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Efficient Sum-Check Protocol for Convolution [PDF]
IEEE Access, 2021 Many applications have recently adopted machine learning and deep learning techniques. Convolutional neural networks (CNNs) are made up of sequential operations including activation, pooling, convolution, and fully connected layer, and their computation cost is enormous, with convolution and fully connected layer dominating.
Chanyang Ju +4 more
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Evaluation of the convolution sum involving the sum of divisors function for 22, 44 and 52
Open Mathematics, 2017 The convolution sum, ∑(l,m)∈N02αl+βm=nσ(l)σ(m), $ \begin{array}{} \sum\limits_{{(l\, ,m)\in \mathbb{N}_{0}^{2}}\atop{\alpha \,l+\beta\, m=n}} \sigma(l)\sigma(m), \end{array} $ where αβ = 22, 44, 52, is evaluated for all natural numbers n. Modular forms
Ntienjem Ebénézer
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Gradient-Controlled Gaussian Kernel for Image Inpainting [PDF]
AUT Journal of Electrical Engineering, 2023 Image inpainting is the process of filling in damaged or missing regions in an image by using information from known regions or known pixels of the image. One of the most important techniques for inpainting is convolution-based methods, in which a kernel
Hossein Noori
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MethodsX, 2021 In probability theory and statistics, the probability distribution of the sum of two or more independent and identically distributed (i.i.d.) random variables is the convolution of their individual distributions.
Arne Johannssen +2 more
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The multinomial convolution sum of a generalized divisor function
Open Mathematics, 2022 The main theorem of this article is to evaluate and express the multinomial convolution sum of the divisor function σr♯(n;N/4,N){\sigma }_{r}^{\sharp }\left(n;\hspace{0.33em}N\hspace{-0.08em}\text{/}\hspace{-0.08em}4,N) in as a simple form as possible ...
Park Ho
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Speed of convergence of complementary probabilities on finite group
Visnik Harkivsʹkogo Nacionalʹnogo Universitetu im. V.N. Karazina. Cepiâ Matematika, Prikladna Matematika i Mehanika, 2021 Let function P be a probability on a finite group G, i.e. $P(g)\geq0\ $ $(g\in G),\ \sum\limits_{g}P(g)=1$ (we write $\sum\limits_{g}$ instead of $\sum\limits_{g\in G})$.
Alexander Vyshnevetskiy
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Frontiers in Earth Science, 2021 The stacked refraction convolution section can be used as an interpretation tool in wide-angle refraction seismic data generated by air gun shooting and recorded by Ocean Bottom Seismometers (OBS).
Antonio González-Fernández
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Computation of the Distribution of the Sum of Independent Negative Binomial Random Variables
Mathematical and Computational Applications, 2023 The distribution of the sum of negative binomial random variables has a special role in insurance mathematics, actuarial sciences, and ecology. Two methods to estimate this distribution have been published: a finite-sum exact expression and a series ...
Marc Girondot, Jon Barry
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CONVOLUTION SUMS INVOLVING THE DIVISOR FUNCTION [PDF]
Proceedings of the Edinburgh Mathematical Society, 2004 AbstractThe series\begin{alignat*}{2} L_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ M_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_3(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \\ N_{r,4}(q)\amp=\sum_{n=0}^\infty\sigma_5(4n+r)q^{4n+r},\amp\quad r\amp=0,1,2,3, \end{alignat*}are evaluated and used to prove convolution formulae such ...
Cheng, Nathalie, Williams, Kenneth S.
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A Novel Hybrid Algorithm for Transient Near-Field Scattering from Rough Surface in 2-D Case
International Journal of Antennas and Propagation, 2021 A novel hybrid algorithm is proposed to reduce the computation cost of the finite-difference time-domain (FDTD) method in calculating the transient near-field scattering from rough surface.
Wei Tian, Bing Wei, Qian Yang
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