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The intersection of algorithmically random closed sets and effective dimension [PDF]
ACM Transactions on Computational Logic, 2021 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 J. Case, Christopher P. Porter
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Rate optimality of Random walk Metropolis algorithm in high-dimension with heavy-tailed target distribution [PDF]
, 2014 The choice of the increment distribution is crucial for the random-walk Metropolis-Hastings (RWM) algorithm. In this paper we study the optimal choice in high-dimension setting among all possible increment distributions. The conclusion is rather counter intuitive, but the optimal rate of convergence is attained by the usual choice, the normal ...
Kengo Kamatani
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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]
, 2012 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.
Michael Gnewuch
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Randomized LOBPCG algorithm with linear dimension reduction
We present a randomized variant of the locally optimal block preconditioned conjugate gradient (LOBPCG) method that incorporates linear dimension reduction for computing a group of eigenpairs of generalized eigenvalue problems. In contrast to the well-established LOBPCG method, we do not assert that our randomized variant always yields a superior ...
Yanfei Xiang
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A biased random key genetic algorithm for open dimension nesting problems using no-fit raster
Expert Systems with Applications, 2017 Irregular 2D cutting problems with one or two open dimensions are tackled.The no-fit raster concept is extended to deal with free form items.A BRKGA combined with bottom-left heuristics is proposed to solve the problems.It outperforms recent methods from the literature on different set of instances.Instances with items as circles, convex and non-convex
Leandro Resende Mundim +2 more
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Performance of global random search algorithms for large dimensions [PDF]
Journal of Global Optimization, 2017 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Andrey Pepelyshev +2 more
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CoRR, 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
Yichuan Deng 0002 +2 more
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Diffusion limits of the random walk Metropolis algorithm in high dimensions [PDF]
The Annals of Applied Probability, 2012 Diffusion limits of MCMC methods in high dimensions provide a useful theoretical tool for studying computational complexity. In particular, they lead directly to precise estimates of the number of steps required to explore the target measure, in stationarity, as a function of the dimension of the state space.
Mattingly, Jonathan C. +2 more
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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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