scholarly journals Inequalities for Shannon Entropy and Kolmogorov Complexity

2000 ◽  
Vol 60 (2) ◽  
pp. 442-464 ◽  
Author(s):  
Daniel Hammer ◽  
Andrei Romashchenko ◽  
Alexander Shen ◽  
Nikolai Vereshchagin
Keyword(s):  
Shannon Entropy ◽  
Kolmogorov Complexity

scholarly journals Quantum Entropy and Complexity

2017 ◽  
Vol 24 (02) ◽  
pp. 1750005
Author(s):  
F. Benatti ◽  
S. Khabbazi Oskouei ◽  
A. Shafiei Deh Abad
Keyword(s):  
Dynamical Systems ◽  
Shannon Entropy ◽  
Kolmogorov Complexity ◽  
Quantum Systems ◽  
Quantum Spin ◽  
Spin Chains ◽  
The Other ◽  
Quantum Entropy ◽  
Quantum Spin Chains ◽  
Quantum Complexity

We study the relations between the recently proposed machine-independent quantum complexity of P. Gacs [1] and the entropy of classical and quantum systems. On one hand, by restricting Gacs complexity to ergodic classical dynamical systems, we retrieve the equality between the Kolmogorov complexity rate and the Shannon entropy rate derived by A. A. Brudno [2]. On the other hand, using the quantum Shannon-McMillan theorem [3], we show that such an equality holds densely in the case of ergodic quantum spin chains.

scholarly journals Characterizing animal movement patterns across different scales and habitats using information theory

2018 ◽  
Author(s):  
Kehinde Owoeye ◽  
Mirco Musolesi ◽  
Stephen Hailes
Keyword(s):  
Information Theory ◽  
Mutual Information ◽  
Shannon Entropy ◽  
Kolmogorov Complexity ◽  
Animal Movement ◽  
Social Systems ◽  
Movement Patterns ◽  
Animal Behaviour ◽  
Migration Routes ◽  
Leibler Divergence

AbstractUnderstanding the movement patterns of animals across different spatio-temporal scales, conditions, habitats and contexts is becoming increasingly important for addressing a series of questions in animal behaviour studies, such as mapping migration routes, evaluating resource use, modelling epidemic spreading in a population, developing strategies for animal conservation as well as understanding several emerging patterns related to feeding, growth and reproduction. In recent times, information theory has been successfully applied in several fields of science, in particular for understanding the dynamics of complex systems and characterizing adaptive social systems, such as dynamics of entities as individuals and as part of groups.In this paper, we describe a series of non-parametric information-theoretic measures that can be used to derive new insights about animal behaviour with a specific focus on movement patterns namely Shannon entropy, Mutual information, Kullback-Leibler divergence and Kolmogorov complexity. In particular, we believe that the metrics presented in this paper can be used to formulate new hypotheses that can be verified potentially through a set of different observations. We show how these measures can be used to characterize the movement patterns of several animals across different habitats and scales. Specifically, we show the effectiveness in using Shannon entropy to characterize the movement of sheep with Batten disease, mutual information to measure association in pigeons, Kullback Leibler divergence to study the flights of Turkey vulture, and Kolmogorov complexity to find similarities in the movement patterns of animals across different scales and habitats. Finally, we discuss the limitations of these methods and we outline the challenges in this research area.

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