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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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A.N. Kolmogorov (b. Tambov 1903, d. Moscow 1987) was one of the most brilliant mathematicians that the world has ever known. Incredibly deep and creative, he was able to approach each subject with a completely new point of view: in a few magnificent pages, which are models of shrewdness and imagination, and which astounded his contemporaries, he changed drastically the landscape of the subject. Most mathematicians prove what they can, Kolmogorov was of those who prove what they want. For this book several world experts were asked to present one part of the mathematical heritage left to us by Kolmogorov. Each chapter treats one of Kolmogorov's research themes, or a subject that was invented as a consequence of his discoveries. His contributions are presented, his methods, the perspectives he opened to us, the way in which this research has evolved up to now, along with examples of recent applications and a presentation of the current prospects. This book can be read by anyone with a master's (even a bachelor's) degree in mathematics, computer science or physics, or more generally by anyone who likes mathematical ideas. Rather than present detailed proofs, the main ideas are described. A bibliography is provided for those who wish to understand the technical details. One can see that sometimes very simple reasoning (with the right interpretation and tools) can lead in a few lines to very substantial results. The Kolmogorov Legacy in Physics was published by Springer in 2004 (ISBN 978-3-540-20307-0).

Kolmogorov complexity. --- Mathematics --- History --- Kolmogorov, A. N. --- Complexity, Kolmogorov --- Kolmogorov-Chaitin complexity --- Electronic data processing --- Machine theory --- Kolmogorov, Andreĭ Nikolaevich, --- Kolmogoroff, A., --- Колмогоров, А. Н. --- Logic, Symbolic and mathematical. --- Distribution (Probability theory. --- Differentiable dynamical systems. --- Fourier analysis. --- Topology. --- Mathematical Logic and Foundations. --- Probability Theory and Stochastic Processes. --- Dynamical Systems and Ergodic Theory. --- Fourier Analysis. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Analysis, Fourier --- Mathematical analysis --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Distribution functions --- Frequency distribution --- Characteristic functions --- Probabilities --- Algebra of logic --- Logic, Universal --- Mathematical logic --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Syllogism --- Mathematical logic. --- Probabilities. --- Dynamics. --- Ergodic theory. --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Dynamical systems --- Kinetics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Physics --- Statics --- Probability --- Statistical inference --- Combinations --- Chance --- Least squares --- Mathematical statistics --- Risk

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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.

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The leading theme of the book is complexity in quantum dynamics. This issue is addressed by comparison with the classical ergodic, information and algorithmic complexity theories. Of particular importance is the notion of Kolmogorov-Sinai dynamical entropy and of its inequivalent quantum extensions formulated by Connes, Narnhofer and Thirring on one hand and Alicki and Fannes on the other. Their connections with extensions to quantum systems of Kolmogorov-Chaitin-Solomonoff algorithmic complexity theory is also presented. The technical tools employed are those of the algebraic approach to quantum statistical mechanics which offers a unifying view of classical and quantum dynamical systems. Proofs and examples are provided in order to make the presentation self consistent.

Computational complexity. --- Differentiable dynamical systems. --- Kolmogorov complexity. --- Quantum entropy. --- Quantum theory. --- Quantum theory --- Kolmogorov complexity --- Quantum entropy --- Differentiable dynamical systems --- Computational complexity --- Physics --- Physical Sciences & Mathematics --- Atomic Physics --- Complexity, Computational --- Quantum dynamics --- Quantum mechanics --- Quantum physics --- Physics. --- Dynamics. --- Ergodic theory. --- Quantum physics. --- Quantum computers. --- Spintronics. --- Statistical physics. --- Dynamical systems. --- Quantum Information Technology, Spintronics. --- Dynamical Systems and Ergodic Theory. --- Quantum Physics. --- Mathematical Methods in Physics. --- Statistical Physics, Dynamical Systems and Complexity. --- Mathematical statistics --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Mechanics --- Statics --- Magnetoelectronics --- Spin electronics --- Microelectronics --- Nanotechnology --- Computers --- Thermodynamics --- Ergodic transformations --- Continuous groups --- Mathematical physics --- Measure theory --- Transformations (Mathematics) --- Natural philosophy --- Philosophy, Natural --- Physical sciences --- Dynamics --- Statistical methods --- Electronic data processing --- Machine theory

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The importance of evapotranspiration is well-established in different disciplines such as hydrology, agronomy, climatology, and other geosciences. Reliable estimates of evapotranspiration are also vital to develop criteria for in-season irrigation management, water resource allocation, long-term estimates of water supply, demand and use, design and management of water resources infrastructure, and evaluation of the effect of land use and management changes on the water balance. The objective of this Special Issue is to define and discuss several ET terms, including potential, reference, and actual (crop) ET, and present a wide spectrum of innovative research papers and case studies.

evapotranspiration --- machine learning --- local --- spatial --- subhumid climate --- agricultural drought --- drought characteristics --- evapotranspiration deficit index --- parameter sensitivity --- temporal scale sensitivity --- water stress anomaly --- interception --- linear storage model --- evaporation --- cover crop --- water balance --- faba bean --- GK2A/AMI --- artificial neural network --- Korean Peninsula --- CWSI --- UAV --- remote sensing --- micrometeorological data --- spatial IRT measurements --- crop irrigation scheduling and management --- infrared radiometer sensors --- real-time data analysis --- water reservoir --- regression --- observed data --- ERA5-Land data --- R language --- precipitation --- drought --- Mann–Kendall --- trend analysis --- actual evapotranspiration --- potential evapotranspiration --- reference evapotranspiration --- evaporation paradox --- global dimming --- wind stilling --- forest fires --- groundwater --- stochastic simulation --- marginal structure --- long-range dependence --- Hurst–Kolmogorov dynamics --- RASPOTION --- parametric model --- hydrological calibration --- evapotranspiration estimation --- urban rain gardens --- lysimeters --- evapotranspiration models --- n/a --- Mann-Kendall --- Hurst-Kolmogorov dynamics