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.

Quantum Neural Computation is a graduate-level monographic textbook. It presents a comprehensive introduction, both non-technical and technical, into modern quantum neural computation, the science behind the fiction movie Stealth. Classical computing systems perform classical computations (i.e., Boolean operations, such as AND, OR, NOT gates) using devices that can be described classically (e.g., MOSFETs). On the other hand, quantum computing systems perform classical computations using quantum devices (quantum dots), that is devices that can be described only using quantum mechanics. Any information transfer between such computing systems involves a state measurement. This book describes this information transfer at the edge of classical and quantum chaos and turbulence, where mysterious quantum-mechanical linearity meets even more mysterious brain's nonlinear complexity, in order to perform a super-high-speed and error-free computations. This monograph describes a crossroad between quantum field theory, brain science and computational intelligence.

Modern Geometrical Machinery; 1 .1 Introduction; 1 .2 Smooth Manifolds; 1.2.1 Intuition Behind a Smooth Manifold; 1.2.2 Definition of a Smooth Manifold; 1.2.3 Smooth Maps Between Manifolds; 1.2.4 (Co)Tangent Bundles of a Smooth Manifold; 1.2.5 Tensor Fields and Bundles of a Smooth Manifold; 1.2.6 Lie Derivative on a Smooth Manifold; 1.2.7 Lie Groups and Associated Lie Algebras; 1.2.8 Lie Symmetries and Prolongations on Manifolds;1.2.9 Riemannian Manifolds; 1.2.10 Finsler Manifolds; 1.2.11 Symplectic Manifolds; 1.2.12 Complex and Kahler Manifolds; 1.2.13 Conformal Killing-Riemannian Geometry; 1.3 Fibre Bundles; 1.3.1 Intuition Behind a Fibre Bundle; 1.3.2 Definition of a Fibre Bundle;1.3.3 Vector and Affine Bundles; 1.3.4 Principal Bundles; 1.3.5 Multivector-Fields and Tangent-Valued Forms; 1.4 Jet Spaces; 1.4.1 Intuition Behind a Jet Space; 1.4.2 Definition of a 1-Jet Space; 1.4.3 Connections as Jet Fields; 1.4.4 Definition of a 2-Jet Space; 1.4.5 Higher-Order Jet Spaces; 1.4.6 Jets in Mechanics;1.4.7 Jets and Action Principle; 1.5 Path Integrals: Extending Smooth Geometrical Machinery; 1.5.1 Intuition Behind a Path Integral; 1.5.2 Path Integral History; 1.5.3 Standard Path-Integral Quantization; 1.5.4 Sum over Geometries/Topologies; 1.5.5 TQFT and Stringy Path Integrals; 2 Dynamics of High-Dimensional Nonlinear Systems; 2.1 Mechanical Systems; 2.1.1 Autonomous Lagrangian/Hamiltonian Mechanics; 2.1.2 Non-Autonomous Lagrangian/Hamiltonian Mechanics; 2.1.3 Semi-Riemannian Geometrical Dynamics; 2.1.4 Relativistic and Multi-Time Rheonomic Dynamics; 2.1.5 Geometrical Quantization; 2.2 Physical Field Systems; 2.2.1 n-Categorical Framework; 2.2.2 Lagrangian Field Theory on Fibre Bundles; 2.2.3 Finsler-Lagrangian Field Theory; 2.2.4 Hamiltonian Field Systems: Path-Integral Quantization; 2.2.5 Gauge Fields on Principal Connections; 2.2.6 Modern Geometrodynamics; 2.2.7 Topological Phase Transitions and Hamiltonian Chaos; 2.2.8 Topological Superstring Theory; 2.2.9 Turbulence and Chaos Field Theory; 2.3 Nonlinear Control Systems; 2.3.1 The Basis of Modern Geometrical Control;2.3.2 Geometrical Control of Mechanical Systems;2.3.3 Hamiltonian Optimal Control and Maximum Principle; 2.3.4 Path-Integral Optimal Control of Stochastic Systems; 2.4 Human-Like Biomechanics; 2.4.1 Lie Groups and Symmetries in Biomechanics; 2.4.2 Muscle-Driven Hamiltonian Biomechanics; 2.4.3 Biomechanical Functors; 2.4.4 Biomechanical Topology; 2.5 Neurodynamics; 2.5.1 Microscopic Neurodynamics and Quantum Brain; 2.5.2 Macroscopic Neurodynamics; 2.5.3 Oscillatory Phase Neurodynamics;2.5.4 Neural Path-Integral Model for the Cerebellum; 2.5.5 Intelligent Robot Control; 2.5.6 Brain-Like Control Functor in Biomechanics; 2.5.7 Concurrent and Weak Functorial Machines; 2.5.8 Brain-Mind Functorial Machines; 26 Psycho-Socio-Economic Dynamics; 2.6.1 Force-Field Psychodynamics; 2.6.2 Geometrical Dynamics of Human Crowd; 2.6.3 Dynamical Games on Lie Groups; 2.6.4 Nonlinear Dynamics of Option Pricing; 2.6.5 Command/Control in Human-Robot Interactions; 2.6.6 Nonlinear Dynamics of Complex Nets; 2.6.7 Complex Adaptive Systems: Common Characteristics; 2.6.8 FAM Functors and Real-Life Games; 2.6.9 Riemann-Finsler Approach to Information Geometry; 3 Appendix: Tensors and Functors; 3.1 Elements of Classical Tensor Analysis; 3.1.1 Transformation of Coordinates and Elementary Tensors; 3.1.2 Euclidean Tensors; 3. 1 .3 Tensor Derivatives on Riemannian Manifolds; 3.1.4 Tensor Mechanics in Brief; 3.1.5 The Covariant Force Law in Robotics and Biomechanics; 3.2 Categories and Functors; 3.2.1 Maps; 3.2.2 Categories; 3.2.3 Functors; 3.2.4 Natural Transformations; 3.2.5 Limits and Colimits; 3.2.6 The Adjunction; 3.2.7 ri-Categories; 3.2.8 Abelian Functorial Algebra; References; Index.

The book "Paradigm Shift for Future Tennis" starts with revelations that make obvious the limitations of today's tennis, which does not use the laws of modern Biomechanics and Neurophysiology. The second part of the book includes a new approach to the quantum mind of a champion. It will reveal the secret weapon of Roger Federer and the blueprint of a future tennis champion. This book will expose the new tennis shot emerging from the field of sports science. It is a real weapon, which can generate a ball-speed similar to that of the first serve: the Power High-Forehand. Its aim is to generate maximal possible racket-head speed while players do not wait for the ball to bounce. This is both a tactical and psychological basis for the future tennis game. This aggressive interceptive psychology will shape the minds of future tennis champions. High racket-head speed can be achieved using the stretch-reflex, without big loops and swings. Weapons of a future tennis game will comprise of whip-like tennis serves and ground strokes, based on the stretch-reflex, and using the whole body in a fluid and integrated manner, thus manifesting a superb combination of speed and strength. Restructure your brain and apply the power of state of the art biomechanical, mathematical, medical, neural, cognitive, and quantum computational intelligence to understand the tennis of today and the future!

The book "Paradigm Shift for Future Tennis" starts with revelations that make obvious the limitations of today's tennis, which does not use the laws of modern Biomechanics and Neurophysiology. The second part of the book includes a new approach to the quantum mind of a champion. It will reveal the secret weapon of Roger Federer and the blueprint of a future tennis champion. This book will expose the new tennis shot emerging from the field of sports science. It is a real weapon, which can generate a ball-speed similar to that of the first serve: the Power High-Forehand. Its aim is to generate maximal possible racket-head speed while players do not wait for the ball to bounce. This is both a tactical and psychological basis for the future tennis game. This aggressive interceptive psychology will shape the minds of future tennis champions. High racket-head speed can be achieved using the stretch-reflex, without big loops and swings. Weapons of a future tennis game will comprise of whip-like tennis serves and ground strokes, based on the stretch-reflex, and using the whole body in a fluid and integrated manner, thus manifesting a superb combination of speed and strength. Restructure your brain and apply the power of state of the art biomechanical, mathematical, medical, neural, cognitive, and quantum computational intelligence to understand the tennis of today and the future

Human-Like Biomechanics is a comprehensive introduction into modern geometrical methods to be used as a unified research approach in two apparently separate and rapidly growing fields: mathematical biomechanics and humanoid robotics. The term human-like biomechanics is used to denote this unified modelling and control approach to humanoid robotics and mathematical biomechanics, based on theoretical mechanics, differential geometry and topology, nonlinear dynamics and control, and path-integral methods. From this geometry-mechanics-control modelling perspective, "human" and "humanoid" means the same. This unified approach enables both design of humanoid systems of immense complexity and prediction/prevention of subtle neuro-musculo-skeletal injuries. This approach has been realized in the form of the world-leading human-motion simulator with 264 powered degrees of freedom, called Human Biodynamics Engine (developed in Defence Science & Technology Organisation, Australia).

The book contains six Chapters and an Appendix. The first Chapter is an Introduction, giving a brief review of mathematical techniques to be used in the text. The second Chapter develops geometrical basis of human-like biomechanics, while the third Chapter develops its mechanical basis, mainly from generalized Lagrangian and Hamiltonian perspective. The fourth Chapter develops topology of human-like biomechanics, while the fifth Chapter reviews related nonlinear control techniques. The sixth Chapter develops covariant biophysics of electro-muscular stimulation. The Appendix consists of two parts: classical muscular mechanics and modern path integral methods, which are both used frequently in the main text. The whole book is based on the authors own research papers in human-like biomechanics. "

This is a graduate level monographic textbook in the field of Computational Intelligence. It presents a modern dynamical theory of the computational mind, combining cognitive psychology, artificial and computational intelligence, and chaos theory with quantum consciousness and computation. The book introduces to human and computational mind, comparing and contrasting main themes of cognitive psychology, artificial and computational intelligence.

This graduate-level textbook is devoted to understanding, prediction and control of high-dimensional chaotic and attractor systems of real life. The objective is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high-dimensional chaotic and attractor dynamics. From introductory material on low-dimensional attractors and chaos, the text explores concepts including Poincare's 3-body problem, high-tech Josephson junctions, and more."

This book represents a comprehensive introduction into both conceptual and rigorous brain and cognition modelling. It is devoted to understanding, prediction and control of the fundamental mechanisms of brain functioning. The reader will be provided with a scientific tool enabling him or her to perform a competitive research in brain and cognition modelling. This is a graduate level monographic textbook.

What are motor abilities of Olympic champions? What are essential psyc- logical characteristics of Mark Spitz, Carl Lewis and Roger Federer? How to discover and maximally develop motor intelligence? How to develop - domitable will power of Olympic champions? What are the secrets of sel- tion for the future Olympic champions? Does for every sport exist a unique model of an Olympic champion? This book gives a modern scienti?c answers to the above questions. Its purpose is to give you the answer to everything you ever wanted to ask about sport champions, but didn't know who or how to ask. In particular, the purpose of this book is to give you the answer to eve- thing you ever wanted to ask about advanced tennis, but didn't know who or how to ask. Its aim is to dispel classical myths of a "biomechanically sound" serve, forehand, and backhand, as well as provide methods for developing superior tennis weapons, a lightning-fast game, and unrivaled mental speed and strength - essential qualities of a future tennis champion.

Quantum Neural Computation is a graduate level monographic textbook. It presents a comprehensive introduction, both non-technical and technical, into modern quantum neural computation, the science behind the fiction movie Stealth. Classical computing systems perform classical computations (i.e., Boolean operations, such as AND, OR, NOT gates) using devices that can be described classically (e.g., MOSFETs). On the other hand, quantum computing systems perform classical computations using quantum devices (quantum dots), that is devices that can be described only using quantum mechanics. Any information transfer between such computing systems involves a state measurement. This book describes this information transfer at the edge of classical and quantum chaos and turbulence, where mysterious quantum-mechanical linearity meets even more mysterious brain s nonlinear complexity, in order to perform a super high speed and error free computations. This monograph describes a crossroad between quantum field theory, brain science and computational intelligence."

This is a graduate level monographic textbook in the field of Computational Intelligence. It presents a modern dynamical theory of the computational mind, combining cognitive psychology, artificial and computational intelligence, and chaos theory with quantum consciousness and computation. The book introduces to human and computational mind, comparing and contrasting main themes of cognitive psychology, artificial and computational intelligence.

This book represents a comprehensive introduction into both conceptual and rigorous brain and cognition modelling. It is devoted to understanding, prediction and control of the fundamental mechanisms of brain functioning. The reader will be provided with a scientific tool enabling him or her to perform a competitive research in brain and cognition modelling. This is a graduate level monographic textbook.

This graduate level textbook is devoted to understanding, prediction and control of high dimensional chaotic and attractor systems of real life. The objective is to provide the serious reader with a serious scientific tool that will enable the actual performance of competitive research in high dimensional chaotic and attractor dynamics. From introductory material on low-dimensional attractors and chaos, the text explores concepts including Poincare s 3-body problem, high-tech Josephson junctions, and more.

Human-Like Biomechanics is a comprehensive introduction into modern geometrical methods to be used as a unified research approach in two apparently separate and rapidly growing fields: mathematical biomechanics and humanoid robotics. The term human-like biomechanics is used to denote this unified modelling and control approach to humanoid robotics and mathematical biomechanics, based on theoretical mechanics, differential geometry and topology, nonlinear dynamics and control, and path-integral methods. From this geometry-mechanics-control modelling perspective, "human" and "humanoid" means the same. This unified approach enables both design of humanoid systems of immense complexity and prediction/prevention of subtle neuro-musculo-skeletal injuries. This approach has been realized in the form of the world-leading human-motion simulator with 264 powered degrees of freedom, called Human Biodynamics Engine (developed in Defence Science & Technology Organisation, Australia).

The book contains six Chapters and an Appendix. The first Chapter is an Introduction, giving a brief review of mathematical techniques to be used in the text. The second Chapter develops geometrical basis of human-like biomechanics, while the third Chapter develops its mechanical basis, mainly from generalized Lagrangian and Hamiltonian perspective. The fourth Chapter develops topology of human-like biomechanics, while the fifth Chapter reviews related nonlinear control techniques. The sixth Chapter develops covariant biophysics of electro-muscular stimulation. The Appendix consists of two parts: classical muscular mechanics and modern path integral methods, which are both used frequently in the main text. Thewhole book is based on the authorsa (TM) own research papers in human-like biomechanics.

Geometrical Dynamics of Complex Systems is a graduate-level monographic textbook. Itrepresentsacomprehensiveintroductionintorigorousgeometrical dynamicsofcomplexsystemsofvariousnatures. By'complexsystems', inthis book are meant high-dimensional nonlinear systems, which can be (but not necessarily are) adaptive. This monograph proposes a uni?ed geometrical - proachtodynamicsofcomplexsystemsofvariouskinds: engineering, physical, biophysical, psychophysical, sociophysical, econophysical, etc. As their names suggest, all these multi-input multi-output (MIMO) systems have something in common: the underlying physics. However, instead of dealing with the pop- 1 ular 'soft complexity philosophy', we rather propose a rigorous geometrical and topological approach. We believe that our rigorous approach has much greater predictive power than the soft one. We argue that science and te- nology is all about prediction and control. Observation, understanding and explanation are important in education at undergraduate level, but after that it should be all prediction and control. The main objective of this book is to show that high-dimensional nonlinear systems and processes of 'real life' can be modelled and analyzed using rigorous mathematics, which enables their complete predictability and controllability, as if they were linear systems. It is well-known that linear systems, which are completely predictable and controllable by de?nition - live only in Euclidean spaces (of various - mensions). They are as simple as possible, mathematically elegant and fully elaborated from either scienti?c or engineering side. However, in nature, no- ing is linear. In reality, everything has a certain degree of nonlinearity, which means: unpredictability, with subsequent uncontrollability.

What are motor abilities of Olympic champions? What are essential psyc- logical characteristics of Mark Spitz, Carl Lewis and Roger Federer? How to discover and maximally develop motor intelligence? How to develop - domitable will power of Olympic champions? What are the secrets of sel- tion for the future Olympic champions? Does for every sport exist a unique model of an Olympic champion? This book gives a modern scienti?c answers to the above questions. Its purpose is to give you the answer to everything you ever wanted to ask about sport champions, but didn't know who or how to ask. In particular, the purpose of this book is to give you the answer to eve- thing you ever wanted to ask about advanced tennis, but didn't know who or how to ask. Its aim is to dispel classical myths of a "biomechanically sound" serve, forehand, and backhand, as well as provide methods for developing superior tennis weapons, a lightning-fast game, and unrivaled mental speed and strength - essential qualities of a future tennis champion.

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.

This book gives a comprehensive introduction into geometrical methods of modern biomechanics. This book is designed for a rigorous, one--semester course at the graduate level. The intended audience includes mechanical, control and biomedical engineers (with stronger mathematical background), mathematicians, physicists, computer scientists and mathematical biologists, as well as all researchers and technical professionals interested in modelling and control of biomechanical systems and humanoid robots.

New Trends in Control Theory is a graduate-level monographic textbook. It is a contemporary overview of modern trends in control theory. The introductory chapter gives the geometrical and quantum background, which is a necessary minimum for comprehensive reading of the book. The second chapter gives the basics of classical control theory, both linear and nonlinear. The third chapter shows the key role that Euclidean group of rigid motions plays in modern robotics and biomechanics. The fourth chapter gives an overview of modern quantum control, from both theoretical and measurement perspectives. The fifth chapter presents modern control and synchronization methods in complex systems and human crowds. The appendix provides the rest of the background material complementary to the introductory chapter. The book is designed as a one-semester course for engineers, applied mathematicians, computer scientists and physicists, both in industry and academia. It includes a most relevant bibliography on the subject and detailed index.