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Kolmogorov complexity --- Computational complexity

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The book is a collection of papers written by a selection of eminent authors from around the world in honour of Gregory Chaitin's 60th birthday. This is a unique volume including technical contributions, philosophical papers and essays. Sample Chapter(s)
Chapter 1: On Random and Hard-to-Describe Numbers (902 KB)

Contents:

• On Random and Hard-to-Describe Numbers (C H Bennett)
• The Implications of a Cosmological Information Bound for Complexity, Quantum Information and the Nature of Physical Law (P C W Davies)
• What is a Computation? <

Kolmogorov complexity. --- Computational complexity. --- Stochastic processes.

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Algorithmic information theory (AIT), or Kolmogorov complexity as it is known to mathematicians, can provide a useful tool for scientists to look at natural systems, however some critical conceptual issues need to be understood and the advances already made collated and put in a form accessible to scientists. This book has been written in the hope that readers will be able to absorb the key ideas behind AIT so that they are in a better position to access the mathematical developments and to apply the ideas to their own areas of interest. The theoretical underpinning of AIT is outlined in the earlier chapters, while later chapters focus on the applications, drawing attention to the thermodynamic commonality between ordered physical systems such as the alignment of magnetic spins, the maintenance of a laser distant from equilibrium, and ordered living systems such as bacterial systems, an ecology, and an economy.

Kolmogorov complexity. --- Information theory. --- Information theory. --- COMPUTERS / Information Theory.

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Quantum-like structure is present practically everywhere. Quantum-like (QL) models, i.e. models based on the mathematical formalism of quantum mechanics and its generalizations can be successfully applied to cognitive science, psychology, genetics, economics, finances, and game theory. This book is not about quantum mechanics as a physical theory. The short review of quantum postulates is therefore mainly of historical value: quantum mechanics is just the first example of the successful application of non-Kolmogorov probabilities, the first step towards a contextual probabilistic description of natural, biological, psychological, social, economical or financial phenomena. A general contextual probabilistic model (Växjö model) is presented. It can be used for describing probabilities in both quantum and classical (statistical) mechanics as well as in the above mentioned phenomena. This model can be represented in a quantum-like way, namely, in complex and more general Hilbert spaces. In this way quantum probability is totally demystified: Born's representation of quantum probabilities by complex probability amplitudes, wave functions, is simply a special representation of this type.

Mathematics. --- Semiconductors. --- Probabilities --- Quantum theory --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Kolmogorov complexity. --- Quantum logic. --- Complexity, Kolmogorov --- Kolmogorov-Chaitin complexity --- Physics. --- Probabilities. --- Quantum physics. --- Economic theory. --- Quantum Physics. --- Probability Theory and Stochastic Processes. --- Economic Theory/Quantitative Economics/Mathematical Methods. --- Algebraic logic --- Mathematical physics --- Electronic data processing --- Machine theory

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This Special Issue collects novel contributions from scientists in the interdisciplinary field of biomolecular evolution. Works listed here use information theoretical concepts as a core but are tightly integrated with the study of molecular processes. Applications include the analysis of phylogenetic signals to elucidate biomolecular structure and function, the study and quantification of structural dynamics and allostery, as well as models of molecular interaction specificity inspired by evolutionary cues.

Research & information: general --- Biology, life sciences --- power law --- Brownian process --- Kolmogorov complexity --- entropy --- chaos --- monofractal --- non-linear --- cumulative sum --- sequence analysis --- protein engineering --- direct coupling analysis --- evolutionary coupling analysis --- contact prediction --- phylogenetic bias --- phylogeny --- co-evolution --- coevolutionary analysis --- direct-coupling analysis --- specificity determining contacts --- sequence reweighting --- maximum entropy models --- protein contact predictions --- TEM-1 --- TOHO-1 --- PBP-A --- DD-transpeptidase --- conformational changes --- catalytic mechanism --- evolution --- epistasis --- allostery --- elastic network model --- protein conformational dynamics --- statistical inference --- mutational phenotypes --- interaction specificity --- phosphorylation --- fitness landscape --- bacterial signaling --- power law --- Brownian process --- Kolmogorov complexity --- entropy --- chaos --- monofractal --- non-linear --- cumulative sum --- sequence analysis --- protein engineering --- direct coupling analysis --- evolutionary coupling analysis --- contact prediction --- phylogenetic bias --- phylogeny --- co-evolution --- coevolutionary analysis --- direct-coupling analysis --- specificity determining contacts --- sequence reweighting --- maximum entropy models --- protein contact predictions --- TEM-1 --- TOHO-1 --- PBP-A --- DD-transpeptidase --- conformational changes --- catalytic mechanism --- evolution --- epistasis --- allostery --- elastic network model --- protein conformational dynamics --- statistical inference --- mutational phenotypes --- interaction specificity --- phosphorylation --- fitness landscape --- bacterial signaling