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We summarize our recent findings, where we proposed a framework for learning a Kolmogorov model, for a collection of binary random variables. More specifically, we derive conditions that link outcomes of specific random variables, and…

Machine Learning · Computer Science 2018-06-07 Hadi Ghauch , Mikael Skoglund , Hossein Shokri-Ghadikolaei , Carlo Fischione , Ali H. Sayed

Link prediction in graphs is an important task in the fields of network science and machine learning. We investigate a flexible means of regularization for link prediction based on an approximation of the Kolmogorov complexity of graphs…

Machine Learning · Computer Science 2021-02-24 Paris D. L. Flood , Ramon Viñas , Pietro Liò

We apply a recently developed measure of multiscale complexity to the Gaussian model consisting of continuous spins with bilinear interactions for a variety of interaction matrix structures. We find two universal behaviors of the complexity…

Statistical Mechanics · Physics 2009-11-10 Richard Metzler , Yaneer Bar-Yam

A measure called Physical Complexity is established and calculated for a population of sequences, based on statistical physics, automata theory, and information theory. It is a measure of the quantity of information in an organism's genome.…

Biological Physics · Physics 2011-12-02 Gerard Briscoe , Philippe De Wilde

We consider an environmental interface regarding as a complex system, in which difference equations for calculating the environmental interface temperature and deeper soil layer temperature are represented by the coupled maps. First…

Chaotic Dynamics · Physics 2014-04-28 Gordan Mimić , Dragutin T. Mihailović , Mirko Budinčević

A comprehensive understanding of the behaviours of the various geophysical processes and an effective evaluation of time series (else referred to as "stochastic") simulation models require, among others, detailed investigations across…

Applications · Statistics 2023-03-06 Georgia Papacharalampous , Hristos Tyralis , Yannis Markonis , Martin Hanel

Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory -- in the discrete setting of bits and Turing machines. Over real numbers, on the other hand, the…

Computational Complexity · Computer Science 2008-03-28 Martin Ziegler , Wouter M. Koolen

In analogy of classical Kolmogorov complexity we develop a theory of the algorithmic information in bits contained in any one of continuously many pure quantum states: quantum Kolmogorov complexity. Classical Kolmogorov complexity coincides…

Quantum Physics · Physics 2007-05-23 Paul Vitanyi

In this work, we propose a testing procedure to distinguish between the different approaches for computing complexity. Our test does not require a direct comparison between the approaches and thus avoids the issue of choice of gates, basis,…

High Energy Physics - Theory · Physics 2019-04-15 Tibra Ali , Arpan Bhattacharyya , S. Shajidul Haque , Eugene H. Kim , Nathan Moynihan

While Kolmogorov complexity is the accepted absolute measure of information content of an individual finite object, a similarly absolute notion is needed for the relation between an individual data sample and an individual model summarizing…

Statistics Theory · Mathematics 2007-07-16 Peter Gacs , John Tromp , Paul Vitanyi

We consider the number of Bowen sets which are necessary to cover a large measure subset of the phase space. This introduce some complexity indicator characterizing different kind of (weakly) chaotic dynamics. Since in many systems its…

Dynamical Systems · Mathematics 2015-06-26 S. Galatolo

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 and review a new complexity measure, called `Krylov complexity', which takes its origins in the field of quantum-chaotic dynamics, serving as a canonical measure of operator growth and spreading. Krylov complexity, underpinned…

High Energy Physics - Theory · Physics 2025-07-10 Eliezer Rabinovici , Adrián Sánchez-Garrido , Ruth Shir , Julian Sonner

Quantifying the complexity of systems consisting of many interacting parts has been an important challenge in the field of complex systems in both abstract and applied contexts. One approach, the complexity profile, is a measure of the…

Pattern Formation and Solitons · Physics 2013-06-03 Yavni Bar-Yam , Dion Harmon , Yaneer Bar-Yam

Measuring the complexity of high-dimensional data in physical systems becomes a critical factor in determining the information and quality of the systems. However, traditional metrics, such as Lyapunov exponent, fractal dimension, and…

Physics and Society · Physics 2026-03-03 Seong-Gyun Im , Taewoo Kang , S. Joon Kwon

Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise…

Information Theory · Computer Science 2012-11-16 Carlos Gershenson , Nelson Fernandez

We present a quantitative measure of physical complexity, based on the amount of information required to build a given physical structure through self-assembly. Our procedure can be adapted to any given geometry, and thus to any given type…

Statistical Mechanics · Physics 2010-09-02 S. E. Ahnert , I. G. Johnston , T. M. A. Fink , J. P. K. Doye , A. A. Louis

The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…

Physics and Society · Physics 2013-04-02 Ernesto Estrada , Juan A. Rodriguez-Velazquez

We have considered the complexity and asymptotic stability in the process of biochemical substance exchange in a coupled ring of cells. We have used coupled maps to model this process. It includes the coupling parameter, cell affinity and…

Dynamical Systems · Mathematics 2015-06-17 Dragutin T. Mihailović , Vladimir Kostić , Igor Balaž , Ljiljana Cvetković

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