Related papers: Toward a dynamical model for prime numbers

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

Any collection can be ranked. Sports and games are common examples of ranked systems: players and teams are constantly ranked using different methods. The statistical properties of rankings have been studied for almost a century in a…

Optimization methods are at the core of many problems in signal/image processing, computer vision, and machine learning. For a long time, it has been recognized that looking at the dual of an optimization problem may drastically simplify…

Information theoretic measures (entropies, entropy rates, mutual information) are nowadays commonly used in statistical signal processing for real-world data analysis. The present work proposes the use of Auto Mutual Information (Mutual…

New families of fourth-order composition methods for the numerical integration of initial value problems defined by ordinary differential equations are proposed. They are designed when the problem can be separated into three parts in such a…

In this work, Bernoulli's Law of Large Numbers, also known as the Golden theorem, has been extended to study the relations between empirical probability and empirical randomness of an otherwise random experiment. Using the example of a coin…

In this paper we propose a data-driven distributionally robust Model Predictive Control framework for constrained stochastic systems with unbounded additive disturbances. Recursive feasibility is ensured by optimizing over an linearly…

We consider a "length-biased" shift-dependent information measure, related to the differential entropy in which higher weight is assigned to large values of observed random variables. This allows us to introduce the notions of "weighted…

We study a mathematical model describing the growth process of a population structured by age and a phenotypical trait, subject to aging, competition between individuals and rare mutations. Our goals are to describe the asymptotic behaviour…

Logarithmic gaps have been used in order to find a periodic component of the sequence of prime numbers, hidden by a random noise (stochastic or chaotic). The recovered period for the sequence of the first 10000 prime numbers is equal to…

Entropy always increases monotonically in a closed system but complexity increases at first and then decreases as equilibrium is approached. Commonsense information-related definitions for entropy and complexity demonstrate that complexity…

Finding interdependency relations between (possibly multivariate) time series provides valuable knowledge about the processes that generate the signals. Information theory sets a natural framework for non-parametric measures of several…

We propose a method based on finite mixture models for classifying a set of observations into number of different categories. In order to demonstrate the method, we show how the component densities for the mixture model can be derived by…

Distributed algorithms for solving additive or consensus optimization problems commonly rely on first-order or proximal splitting methods. These algorithms generally come with restrictive assumptions and at best enjoy a linear convergence…

The estimation of information measures of continuous distributions based on samples is a fundamental problem in statistics and machine learning. In this paper, we analyze estimates of differential entropy in $K$-dimensional Euclidean space,…

Distribution functions of many static transport equations are found using the Maximum Entropy Principle. The equations of constraint which contain the relevant dynamical information are simply the low-lying moments of the distributions.…

This survey provides an exposition of a suite of techniques based on the theory of polynomials, collectively referred to as polynomial methods, which have recently been applied to address several challenging problems in statistical…

Comparisons of different treatments or production processes are the goals of a significant fraction of applied research. Unsurprisingly, two-sample problems play a main role in Statistics through natural questions such as `Is the the new…

We provide a computational complexity lens to understand the power of machine learning models, particularly their ability to model complex systems. Machine learning models are often trained on data drawn from sampleable or more complex…

The information entropy of a nuclear density distribution is calculated for a number of nuclei. Various phenomenological models for the density distribution using different geometry are employed. Nuclear densities calculated within various…