficient between X 1 {\displaystyle X_{1}} and X 2 {\displaystyle
Chebyshev's_inequality
Action of a massive abelian gauge field
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Proca_action
Stochastic differential equation
{\boldsymbol {\eta }}(t)} has a Gaussian probability distribution with correlation function ⟨ η i ( t ) η j ( t ′ ) ⟩ = 2 λ k B T δ i , j δ ( t − t ′ )
Langevin_equation
Predicting and managing water resources
flow peaks. The degree and nature of correlation may be quantified, by using a method such as the Pearson correlation coefficient, autocorrelation, or the
Hydrological_model
Stochastic process generalizing Brownian motion
evolution. In applied mathematics, the Wiener process is used to represent the integral of a white noise Gaussian process, and so is useful as a model of noise
Wiener_process
Ability to easily switch cryptographic primitives
stream mode shift register LFSR NLFSR T-function IV Attacks correlation attack correlation immunity stream cipher attacks v t e Cryptography General History
Cryptographic_agility
Statistical measure of how far values spread from their average
the average correlation remains constant or converges too. So for the variance of the mean of standardized variables with equal correlations or converging
Variance
Input to a cryptographic primitive
stream mode shift register LFSR NLFSR T-function IV Attacks correlation attack correlation immunity stream cipher attacks v t e Cryptography General History
Initialization_vector
Phase transition in the two-dimensional (2-D) XY model
seen. However, one finds a low-temperature quasi-ordered phase with a correlation function (see statistical mechanics) that decreases with the distance
Berezinskii–Kosterlitz–Thouless transition
Berezinskii–Kosterlitz–Thouless_transition
Topics referred to by the same term
decomposition of multiple integrals Integration by reduction formulae, expressing an integral in terms of the same integral but in lower powers LSZ reduction
Reduction_formula
Psychometric factor also known as "general intelligence"
abilities and human intelligence. It is a variable that summarizes positive correlations among different cognitive tasks, reflecting the assertion that an individual's
G_factor_(psychometrics)
Quantity relating heat flux and temperature difference
The Dittus-Bölter correlation (1930) is a common and particularly simple correlation useful for many applications. This correlation is applicable when
Heat_transfer_coefficient
Theory of quantum gauge fields on a lattice
infinite-dimensional path integral, which is computationally intractable. By working on a discrete spacetime, the path integral becomes finite-dimensional
Lattice_gauge_theory
Topics referred to by the same term
temperatures Supersymmetric localization, a method to compute exact correlation functions of certain supersymmetric operators in supersymmetric quantum
Localization
Nondimensional heat transfer coefficient
identified this dimensionless group in 1915. Analytical results and empirical correlations allow the Nusselt number to be estimated in many situations. For forced
Nusselt_number
Jerome K. Percus and George J. Yevick. The direct correlation function represents the direct correlation between two particles in a system containing N − 2
Percus–Yevick_approximation
Function that encodes the dependence of a coupling parameter on the energy scale
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Beta_function_(physics)
Quantum field theory of electromagnetism
physical meaning at certain divergences appearing in the theory through integrals, became one of the fundamental aspects of quantum field theory and is
Quantum_electrodynamics
in equilibrium. In this relation, Euclidean Green's functions become correlation functions in the statistical mechanical system. A statistical mechanical
Stochastic_quantization
Theorem for reducing high-order derivatives
theorem applied to fields is proved in essentially the same way. The correlation function that appears in quantum field theory can be expressed by a contraction
Wick's_theorem
Sampling algorithm
integrator.[citation needed] The reduced correlation means fewer Markov chain samples are needed to approximate integrals with respect to the target probability
Hamiltonian_Monte_Carlo
Probabilistic problem-solving algorithm
precisely one would have to already know the integral, but one can approximate the integral by an integral of a similar function or use adaptive routines
Monte_Carlo_method
Measure of statistical dispersion
a number such that integral of the PDF from -∞ to Q1 equals 0.25, while the upper quartile, Q3, is such a number that the integral from -∞ to Q3 equals
Interquartile_range
Relativistic wave equation describing massless fermions
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Weyl_equation
Decomposition of periodic functions
original function. The coefficients of the Fourier series are determined by integrals of the function multiplied by trigonometric functions, described in Fourier
Fourier_series
Measure of variation in statistics
parameters Coefficient of variation Cumulant Deviation (statistics) Distance correlation Distance standard deviation Error bar Geometric standard deviation Mahalanobis
Standard_deviation
Quantum field that enables consistent quantization
anticommuting fields that are introduced to maintain the consistency of the path integral formulation in non-abelian gauge theories, such as the ones describing
Ghost_(physics)
Attempts to develop a quantum mechanical theory of cosmology
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Quantum_cosmology
Type of approximation to an underlying physical theory
Topological charge Tools Anomaly Background field method BRST quantization Correlation function Crossing Effective action Effective field theory Expectation
Effective_field_theory
Identity in abelian theories due to gauge invariance
quantum field theory, a Ward–Takahashi identity is an identity between correlation functions that follows from the global or gauge symmetries of the theory
Ward–Takahashi_identity
Statistical distribution for dependence between random variables
{\displaystyle \mathbb {R} ^{d}} by using the probability integral transform. For a given correlation matrix R ∈ [ − 1 , 1 ] d × d {\displaystyle R\in [-1
Copula_(statistics)
Type of Feynman diagram
diagram with one external leg, giving a contribution to a one-point correlation function (i.e., the field's vacuum expectation value). One-loop diagrams
Tadpole_(physics)
Type of degradation in signal transmission
phase of delay correlation of weighted signals. For integer CFO, frequency-domain cross-correlation and frequency-domain PN correlation can be used with
Carrier_frequency_offset
Pattern-recognition performance metrics
(the weighted harmonic mean of precision and recall), or the Matthews correlation coefficient, which is a geometric mean of the chance-corrected variants:
Precision_and_recall
CORRELATION INTEGRAL
CORRELATION INTEGRAL
CORRELATION INTEGRAL
Boy/Male
Hindu, Indian
Lord Shiva
Girl/Female
Muslim
Miracle, Verses in the Quran
Girl/Female
Assamese, Hindu, Indian, Kannada, Marathi, Telugu, Traditional
Garland of Rays
Boy/Male
Hindu, Indian, Sanskrit
Penance; To Burn; Shine; Suffer
Surname or Lastname
English (Somerset)
English (Somerset) : variant spelling of Pepin.
Boy/Male
Arabic, Muslim
Father of Hasan
Boy/Male
English French
Courtier; court attendant.
Boy/Male
Indian, Punjabi, Sikh
Protected Lamp
Boy/Male
Latin
In bloom.
Girl/Female
Spanish
Warring.
CORRELATION INTEGRAL
CORRELATION INTEGRAL
CORRELATION INTEGRAL
CORRELATION INTEGRAL
CORRELATION INTEGRAL
n.
Reciprocal relation; corresponding similarity or parallelism of relation or law; capacity of being converted into, or of giving place to, one another, under certain conditions; as, the correlation of forces, or of zymotic diseases.
n.
Quality of being correlative.
a.
Having or indicating a reciprocal relation.
n.
Abatement of noxious qualities; the counteraction of what is inconvenient or hurtful in its effects; as, the correction of acidity in the stomach.
n.
The quality of correlation; reciprocation; interchange; interaction; interdependence.
n.
The flowing of different streams into one.
n.
Emendation; correction.
n.
One who, or that which, stands in a reciprocal relation, or is correlated, to some other person or thing.
n.
The act corrugating; contraction into wrinkles or alternate ridges and grooves.
n.
Correction; chastisement; punishment inflicted by way of correction and training.
a.
Submissive to correction; docile.
n.
The state of being congealed.
n.
The quality or state of being irrelative; want of connection or relation.
adv.
In a correlative relation.
n.
The act or process of passing, or causing to pass, from a fluid to a solid state, as by the abstraction of heat; the act or process of freezing.
p. pr. & vb. n.
of Correlate
n.
Mutual or reciprocal relation; correlation.
n.
That which is congealed.
n.
An allowance made for inaccuracy in an instrument; as, chronometer correction; compass correction.
n.
The antecedent of a pronoun.