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Special class of quantum states
information theory, a Gaussian state (also called a quasi-free state in quantum field theory) is a specific type of mixed quantum state of either multiple
Gaussian_state
Filter in electronics and signal processing
processing, a Gaussian filter is a filter whose impulse response is a Gaussian function (or an approximation to it, since a true Gaussian response would
Gaussian_filter
Recursive state estimator for state-space models derived via dynamic programming
(latent) states in a state-space model from noisy observations. It is typically formulated for models with a linear–Gaussian state transition and a possibly
Bellman_filter
Volume rendering technique
Gaussian splatting is a volume rendering technique that deals with the direct rendering of volume data without converting the data into surface or line
Gaussian_splatting
Mathematical function
In mathematics, a Gaussian function, often simply referred to as a Gaussian, is a function of the base form f ( x ) = exp ( − x 2 ) {\displaystyle f(x)=\exp(-x^{2})}
Gaussian_function
Short "burst" or "envelope" of restricted wave action that travels as a unit
frequency within a bandwidth inversely proportional to that width; even a Gaussian function is considered a wave packet because its Fourier transform is a
Wave_packet
Probability distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued
Normal_distribution
Integral of the Gaussian function, equal to sqrt(π)
The Gaussian integral, also known as the Euler–Poisson integral, is the integral of the Gaussian function over the entire real line. Named after the German
Gaussian_integral
Statistical concept
multivariate Gaussian mixture model is used to cluster the feature data into k number of groups where k represents each state of the machine. The machine state can
Mixture_model
Approximation of the definite integral of a function
In numerical analysis, an n-point Gaussian quadrature rule, named after Carl Friedrich Gauss, is a quadrature rule constructed to yield an exact result
Gaussian_quadrature
Product of the principal curvatures of a surface
In differential geometry, the Gaussian curvature or Gauss curvature (symbol Κ, named after Carl Friedrich Gauss) of a smooth surface in three-dimensional
Gaussian_curvature
Application of quantum entanglement to high-precision measurement
in each degree of freedom. Dimensional metrology Forensic metrology Gaussian state Quantum metrological gain Smart Metrology Time metrology Braunstein
Quantum_metrology
Monochrome light beam whose amplitude envelope is a Gaussian function
optics, a Gaussian beam is an idealized beam of electromagnetic radiation whose amplitude envelope in the transverse plane is given by a Gaussian function;
Gaussian_beam
Complex number whose real and imaginary parts are both integers
In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers. The Gaussian integers, with ordinary addition
Gaussian_integer
Computational chemistry software
methods Gaussian 70, Gaussian 76, Gaussian 80, Gaussian 82, Gaussian 86, Gaussian 88, Gaussian 90, Gaussian 92, Gaussian 92/DFT, Gaussian 94, Gaussian 98,
Gaussian_(software)
Algorithm that estimates unknowns from a series of measurements over time
Markov model such that the state space of the latent variables is continuous and all latent and observed variables have Gaussian distributions. Kalman filtering
Kalman_filter
Quantum error correcting code
protects against random shifts in the quadratures, which can be modeled as a Gaussian random displacement channel. N ( ρ ) = ∫ d x e − | | x | | 2 / 2 σ ~ 2
Gottesman–Kitaev–Preskill code
Gottesman–Kitaev–Preskill_code
Random matrix with gaussian entries
the Gaussian ensembles are specific probability distributions over self-adjoint matrices whose entries are independently sampled from the gaussian distribution
Gaussian_ensemble
Mathematical function
computational chemistry and molecular physics, Gaussian orbitals (also known as Gaussian type orbitals, GTOs or Gaussians) are functions used as atomic orbitals
Gaussian_orbital
Restricted model of non-universal quantum computation
concluded by Gaussian measurements (more specifically, by eight-port homodyne detection that projects each output mode onto a squeezed coherent state). Such
Boson_sampling
Continuous deformation between two continuous functions
complex non-Gaussian states is a challenging task. Using deep learning and homotopy, such complex states can be transformed to Gaussian state and mildly
Homotopy
Feature enhancement algorithm in imaging science
imaging science, difference of Gaussians (DoG) is a feature enhancement algorithm that involves the subtraction of one Gaussian blurred version of an original
Difference_of_Gaussians
baseline for the state survey of the Duchy of Holstein, the Danish state, the city of Hamburg and the Kingdom of Hanover (Gaussian State Survey). Its length
Braak_Base_Line
Model of interest rate curves
instantaneous forward rate are assumed to be deterministic, this is known as the Gaussian Heath–Jarrow–Morton (HJM) model of forward rates. For direct modeling of
Heath–Jarrow–Morton_framework
Quantum mechanical waves describing matter
free space he worked out the propagation of the wave, assuming an initial Gaussian wave packet. Darwin showed that at time t {\displaystyle t} later the position
Matter_wave
q-Gaussian processes are deformations of the usual Gaussian distribution. There are several different versions of this; here we treat a multivariate deformation
Q-Gaussian_process
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
Feature observed in spectroscopy
weaker intensity in the spectrum. Ideal line shapes include Lorentzian, Gaussian and Voigt functions, whose parameters are the line position, maximum height
Spectral_line_shape
Family of polynomials
In mathematics, the Gaussian binomial coefficients (also called Gaussian coefficients, Gaussian numbers, Gaussian polynomials, or q-binomial coefficients)
Gaussian_binomial_coefficient
Linear optimal control technique
measurements are assumed to be corrupted by Gaussian noise and the initial state, likewise, is assumed to be a Gaussian random vector. Under these assumptions
Linear–quadratic–Gaussian control
Linear–quadratic–Gaussian_control
Measure of nonclassical correlations between two subsystems of a quantum system
Gaussian states. Work has demonstrated that the upper-bound of Gaussian discord indeed coincides with the actual quantum discord of a Gaussian state,
Quantum_discord
occur and any quantum state can be expressed as a real probability distribution. Corney, J. F.; Drummond, P. D. (2004-12-20). "Gaussian Quantum Monte Carlo
Gaussian_quantum_Monte_Carlo
Polynomial sequence
theory in connection with nonlinear operations on Gaussian noise. random matrix theory in Gaussian ensembles. Hermite polynomials were defined by Pierre-Simon
Hermite_polynomials
Theorem that tells the maximum rate at which information can be transmitted
archetypal case of a continuous-time analog communications channel subject to Gaussian noise. The theorem establishes Shannon's channel capacity for such a communication
Shannon–Hartley_theorem
Combining information from two detectors
; Shapiro, Jeffrey H. (2008). "Unified theory of ghost imaging with Gaussian-state light". Physical Review A. 77 (4) 043809. arXiv:0712.3554. Bibcode:2008PhRvA
Ghost_imaging
Laser which uses a solid gain medium
A solid-state laser is a laser that uses a gain medium that is a solid, usually a crystal or glass. Semiconductor-based lasers such as laser diodes are
Solid-state_laser
Set of functions used to represent the electronic wave function
typically used within the solid state community, or real-space approaches. Several types of atomic orbitals can be used: Gaussian-type orbitals, Slater-type
Basis_set_(chemistry)
Statistical distribution for dependence between random variables
applying the Gaussian copula to credit derivatives to be one of the causes of the 2008 financial crisis; see David X. Li § CDOs and Gaussian copula. Despite
Copula_(statistics)
exponentially modified Gaussian distribution, a convolution of a normal distribution with an exponential distribution, and the Gaussian minus exponential distribution
List of probability distributions
List_of_probability_distributions
Device measuring quantum mechanical effects
S2CID 6470118. Guha, Saikat; Erkmen, Baris I. (November 10, 2009). "Gaussian-state quantum-illumination receivers for target detection". Physical Review
Quantum_sensor
Probabilistic numerical ODE solver
specifically, as Gauss–Markov processes. Discretization results in nonlinear Gaussian state space models. Second, use a general Bayesian filtering and smoothing
ODE_filter
Result of differential geometry proved by Gauss
in 1827, that concerns the curvature of surfaces. The theorem says that Gaussian curvature can be determined entirely by measuring angles, distances and
Theorema_Egregium
Free and open-source statistical program
T-Tests, ANOVA, Regression, Variances) BSTS: Bayesian take on linear Gaussian state space models suitable for time series analysis. Circular Statistics:
JASP
Type of reservoir computer
training data. This idea has been demonstrated in by using Gaussian priors, whereby a Gaussian process model with ESN-driven kernel function is obtained
Echo_state_network
Indian statistician (1936–2023)
ISSN 0003-486X. JSTOR 1970351. Parthasarathy, K R (2010). "What is a Gaussian state?". Communications on Stochastic Analysis. 4 (2). doi:10.31390/cosa.4
K. R. Parthasarathy (probabilist)
K._R._Parthasarathy_(probabilist)
Constant used in orbital mechanics
The Gaussian gravitational constant (symbol k) is a parameter used in the orbital mechanics of the Solar System. It relates the orbital period to the orbit's
Gaussian gravitational constant
Gaussian_gravitational_constant
Mathematical transform that expresses a function of time as a function of frequency
distribution (e.g., diffusion). The Fourier transform of a Gaussian function is another Gaussian function. Joseph Fourier introduced sine and cosine transforms
Fourier_transform
Field of knowledge
contributions of Adrien-Marie Legendre and Carl Friedrich Gauss. Many easily stated number problems have solutions that require sophisticated methods, often
Mathematics
Specific quantum state of a quantum harmonic oscillator
standard coherent states, Gaussian states, or oscillator states. In quantum optics the coherent state refers to a state of the quantized electromagnetic
Coherent_state
Formulation of quantum mechanics
Gaussian state, with the expectation values of position and momentum both centered at the origin in phase space. The Wigner function for such a state
Phase-space_formulation
Physics phenomenon
{\displaystyle 1\oplus n} -mode Gaussian states, but no longer sufficient for 2 ⊕ 2 {\displaystyle 2\oplus 2} -mode Gaussian states. Simon's condition can
Quantum_entanglement
Quantum states that are not entangled
{\displaystyle 1\oplus n} -mode Gaussian states, but no longer sufficient for 2 ⊕ 2 {\displaystyle 2\oplus 2} -mode Gaussian states. Simon's condition can
Separable_state
American academic administrator (born 1939)
to receive a Ph.D. in electrical engineering. His early research on non-Gaussian random processes and signal detection, funded by the Navy for sonar applications
Percy_A._Pierre
In mathematics, in the area of number theory, a Gaussian period is a certain kind of sum of roots of unity. The periods permit explicit calculations in
Gaussian_period
Theory of stochastic processes
a centered process. Moreover, if the process is Gaussian, then the random variables Zk are Gaussian and stochastically independent. This result generalizes
Kosambi–Karhunen–Loève theorem
Kosambi–Karhunen–Loève_theorem
Branch of mathematics
Theorema Egregium ("remarkable theorem") that asserts roughly that the Gaussian curvature of a surface is independent from any specific embedding in a
Geometry
Proposal to test the uncertainty principle of quantum mechanics
narrow slit on particle 1 can be thought of as reducing it to a narrow Gaussian state: ϕ 1 ( y 1 ) = 1 ( 2 π ϵ 2 ) 1 4 e − y 1 2 4 ϵ 2 {\displaystyle \phi
Popper's_experiment
Measure of laser beam quality
beam from an ideal Gaussian beam. It is calculated from the ratio of the beam parameter product (BPP) of the beam to that of a Gaussian beam with the same
M_squared
Diffraction pattern in optics
{\textstyle \omega _{0}} is the Gaussian RMS width (in one dimension). If we equate the peak amplitude of the Airy pattern and Gaussian profile, that is, I 0 ′
Airy_disk
English polymath (1642–1727)
credited as founding stereology. Newton was responsible for the origin of Gaussian elimination in Europe. In 1669 to 1670, Newton wrote that all the algebra
Isaac_Newton
Evolutionary algorithm designed for maximizing manufacturing yield
Gaussian adaptation (GA), also called normal or natural adaptation (NA) is an evolutionary algorithm designed for the maximization of manufacturing yield
Gaussian_adaptation
German polymath and scholar (1777–1855)
polygon construction in over 2000 years. He also introduced the concept of Gaussian curvature and proved its key properties, especially with his Theorema Egregium
Carl_Friedrich_Gauss
Type of recurrent neural network with random and non-trainable internal structure
universal quantum computing because transformations that preserve the Gaussian nature of a state are linear. Normally, linear dynamics would not be sufficient
Reservoir_computing
Natural number
Numbers Indicating the Filling of Subshells Within Those Shells". San José State University. Archived from the original on 2019-12-02. Retrieved 2019-12-22
2
Type of error-correcting code using convolution
designate such a state as "10". According to an input bit the encoder at the next turn can convert either to the "01" state or the "11" state. One can see
Convolutional_code
Measure of distance to normality
Out of all probability distributions with a given mean and variance, the Gaussian or normal distribution is the one with the highest entropy.[clarification
Negentropy
Matrix-valued random variable
components per matrix element. The Gaussian unitary ensemble GUE ( n ) {\displaystyle {\text{GUE}}(n)} is described by the Gaussian measure with density 1 Z GUE
Random_matrix
Technique for the generative modeling of a continuous probability distribution
training a neural network to sequentially denoise images blurred with Gaussian noise. The model is trained to reverse the process of adding noise to an
Diffusion_model
Sequential model-based optimization of expensive black-box functions
method constructs a probabilistic model of the unknown function, often a Gaussian process (GP), and uses the resulting predictive distribution to choose
Bayesian_optimization
state prediction density is approximately Gaussian. Masreliez discovered in 1975 that this approximation yields an intuitively appealing non-Gaussian
Masreliez's_theorem
Stochastic process modeling random walk with friction
process is a stationary Gauss–Markov process, which means that it is a Gaussian process, a Markov process, and is temporally homogeneous. In fact, it is
Ornstein–Uhlenbeck_process
Physical theory of the cosmos
predicts that the primordial fluctuations are nearly scale invariant and Gaussian, which has been confirmed by measurements of the CMB. A related issue to
Big_Bang
Statistician and econometrician
squared observations, the model can be represented as a state-space model whose principal non-Gaussian component is a log-chi-squared observation error. The
Siddhartha_Chib
Spectroscopic technique
The mentioned static (harmonic) method also has been integrated into the Gaussian software as default, using the keyword Opt Freq=Raman to calculate. The
Raman_spectroscopy
English computer scientist (1912–1954)
was awarded first-class honours in mathematics. His dissertation, On the Gaussian error function, written during his senior year and delivered in November
Alan_Turing
Exterior structure on infrastructure used to prevent loud sounds from escaping
dozens of different existing and planned highways. Most were commissioned by state highway departments and conducted by one of the four research groups mentioned
Noise_barrier
Study involving matter and electromagnetic radiation
type of element or molecule. Most elements are first put into a gaseous state to allow the spectra to be examined, although today other methods can be
Spectroscopy
Power engineering technique
eliminate the desired node without need of repeating the steps like in Gaussian elimination. It is named after Hungarian American electrical engineer Gabriel
Kron_reduction
Signal processing computational method
subcomponents. This is done by assuming that at most one subcomponent is Gaussian and that the subcomponents are statistically independent from each other
Independent component analysis
Independent_component_analysis
Subset of artificial intelligence
solve decision problems under uncertainty are called influence diagrams. A Gaussian process is a stochastic process in which every finite collection of the
Machine_learning
In mathematics, invariant of square matrices
entries in a row or column. Determinants can be efficiently computed with Gaussian elimination and singular value decomposition. Determinants can also be
Determinant
Probability distribution
are also ratio distributions: the Student's t-distribution arises from a Gaussian random variable divided by an independent chi-distributed random variable
Ratio_distribution
Quantum state, of opposed conditions
separation between the two Gaussian peaks in the Wigner function. More methods have been proposed to produce larger coherent state superpositions through
Cat_state
Modern form of the metric system
measurements: a CGS-based system for electrostatic units, also known as the Gaussian or ESU system, a CGS-based system for electromechanical units (EMU), and
International_System_of_Units
Integer side lengths of a right triangle
the square of a Gaussian integer. This can be proved using the property that every Gaussian integer can be factored uniquely into Gaussian primes up to units
Pythagorean_triple
Vast empty spaces between filaments with few or no galaxies
This unique mix supports the biased galaxy formation picture predicted in Gaussian adiabatic cold dark matter models. This phenomenon provides an opportunity
Void_(astronomy)
approximated by a simple two-gaussian model where a perfect point-like electron beam is broadened to a superposition of a Gaussian with a width α {\displaystyle
Proximity effect (electron beam lithography)
Proximity_effect_(electron_beam_lithography)
Type of activation function
\sigma (x)))} , where N {\displaystyle {\mathcal {N}}} stands for the gaussian distribution. They also argued for another reason for using ReLU: that
Rectified_linear_unit
Type of matrix factorization
permutation matrix as well. LU decomposition can be viewed as the matrix form of Gaussian elimination. Computers usually solve square systems of linear equations
LU_decomposition
Probability distribution and special case of gamma distribution
unit-variance Gaussian random variables. Generalizations of this distribution can be obtained by summing the squares of other types of Gaussian random variables
Chi-squared_distribution
Fortunate number is composite. The Gaussian moat problem: is it possible to find an infinite sequence of distinct Gaussian prime numbers such that the difference
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Relativistic vector field
indices for more details on notation. Formulae are given in SI units and Gaussian-cgs units. The contravariant electromagnetic four-potential can be defined
Electromagnetic four-potential
Electromagnetic_four-potential
Number, approximately 3.14
uncertainty principle only for the Gaussian function. Equivalently, π is the unique constant making the Gaussian normal distribution e−πx2 equal to its
Pi
Medical use of laser to cut tissues
Beam expander Beam homogenizer Chirped pulse amplification Gain-switching Gaussian beam Injection seeder Laser beam profiler M squared Mode locking Multiple-prism
Laser_surgery
Measure for evaluating probabilistic forecasts
probabilistic model that predicts (based on an input x {\displaystyle x} ) a gaussian distribution N ( μ , σ 2 ) {\displaystyle {\mathcal {N}}(\mu ,\sigma ^{2})}
Scoring_rule
vector-valued Wiener process, x ( 0 ) {\displaystyle x(0)} is a zero-mean Gaussian random vector independent of w {\displaystyle w} , y ( 0 ) = 0 {\displaystyle
Separation principle in stochastic control
Separation_principle_in_stochastic_control
Trace radiation from the early universe
such as very large scale anisotropies, anomalous alignments, and non-Gaussian distributions. The most longstanding of these is the low-ℓ multipole controversy
Cosmic_microwave_background
Multivalued function in mathematics
denotes the gamma function. The first identity can be found by writing the Gaussian integral in polar coordinates. The second identity can be derived by making
Lambert_W_function
result of centralized linear–quadratic–Gaussian control systems—that in a system with linear dynamics, Gaussian disturbance, and quadratic cost, affine
Witsenhausen's_counterexample
Measure of the level of acidity or basicity of an aqueous solution
(2019). "Mapping LUCAS topsoil chemical properties at European scale using Gaussian process regression". Geoderma. 355 113912. Bibcode:2019Geode.35513912B
PH
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GAUSSIAN STATE
GAUSSIAN STATE
Male
Russian
(РоÑÑ) Russian pet form of Czech/Russian Rostislav, ROSTYA means "usurp-glory."
Female
Russian
(Людмила) Russian feminine form of Czech/Russian Ludmil, LUDMILA means "people's favor."Â
Male
Russian
Variant spelling of Russian Afanasiy, AFANASY means "immortal."
Male
Russian
Variant spelling of Russian Arseniy, ARSENI means "virile."
Male
Russian
Variant spelling of Russian Aleksey, ALEXEY means "defender."
Boy/Male
Australian, French, German, Irish
Curly-headed
Male
Russian
Variant spelling of Russian Arseniy, ARSENIY means "virile."
Male
Russian
Variant spelling of Russian Vasiliy, VASSILY means "king."
Male
Russian
(Паша) Russian pet form of Czech/Russian Pavel, PASHA means "small."
Male
Russian
Variant spelling of Russian Faddei, FADEI means "courageous."
Male
Russian
Variant spelling of Russian Gennadiy, GENNADY means "noble."
Male
Russian
Variant spelling of Russian Vikentiy, VIKENTI means "conquering."
Male
Russian
Variant spelling of Russian Vasiliy, VASILI means "king."
Male
Russian
Variant spelling of Russian Vasiliy, VASILY means "king."
Male
Russian
Variant spelling of Russian Afanasiy, AFANASEI means "immortal."
Male
Russian
Variant spelling of Russian Irinei, IRINEY means "peaceful."
Female
Russian
(Russian Ева): Armenian and Russian form of Greek Eva, YEVA means "life."Â
Male
Russian
Variant spelling of Russian Afanasiy, AFANASII means "immortal."
Male
Russian
Variant spelling of Russian Gennadiy, GENNADI means "noble."
Male
Russian
(Russian ИÑидор): Russian form of Greek Isidoros, ISIDOR means "gift of Isis."
GAUSSIAN STATE
GAUSSIAN STATE
GAUSSIAN STATE
GAUSSIAN STATE
GAUSSIAN STATE
GAUSSIAN STATE
GAUSSIAN STATE
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