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Proof technique in probability theory
In probability theory, coupling is a proof technique that allows one to compare two unrelated random variables (distributions) X and Y by creating a random
Coupling_(probability)
process Chapman–Kolmogorov equation Chinese restaurant process Coupling (probability) Ergodic theory Maximal ergodic theorem Ergodic (adjective) Galton–Watson
List_of_probability_topics
Topics referred to by the same term
(genetics), a type of genetic linkage Coupling (probability), a proof technique in probability theory Coupling (piping), a short length of pipe or tube
Coupling_(disambiguation)
Card trick and probabilistic concept
initially chosen number and therefore the magician can predict it. Coupling (probability) Discrete logarithm Equifinality Ergodic theory Geometric distribution
Kruskal_count
Statistical distribution for dependence between random variables
In probability theory and statistics, a copula is a multivariate cumulative distribution function for which the marginal probability distribution of each
Copula_(statistics)
Quantum field theory of electromagnetism
quantities called probability amplitudes. The probability is the square of the absolute value of total probability amplitude, probability = | f ( amplitude
Quantum_electrodynamics
Bibliographic coupling occurs when two works reference a common third work in their bibliographies. It is an indication that a probability exists that the
Bibliographic_coupling
Machine learning problem
application of the pairwise coupling algorithm by Hastie and Tibshirani. A method used to assign scores to pairs of predicted probabilities and actual discrete
Probabilistic_classification
Direct coupling analysis or DCA is an umbrella term comprising several methods for analyzing sequence data in computational biology. The common idea of
Direct_coupling_analysis
Mechanism of beta decay proposed in 1933
direct coupling of a neutron with an electron, a neutrino (later determined to be an antineutrino) and a proton. Fermi first introduced this coupling in his
Fermi's_interaction
lists articles related to probability theory. In particular, it lists many articles corresponding to specific probability distributions. Such articles
Catalog of articles in probability theory
Catalog_of_articles_in_probability_theory
Topics referred to by the same term
up decoupling or coupling in Wiktionary, the free dictionary. Decoupling usually refers to the ending, removal or reverse of coupling. Decoupling may also
Decoupling
Ambiguous term in statistics
class membership probabilities in the case with classes count greater than two: Reduction to binary tasks and subsequent pairwise coupling, see Hastie and
Calibration_(statistics)
Exactly solvable model of coupled oscillators
model. The model makes several assumptions, including that there is weak coupling, that the oscillators are identical or nearly identical, and that interactions
Kuramoto_model
Principle of quantum mechanics
solutions to the Schrödinger equation in Dirac notation weighted by the two probability amplitudes c 0 {\displaystyle c_{0}} and c 1 {\displaystyle c_{1}} that
Quantum_superposition
Intereference effect in quantum optics
stronger "coupling" field is tuned near resonance at a different transition. If the states are selected properly, the presence of the coupling field will
Electromagnetically induced transparency
Electromagnetically_induced_transparency
Electrical engineering concept
known equally as susceptibility or immunity. A third class studied is coupling, which is the mechanism by which emitted interference reaches the victim
Electromagnetic_compatibility
Concept in theoretical physics
describe the interactions of the objects; they may be variable ("running") couplings which measure the strength of various forces, mass parameters, or the
Renormalization_group
non-relativistic couplings responsible for mixing between states are a driving force of transition. For example, the larger spin-orbit coupling at MECP the
Nonadiabatic transition state theory
Nonadiabatic_transition_state_theory
Concept in quantum mechanics
is insufficient time for the functional form to adapt, so the spatial probability density remains unchanged. At the 1911 Solvay conference, Einstein gave
Adiabatic_theorem
Design guideline for software development
object-oriented programs. In its general form, the LoD is a specific case of loose coupling. The guideline was proposed by Ian Holland at Northeastern University towards
Law_of_Demeter
Scientific study of digital information
coin, they gain information about the outcome. For a fair coin, the probability of either heads or tails is 1/2 and the amount of information is expressed
Information_theory
Process forming a path from many random steps
namely manifested on the same probability space in a dependent way that forces them to be quite close. The simplest such coupling is the Skorokhod embedding
Random_walk
In probability and statistics, decoupling is a reduction of a sample statistic to an average of the statistic evaluated on several independent sequences
Decoupling_(probability)
average IRI of the schedule (Killeen, 1994). To derive the coupling coefficient, the probability of the schedule not having ended, weighted by the contents
Mathematical principles of reinforcement
Mathematical_principles_of_reinforcement
Quantum mechanical phenomenon
appear outside of the barrier representing a probability for tunnelling through the barrier. Since the probability of transmission of a wave packet through
Quantum_tunnelling
Formula for the probability that a system will change between two energy states
the two states is a linear function of time. The formula, giving the probability of a non-adiabatic transition between the two adiabatic energy states
Landau–Zener_formula
Direct interaction between two magnetic dipoles
Magnetic dipole–dipole interaction, also called dipolar coupling or dipolar interaction, refers to the direct interaction between two magnetic dipoles
Magnetic dipole–dipole interaction
Magnetic_dipole–dipole_interaction
Calculation of complex statistical distributions
is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a Markov chain whose
Markov_chain_Monte_Carlo
Distance function defined between probability distributions
)} and corresponds to a supremum norm. Here, a coupling γ {\displaystyle \gamma } is a joint probability measure on M × M {\displaystyle M\times M} whose
Wasserstein_metric
Theorem in classical statistical mechanics
nuclear magnetic resonance, particularly protein NMR and residual dipolar couplings. Rotational diffusion can also be observed by other biophysical probes
Equipartition_theorem
Mathematical description of quantum state
interpretation of quantum mechanics, the Born rule, relating transition probabilities to inner products. The Schrödinger equation determines how wave functions
Wave_function
Quantum measurement phenomenon
period of time; the probability of decaying increases with time. Then frequent measurement reestablishes or strengthens the coupling, and with it the measured
Quantum_Zeno_effect
Physical and science fiction concept
M.; Neunzig, O. (21 August 2024). "In-depth experimental search for a coupling between gravity and electromagnetism with steady fields". Scientific Reports
Anti-gravity
Technique for the generative modeling of a continuous probability distribution
2015 as a method to train a model that can sample from a highly complex probability distribution. They used techniques from non-equilibrium thermodynamics
Diffusion_model
Compare and contrast article
"split" into an electron plus a photon, with a certain probability (which is roughly the coupling constant). This is described in string theory as one string
Relationship between string theory and quantum field theory
Relationship_between_string_theory_and_quantum_field_theory
Quantum physical phenomenon
related to the probability of an electron to propagate between two given points in space. Classical physics assumes that the total probability is just the
Weak_localization
Transition rate formula
Fermi's golden rule is a formula that describes the transition rate (the probability of a transition per unit time) from one energy eigenstate of a quantum
Fermi's_golden_rule
Method to identify covarying pairs of amino acids in proteins
Statistical Coupling Analysis (SCA) is a method used in bioinformatics to study how pairs of amino acids in a protein sequence evolve together. It analyzes
Statistical_coupling_analysis
target, due to spin-orbit coupling. It can assume values ranging from -1 (spin-up electron is scattered with 100% probability to the left of the target)
Sherman_function
Concept in physics
becomes likely below about 40 kelvins, but depends also on the strength of coupling between the chromophore and the host lattice. The transition between the
Zero-phonon line and phonon sideband
Zero-phonon_line_and_phonon_sideband
Explanation for the rates of electron transfer reactions
system has a certain probability to jump from the initial to the final potential energy curves. In the adiabatic case the coupling is considerable and
Marcus_theory
Observed inability to reproduce scientific studies
significance, the probability of replication increases with power, and prior probability for H 1 {\displaystyle H_{1}} . If the prior probability for H 1 {\displaystyle
Replication_crisis
Method of sampling from a Markov chain
Propp, James; Wilson, David (1998), "Coupling from the past: a user's guide", Microsurveys in discrete probability (Princeton, NJ, 1997), DIMACS Ser. Discrete
Coupling_from_the_past
Loss of quantum coherence
phase space created by coupling with the environment. In phase space, this decoupling is monitored through the Wigner quasi-probability distribution. The original
Quantum_decoherence
Damped oscillation in quantum optics
volume V in an optical cavity. Spontaneous emission is a consequence of coupling between the atom and the vacuum fluctuations of the cavity field. A mathematical
Vacuum_Rabi_oscillation
Model in quantum optics
of probabilities predicted by the model. Before that time, research groups were unable to build experimental setups capable of enhancing the coupling of
Jaynes–Cummings_model
Type of artificial neural network
representations for higher capsules. The output is a vector consisting of the probability of an observation, and a pose for that observation. This vector is similar
Capsule_neural_network
Atom of the element hydrogen
electron. Using the time-independent Schrödinger equation, ignoring all spin-coupling interactions and using the reduced mass μ = m e M / ( m e + M ) {\displaystyle
Hydrogen_atom
positions, dipole coupling is averaged partially due to water diffusion which proceeds according to the symmetry of the solids and the probability distribution
Pake_doublet
Equivalence of two physical theories
coupling constant must be less than 1 so that the higher powers of g {\displaystyle g} become negligibly small and the sum is finite. If the coupling
S-duality
Chemical reaction
on the sodium-induced coupling of alkyl halides (the Wurtz reaction), Wilhelm Rudolph Fittig extended the approach to the coupling of an alkyl halide with
Wurtz–Fittig_reaction
Measure of dependence between two variables
In probability theory and information theory, the mutual information (MI) of two random variables is a measure of the mutual dependence between the two
Mutual_information
Systems design methodology
assess and mitigate the effects of coupling. Axiom 2, the Information Axiom, provides a metric of the probability that a specific DP will deliver the
Axiomatic_design
Aspect of electron emission of a compound
models were able to qualitatively explain the effect using spin-orbit coupling (SOC). But quantitatively, the predicted effect was always orders of magnitude
Chirality-induced spin selectivity
Chirality-induced_spin_selectivity
Mathematical theory on behavior of connected clusters in a random graph
the probability that an infinite cluster exists is either zero or one. Since this probability is an increasing function of p (proof via coupling argument)
Percolation_theory
Random fluctuation in an electrical signal
into a circuit from the external environment, by inductive coupling or capacitive coupling, or through the antenna of a radio receiver. Intermodulation
Noise_(electronics)
Process by which atoms or molecules acquire charge by gaining or losing electrons
{\displaystyle \Gamma (t)=\Gamma _{m}I(t)^{m/2}} coupling the two states. According to Story et al., the probability of remaining in the ground state, P g {\displaystyle
Ionization
Superconducting qubit implementation
the coupling energy and charging energy of its junctions. In the charge qubit regime the charging energy of the junctions dominates the coupling energy
Flux_qubit
Mathematical model of ferromagnetism in statistical mechanics
{\displaystyle f} . The configuration probabilities P β ( σ ) {\displaystyle P_{\beta }(\sigma )} represent the probability that (in equilibrium) the system
Ising_model
Probability theorem
doi:10.2307/2325124. JSTOR 2325124. den Hollander, Frank. Probability Theory: the Coupling Method. Weisstein, Eric W. "Le Cam's Inequality". MathWorld
Le_Cam's_theorem
Time required for a Markov chain to reach a stationary distribution
In probability theory, the mixing time of a Markov chain is the time until the Markov chain is "close" to its steady state distribution. More precisely
Markov_chain_mixing_time
Elementary particle involved with rest mass
boson's self-coupling remains unmeasured. The shape of the Higgs potential in the Standard Model includes both trilinear and quartic self-couplings, which are
Higgs_boson
Branch of probability theory
Renewal theory is the branch of probability theory that generalizes the Poisson process for arbitrary holding times. Instead of exponentially distributed
Renewal_theory
Restricted model of non-universal quantum computation
computers. As explained by Philip Ball, it "entails calculating the probability distribution of many bosons — a category of fundamental particle that
Boson_sampling
Pattern of oscillating motion in a system
isolated, the self-coupling approximation, or that many modes close in frequency resonate, the cross-coupling approximation. Self-coupling will solely change
Normal_mode
Method for stochastic equation systems
In probability theory, the Gillespie algorithm (or the Doob–Gillespie algorithm or stochastic simulation algorithm, the SSA) generates a statistically
Gillespie_algorithm
Topics referred to by the same term
dependence, dependent or depend may refer to: Dependency (computer science) or coupling, a state in which one object uses a function of another object Data dependency
Dependency
Theoretical framework in physics
The renormalized coupling constant, which changes with the energy scale, is also called the running coupling constant. The coupling constant g in quantum
Quantum_field_theory
Formal constraint in quantum mechanics
moment operator. This integral represents the propagator (and thus the probability) of the transition between states 1 and 2; if the value of this integral
Selection_rule
Cardiorespiratory condition
through the capillary beds. Under normal conditions, ventilation-perfusion coupling keeps ventilation (V) at approximately 4 L/min and normal perfusion (Q)
Ventilation–perfusion mismatch
Ventilation–perfusion_mismatch
Type of quark
recent evidence that intrinsic charm quarks exist in the proton, and the coupling of the charm quark and the Higgs boson has been studied. Recent evidence
Charm_quark
Allowing for contactless payments in credit and debit cards
they use a built-in inductor, using the principle of resonant inductive coupling, to capture some of the incident electromagnetic signal, rectify it, and
Contactless_smart_card
Probability theory routinely uses results from other fields of mathematics (mostly, analysis). The opposite cases, collected below, are relatively rare;
List of probabilistic proofs of non-probabilistic theorems
List_of_probabilistic_proofs_of_non-probabilistic_theorems
Interaction between subatomic particles
interaction has a coupling constant (an indicator of how frequently interactions occur) between 10−7 and 10−6, compared to the electromagnetic coupling constant
Weak_interaction
American mathematician
Propp, James; Wilson, David (1998). "Coupling from the past: a user's guide". Microsurveys in discrete probability (Princeton, NJ, 1997). DIMACS Ser. Discrete
Jim_Propp
Measurement of a quantum system which minimally disturbs it
∑ q E q = I {\textstyle \sum _{q}E_{q}=I} so that the corresponding probabilities sum to unity: ∑ q Pr ( q | ψ ) = ∑ q ⟨ ψ | E q | ψ ⟩ = 1 {\textstyle
Weak_measurement
Excited state dynamic
spin-orbit coupling promotes the formation of the triplet MLCT excited state, which could improve exciton diffusion length and reduce the probability of recombination
Intersystem_crossing
Differential equations involving stochastic processes
of the probability distribution function. [citation needed] The notation used in probability theory (and in many applications of probability theory,
Stochastic differential equation
Stochastic_differential_equation
Brainwaves, repetitive patterns of neural activity in the central nervous system
on the properties of the connection, such as the coupling strength, time delay and whether coupling is excitatory or inhibitory, the spike trains of the
Neural_oscillation
Statistical method for molecular phylogenetics
posterior probability. Some of the most common algorithms used in MCMC methods include the Metropolis–Hastings algorithms, the Metropolis-Coupling MCMC (MC³)
Bayesian inference in phylogeny
Bayesian_inference_in_phylogeny
Statistical modeling framework
methods. DCM is typically used to estimate the coupling among brain regions and the changes in coupling due to experimental changes (e.g., time or context)
Dynamic_causal_modeling
Elementary quasiparticle
of TI-polaron is a delocalized state of electron-phonon system: the probabilities of electron's occurrence at any point of a space are similar. Both the
TI-polaron
Pictorial representation of the behavior of subatomic particles
Richard Feynman, who introduced the diagrams in 1948. The calculation of probability amplitudes in theoretical particle physics requires the use of large
Feynman_diagram
Statistical mechanics hypothesis that all microstates are equiprobable for a given energy
the Mode-Coupling theory of Götze, W. (2008). Dynamics of Glass Forming Liquids. Oxford Univ. Press. Taleb, Nassim Nicholas (2019), "Probability, Risk,
Ergodic_hypothesis
2009 non-fiction book discussing mathematics
stochastic process defined by a set of states and, for each state, a probability distribution on the states. Starting from an initial state, it follows
Markov Chains and Mixing Times
Markov_Chains_and_Mixing_Times
Mathematical concept
named after Josiah Willard Gibbs, is a probability measure frequently seen in many problems of probability theory, statistical mechanics, and dynamical
Gibbs_measure
Hypothetical particle decay process of a proton
Model unification occurs, the three fundamental forces have comparable couplings, suggesting unification in Grand Unified Theories (GUTs). Historical models
Proton_decay
Russian-American mathematician
Forum Mathematicum, the Electronic Journal of Probability, and Electronic Communications in Probability. Gordina was awarded a Humboldt Research fellowship
Maria_Gordina
Measure of similarity between curves
associated grid graph. The discrete Fréchet distance, also called the coupling distance, is an approximation of the Fréchet metric for polygonal curves
Fréchet_distance
Physical theory with fields invariant under the action of local "gauge" Lie groups
{\displaystyle \ D_{\mu }=\partial _{\mu }-igA_{\mu }} where g is called the coupling constant; a quantity defining the strength of an interaction. After a simple
Gauge_theory
Calculation method in computational fluid dynamics
using a finite volume approach. The particle phase is described by a probability distribution function (PDF), ϕ ( x , u f , ρ p , Ω p , t ) ; {\displaystyle
Multiphase particle-in-cell method
Multiphase_particle-in-cell_method
Absence of diffusion waves in disordered media
dimensions (3D) at zero magnetic field and in the absence of spin-orbit coupling. Much further work has subsequently supported these scaling arguments both
Anderson_localization
Class of organic compounds with general structure RN=C=NR'
increases the probability of sensitization to the compound. Clinical reports of individuals who cannot enter rooms where peptide coupling agents are used
Carbodiimide
Model of quantum optics
while the matter is described as a set of two-level systems. When the coupling between the light and matter crosses a critical value, the Dicke model
Dicke_model
Structure connecting neurons in the nervous system
synaptic transmission. Synaptic communication is distinct from an ephaptic coupling, in which communication between neurons occurs via indirect electric fields
Synapse
Nonlinear infrared spectroscopy technique
the vibrational coupling in solution, since the solvent modify both vibrational frequencies, transition probabilities and couplings. Computer simulations
Two-dimensional infrared spectroscopy
Two-dimensional_infrared_spectroscopy
Indian tea estate worker
many people. However, the probability of this gene expressing is very low: it can happen because of rare recessive gene coupling, or some form of mutation
Chandre_Oram
electric, magnetic, and electromagnetic means. Common Mode coupling as well as Differential Mode coupling can occur in both a conducted and radiated way. Differential
Common_mode_current
Technique in theoretical physics
are known as flux compactifications. The coupling constant of string theory, which determines the probability of strings splitting and reconnecting, can
Compactification_(physics)
COUPLING PROBABILITY
COUPLING PROBABILITY
Surname or Lastname
English (Lancashire)
English (Lancashire) : possibly a variant of Colling.
Girl/Female
Arabic, Muslim
Cooling or Delight of the Eye; Joy; Pleasure; Darling; Sweetheart
Surname or Lastname
English and Scottish
English and Scottish : variant of Copeland.
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : from a double diminutive of Codd.English (Yorkshire) : from Old French ceur de lion ‘lion heart’, applied as a nickname for a brave man, or ironically for an exceptionally timorous one.
Surname or Lastname
English
English : variant of Colling.
Girl/Female
Muslim
Complex, Zigzag, Curling
Girl/Female
Australian, British, English
Copying Something
Surname or Lastname
English
English : from the Old Norse personal name Kollungr, a derivative of Koli, or from an Old English cognate, Colling, a derivative of Cola (see Cole 2).English : from a pet form of Coll 1.Altered spelling of German Kölling (see Kolling).
Biblical
fifty count or the counting of fifty days
Boy/Male
Hindu, Indian
Counting
Surname or Lastname
English
English : from Middle English crulling ‘the curly one’, a nickname for someone with curly hair.Possibly an Americanized spelling of German Gerling.
Surname or Lastname
English
English : variant of Joplin.
Girl/Female
Arabic, Muslim
Complex; Zigzag; Curling
Girl/Female
Hindu, Indian, Marathi, Sanskrit
A Cooling Note
Surname or Lastname
English
English : variant of Coppin.English : topographic name for someone who lived on the top of a hill, from a derivative Old English of copp ‘summit’ (see Copp 1).
Surname or Lastname
English
English : variant of Cooling.
Surname or Lastname
English
English : from a medieval personal name, originally an Old English patronymic from the personal names Cūl(a) or Cēola. The former may be from a Germanic root kūl ‘swollen’; the latter is a short form of various compound names with the first element cēol ‘ship’.English : habitational name from a place in Kent named Cooling, from the Old English tribal name Cūlingas ‘people of Cūl(a)’.
Surname or Lastname
English
English : patronymic from Colling.
Boy/Male
Indian, Punjabi, Sikh
Imbued with Cooling Peace
Surname or Lastname
English
English : topographic name for someone who lived on a hilltop, from Copping 2 + the suffix -er denoting an inhabitant.Possibly an Americanized spelling of German Kapfinger, Gapfinger, or Kopfinger, habitational names for someone from a place named Kapfingen or Köpfingen, in southern Germany.
COUPLING PROBABILITY
COUPLING PROBABILITY
Girl/Female
Indian, Punjabi, Sikh
Gold Dust
Boy/Male
American, Australian, British, Christian, Danish, English, Finnish, German, Greek
Rock; Form of Peter; Stone
Boy/Male
Muslim
A prophets name
Boy/Male
Indian, Modern, Sikh
The Diamond of God
Girl/Female
Arabic, Muslim
Thankfulness
Boy/Male
Arabic
Morning; Dawn
Boy/Male
Hindu
Gift of the God of religion
Surname or Lastname
English (East Anglia)
English (East Anglia) : nickname for a clever person, from Anglo-Norman French sotil ‘subtle’, ‘clever’, ‘cunning’.English (East Anglia) : habitational name from Soothill in West Yorkshire.
Boy/Male
Arabic
Imagination; Conception
Boy/Male
Gujarati, Hindu, Indian, Sanskrit
Fighter; Stronger; Strength; One who has Strength in his Arms
COUPLING PROBABILITY
COUPLING PROBABILITY
COUPLING PROBABILITY
COUPLING PROBABILITY
COUPLING PROBABILITY
n.
A coupling pin. See under Coupling.
n.
A coupling pin. See under Coupling.
n.
A coursing back, or coursing again, along the line of a previous coursing; renewed course; return; retreat; recurence.
a.
Sacramental; as, housling fire.
a.
Same as Housling.
n.
Alt. of Complin
n.
A turning and winding; as, the doubling of a hunted hare; shift; trick; artifice.
n.
The act of bringing or coming together; connection; sexual union.
n.
The cap or coupling of a flail, through which the thongs pass which connect the handle and swingel.
n.
Same as Compline.
n.
An erroneous counting.
n.
A cupping glass.
v. t.
To apply a cupping apparatus to; to subject to the operation of cupping. See Cupping.
a.
Cooling.
p. pr. & vb. n.
of Couple
n.
A device or contrivance which serves to couple or connect adjacent parts or objects; as, a belt coupling, which connects the ends of a belt; a car coupling, which connects the cars in a train; a shaft coupling, which connects the ends of shafts.
n.
The act or state of that which curls; as, the curling of smoke when it rises; the curling of a ringlet; also, the act or process of one who curls something, as hair, or the brim of hats.
n.
Union; combination; a coupling; a pair.
n.
A stone for coping. See Coping.
n.
The act of coupling or joining; union; conjunction.