Results 1 to 10 of about 1,582,759 (205)
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 ...
Chanyang Ju +4 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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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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On a shifted convolution sum problem
Journal of Number Theory, 2021 Let f be a holomorphic newform of prime level p and trivial nebentypus. For p 1 + e ≪ M ≪ p 3 − e , and 0 | u | ≪ M / p we prove that ∑ m = 1 ∞ λ f ( m ) λ f ( m + p u ) F ( m M ) ≪ p 1 / 4 + e M 3 / 4 where F is a compactly supported smooth bump ...
R. Munshi
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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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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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Top-𝑘-convolution and the quest for near-linear output-sensitive subset sum [PDF]
Symposium on the Theory of Computing, 2020 In the classical SubsetSum problem we are given a set X and a target t, and the task is to decide whether there exists a subset of X which sums to t. A recent line of research has resulted in (t · poly (logt))-time algorithms, which are (near-)optimal ...
K. Bringmann, Vasileios Nakos
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Faster Algorithms for Bounded Knapsack and Bounded Subset Sum Via Fine-Grained Proximity Results [PDF]
ACM-SIAM Symposium on Discrete Algorithms, 2023 We investigate pseudopolynomial-time algorithms for Bounded Knapsack and Bounded Subset Sum. Recent years have seen a growing interest in settling their fine-grained complexity with respect to various parameters. For Bounded Knapsack, the number of items
Lin Chen +3 more
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