convolution

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convolution

Anatomy any of the numerous convex folds or ridges of the surface of the brain

convolution

(kon-vŏ-loo -shŏn) A mathematical operation that is performed on two functions and expresses how the shape of one is ‘smeared’ by the other. Mathematically, the convolution of the functions f(x) and g(x) is given by
(u )g(x u )du

It finds wide application in physics; it describes, for example, how the transfer function of an instrument affects the response to an input signal. See also autocorrelation function; radio-source structure.

Convolution

 

The convolution of the two functions f1(x) and f2(x) is the function

The convolution of f1(x) and f2(x) is sometimes denoted by f1 * f2

If f1 and f2 are the probability density functions of two independent random variables X and Y, then f1 * f2 is the probability density function of the random variable X + Y. If Fk(x) is the Fourier transform of the function fk(x), that is,

then F1(x) F2(x) is the Fourier transform of the function f1 * f2. This property of convolutions has important applications in probability theory. The convolution of two functions exhibits an analogous property with respect to the Laplace transform; this fact underlies broad applications of convolutions in operational calculus.

The operation of convolution of functions is commutative and associative—that is, f1 * f2 = f2 * f1 and f1 * (f2 * f3) = (f1 * f2) * f3. For this reason, the convolution of two functions can be regarded as a type of multiplication. Consequently, the theory of normed rings can be applied to the study of convolutions of functions.

convolution

[‚kän·və′lü·shən]
(anatomy)
A fold, twist, or coil of any organ, especially any one of the prominent convex parts of the brain, separated from each other by depressions or sulci.
(geology)
The process of developing convolute bedding.
A structure resulting from a convolution process, such as a small-scale but intricate fold.
(mathematics)
The convolution of the functions ƒ and g is the function F, defined by
(statistics)
A method for finding the distribution of the sum of two or more random variables; computed by direct integration or summation as contrasted with, for example, the method of characteristic functions.
References in periodicals archive ?
Richard, "Feature Adapted Convolutional neural Networks for Downbeat Tracking," in Proc.
and Wallace, B, "A sensitive Analysis of (and Practitioners' Guide to) Convolutional Neural Networks for Sentence Classification", arXiv preprint arXiv:1510.
Another Matlab toolbox is MatConvNet that implements Convolutional Neural Networks (CNNs) and is useful in applications that require the automated extraction of information from images.
Decomposing convolutional layers [15] for accelerating time computation of CNNs is composed of two components: (i) a layer decomposition design, for example, low-rank decompositions and CP-decomposition and (ii) an optimization scheme, such as conjugate gradient descent and SGD.
Hinton, Imagenet classification with deep convolutional neural networks.
Besides, each frame incorporates a number of information bit denoted by B together with Bo overhead bits which could be encoded via a convolutional encoding through different coding rates.
Cox, "Fine-tuning convolutional neural networks using harmony search," in Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications, A.
Taking 48 * 48 block size, for example, we design seven-layer architecture, including one input layer, five convolutional layers (noted as C1, C2, C3, C4, and C5), and one max pooling layer.
In [8-15], some blind recognition methods of convolutional codes are proposed.
com) reports that Stanford University computer science graduate student Andrej Karpathy sought to answer that question by using a Convolutional Neural Network data mining computer tool.
In this paper we consider joint network-channel coding for multiple-access relay channel when the transmitting node employs Reed-Solomon (RS code) error correcting code and punctured recursive systematic convolutional code (RSCC) is used as network code.
The precise neuropathology of cortical dysgenesis cannot be based on neuroimaging findings; the histologic examination performed in one case revealed a polymicrogyric convolutional pattern.