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scale convolution of two functions s ( t ) {\displaystyle s(t)} and r ( t ) {\displaystyle r(t)} , also known as their logarithmic convolution or log-volution
Logarithmic_convolution
Topics referred to by the same term
convolution Logarithmic convolution Vandermonde convolution Convolution, in digital image processing, with a Kernel (image processing) Convolutional code
Convolution_(disambiguation)
distribution Logarithmic algorithm Logarithmic convolution Logarithmic decrement Logarithmic derivative Logarithmic differential Logarithmic differentiation
Index_of_logarithm_articles
Problem in computational complexity theory
S2CID 30368541 Chan, Timothy M. (2020), "More logarithmic-factor speedups for 3SUM, (median,+)-convolution, and some geometric 3SUM-hard problems", ACM
3SUM
Type of mathematical function
In convex analysis, a non-negative function f : Rn → R+ is logarithmically concave (or log-concave for short) if its domain is a convex set, and if it
Logarithmically concave function
Logarithmically_concave_function
Estimate of time taken for running an algorithm
input cannot take logarithmic time, as the time taken for reading an input of size n is of the order of n. An example of logarithmic time is given by dictionary
Time_complexity
Mathematical algorithm
obtain the convolution of a and b, according to the usual convolution theorem. Let us also be more precise about what type of convolution is required
Chirp_Z-transform
density is a logarithmically concave function. Thus, any Gaussian measure is log-concave. The Prékopa–Leindler inequality shows that a convolution of log-concave
Logarithmically concave measure
Logarithmically_concave_measure
Power spectrum of a noise signal
intervals are 20 Hz wide. Note that spectra are often plotted with a logarithmic frequency axis rather than a linear one, in which case equal physical
Colors_of_noise
before the first success (i.e. one less). The Hermite distribution The logarithmic (series) distribution The mixed Poisson distribution The negative binomial
List of probability distributions
List_of_probability_distributions
Signal processing conducted on analog signals
_{a}^{b}x(\tau )h(t-\tau )\,d\tau } That is the convolution integral and is used to find the convolution of a signal and a system; typically a = −∞ and
Analog_signal_processing
Signal representation used in automatic speech recognition
Hence, y ( n ) = x ( n ) ∗ h ( n ) {\displaystyle y(n)=x(n)*h(n)} (convolution) As speech is not stationary signal, it is divided into overlapped frames
Mel-frequency_cepstrum
Arithmetic function
f(q)b ... While the Dirichlet convolution of two multiplicative functions is multiplicative, the Dirichlet convolution of two completely multiplicative
Completely multiplicative function
Completely_multiplicative_function
Effect in signal processing
{\displaystyle s(t)} and a Dirac comb function. The spectrum of a product is the convolution between S ( f ) {\displaystyle S(f)} and another function, which inevitably
Spectral_leakage
Smooth approximation to the maximum function
encountered when the usual arithmetic computations are performed on a logarithmic scale, as in log probability. Similar to multiplication operations in
LogSumExp
Local pressure deviation caused by a sound wave
is the particle velocity, ∗ {\displaystyle *} is the convolution operator, z−1 is the convolution inverse of the specific acoustic impedance, hence the
Sound_pressure
Integral inequality
f\star g} is the pdf of X + Y {\displaystyle X+Y} , we also have that the convolution of two log-concave functions is log-concave. Suppose that H(x,y) is a
Prékopa–Leindler_inequality
Mathematical transform that expresses a function of time as a function of frequency
Borel measures, with multiplication given by convolution of measures. With the convention above, convolution corresponds to operator multiplication with
Fourier_transform
Technique in signal processing
interpolated at an arbitrary real argument x is obtained by the discrete convolution of those samples with the Lanczos kernel: S ( x ) = ∑ i = ⌊ x ⌋ − a +
Lanczos_resampling
Multiplication algorithm
n + 1 {\displaystyle 2^{n}+1} ) can be calculated by evaluating the convolution of A , B {\displaystyle A,B} . Also, with g = 2 2 M ′ {\displaystyle
Schönhage–Strassen_algorithm
Probability distribution
{\displaystyle F} , the convolution of F {\displaystyle F} with itself, written F ∗ 2 {\displaystyle F^{*2}} and called the convolution square, is defined
Heavy-tailed_distribution
Measure of the shape of a function
] {\displaystyle \operatorname {E} \left[X^{-n}\right]} and the nth logarithmic moment about zero is E [ ln n ( X ) ] . {\displaystyle \operatorname
Moment_(mathematics)
Function whose domain is the positive integers
called the Dirichlet convolution of a and b, and is denoted by a ∗ b {\displaystyle a*b} . A particularly important case is convolution with the constant
Arithmetic_function
Mathematical function having a characteristic S-shaped curve or sigmoid curve
functions.. These include algebraic transformations, integration and convolution methods, constructions from bell-shaped functions, solutions of ordinary
Sigmoid_function
transforms, list of Fourier-related transforms Kernel (integral operator) Convolution Radon transform Buffon's needle Hadwiger's theorem mean width intrinsic
List of integration and measure theory topics
List_of_integration_and_measure_theory_topics
French mathematician and engineer (1755–1839)
technical school in Paris. In 1791, Prony embarked on the task of producing logarithmic and trigonometric tables for the French Cadastre (geographic survey)
Gaspard_de_Prony
Visual representation of the spectrum of frequencies of a signal as it varies with time
either linear or logarithmic, depending on what the graph is being used for. Audio would usually be represented with a logarithmic amplitude axis (probably
Spectrogram
On the distribution of prime numbers in arithmetic progressions
Iwaniec generalized the Elliott-Halberstam conjecture, using Dirichlet convolution of arithmetic functions related to the von Mangoldt function. The Elliott–Halberstam
Elliott–Halberstam_conjecture
Correlation of a signal with a time-shifted copy of itself, as a function of shift
cross-correlation. By using the symbol ∗ {\displaystyle *} to represent convolution and g − 1 {\displaystyle g_{-1}} is a function which manipulates the
Autocorrelation
Integral transform useful in probability theory, physics, and engineering
integral equations with algebraic polynomial equations, and by replacing convolution with multiplication. For example, through the Laplace transform, the
Laplace_transform
Arithmetic function related to the divisors of an integer
(s-a-b)}{\zeta (2s-a-b)}},} which is a special case of the Rankin–Selberg convolution. A Lambert series involving the divisor function is: ∑ n = 1 ∞ q n σ
Divisor_function
Interdisciplinary research area
polynomially in the number of qubits n {\displaystyle n} , which amounts to a logarithmic time complexity in the number of amplitudes and thereby the dimension
Quantum_machine_learning
Mathematical function
figure. The product of two Gaussian functions is a Gaussian, and the convolution of two Gaussian functions is also a Gaussian, with variance being the
Gaussian_function
Functional relationship between two quantities
statistical models characterized by closure under additive and reproductive convolution as well as under scale transformation. Consequently, these models all
Power_law
n cryptanalysis Multiplicative function Additive function Dirichlet convolution Erdős–Kac theorem Möbius function Möbius inversion formula Divisor function
List_of_number_theory_topics
Mapping involving integration between function spaces
integration kernels are then biperiodic functions; convolution by functions on the circle yields circular convolution. If one uses functions on the cyclic group
Integral_transform
length. The main idea is that if the inner block length is selected to be logarithmic in the size of the outer code then the decoding algorithm for the inner
Concatenated error correction code
Concatenated_error_correction_code
Framework for multi-scale signal representation
derived signals L ( x , y ; t ) {\displaystyle L(x,y;t)} defined by the convolution of f ( x , y ) {\displaystyle f(x,y)} with the two-dimensional Gaussian
Scale_space
Video editing software
Lens Flare, Light Rays, Film FX, Color Curves, Mirror, Remap, Deform, Convolution, Linear Blur, Black Restore, Levels, Unsharp Mask, Color Grading, and
Vegas_Pro
Special function defined by an integral
Related is the Gibbs phenomenon: If the sine integral is considered as the convolution of the sinc function with the Heaviside step function, this corresponds
Trigonometric_integral
Mathematical problem in classical harmonic analysis
D N {\displaystyle S_{N}(f)=f*D_{N}} where ∗ stands for the periodic convolution and D N {\displaystyle D_{N}} is the Dirichlet kernel, which has an explicit
Convergence_of_Fourier_series
Mathematical operation
based on the observation that it can be cast in the form of a convolution by a logarithmic change of variables r = r 0 e − ρ , k = k 0 e κ . {\displaystyle
Hankel_transform
\left(\left(n+{\frac {1}{2}}\right)x\right)}{\sin \left({\frac {1}{2}}x\right)}}.} The convolution of any integrable function of period 2 π {\displaystyle 2\pi } with the
List of trigonometric identities
List_of_trigonometric_identities
measures Convergence of random variables Convex hull Convolution of probability distributions Convolution random number generator Conway–Maxwell–Poisson distribution
List_of_statistics_articles
measure for the angle estimation. Logarithmic spirals, including circles, can for instance be detected by (complex) convolutions and non-linear mappings. The
Generalized_structure_tensor
Mathematical series
following series may be obtained by applying Möbius inversion and Dirichlet convolution to known series. For example, given a Dirichlet character χ(n) one has
Dirichlet_series
Mathematical term
where the coefficients of the new series are given by the Dirichlet convolution of an with the constant function 1(n) = 1: b m = ( a ∗ 1 ) ( m ) = ∑
Lambert_series
Lists of integrals List of laws List of lemmas List of limits List of logarithmic identities List of mathematical functions List of mathematical identities
List_of_theorems
Function used in signal processing
spectral nulls are actually zero-crossings, which cannot be shown on a logarithmic scale such as this.) This property is unique to the rectangular window
Window_function
Branch of mathematical analysis
fractional derivative. In particular, the ABC operator can be written as a convolution of the Caputo derivative with a nontrivial Mittag–Leffler kernel, which
Fractional_calculus
Method to draw shadows in computer graphic images
"Exponential" https://discovery.ucl.ac.uk/id/eprint/10001/1/10001.pdf CSM "Convolution" https://doclib.uhasselt.be/dspace/bitstream/1942/8040/1/3227.pdf VSM
Shadow_mapping
Type of signal filter
by the rectangular function in the frequency domain or, equivalently, convolution with its impulse response, a sinc function, in the time domain. However
Low-pass_filter
Differential operator in mathematics
0<\alpha <n} , the Riesz potential of order α {\displaystyle \alpha } is convolution with the kernel c n , α | x | α − n {\displaystyle c_{n,\alpha }|x|^{\alpha
Laplace_operator
Quantum computing protocol
protocol for predicting expectation values of a quantum state using only a logarithmic number of measurements. Given an unknown state ρ {\displaystyle \rho
Classical_shadow
Class of organic compounds
inert, their concentration in the ocean interior reflects simply the convolution of their atmospheric time evolution and ocean circulation and mixing
Chlorofluorocarbon
Measurable property or characteristic
include noise ratios, length of sounds, relative power, filter matches, logarithmic Mel-scale spectral vectors and Mel-frequency cepstral coefficients, which
Feature_(machine_learning)
) y ( t − s ) d s {\displaystyle F[x,y]=x*y=\int _{E}x(s)y(t-s)\,ds} Convolution F [ y ] = ∫ E y ln y d t {\displaystyle F[y]=\int _{E}y\ln y\,dt} Differential
List_of_mathematic_operators
Function for integral Fourier-like transform
(For instance, a logarithmic Fourier Transform also exists with O(N) complexity, but the original signal must be sampled logarithmically in time, which
Wavelet
Fast Fourier transform algorithm
modulo operations for that level take O(N) time; since there will be a logarithmic number of levels, the overall complexity is O (N log N). More explicitly
Bruun's_FFT_algorithm
Study of the deformation of solids that touch each other
{\displaystyle F_{n}(h)} terms are calculated for the given surfaces using the convolution of the surface roughness ϕ ∗ ( s ) {\displaystyle \phi ^{*}(s)} . Several
Contact_mechanics
Spiral-shaped regions of enhanced brightness within the galactic disc in spiral galaxies
manner as a logarithmic spiral. However, spiral arms may also be described as an Archimedean or hyperbolic spiral. In the case of the logarithmic spiral,
Spiral_arm
Generating pseudo-random numbers that follow a probability distribution
decreasing density functions as well as symmetric unimodal distributions Convolution random number generator, not a sampling method in itself: it describes
Non-uniform random variate generation
Non-uniform_random_variate_generation
Outer layer of the cerebrum of the mammalian brain
gyri) and a groove is termed a sulcus (plural sulci). These surface convolutions appear during fetal development and continue to mature after birth through
Cerebral_cortex
Description of a quantum-mechanical system
mechanics Lamé equation List of things named after Erwin Schrödinger Logarithmic Schrödinger equation Nonlinear Schrödinger equation Pauli equation Quantum
Schrödinger_equation
Sequence in computer science
arbitrary rectangular subarrays. This can be a helpful primitive in image convolution operations. Counting sort is an integer sorting algorithm that uses the
Prefix_sum
Exploring properties of the integers with complex analysis
Gustav Lejeune Dirichlet came up with his own approximating function, the logarithmic integral li(x) (under the slightly different form of a series, which
Analytic_number_theory
Method of data analysis
(2008). "Randomized online PCA algorithms with regret bounds that are logarithmic in the dimension" (PDF). Journal of Machine Learning Research. 9: 2287–2320
Principal_component_analysis
Operation in mathematical calculus
resulting infinite series can be summed analytically. The method of convolution using Meijer G-functions can also be used, assuming that the integrand
Integral
Method of analyzing electrochemical reactions
square-wave voltammetry, cyclic voltammetry, anodic stripping voltammetry, convolution techniques, and elimination methods. Lastly, there was also an advancement
Voltammetry
Arithmetic operation
this sense, the maximum operation is a dequantized version of addition. Convolution is used to add two independent random variables defined by distribution
Addition
Property of solid materials under mechanical stress
Newtonian dashpot in parallel. The creep strain is given by the following convolution integral: ε ( t ) = σ C 0 + σ C ∫ 0 ∞ f ( τ ) ( 1 − e − t / τ ) d τ {\displaystyle
Creep_(deformation)
Book by Hiroshi Yūki
Catalan numbers Convolution Propositions Elements Sets The Riemann zeta function The Basel problem Euler product Harmonic series Logarithmic function Oresme's
Math_Girls
Process in quantum computing
Quantum Error Correction: Symmetric, Asymmetric, Synchronizable, and Convolutional Codes. Springer Nature. Frank Gaitan (2008). Quantum Error Correction
Quantum_error_correction
Mathematical function
polynomials, σ(α) n(x) where σ(1) n(x) ≡ σn(x), which generalize the Stirling convolution polynomials from the single factorial case to the multifactorial cases
Double_factorial
Iterative method for finding maximum likelihood estimates in statistical models
(2003). "The α-EM algorithm: Surrogate likelihood maximization using α-logarithmic information measures". IEEE Transactions on Information Theory. 49 (3):
Expectation–maximization algorithm
Expectation–maximization_algorithm
Computer hardware and software capable of playing chess
the bounds coincided, reduced the branching factor of the game tree logarithmically, but it still was not feasible for chess programs at the time to exploit
Computer_chess
coefficients of the expansions for V and 1/V are related by the simple convolution formulas derived from the following identity: so that the right-hand
Holomorphic Embedding Load-flow method
Holomorphic_Embedding_Load-flow_method
Logarithmic identities Several important formulas, sometimes called logarithmic identities or log laws, relate logarithms to one another. Logarithmic
Glossary_of_engineering:_A–L
Chinese-American computer engineer and neuroscientist
development of techniques like learning large-scale 3D objects with a deep convolutional neural network (CNN) and feature-independent learning for extensive
Juyang_Weng
Characteristic of an optical system
function can also be calculated directly from the pupil function. From the convolution theorem it can be seen that the optical transfer function is in fact
Optical_transfer_function
Features that do not change if length or energy scales are multiplied by a common factor
linear model and characterized by closure under additive and reproductive convolution as well as under scale transformation. These include a number of common
Scale_invariance
Ensemble learning method
the feature sharing detectors, is observed to scale approximately logarithmically with the number of class, i.e., slower than linear growth in the non-sharing
Boosting_(machine_learning)
Probability distribution
Discussion Paper 865. Grinshpan, A. Z. (2017). "An inequality for multiple convolutions with respect to Dirichlet probability measure". Advances in Applied Mathematics
Dirichlet_distribution
Very general problem in computer science
polynomial number of measurements. The size of a generating set will be logarithmically small compared to the size of G {\displaystyle G} . Let T {\displaystyle
Hidden_subgroup_problem
Integral transform
(k+1)}{\Gamma (\alpha +k+1)}}t^{\alpha +k}} as expected. Indeed, given the convolution rule L { f ∗ g } = ( L { f } ) ( L { g } ) {\displaystyle {\mathcal {L}}\{f*g\}={\bigl
Riemann–Liouville_integral
Quantum algorithm for solving systems of linear equations
was developed by Childs et al. Since the HHL algorithm maintains its logarithmic scaling in N {\displaystyle N} only for sparse or low rank matrices,
HHL_algorithm
NASA satellite of the Explorer program
spacecraft. The electric field spectrum measurements were made in 16 logarithmically spaced frequency channels extending from 1.78 Hz to 178 kHz, and DC
Explorer_52
Time behavior of a system controlled by Heaviside step functions
S} for notational convenience: the step response can be obtained by convolution of the Heaviside step function control and the impulse response h(t)
Step_response
Artificial structures such as pavements covered with water-tight materials
and environmental monitoring. Deep learning algorithms, particularly convolutional neural networks (CNNs), have revolutionized our capacity to identify
Impervious_surface
Certain vector fields are the sum of an irrotational and a solenoidal vector field
kernel K ( r , r ′ ) {\displaystyle K(\mathbf {r} ,\mathbf {r} ')} in the convolution integrals has to be replaced by K ′ ( r , r ′ ) = K ( r , r ′ ) − K (
Helmholtz_decomposition
Quantum algorithm for counting solutions to search problems
else it returns NO. Quantum relation testing combined with classical logarithmic search forms an efficient quantum min/max searching algorithm. Quantum
Quantum_counting_algorithm
have lymphoma. The artificial intelligence within the tool uses a deep convolutional neural network to recognize patterns of distinct subtypes. All data
Flow_cytometry_bioinformatics
Academic field
is connected to a component of size n {\displaystyle n} is given by convolution powers of the degree distribution: w ( n ) = { E [ k ] n − 1 u 1 ∗ n
Network_science
Quantization procedure in quantum field theory
}={\vec {k}}_{\perp }-x_{1}{\vec {q}}_{\perp }} . The result of the convolution gives the form factor exactly for all momentum transfer when one sums
Light-front quantization applications
Light-front_quantization_applications
Statistical physics approach
same as an ordinary logarithmic function. Basic properties The κ-logarithm function has the following properties of a logarithmic function: ln κ ( x
Kaniadakis_statistics
Infinite sum that is considered independently from any notion of convergence
product of the two sequences of coefficients, and is a sort of discrete convolution. With these operations, R N {\displaystyle R^{\mathbb {N} }} becomes
Formal_power_series
Experimental technology level
the Bernstein-Vazirani problem, where quantum advantage requires only logarithmic query complexity. For quantum state learning problems, NISQ devices face
Noisy intermediate-scale quantum computing
Noisy_intermediate-scale_quantum_computing
Technique for the generative modeling of a discrete probability distribution
(t)}}dW_{t}} . This changes the probability density function, by first a convolution with the density of a gaussian, followed by a scaling. In the case of
Discrete_diffusion_model
a protocol for predicting functions of a quantum state using only a logarithmic number of measurements. Given an unknown state ρ {\displaystyle \rho
Glossary_of_quantum_computing
LOGARITHMIC CONVOLUTION
LOGARITHMIC CONVOLUTION
LOGARITHMIC CONVOLUTION
LOGARITHMIC CONVOLUTION
Boy/Male
English Teutonic
Noble guardian/protector.
Boy/Male
Indian, Punjabi, Sikh
Tremendous Love
Surname or Lastname
English
English : habitational name from places in Derbyshire and Hampshire, named from the Old English byname Wicga (meaning ‘beetle’, ‘insect’) or Old English wicga ‘beetle’, ‘insect’ + lēah ‘wood’, ‘woodland clearing’.
Boy/Male
Muslim
Old Arabic name
Girl/Female
Hindu, Indian, Marathi
Most Beautiful; Well Adorned
Boy/Male
Norse English
Happy.
Boy/Male
Indian
Grand.
Girl/Female
Arabic, Indian
Beautiful
Boy/Male
Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Telugu
Star
Girl/Female
Tamil
Rich or from hadria, Dissolved
LOGARITHMIC CONVOLUTION
LOGARITHMIC CONVOLUTION
LOGARITHMIC CONVOLUTION
LOGARITHMIC CONVOLUTION
LOGARITHMIC CONVOLUTION
n.
An expression of the condition of equality between two algebraic quantities or sets of quantities, the sign = being placed between them; as, a binomial equation; a quadratic equation; an algebraic equation; a transcendental equation; an exponential equation; a logarithmic equation; a differential equation, etc.
n.
Any collection and arrangement in a condensed form of many particulars or values, for ready reference, as of weights, measures, currency, specific gravities, etc.; also, a series of numbers following some law, and expressing particular values corresponding to certain other numbers on which they depend, and by means of which they are taken out for use in computations; as, tables of logarithms, sines, tangents, squares, cubes, etc.; annuity tables; interest tables; astronomical tables, etc.
n.
The decimal part of a logarithm, as distinguished from the integral part, or characteristic.
n.
A logarithm of the cosine or cotangent.
n.
A number or quantity which is arbitrarily made the fundamental number of any system; a base. Thus, 10 is the radix, or base, of the common system of logarithms, and also of the decimal system of numeration.
n.
An irregular, tortuous folding of an organ or part; as, the convolutions of the intestines; the cerebral convolutions. See Brain.
a.
See Logarithmic.
a.
Alt. of Logarithmetical
a.
Of or pertaining to logarithms; consisting of logarithms.
n.
One of a class of auxiliary numbers, devised by John Napier, of Merchiston, Scotland (1550-1617), to abridge arithmetical calculations, by the use of addition and subtraction in place of multiplication and division.
n.
The number corresponding to a logarithm. The word has been sometimes, though rarely, used to denote the complement of a given logarithm; also the logarithmic cosine corresponding to a given logarithmic sine.
n.
The number from which a mathematical table is constructed; as, the base of a system of logarithms.
n.
The act of finding out or inventing; contrivance or construction of that which has not before existed; as, the invention of logarithms; the invention of the art of printing.
a.
Alt. of Logarithmical
adv.
By the use of logarithms.
a.
Consisting of many folds, coils, or convolutions.
n.
The integral part (whether positive or negative) of a logarithm.
n.
Anything of a rounded or swelling form resembling a roll; a turn; a convolution; a coil.