Vladimir G. Ivancevic Livres

The book delves into the concepts of smooth manifolds, providing both intuitive insights and formal definitions. It explores the foundational aspects of modern geometrical machinery, emphasizing the significance of smooth manifolds in advanced mathematical contexts. Readers will gain a deeper understanding of the structure and properties of these manifolds, which play a crucial role in various fields of mathematics and physics.

Neuro–Fuzzy Associative Machinery for Comprehensive Brain and Cognition Modelling" is a graduate–level monographic textbook. It 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 to perform a competitive research in brain and cognition modelling.

Computational Mind: A Complex Dynamics Perspective 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. It presents brain/mind dynamics from the chaos theory perspective, including sections on chaos in human EEG, basics of nonlinear dynamics and chaos, techniques of chaos control, synchronization in chaotic systems and complexity in humanoid robots. This book presents modern theory of quantum computational mind, including sections on Dirac–Feynman quantum dynamics, quantum consciousness, and quantum computation using Josephson junctions. The book is designed as a one–semester course for computer scientists, engineers, physicists and applied mathematicians, both in industry and academia. It includes a strong bibliography on the subject and detailed index.

Exploring the intersection of quantum computation and neural networks, this book offers both non-technical and technical insights into modern quantum neural computation. It outlines foundational concepts and presents a visionary blueprint for the future of quantum brains, merging advanced computational theories with practical applications in neural processing.

Exploring the intersection of cognitive psychology and computational intelligence, this graduate-level textbook offers a modern dynamical theory of the mind. It delves into chaos theory, examining brain dynamics through human EEG and nonlinear dynamics, while discussing chaos control and synchronization in systems. Additionally, it introduces quantum computational concepts, including Dirac-Feynman dynamics and the role of Josephson junctions. Designed for professionals in various scientific fields, the book includes extensive references and a detailed index for further study.

Exploring the intricacies of human-like biomechanics, this book delves into the principles that govern human movement and how these principles can be applied to robotics and artificial intelligence. It examines the anatomical and physiological aspects of human motion, providing insights into the design of more efficient and adaptable machines. The text combines theoretical frameworks with practical applications, making it a valuable resource for engineers, researchers, and anyone interested in the intersection of biology and technology.

Exploring the complexities of high-dimensional chaos, this book delves into the dynamics of nonlinear systems, emphasizing the need to understand and control life's unpredictability. Building on previous work, it focuses on extreme cases of chaos and attractor systems, revealing their inherent order despite appearances of disorder. Unlike introductory texts that oversimplify chaos, this work aims to equip readers with a deeper understanding of real-world chaotic dynamics, encouraging them to engage with the complexities of life.

This book explores the prediction and control of nonlinear and chaotic dynamics in high-dimensional complex systems, addressing both physical and non-physical phenomena and their underlying geometro-topological changes. It begins with a foundational overview of nonlinear dynamics, attractors, and chaos, including contemporary chaos-control techniques. The second chapter examines the edge of chaos through various phase transitions—equilibrium, non-equilibrium, oscillatory, fractal, and noise-induced—while also touching on synergetics. Unlike linear dynamics, which operates in flat, Euclidean spaces, nonlinear dynamics is grounded in curved, Riemannian geometry, necessitating tools from nonlinear tensor algebra and analysis. The extreme nonlinearity of chaos is linked to changes in the topology of the configuration manifold. The third chapter delves into the relationship between geometry, topology change, and complex nonlinearity. The fourth chapter introduces general nonlinear dynamics through path integrals and their action-amplitude formalism, building on Feynman’s sum over histories and extending it to sums over geometries and topologies. The final chapter synthesizes these concepts, presenting a unified framework that integrates chaos, phase transitions, geometrical dynamics, and topology change via path integrals. A comprehensive bibliography and detailed index support researchers and students across various fields, includ