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We apply a common measure of randomness, the entropy, in the context of iterated functions on a finite set with n elements. For a permutation, it turns out that this entropy is asymptotically (for a growing number of iterations) close to…

Number Theory · Mathematics 2017-12-20 Joachim von zur Gathen

We apply numerical optimization and linear algebra algorithms for classical computers to the problem of automatically synthesizing algorithms for quantum computers. Using our framework, we apply several common techniques from these…

Numerical Analysis · Mathematics 2025-09-16 Yuxin Huang , Benjamin E. Grossman-Ponemon , David A. B. Hyde

Consider a probability measure supported by a regular geodesic ball in a manifold. For any p larger than or equal to 1 we define a stochastic algorithm which converges almost surely to the p-mean of the measure. Assuming furthermore that…

Probability · Mathematics 2011-06-28 Marc Arnaudon , Clément Dombry , Anthony Phan , Le Yang

Numerical approximate computation can solve large and complex problems fast. It has the advantage of high efficiency. However it only gives approximate results, whereas we need exact results in many fields. There is a gap between…

Algebraic Geometry · Mathematics 2007-05-23 Jingzhong Zhang , Yong Feng

This article describes a method for constructing approximations to periodic solutions of dynamic Lorenz system with classical values of the system parameters. The author obtained a system of nonlinear algebraic equations in general form…

Numerical Analysis · Mathematics 2021-02-10 Alexander N. Pchelintsev

Permutations can be represented as linear combinations of natural numbers with different powers. In this paper, its coefficient matrix and inverse matrix is derived, and the results show the coefficient matrix is a lower triangular matrix…

General Mathematics · Mathematics 2018-05-30 Yuyang Zhu

We study the question of constructive approximation of the harmonic measure $\omega_x^\Omega$ of a connected bounded domain $\Omega$ with respect to a point $x\in\Omega$. In particular, using a new notion of computable harmonic…

Complex Variables · Mathematics 2020-11-20 Ilia Binder , Adi Glucksam , Cristobal Rojas , Michael Yampolsky

We consider the complexity for computing the approximate sum $a_1+a_2+...+a_n$ of a sorted list of numbers $a_1\le a_2\le ...\le a_n$. We show an algorithm that computes an $(1+\epsilon)$-approximation for the sum of a sorted list of…

Data Structures and Algorithms · Computer Science 2012-01-24 Bin Fu

In the paper, the authors concisely survey and review some functions involving the gamma function and its various ratios, simply state their logarithmically complete monotonicity and related results, and find necessary and sufficient…

Classical Analysis and ODEs · Mathematics 2015-07-07 Feng Qi , Wen-Hui Li

This paper is an attempt to remedy the problem of slow convergence for first-order numerical algorithms by proposing an adaptive conditioning heuristic. First, we propose a parallelizable numerical algorithm that is capable of solving…

Optimization and Control · Mathematics 2021-03-02 Muhammad Adil , Sasan Tavakkol , Ramtin Madani

We introduce harmonization, an ensembling method that combines several "noisy" decoders to generate highly accurate decoding predictions. Harmonized ensembles of MWPM-based decoders achieve lower logical error rates than their individual…

Quantum Physics · Physics 2024-03-18 Noah Shutty , Michael Newman , Benjamin Villalonga

Inspired by regularization techniques in statistics and machine learning, we study complementary composite minimization in the stochastic setting. This problem corresponds to the minimization of the sum of a (weakly) smooth function endowed…

Machine Learning · Computer Science 2024-01-24 Alexandre d'Aspremont , Cristóbal Guzmán , Clément Lezane

This paper presents a stochastic algorithm for iterative error control decoding. We show that the stochastic decoding algorithm is an approximation of the sum-product algorithm. When the code's factor graph is a tree, as with trellises, the…

Information Theory · Computer Science 2007-07-13 Chris Winstead , Anthony Rapley , Vincent C. Gaudet , Christian Schlegel

We propose a simple algorithm for generating normally distributed pseudo random numbers. The algorithm simulates N molecules that exchange energy among themselves following a simple stochastic rule. We prove that the system is ergodic, and…

Condensed Matter · Physics 2009-10-31 J. F. Fernandez , Carlos Criado

In this paper, we study the theory of the harmonic and the hyperharmonic Fibonacci numbers. Also, we get some combinatoric identities like as harmonic and hyperharmonic numbers and we obtain some useful formulas for $\mathbb{F}_{n}$, which…

Number Theory · Mathematics 2016-03-28 Naim Tuglu , Can Kızılateş , Seyhun Kesim

We study the random rotation number for random circle homeomorphisms. We introduce two new definitions of the random rotation number that can be stated without reference to any choice of lift of the dynamics to the real line, and prove that…

Dynamical Systems · Mathematics 2026-03-27 Zixu Li , Simon Lloyd

We consider the problem of sampling and approximately counting an arbitrary given motif $H$ in a graph $G$, where access to $G$ is given via queries: degree, neighbor, and pair, as well as uniform edge sample queries. Previous algorithms…

Data Structures and Algorithms · Computer Science 2021-07-20 Amartya Shankha Biswas , Talya Eden , Ronitt Rubinfeld

Matrix multiplication is a fundamental building block for large scale computations arising in various applications, including machine learning. There has been significant recent interest in using coding to speed up distributed matrix…

Information Theory · Computer Science 2019-05-17 Wei-Ting Chang , Ravi Tandon

In this paper, we consider robust control using randomized algorithms. We extend the existing order statistics distribution theory to the general case in which the distribution of population is not assumed to be continuous and the order…

Optimization and Control · Mathematics 2008-05-13 Xinjia Chen , Kemin Zhou

In the era of big data, one of the key challenges is the development of novel optimization algorithms that can accommodate vast amounts of data while at the same time satisfying constraints and limitations of the problem under study. The…

Optimization and Control · Mathematics 2019-09-27 Nicolas Loizou