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Calibration methods have been widely studied in survey sampling over the last decades. Viewing calibration as an inverse problem, we extend the calibration technique by using a maximum entropy method. Finding the optimal weights is achieved…

Methodology · Statistics 2009-09-23 Fabrice Gamboa , Jean-Michel Loubes , Paul Rochet

We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and…

Functional Analysis · Mathematics 2024-05-21 Thomas Allard , Helmut Bölcskei

Complex systems are characterised by a tight, nontrivial interplay of their constituents, which gives rise to a multi-scale spectrum of emergent properties. In this scenario, it is practically and conceptually difficult to identify those…

Statistical Mechanics · Physics 2022-10-19 Roi Holtzman , Marco Giulini , Raffaello Potestio

The estimation of various matrix integrals as the size of the matrices goes to infinity is motivated by theoretical physics, geometry and free probability questions. On a rigorous ground, only integrals of one matrix or of several matrices…

Probability · Mathematics 2007-05-23 Alice Guionnet , Mylene Maida

We present a method for computing the topological entropy of one-dimensional maps. As an approximation scheme, the algorithm converges rapidly and provides both upper and lower bounds.

chao-dyn · Physics 2009-10-22 N. J. Balmforth , E. A. Spiegel , C. Tresser

The aim of this study is to generalise recent results of the two last authors on en-tropy methods for measure solutions of the renewal equation to other classes of structured population problems. Specifically, we develop a generalised…

Analysis of PDEs · Mathematics 2018-04-11 Tomasz Dębiec , Marie Doumic , Piotr Gwiazda , Emil Wiedemann

We show that various formulations (e.g., dual and Kullback-Csiszar iterations) of estimation of maximum entropy (ME) models can be transformed to solving systems of polynomial equations in several variables for which one can use celebrated…

Information Theory · Computer Science 2008-04-08 Ambedkar Dukkipati

The `deautonomisation' of an integrable mapping of the plane consists in treating the free parameters in the mapping as functions of the independent variable, the precise expressions of which are to be determined with the help of a suitable…

Exactly Solvable and Integrable Systems · Physics 2016-02-17 Takafumi Mase , Ralph Willox , Basil Grammaticos , Alfred Ramani

We describe a framework in which is possible to develop and implement algorithms for the approximation of invariant measures of dynamical systems with a given bound on the error of the approximation. Our approach is based on a general…

Dynamical Systems · Mathematics 2017-10-05 Stefano Galatolo , Isaia Nisoli

Entropy is a fundamental thermodynamic quantity indicative of the accessible degrees of freedom in a system. While it has been suggested that the entropy of a mesoscopic system can yield nontrivial information on emergence of exotic states,…

Mesoscale and Nanoscale Physics · Physics 2020-01-23 Yaakov Kleeorin , Holger Thierschmann , Hartmut Buhmann , Antoine Georges , Laurens W. Molenkamp , Yigal Meir

We propose a formal expansion of the transfer entropy to put in evidence irreducible sets of variables which provide information for the future state of each assigned target. Multiplets characterized by a large contribution to the expansion…

Quantitative Methods · Quantitative Biology 2015-06-04 S. Stramaglia , Guo-Rong Wu , M. Pellicoro , D. Marinazzo

The topological entropy of piecewise affine maps is studied. It is shown that singularities may contribute to the entropy only if there is angular expansion and we bound the entropy via the expansion rates of the map. As a corollary we…

Dynamical Systems · Mathematics 2007-05-23 Boris Kruglikov , Martin Rypdal

We examine the notion of anticonfinement and the role it has to play in the singularity analysis of discrete systems. A singularity is said to be anticonfined if singular values continue to arise indefinitely for the forward and backward…

Mathematical Physics · Physics 2017-11-17 Takafumi Mase , Ralph Willox , Alfred Ramani , Basil Grammaticos

We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…

Information Theory · Computer Science 2011-04-05 Paul M. B. Vitányi

We study entropy-bounded computational geometry, that is, geometric algorithms whose running times depend on a given measure of the input entropy. Specifically, we introduce a measure that we call range-partition entropy, which unifies and…

Computational Geometry · Computer Science 2025-08-29 David Eppstein , Michael T. Goodrich , Abraham M. Illickan , Claire A. To

Two important notions of integrability for discrete mappings are algebraic integrability and singularity confinement, have been used for discrete mappings. Algebraic integrability is related to the existence of sufficiently many conserved…

Exactly Solvable and Integrable Systems · Physics 2015-06-26 S. Lafortune , A. Goriely

This paper shows how to evolve numerically the maximum entropy probability distributions for a given set of constraints, which is a variational calculus problem. An evolutionary algorithm can obtain approximations to some well-known…

Methodology · Statistics 2020-02-07 Raul Rojas

This paper addresses the problem of measuring complexity from embedded attractors as a way to characterize changes in the dynamical behaviour of different types of systems by observing their outputs. With the aim of measuring the stability…

Information Theory · Computer Science 2023-07-19 Julián D. Arias-Londoño , Juan I. Godino-Llorente

In this paper, we propose a numerical method for computing Hadamard finite-part integrals with an integral-power singularity at an endpoint, the part of the divergent integral which is finite as a limiting procedure. In the proposed method,…

Numerical Analysis · Mathematics 2019-09-20 Hidenori Ogata

We study a curve of Gibbsian families of complex 3x3-matrices and point out new features, absent in commutative finite-dimensional algebras: a discontinuous maximum-entropy inference, a discontinuous entropy distance and non-exposed faces…

Mathematical Physics · Physics 2016-05-17 Andreas Knauf , Stephan Weis