Mutual information of ising systems

Matsuda, Hiroyuki; Kudo, Kiyoshi; Nakamura, Ryoku; Yamakawa, Osamu; Murata, Takuo

doi:10.1007/bf02330576

Cited by 47 publications

(49 citation statements)

References 7 publications

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“…It has been established previously that pairwise mutual information peaks at the phase transition for the 2D lattice Ising model [1,2]. Our results show that so too does pairwise transfer entropy.…”

Section: Critical Inverse Temperaturesupporting

confidence: 58%

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Information Flow in a Kinetic Ising Model Peaks in the Disordered Phase

et al. 2013

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Section: Critical Inverse Temperaturesupporting

confidence: 58%

“…This is essentially the quantity previously considered in Refs. [1,2]; Ref. [17] also considers the mutual information between two halves of a cylindrical 2D lattice.…”

mentioning

confidence: 99%

Information Flow in a Kinetic Ising Model Peaks in the Disordered Phase

et al. 2013

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“…It has been analytically shown that, in a two-dimensional Ising model, the mutual information between joint states of two spin systems peaks at the critical temperature [33]. Barnett et al [26] show empirically that mutual information measured between pairs of neighboring spins peaks at the phase transition.…”

Section: Related Workmentioning

confidence: 99%

Analyzing Information Distribution in Complex Systems

Sootla

Theis

Vicente

2017

Entropy

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Information theory is often utilized to capture both linear as well as nonlinear relationships between any two parts of a dynamical complex system. Recently, an extension to classical information theory called partial information decomposition has been developed, which allows one to partition the information that two subsystems have about a third one into unique, redundant and synergistic contributions. Here, we apply a recent estimator of partial information decomposition to characterize the dynamics of two different complex systems. First, we analyze the distribution of information in triplets of spins in the 2D Ising model as a function of temperature. We find that while redundant information obtains a maximum at the critical point, synergistic information peaks in the disorder phase. Secondly, we characterize 1D elementary cellular automata rules based on the information distribution between neighboring cells. We describe several clusters of rules with similar partial information decomposition. These examples illustrate how the partial information decomposition provides a characterization of the emergent dynamics of complex systems in terms of the information distributed across their interacting units.

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“…In particular, mutual information is adopted as a general measure of correlation between two systems. Mutual information, as well as entropy, have found significance in various applications in diverse fields, such as in analyzing experimental time series [37][38][39], in characterizing symbol sequences such as DNA sequences [40][41][42] and in providing a theoretical basis for the notion of complexity [43][44][45][46][47], just to name a few.…”

Section: Mathematical Toolsmentioning

confidence: 99%

Analysis and Visualization of Seismic Data Using Mutual Information

Machado

Lopes

2013

Entropy

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Abstract:Seismic data is difficult to analyze and classical mathematical tools reveal strong limitations in exposing hidden relationships between earthquakes. In this paper, we study earthquake phenomena in the perspective of complex systems. Global seismic data, covering the period from 1962 up to 2011 is analyzed. The events, characterized by their magnitude, geographic location and time of occurrence, are divided into groups, either according to the Flinn-Engdahl (F-E) seismic regions of Earth or using a rectangular grid based in latitude and longitude coordinates. Two methods of analysis are considered and compared in this study. In a first method, the distributions of magnitudes are approximated by Gutenberg-Richter (G-R) distributions and the parameters used to reveal the relationships among regions. In the second method, the mutual information is calculated and adopted as a measure of similarity between regions. In both cases, using clustering analysis, visualization maps are generated, providing an intuitive and useful representation of the complex relationships that are present among seismic data. Such relationships might not be perceived on classical geographic maps. Therefore, the generated charts are a valid alternative to other visualization tools, for understanding the global behavior of earthquakes.

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Mutual information of ising systems

Cited by 47 publications

References 7 publications

Information Flow in a Kinetic Ising Model Peaks in the Disordered Phase

Information Flow in a Kinetic Ising Model Peaks in the Disordered Phase

Analyzing Information Distribution in Complex Systems

Analysis and Visualization of Seismic Data Using Mutual Information

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