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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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The dispersion of particles in a flow is of central importance in various geophysical and environmental problems. The spreading of aerosols and soot in the air, the growth and dispersion of plankton blooms in seas and oceans, or the transport of sediment in rivers, estuaries and coastal regions are striking examples. These problems are characterized by strong nonlinear coupling between several dynamical mechanisms. As a result, processes on widely different length and time scales are simultaneously of importance. The multiscale nature of this challenging field motivated the EUROMECH colloquium

Fluid dynamics --- Fluid dynamic measurements. --- Particles --- Kolmogorov complexity. --- Mathematical models. --- Data processing. --- Environmental aspects. --- Complexity, Kolmogorov --- Kolmogorov-Chaitin complexity --- Electronic data processing --- Machine theory --- CFD (Computational fluid dynamics) --- Measurements, Fluid dynamic --- Physical measurements --- Computer simulation --- Data processing --- Measurement --- Ecology. --- Mechanical engineering. --- Civil engineering. --- Geotechnical Engineering & Applied Earth Sciences. --- Theoretical, Mathematical and Computational Physics. --- Mechanical Engineering. --- Civil Engineering. --- Engineering --- Public works --- Engineering, Mechanical --- Machinery --- Steam engineering --- Balance of nature --- Biology --- Bionomics --- Ecological processes --- Ecological science --- Ecological sciences --- Environment --- Environmental biology --- Oecology --- Environmental sciences --- Population biology --- Ecology --- Geotechnical engineering. --- Ecology . --- Mathematical physics. --- Engineering, Geotechnical --- Geotechnics --- Geotechnology --- Engineering geology --- Physical mathematics --- Physics --- Mathematics --- Computational fluid dynamics.

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This ongoing bestseller, now in its third edition, is considered the standard reference on Kolmogorov complexity, a modern theory of information that is concerned with information in individual objects. New key features and topics in the 3rd edition: * New results on randomness * Kolmogorov's structure function, model selection, and MDL * Incompressibility method: counting unlabeled graphs, Shellsort, communication complexity * Derandomization * Kolmogorov complexity versus Shannon information, rate distortion, lossy compression, denoising * Theoretical results on information distance * The similarity metric with applications to genomics, phylogeny, clustering, classification, semantic meaning, question-answer systems *Quantum Kolmogorov complexity Written by two experts in the field, this book is ideal for advanced undergraduate students, graduate students, and researchers in all fields of science. It is self-contained: it contains the basic requirements from mathematics, probability theory, statistics, information theory, and computer science. Included are history, theory, new developments, a wide range of applications, numerous (new) problem sets, comments, source references, and hints to solutions of problems. This is the only comprehensive treatment of the central ideas of Kolmogorov complexity and their applications. ``Li and Vitányi have provided an ideal book for the exploration of a deep, beautiful and important part of computer science.'' -- Juris Hartmanis, Turing Award Winner 1993, Cornell University, Ithaca, NY. ``The book is likely to remain the standard treatment of Kolmogorov complexity for a long time.'' -- Jorma J. Rissanen, IBM Research, California. ``The book of Li and Vitányi is unexcelled.'' -- Ray J. Solomonoff, Oxbridge Research, Cambridge, Massachusetts "The book is outstanding...the authors did their job unbelievably well...necessary reading for all kinds of readers from undergraduate students to top authorities in the field." -- Vladimir A. Uspensky and Alexander K. Shen, Journal of Symbolic Logic [Review] ``Careful and clear introduction to a subtle and deep field.'' --David G. Stork, Ricoh Innovations, California, Amazon [Review] ``THE book on Kolmogorov Complexity.'' --Lance Fortnow, University of Chicago, IL, Amazon [Review].

Computer Science. --- Coding and Information Theory. --- Theory of Computation. --- Algorithms. --- Statistical Theory and Methods. --- Pattern Recognition. --- Computer science. --- Coding theory. --- Information theory. --- Optical pattern recognition. --- Mathematical statistics. --- Informatique --- Codage --- Théorie de l'information --- Reconnaissance optique des formes (Informatique) --- Algorithmes --- Statistique mathématique --- Electronic books. -- local. --- Electronic data processing. --- Kolmogorov complexity. --- Kolmogorov complexity --- Algebra --- Mathematics --- Physical Sciences & Mathematics --- ADP (Data processing) --- Automatic data processing --- Data processing --- EDP (Data processing) --- IDP (Data processing) --- Integrated data processing --- Complexity, Kolmogorov --- Kolmogorov-Chaitin complexity --- Mathematics. --- Computers. --- Pattern recognition. --- Applied mathematics. --- Engineering mathematics. --- Statistics. --- Applications of Mathematics. --- Computers --- Office practice --- Electronic data processing --- Machine theory --- Automation --- Optical data processing --- Pattern perception --- Perceptrons --- Visual discrimination --- Statistical inference --- Statistics, Mathematical --- Statistics --- Probabilities --- Sampling (Statistics) --- Algorism --- Arithmetic --- Communication theory --- Communication --- Cybernetics --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Signal theory (Telecommunication) --- Computer programming --- Math --- Science --- Statistical methods --- Foundations --- Statistics . --- Design perception --- Pattern recognition --- Form perception --- Perception --- Figure-ground perception --- Statistical analysis --- Statistical data --- Statistical science --- Econometrics --- Automatic computers --- Automatic data processors --- Computer hardware --- Computing machines (Computers) --- Electronic brains --- Electronic calculating-machines --- Electronic computers --- Hardware, Computer --- Computer systems --- Calculators --- Cyberspace --- Engineering --- Engineering analysis --- Mathematical analysis --- Pattern perception.