An Algorithmic Complexity Interpretation of Lin's Third Law of Information Theory

Ratsaby, Joel

doi:10.3390/entropy-e10010006

Cited by 14 publications

(42 citation statements)

References 18 publications

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“…This selection mechanism is intrinsically connected to the solid's complex non-linear structure (partly a consequence of its internal atomic vibrations) and its intricate time-response to external stimulus. As postulated in [4], a simple solid is one whose information content is small. Its selection behavior is of low complexity since it can be described by a more concise time-response model (shorter computer program).…”

Section: Introductionmentioning

confidence: 98%

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On the algorithmic complexity of static structures

Chaskalovic

2010

J Syst Sci Complex

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This paper provides a first indication that this is true for a system comprised of a static structure described by hyperbolic partial differential equations and is subjected to an external random input force. The system deforms the randomness of an input force sequence in proportion to its algorithmic complexity. The authors demonstrate this by numerical analysis of a one-dimensional vibrating elastic solid (the system) on which we apply a maximally-random force sequence (input). The level of complexity of the system is controlled via external parameters. The output response is the field of displacements observed at several positions on the body. The algorithmic complexity and stochasticity of the resulting output displacement sequence is measured and compared against the complexity of the system. The results show that the higher the system complexity, the more random-deficient the output sequence.

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Section: Introductionmentioning

confidence: 98%

“…Ratsaby [4] introduced a quantitative definition of the information content of a static structure (a solid) and explained its relationship to the stability and symmetry of the solid. His model is based on concepts of the theory of algorithmic information and randomness.…”

Section: Introductionmentioning

confidence: 99%

On the algorithmic complexity of static structures

Chaskalovic

2010

J Syst Sci Complex

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“…In effect, those structures or configurations that show order or pattern will be described by much shorter algorithms than those that are random. For example, Ratsaby [7] argues that the algorithmic complexity (i.e. the algorithmic entropy) of a static structure is a measure of its order.…”

Section: Introductionmentioning

confidence: 99%

The Insights of Algorithmic Entropy

Devine

2009

Entropy

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Abstract:The algorithmic entropy of a system, the length of the shortest algorithm that specifies the system's exact state adds some missing pieces to the entropy jigsaw. Because the approach embodies the traditional entropies as a special case, problematic issues such as the coarse graining framework of the Gibbs' entropy manifest themselves in a different and more manageable form, appearing as the description of the system and the choice of the universal computing machine. The provisional algorithmic entropy combines the best information about the state of the system together with any underlying uncertainty; the latter represents the Shannon entropy. The algorithmic approach also specifies structure that the traditional entropies take as given. Furthermore, algorithmic entropy provides insights into how a system can maintain itself off equilibrium, leading to Ashby's law of requisite variety. This review shows how the algorithmic approach can provide insights into real world systems, by outlining recent work on how replicating structures that generate order can evolve to maintain a system far from equilibrium.

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“…The paper of Prof. Joel Ratsaby is also very inspiring [31]. He introduces an algorithmic complexity framework for representing Lin's concepts of static entropy, stability and their connection to the second law of thermodynamic.…”

Section: New Lines Of Researchmentioning

confidence: 99%

“…Also, they are topological objects, not geometrical entities. And they may exhibit symmetries under transformations that are not node permutations: e.g., by scale invariance on fractals [31].…”

Section: Symmetry As Invariancementioning

confidence: 99%

Symmetry in Complex Networks

Garrido

2011

Symmetry

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Abstract:In this paper, we analyze a few interrelated concepts about graphs, such as their degree, entropy, or their symmetry/asymmetry levels. These concepts prove useful in the study of different types of Systems, and particularly, in the analysis of Complex Networks. A System can be defined as any set of components functioning together as a whole. A systemic point of view allows us to isolate a part of the world, and so, we can focus on those aspects that interact more closely than others. Network Science analyzes the interconnections among diverse networks from different domains: physics, engineering, biology, semantics, and so on. Current developments in the quantitative analysis of Complex Networks, based on graph theory, have been rapidly translated to studies of brain network organization. The brain's systems have complex network features-such as the small-world topology, highly connected hubs and modularity. These networks are not random. The topology of many different networks shows striking similarities, such as the scale-free structure, with the degree distribution following a Power Law. How can very different systems have the same underlying topological features? Modeling and characterizing these networks, looking for their governing laws, are the current lines of research. So, we will dedicate this Special Issue paper to show measures of symmetry in Complex Networks, and highlight their close relation with measures of information and entropy.

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An Algorithmic Complexity Interpretation of Lin's Third Law of Information Theory

Cited by 14 publications

References 18 publications

On the algorithmic complexity of static structures

On the algorithmic complexity of static structures

The Insights of Algorithmic Entropy

Symmetry in Complex Networks

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