Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics
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Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics
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Author : Marco Pettini
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-06-14
Geometry And Topology In Hamiltonian Dynamics And Statistical Mechanics written by Marco Pettini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-14 with Mathematics categories.
Itisaspecialpleasureformetowritethisforewordforaremarkablebookbya remarkableauthor.MarcoPettiniisadeepthinker,whohasspentmanyyears probing the foundations of Hamiltonian chaos and statistical mechanics, in particular phase transitions, from the point of view of geometry and topology. Itisinparticularthequalityofmindoftheauthorandhisdeepphysical,as well as mathematical insights which make this book so special and inspiring. It is a “must” for those who want to venture into a new approach to old problems or want to use new tools for new problems. Although topology has penetrated a number of ?elds of physics, a broad participationoftopologyintheclari?cationandprogressoffundamentalpr- lems in the above-mentioned ?elds has been lacking. The new perspectives topology gives to the above-mentioned problems are bound to help in their clari?cation and to spread to other ?elds of science. The sparsity of geometric thinking and of its use to solve fundamental problems, when compared with purely analytical methods in physics, could be relieved and made highly productive using the material discussed in this book. It is unavoidable that the physicist reader may have then to learn some new mathematics and be challenged to a new way of thinking, but with the author as a guide, he is assured of the best help in achieving this that is presently available.
An Introduction To The Geometry And Topology Of Fluid Flows
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Author : Renzo L. Ricca
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
An Introduction To The Geometry And Topology Of Fluid Flows written by Renzo L. Ricca and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.
Computational Psychiatry
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Author : Rodrick Wallace
language : en
Publisher: Springer
Release Date : 2017-04-20
Computational Psychiatry written by Rodrick Wallace and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-20 with Science categories.
This book explores mental disorders from a uniquely evolutionary perspective. Although there have been many attempts to mathematically model neural processes and, to some extent, their dysfunction, there is very little literature that models mental function within a sociocultural, socioeconomic, and environmental context. Addressing this gap in the extant literature, this book explores essential aspects of mental disorders, recognizing the ubiquitous role played by the exaptation of crosstalk between cognitive modules at many different scales and levels of organization, the missing heritability of complex diseases, and cultural epigenetics. Further, it introduces readers to valuable control theory tools that permit the exploration of the environmental induction of neurodevelopmental disorders, as well as the study of the synergism between culture, psychopathology and sleep disorders, offering a distinctively unique resource.
Essays On The Extended Evolutionary Synthesis
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Author : Rodrick Wallace
language : en
Publisher: Springer Nature
Release Date : 2023-05-18
Essays On The Extended Evolutionary Synthesis written by Rodrick Wallace and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-05-18 with Science categories.
From the ‘punctuated equilibrium' of Eldrege and Gould, through Lewontin's ‘triple helix' and the various visions and revisions of the Extended Evolutionary Synthesis (EES) of Laland and others, both data and theory have demanded an opening-up of the 1950's Evolutionary Synthesis that so firmly wedded evolutionary theory to the mathematics of gene frequency analysis. It can, however, be argued that a single deep and comprehensive mathematical theory may simply not be possible for the almost infinite varieties of evolutionary process active at and across the full range of scales of biological, social, institutional, and cultural phenomena. Indeed, the case history of 'meme theory' should have raised a red flag that narrow gene-centered models of evolutionary process may indeed have serious limitations. What is attempted here is less grand, but still broader than a gene-centered analysis. Following the instruction of Maturana and Varela that all living systems are cognitive, in a certainsense, and that living as a process is a process of cognition, the asymptotic limit theorems of information and control theories that bound all cognition provide a basis for constructing an only modestly deep but wider-ranging series of probability models that might be converted into useful statistical tools for the analysis of observational and experimental data related to evolutionary process. The line of argument in this series of interrelated essays proves to be surprisingly direct.
Dynamical Systems And Geometric Mechanics
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Author : Jared Maruskin
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2018-08-21
Dynamical Systems And Geometric Mechanics written by Jared Maruskin and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-21 with Science categories.
Introduction to Dynamical Systems and Geometric Mechanics provides a comprehensive tour of two fields that are intimately entwined: dynamical systems is the study of the behavior of physical systems that may be described by a set of nonlinear first-order ordinary differential equations in Euclidean space, whereas geometric mechanics explore similar systems that instead evolve on differentiable manifolds. The first part discusses the linearization and stability of trajectories and fixed points, invariant manifold theory, periodic orbits, Poincaré maps, Floquet theory, the Poincaré-Bendixson theorem, bifurcations, and chaos. The second part of the book begins with a self-contained chapter on differential geometry that introduces notions of manifolds, mappings, vector fields, the Jacobi-Lie bracket, and differential forms.
Complex Nonlinearity
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Author : Vladimir G. Ivancevic
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-05-31
Complex Nonlinearity written by Vladimir G. Ivancevic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-05-31 with Science categories.
Complex Nonlinearity: Chaos, Phase Transitions, Topology Change and Path Integrals is a book about prediction & control of general nonlinear and chaotic dynamics of high-dimensional complex systems of various physical and non-physical nature and their underpinning geometro-topological change. The book starts with a textbook-like expose on nonlinear dynamics, attractors and chaos, both temporal and spatio-temporal, including modern techniques of chaos–control. Chapter 2 turns to the edge of chaos, in the form of phase transitions (equilibrium and non-equilibrium, oscillatory, fractal and noise-induced), as well as the related field of synergetics. While the natural stage for linear dynamics comprises of flat, Euclidean geometry (with the corresponding calculation tools from linear algebra and analysis), the natural stage for nonlinear dynamics is curved, Riemannian geometry (with the corresponding tools from nonlinear, tensor algebra and analysis). The extreme nonlinearity – chaos – corresponds to the topology change of this curved geometrical stage, usually called configuration manifold. Chapter 3 elaborates on geometry and topology change in relation with complex nonlinearity and chaos. Chapter 4 develops general nonlinear dynamics, continuous and discrete, deterministic and stochastic, in the unique form of path integrals and their action-amplitude formalism. This most natural framework for representing both phase transitions and topology change starts with Feynman’s sum over histories, to be quickly generalized into the sum over geometries and topologies. The last Chapter puts all the previously developed techniques together and presents the unified form of complex nonlinearity. Here we have chaos, phase transitions, geometrical dynamics and topology change, all working together in the form of path integrals. The objective of this book is to provide a serious reader with a serious scientific tool that will enable them to actually perform a competitive research in modern complex nonlinearity. It includes a comprehensive bibliography on the subject and a detailed index. Target readership includes all researchers and students of complex nonlinear systems (in physics, mathematics, engineering, chemistry, biology, psychology, sociology, economics, medicine, etc.), working both in industry/clinics and academia.
Consciousness Cognition And Crosstalk The Evolutionary Exaptation Of Nonergodic Groupoid Symmetry Breaking
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Author : Rodrick Wallace
language : en
Publisher: Springer Nature
Release Date : 2021-10-20
Consciousness Cognition And Crosstalk The Evolutionary Exaptation Of Nonergodic Groupoid Symmetry Breaking written by Rodrick Wallace and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-20 with Technology & Engineering categories.
This book makes application to the dynamics of arousal and distraction, and to other examples. A modified version of the Kadanoff picture of phase transitions in consciousness emerges from the Morse Function itself in a surprisingly standard manner, closely associated with the breaking of groupoid symmetries driven by fundamental equivalence class algebras. Although this is far indeed from the familiar world of physical theory, it should be possible, on the basis of the probability models developed in the book, to develop new statistical tools for the analysis of observational and empirical data regarding cognition and consciousness.
Nonlinear Dynamics New Directions
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Author : Hernán González-Aguilar
language : en
Publisher: Springer
Release Date : 2015-02-10
Nonlinear Dynamics New Directions written by Hernán González-Aguilar and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-02-10 with Technology & Engineering categories.
This book, along with its companion volume, Nonlinear Dynamics New Directions: Theoretical Aspects, covers topics ranging from fractal analysis to very specific applications of the theory of dynamical systems to biology. This second volume contains mostly new applications of the theory of dynamical systems to both engineering and biology. The first volume is devoted to fundamental aspects and includes a number of important new contributions as well as some review articles that emphasize new development prospects. The topics addressed in the two volumes include a rigorous treatment of fluctuations in dynamical systems, topics in fractal analysis, studies of the transient dynamics in biological networks, synchronization in lasers, and control of chaotic systems, among others. This book also: · Develops applications of nonlinear dynamics on a diversity of topics such as patterns of synchrony in neuronal networks, laser synchronization, control of chaotic systems, and the study of transient dynamics in biological · Includes a study of self-organized regularity in long-range systems · Explains use of Levenstein's distance for measuring lexical evolution rates
Mathematical Essays On Embodied Cognition
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Author : Rodrick Wallace
language : en
Publisher: Springer Nature
Release Date : 2025-05-13
Mathematical Essays On Embodied Cognition written by Rodrick Wallace and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-05-13 with Technology & Engineering categories.
This book provides a unique formal foundation for the development of statistical tools useful in the exploration of observational and experimental data related to embodied cognition. The asymptotic limit theorems of information and control theories can be used to construct statistical tools analogous to -- but different from -- regression models for the study of the often highly punctuated cognitive phenomena embedded in and hence influenced by a surrounding ecosystem of which the phenomena are themselves part. The book builds probability models based on those theorems that incorporate embodiment at a number of scales and levels of organization, ranging from the effects of stress on the immune system within a higher organism, through institutional (and machine) cognition under challenge from adversaries, to the failure of public health institutions under pathogen challenge. In distinct contrast to the existing literature, many detailed, worked-out examples provide templates for sophisticated readers to build their own model/tool constructs.
Information Geometry
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Author : Geert Verdoolaege
language : en
Publisher: MDPI
Release Date : 2019-04-04
Information Geometry written by Geert Verdoolaege and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-04-04 with Juvenile Nonfiction categories.
This Special Issue of the journal Entropy, titled “Information Geometry I”, contains a collection of 17 papers concerning the foundations and applications of information geometry. Based on a geometrical interpretation of probability, information geometry has become a rich mathematical field employing the methods of differential geometry. It has numerous applications to data science, physics, and neuroscience. Presenting original research, yet written in an accessible, tutorial style, this collection of papers will be useful for scientists who are new to the field, while providing an excellent reference for the more experienced researcher. Several papers are written by authorities in the field, and topics cover the foundations of information geometry, as well as applications to statistics, Bayesian inference, machine learning, complex systems, physics, and neuroscience.