Dynamical Search
Dynamical Search

Author: Luc Pronzato

Publisher: CRC Press

Published: 1999-08-27

Total Pages: 240

ISBN-13: 9780849303364

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Certain algorithms that are known to converge can be renormalized or "blown up" at each iteration so that their local behavior can be seen. This creates dynamical systems that we can study with modern tools, such as ergodic theory, chaos, special attractors, and Lyapounov exponents. Furthermore, we can translate the rates of convergence into less studied exponents known as Renyi entropies. This all feeds back to suggest new algorithms with faster rates of convergence. For example, in line-search, we can improve upon the Golden Section algorithm with new classes of algorithms that have their own special-and sometimes chaotic-dynamical systems. The ellipsoidal algorithms of linear and convex programming have fast, "deep cut" versions whose dynamical systems contain cyclic attractors. And ordinary steepest descent has, buried within, a beautiful fractal that controls the gateway to a special two-point attractor. Faster "relaxed" versions exhibit classical period doubling. Dynamical Search presents a stimulating introduction to a brand new field - the union of dynamical systems and optimization. It will prove fascinating and open doors to new areas of investigation for researchers in both fields, plus those in statistics and computer science.

Multi-UAS Minimum Time Search in Dynamic and Uncertain Environments
Multi-UAS Minimum Time Search in Dynamic and Uncertain Environments

Author: Sara Pérez Carabaza

Publisher: Springer Nature

Published: 2021-06-30

Total Pages: 183

ISBN-13: 3030765598

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This book proposes some novel approaches for finding unmanned aerial vehicle trajectories to reach targets with unknown location in minimum time. At first, it reviews probabilistic search algorithms that have been used for dealing with the minimum time search (MTS) problem, and discusses how metaheuristics, and in particular the ant colony optimization algorithm (ACO), can help to find high-quality solutions with low computational time. Then, it describes two ACO-based approaches to solve the discrete MTS problem and the continuous MTS problem, respectively. In turn, it reports on the evaluation of the ACO-based discrete and continuous approaches to the MTS problem in different simulated scenarios, showing that the methods outperform in most all the cases over other state-of-the-art approaches. In the last part of the thesis, the work of integration of the proposed techniques in the ground control station developed by Airbus to control ATLANTE UAV is reported in detail, providing practical insights into the implementation of these methods for real UAVs.

Invitation to Dynamical Systems
Invitation to Dynamical Systems

Author: Edward R. Scheinerman

Publisher: Courier Corporation

Published: 2012-01-01

Total Pages: 402

ISBN-13: 0486485943

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This text is designed for those who wish to study mathematics beyond linear algebra but are not ready for abstract material. Rather than a theorem-proof-corollary-remark style of exposition, it stresses geometry, intuition, and dynamical systems. An appendix explains how to write MATLAB, Mathematica, and C programs to compute dynamical systems. 1996 edition.

Random Dynamical Systems
Random Dynamical Systems

Author: Ludwig Arnold

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 590

ISBN-13: 3662128780

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The first systematic presentation of the theory of dynamical systems under the influence of randomness, this book includes products of random mappings as well as random and stochastic differential equations. The basic multiplicative ergodic theorem is presented, providing a random substitute for linear algebra. On its basis, many applications are detailed. Numerous instructive examples are treated analytically or numerically.

Dynamical Systems in Neuroscience
Dynamical Systems in Neuroscience

Author: Eugene M. Izhikevich

Publisher: MIT Press

Published: 2010-01-22

Total Pages: 459

ISBN-13: 0262514206

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Explains the relationship of electrophysiology, nonlinear dynamics, and the computational properties of neurons, with each concept presented in terms of both neuroscience and mathematics and illustrated using geometrical intuition. In order to model neuronal behavior or to interpret the results of modeling studies, neuroscientists must call upon methods of nonlinear dynamics. This book offers an introduction to nonlinear dynamical systems theory for researchers and graduate students in neuroscience. It also provides an overview of neuroscience for mathematicians who want to learn the basic facts of electrophysiology. Dynamical Systems in Neuroscience presents a systematic study of the relationship of electrophysiology, nonlinear dynamics, and computational properties of neurons. It emphasizes that information processing in the brain depends not only on the electrophysiological properties of neurons but also on their dynamical properties. The book introduces dynamical systems, starting with one- and two-dimensional Hodgkin-Huxley-type models and continuing to a description of bursting systems. Each chapter proceeds from the simple to the complex, and provides sample problems at the end. The book explains all necessary mathematical concepts using geometrical intuition; it includes many figures and few equations, making it especially suitable for non-mathematicians. Each concept is presented in terms of both neuroscience and mathematics, providing a link between the two disciplines. Nonlinear dynamical systems theory is at the core of computational neuroscience research, but it is not a standard part of the graduate neuroscience curriculum—or taught by math or physics department in a way that is suitable for students of biology. This book offers neuroscience students and researchers a comprehensive account of concepts and methods increasingly used in computational neuroscience. An additional chapter on synchronization, with more advanced material, can be found at the author's website, www.izhikevich.com.

Advanced Topics in the Arithmetic of Elliptic Curves
Advanced Topics in the Arithmetic of Elliptic Curves

Author: Joseph H. Silverman

Publisher: Springer Science & Business Media

Published: 2013-12-01

Total Pages: 482

ISBN-13: 1461208513

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In the introduction to the first volume of The Arithmetic of Elliptic Curves (Springer-Verlag, 1986), I observed that "the theory of elliptic curves is rich, varied, and amazingly vast," and as a consequence, "many important topics had to be omitted." I included a brief introduction to ten additional topics as an appendix to the first volume, with the tacit understanding that eventually there might be a second volume containing the details. You are now holding that second volume. it turned out that even those ten topics would not fit Unfortunately, into a single book, so I was forced to make some choices. The following material is covered in this book: I. Elliptic and modular functions for the full modular group. II. Elliptic curves with complex multiplication. III. Elliptic surfaces and specialization theorems. IV. Neron models, Kodaira-Neron classification of special fibers, Tate's algorithm, and Ogg's conductor-discriminant formula. V. Tate's theory of q-curves over p-adic fields. VI. Neron's theory of canonical local height functions.

Theory of Complexity
Theory of Complexity

Author: Ricardo López-Ruiz

Publisher: BoD – Books on Demand

Published: 2021-06-30

Total Pages: 112

ISBN-13: 1789852137

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Over two parts, this book examines the meaning of complexity in the context of systems both social and natural. Chapters cover such topics as the traveling salesman problem, models of opinion dynamics creation, a universal theory for knowledge formation in children, the evaluation of landscape organization and dynamics through information entropy indicators, and studying the performance of wind farms using artificial neural networks. We hope that this book will be useful to an audience interested in the different problems and approaches that are used within the theory of complexity

Search Algorithms for Engineering Optimization
Search Algorithms for Engineering Optimization

Author: Taufik Abrão

Publisher: BoD – Books on Demand

Published: 2013-02-13

Total Pages: 296

ISBN-13: 9535109839

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Heuristic Search is an important sub-discipline of optimization theory and finds applications in a vast variety of fields, including life science and engineering. Search methods have been useful in solving tough engineering-oriented problems that either could not be solved any other way or solutions take a very long time to be computed. This book explores a variety of applications for search methods and techniques in different fields of electrical engineering. By organizing relevant results and applications, this book will serve as a useful resource for students, researchers and practitioners to further exploit the potential of search methods in solving hard optimization problems that arise in advanced engineering technologies, such as image and video processing issues, detection and resource allocation in telecommunication systems, security and harmonic reduction in power generation systems, as well as redundancy optimization problem and search-fuzzy learning mechanisms in industrial applications.

Reviews of Nonlinear Dynamics and Complexity
Reviews of Nonlinear Dynamics and Complexity

Author: Heinz Georg Schuster

Publisher: John Wiley & Sons

Published: 2010-07-06

Total Pages: 260

ISBN-13: 9783527630974

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Written in a style that breaks the barriers between the disciplines, this monograph enables researchers from life science, physics, engineering, or chemistry to access the most recent results in a common language. The resulting review character of this project sets it apart from specialized journals, and allows each volume to respond quickly to new developments. This third volume contains new topics ranging from chaotic computing, via random dice tossing and stochastic limit-cycle oscillators, to a number theoretic example of self-organized criticality, wave localization in complex networks and anomalous diffusion. A first-class board of international scientists advises the editor, such that the carefully selected and invited contributions represent the latest and most relevant findings.

Differential Dynamical Systems, Revised Edition
Differential Dynamical Systems, Revised Edition

Author: James D. Meiss

Publisher: SIAM

Published: 2017-01-24

Total Pages: 410

ISBN-13: 161197464X

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Differential equations are the basis for models of any physical systems that exhibit smooth change. This book combines much of the material found in a traditional course on ordinary differential equations with an introduction to the more modern theory of dynamical systems. Applications of this theory to physics, biology, chemistry, and engineering are shown through examples in such areas as population modeling, fluid dynamics, electronics, and mechanics. Differential Dynamical Systems begins with coverage of linear systems, including matrix algebra; the focus then shifts to foundational material on nonlinear differential equations, making heavy use of the contraction-mapping theorem. Subsequent chapters deal specifically with dynamical systems concepts?flow, stability, invariant manifolds, the phase plane, bifurcation, chaos, and Hamiltonian dynamics. This new edition contains several important updates and revisions throughout the book. Throughout the book, the author includes exercises to help students develop an analytical and geometrical understanding of dynamics. Many of the exercises and examples are based on applications and some involve computation; an appendix offers simple codes written in Maple, Mathematica, and MATLAB software to give students practice with computation applied to dynamical systems problems.