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We review several statistical complexity measures proposed over the last decade and a half as general indicators of structure or correlation. Recently, Lopez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209 (1995) 321] introduced another…

Statistical Mechanics · Physics 2008-02-03 David P. Feldman , James P. Crutchfield

We describe recent work that extends some of the measure and topological rigidity results in dynamical systems from situations homogeneous under a Lie group to quite general manifolds.

Dynamical Systems · Mathematics 2025-12-17 Simion Filip

We propose to examine the predictability and the complexity characteristics of the Standard&Poor500 dynamics behaviors in a coarse-grained way using the symbolic dynamics method and under the prism of the Information theory through the…

Statistical Finance · Quantitative Finance 2021-05-11 Geoffrey Ducournau

We introduce a new type of shift dynamics as an extended model of symbolic dynamics, and investigate the characteristics of shift spaces from the viewpoints of both dynamics and computation. This shift dynamics is called a functional shift…

Chaotic Dynamics · Physics 2009-11-10 Jun Namikawa , Takashi Hashimoto

We give a general method on the way of approximating equilibrium states for a dynamical system of a compact metric space.

Dynamical Systems · Mathematics 2013-06-04 Abdelhamid Amroun

We consider the dynamical behavior of Martin-L\"of random points in dynamical systems over metric spaces with a computable dynamics and a computable invariant measure. We use computable partitions to define a sort of effective symbolic…

Dynamical Systems · Mathematics 2008-04-29 Stefano Galatolo , Mathieu Hoyrup , Cristobal Rojas

Complexity science offers a wide range of measures for quantifying unpredictability, structure, and information. Yet, a systematic conceptual organization of these measures is still missing. We present a unified framework that locates…

Machine Learning · Computer Science 2025-05-13 Nima Dehghani

In this paper we study speedups of dynamical systems in the topological category. Specifically, we characterize when one minimal homeomorphism on a Cantor space is the speedup of another. We go on to provide a characterization for strong…

Dynamical Systems · Mathematics 2022-08-17 Drew D. Ash , Nicholas Ormes

Let f be a rational mapping of a space X . The complexity of (f,X) as a dynamical system is measured by the dynamical degrees $\delta_p(f)$, $1\le p\le {\rm dim}(X)$. We give the definition of the dynamical degrees show how they are…

Dynamical Systems · Mathematics 2011-10-11 Eric Bedford

Two different notions of {\mu}-equicontinuity that apply to topological dynamical systems and probability measures were studied by Gilman (1987) and Huang-Lu-Ye (2011). One was used to classify measure preserving topological dynamical…

Dynamical Systems · Mathematics 2019-11-05 Felipe García-Ramos

Background: Transitioning from an old medical coding system to a new one can be challenging, especially when the two coding systems are significantly different. The US experienced such a transition in 2015. Objective: This research aims to…

Information Theory · Computer Science 2020-12-24 Jerome Niyirora

A good process model is expected not only to reflect the behavior of the process, but also to be as easy to read and understand as possible. Because preferences vary across different applications, numerous measures provide ways to reflect…

Formal Languages and Automata Theory · Computer Science 2024-08-23 Patrizia Schalk , Adam Burke , Robert Lorenz

Forests are complex systems, and it is necessary to include this characteristic in every forest definition, in order to consider the restriction that this imposes in terms of prediction and control. This lost of predictability and…

The topological pressure introduced by Ruelle and similar quantities describe dynamical multifractal properties of dynamical systems. These are important characteristics of mesoscopic systems in the classical regime. Original definition of…

chao-dyn · Physics 2009-10-28 Péter Pollner , Gábor Vattay

We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…

Data Analysis, Statistics and Probability · Physics 2012-08-20 Peter Grassberger

We introduce amorphic complexity as a new topological invariant that measures the complexity of dynamical systems in the regime of zero entropy. Its main purpose is to detect the very onset of disorder in the asymptotic behaviour. For…

Dynamical Systems · Mathematics 2016-02-17 G. Fuhrmann , M. Gröger , T. Jäger

We study some dynamical aspects of the action of automorphisms in model theory in particular in the presence of invariant measures. We give some characterizations for NIP theories in terms of dynamics of automorphisms and invariant measures…

Logic · Mathematics 2022-12-19 Alireza Mofidi

We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the…

Chaotic Dynamics · Physics 2018-11-08 Agnes Fülöp

In this chapter, a statistical measure of complexity is introduced and some of its properties are discussed. Also, some straightforward applications are shown.

Adaptation and Self-Organizing Systems · Physics 2010-09-09 Ricardo Lopez-Ruiz , Hector Mancini , Xavier Calbet

The spatial character of territorial systems plays a crucial role in the emergence of their complexities. This contribution aims at illustrating to what extent different types of complexities can be exhibited in models of such systems. We…

Physics and Society · Physics 2019-01-29 Juste Raimbault