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The Intersection of Algorithmically Random Closed Sets and Effective Dimension
ACM Transactions on Computational Logic, 2022 In this article, we study several aspects of the intersections of algorithmically random closed sets. First, we answer a question of Cenzer and Weber, showing that the operation of intersecting relatively random closed sets (random with respect to certain underlying measures induced by Bernoulli measures on the space of codes of closed sets), which ...
Adam Case, Christopher P. Porter
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Journal of Global Optimization, 2023 AbstractWe consider global optimization problems, where the feasible region $${\mathcal {X}}$$ X is a compact subset of $$\mathbb {R}^d$$ R d with $$d \ge 10$$
Jack Noonan, Anatoly Zhigljavsky
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, 2023 Large language models (LLMs) have shown their power in different areas. Attention computation, as an important subroutine of LLMs, has also attracted interests in theory. Recently the static computation and dynamic maintenance of attention matrix has been studied by [Alman and Song 2023] and [Brand, Song and Zhou 2023] from both algorithmic perspective
Deng, Yichuan +2 more
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Random field Ising model in two dimensions: Bethe approximation, cluster variational method and message passing algorithms [PDF]
Journal of Statistical Mechanics: Theory and Experiment, 2015 We study two free energy approximations (Bethe and plaquette-CVM) for the Random Field Ising Model in two dimensions. We compare results obtained by these two methods in single instances of the model on the square grid, showing the difficulties arising in defining a robust critical line.
DomÃnguez, Eduardo +2 more
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Performance Analysis of Turbo-Code with Random (and s-random) Interleaver based on 3-Dimension Algorithm [PDF]
The KIPS Transactions:PartA, 2002 In this paper, we apply the 3-dimension algorithm to the random interleaver and s-random interleaver and analyze the performance of the turbo code system with random interleaver (or s-random interleaver). In general, the performance of interleaver is determined by minimum distance between neighbor data, thus we could improve the performance of ...
Hyung-Yun Kong, Ji-Woong Choi
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Lower Error Bounds for Randomized Multilevel and Changing Dimension Algorithms [PDF]
, 2013 We provide lower error bounds for randomized algorithms that approximate integrals of functions depending on an unrestricted or even infinite number of variables. More precisely, we consider the infinite-dimensional integration problem on weighted Hilbert spaces with an underlying anchored decomposition and arbitrary weights.
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Scientific ReportsThe growing urgency for low-carbon lifestyles necessitates developing effective strategies to promote sustainable consumer choices. This study investigates key dimensions of information quality that shape consumer behavior within digital marketing to achieve this goal.
Weiji Gao +3 more
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The Algorithm of Chaos: WL and Random Dimensions
This paper explores the theoretical construct of "WL," a hypothetical world governed entirely by randomness, devoid of compliance with established laws. In WL, randomness is not entirely without structure, and its governing principles introduce profound implications for dimensions, time, life, and permanence.
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Hybrid optimization algorithm for solving path planning problems based on grey wolf optimization algorithm. [PDF]
Sci RepCheng G, Liu Y.
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A Novel Image Encryption Scheme Based on Two-Dimensional Chaotic Map Constructed from Ackley Function and DNA Operations. [PDF]
Entropy (Basel)Jiang C, Zhang X, Zhang X.
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