Generalized kolmogorov complexity and other dual complexity measures

Cybernetics ◽  
1991 ◽  
Vol 26 (4) ◽  
pp. 481-490 ◽  
Author(s):  
M. S. Burgin
Keyword(s):  
Kolmogorov Complexity ◽  
Complexity Measures

scholarly journals Randomness Representation of Turbulence in Canopy Flows Using Kolmogorov Complexity Measures

Entropy ◽  
2017 ◽  
Vol 19 (10) ◽  
pp. 519 ◽  
Author(s):  
Dragutin Mihailović ◽  
Gordan Mimić ◽  
Paola Gualtieri ◽  
Ilija Arsenić ◽  
Carlo Gualtieri
Keyword(s):  
Kolmogorov Complexity ◽  
Complexity Measures ◽  
Canopy Flows

scholarly journals On Measuring the Complexity of Networks: Kolmogorov Complexity versus Entropy

Complexity ◽  
2017 ◽  
Vol 2017 ◽  
pp. 1-12 ◽  
Author(s):  
Mikołaj Morzy ◽  
Tomasz Kajdanowicz ◽  
Przemysław Kazienko
Keyword(s):  
Kolmogorov Complexity ◽  
Degree Sequences ◽  
Empirical Comparison ◽  
Reliable Measure ◽  
Complexity Measures ◽  
Information Theoretic ◽  
Generative Process ◽  
Evolving Networks ◽  
Original Contribution ◽  
Information Theoretic Measures

One of the most popular methods of estimating the complexity of networks is to measure the entropy of network invariants, such as adjacency matrices or degree sequences. Unfortunately, entropy and all entropy-based information-theoretic measures have several vulnerabilities. These measures neither are independent of a particular representation of the network nor can capture the properties of the generative process, which produces the network. Instead, we advocate the use of the algorithmic entropy as the basis for complexity definition for networks. Algorithmic entropy (also known as Kolmogorov complexity or K-complexity for short) evaluates the complexity of the description required for a lossless recreation of the network. This measure is not affected by a particular choice of network features and it does not depend on the method of network representation. We perform experiments on Shannon entropy and K-complexity for gradually evolving networks. The results of these experiments point to K-complexity as the more robust and reliable measure of network complexity. The original contribution of the paper includes the introduction of several new entropy-deceiving networks and the empirical comparison of entropy and K-complexity as fundamental quantities for constructing complexity measures for networks.

Complexity Measures of Brain Electrophysiological Activity

2010 ◽  
Vol 24 (2) ◽  
pp. 131-135 ◽  
Author(s):  
Włodzimierz Klonowski ◽  
Pawel Stepien ◽  
Robert Stepien
Keyword(s):  
Brain Activity ◽  
Deterministic Chaos ◽  
Epileptic Seizures ◽  
Eeg Signal ◽  
Eeg Signals ◽  
Complexity Measures ◽  
Electrophysiological Activity ◽  
Signal Complexity ◽  
Physiological Sleep ◽  
The Brain

Over 20 years ago, Watt and Hameroff (1987 ) suggested that consciousness may be described as a manifestation of deterministic chaos in the brain/mind. To analyze EEG-signal complexity, we used Higuchi’s fractal dimension in time domain and symbolic analysis methods. Our results of analysis of EEG-signals under anesthesia, during physiological sleep, and during epileptic seizures lead to a conclusion similar to that of Watt and Hameroff: Brain activity, measured by complexity of the EEG-signal, diminishes (becomes less chaotic) when consciousness is being “switched off”. So, consciousness may be described as a manifestation of deterministic chaos in the brain/mind.

scholarly journals Normalized Sombor Indices as Complexity Measures of Random Networks

Entropy ◽  
2021 ◽  
Vol 23 (8) ◽  
pp. 976
Author(s):  
R. Aguilar-Sánchez ◽  
J. Méndez-Bermúdez ◽  
José Rodríguez ◽  
José Sigarreta
Keyword(s):  
Random Matrix ◽  
Adjacency Matrix ◽  
Matrix Theory ◽  
Computational Study ◽  
Random Networks ◽  
Geometric Graphs ◽  
Theory Approach ◽  
Complexity Measures ◽  
Random Geometric Graphs ◽  
Highly Correlated

We perform a detailed computational study of the recently introduced Sombor indices on random networks. Specifically, we apply Sombor indices on three models of random networks: Erdös-Rényi networks, random geometric graphs, and bipartite random networks. Within a statistical random matrix theory approach, we show that the average values of Sombor indices, normalized to the order of the network, scale with the average degree. Moreover, we discuss the application of average Sombor indices as complexity measures of random networks and, as a consequence, we show that selected normalized Sombor indices are highly correlated with the Shannon entropy of the eigenvectors of the adjacency matrix.

scholarly journals Crystal Chemical Relations in the Shchurovskyite Family: Synthesis and Crystal Structures of K2Cu[Cu3O]2(PO4)4 and K2.35Cu0.825[Cu3O]2(PO4)4

Crystals ◽  
2021 ◽  
Vol 11 (7) ◽  
pp. 807
Author(s):  
Ilya V. Kornyakov ◽  
Sergey V. Krivovichev
Keyword(s):  
Crystal Structure ◽  
Crystal Structures ◽  
Structural Complexity ◽  
Crystal Chemical ◽  
X Ray Diffraction ◽  
Complexity Measures ◽  
X Ray ◽  
The Family ◽  
Similarities And Differences ◽  
Related Compounds

Single crystals of two novel shchurovskyite-related compounds, K2Cu[Cu3O]2(PO4)4 (1) and K2.35Cu0.825[Cu3O]2(PO4)4 (2), were synthesized by crystallization from gaseous phase and structurally characterized using single-crystal X-ray diffraction analysis. The crystal structures of both compounds are based upon similar Cu-based layers, formed by rods of the [O2Cu6] dimers of oxocentered (OCu4) tetrahedra. The topologies of the layers show both similarities and differences from the shchurovskyite-type layers. The layers are connected in different fashions via additional Cu atoms located in the interlayer, in contrast to shchurovskyite, where the layers are linked by Ca2+ cations. The structures of the shchurovskyite family are characterized using information-based structural complexity measures, which demonstrate that the crystal structure of 1 is the simplest one, whereas that of 2 is the most complex in the family.

Computable Følner monotilings and a theorem of Brudno

2020 ◽  
pp. 1-28
Author(s):  
NIKITA MORIAKOV
Keyword(s):  
Kolmogorov Complexity

Abstract A theorem of Brudno says that the Kolmogorov–Sinai entropy of an ergodic subshift over $\mathbb {N}$ equals the asymptotic Kolmogorov complexity of almost every word in the subshift. The purpose of this paper is to extend this result to subshifts over computable groups that admit computable regular symmetric Følner monotilings, which we introduce in this work. For every $d \in \mathbb {N}$ , the groups $\mathbb {Z}^d$ and $\mathsf{UT}_{d+1}(\mathbb {Z})$ admit computable regular symmetric Følner monotilings for which the required computing algorithms are provided.

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