This book focuses on the control of fractal behaviors in nonlinear dynamics systems, addressing both the principles and purposes of control. For fractals in different systems, it presents revealing studies on the theory and applications of control, reflecting a spectrum of different control methods used with engineering technology. As such, it will benefit researchers, engineers, and graduate students in fields of fractals, chaos, engineering, etc.

This book reports on the latest findings concerning nonlinear control theory and applications. It presents novel work on several kinds of commonly encountered nonlinear time-delay systems, including those whose nonlinear terms satisfy high-order polynomial form or general nonlinear form, those with nonlinear input or a triangular structure, and so on. As such, the book will be of interest to university researchers, R&D engineers and graduate students in the fields of control theory and control engineering who wish to learn about the core principles, methods, algorithms, and applications of nonlinear time-delay systems.

This book is the first to present the application of the hybrid system theory to systems with EPCA (equations with piecewise continuous arguments). The hybrid system paradigm is a valuable modeling tool for describing a wide range of real-world applications. Moreover, although new technology has produced, and continues to produce highly hierarchical sophisticated machinery that cannot be analyzed as a whole system, hybrid system representation can be used to reduce the structural complexity of these systems. That is to say, hybrid systems have become a modeling priority, which in turn has led to the creation of a promising research field with several application areas. As such, the book explores recent developments in the area of deterministic and stochastic hybrid systems using the Lyapunov and Razumikhin-Lyapunov methods to investigate the systems' properties. It also describes properties such as stability, stabilization, reliable control, H-infinity optimal control, input-to-state stability (ISS)/stabilization, state estimation, and large-scale singularly perturbed systems.

This book expands the foundations of general systems theory to enable progress beyond the rich heuristic practices available today. It establishes a foundational framework for the development of scientific transdisciplinary systems principles and shows how these can amplify the potential of individuals and teams working in multi-, inter- and transdisciplinary contexts or striving to translate their progress across disciplinary boundaries. Three general scientific systems principles are presented, and their relevance to the design, analysis, management and transformation of systems is explored. Applying lessons from the history and philosophy science, this book disambiguates key concepts of general systemology, clarifies the role of general systemology within the field of systemology, and explains how general systemology supports other forms of transdisciplinarity. These insights are used to develop new perspectives, strategies and tools for addressing long-standing challenges to the advancement and transdisciplinary application of general insights into the nature of complex systems.The material presented in this book includes comprehensive models of the structure of systemology as a disciplinary field, the structure and significance of the general systems worldview, and the role of general systemology as the heart of systems science, systems engineering and systems practice. It explains what a fully-fledged general theory of systems would look like, what its potential is, what routes are available to us to develop it further, and how to leverage the knowledge we have attained so far. Many examples and analogies show how general systemology has the potential to enable scientific discovery, insightful theory building, and practical innovation in all the disciplines as they study, design, nurture or transform complex systems. This book is essential reading for anyone wishing to master the concepts, terminology, models and strategies needed to make effective use of current general systems knowledge and to engage in the further development of the philosophy, science, and practice of general systemology.

Around the globe, there is an increasingly urgent need to provide opportunities for learners to embrace complexity; to develop the many skills and habits of mind that are relevant to today's complex and interconnected world; and to make learning more connected to our rapidly changing workplace and society. This presents an opportunity to (1) leverage new paradigms for understanding the structure and function of teaching and learning communities, and (2) to promote new approaches to developing methods, curricular materials, and resources. Network science - the study of connectivity - can play an important role in these activities, both as an important subject in teaching and learning and as a way to develop interconnected curricula. Since 2010, an international community of network science researchers and educators has come together to raise the global level of network literacy by applying ideas from network science to teaching and learning. Network Science in Education - which refers to both this community and to its activities - has evolved in response to the escalating activity in the field of network science and the need for people to be able to access the field through education channels. Network Science In Education: Transformational Approaches in Teaching and Learning appeals to both instructors and professionals, while offering case studies from a wide variety of activities that have been developed around the globe: the creation of entirely new courses and degree programs; tools for K-20 learners, teachers, and the general public; and in-depth analysis of selected programs. As network-based pedagogy and the community of practice continues to grow, we hope that the book's readers will join this vibrant network education community to build on these nascent ideas and help deepen the understanding of networks for all learners.

Control of Discrete-Time Descriptor Systems takes an anisotropy-based approach to the explanation of random input disturbance with an information-theoretic representation. It describes the random input signal more precisely, and the anisotropic norm minimization included in the book enables readers to tune their controllers better through the mathematical methods provided. The book contains numerous examples of practical applications of descriptor systems in various fields, from robotics to economics, and presents an information-theoretic approach to the mathematical description of coloured noise. Anisotropy-based analysis and design for descriptor systems is supplied along with proofs of basic statements, which help readers to understand the algorithms proposed, and to undertake their own numerical simulations. This book serves as a source of ideas for academic researchers and postgraduate students working in the control of discrete-time systems. The control design procedures outlined are numerically effective and easily implementable in MATLAB (R)

This book introduces characteristic features of the protein structure prediction (PSP) problem. It focuses on systematic selection and improvement of the most appropriate metaheuristic algorithm to solve the problem based on a fitness landscape analysis, rather than on the nature of the problem, which was the focus of methodologies in the past. Protein structure prediction is concerned with the question of how to determine the three-dimensional structure of a protein from its primary sequence. Recently a number of successful metaheuristic algorithms have been developed to determine the native structure, which plays an important role in medicine, drug design, and disease prediction. This interdisciplinary book consolidates the concepts most relevant to protein structure prediction (PSP) through global non-convex optimization. It is intended for graduate students from fields such as computer science, engineering, bioinformatics and as a reference for researchers and practitioners.

This book explores Probabilistic Cellular Automata (PCA) from the perspectives of statistical mechanics, probability theory, computational biology and computer science. PCA are extensions of the well-known Cellular Automata models of complex systems, characterized by random updating rules. Thanks to their probabilistic component, PCA offer flexible computing tools for complex numerical constructions, and realistic simulation tools for phenomena driven by interactions among a large number of neighboring structures. PCA are currently being used in various fields, ranging from pure probability to the social sciences and including a wealth of scientific and technological applications. This situation has produced a highly diversified pool of theoreticians, developers and practitioners whose interaction is highly desirable but can be hampered by differences in jargon and focus. This book - just as the workshop on which it is based - is an attempt to overcome these difference and foster interest among newcomers and interaction between practitioners from different fields. It is not intended as a treatise, but rather as a gentle introduction to the role and relevance of PCA technology, illustrated with a number of applications in probability, statistical mechanics, computer science, the natural sciences and dynamical systems. As such, it will be of interest to students and non-specialists looking to enter the field and to explore its challenges and open issues.

This book reveals how open innovation utilizes the developing circle of business models to establish new ones that define a unique link between technology and markets, focusing on how to develop and maintain successful business models. It draws readers into the philosophy and economic effects of open innovation from the outset.It presents four different developing circle business models for customers in the role of consumers, entrepreneurs, social entrepreneurs and engineers respectively, enabling each group to develop, utilize and enlarge creative business models, and even switch business models.In addition to these four circles, it takes a systemic approach to describe the relationship between technology and markets. From this relationship an open innovation strategy towards entrepreneurship can be adopted. From Open Innovation to a Creative Developing-Circle Business Model is an essential resource for start-up entrepreneurs, as well as for students of technology management, strategy and open innovation.

This volume, which is dedicated to Heinz Langer, includes biographical material and carefully selected papers. Heinz Langer has made fundamental contributions to operator theory. In particular, he has studied the domains of operator pencils and nonlinear eigenvalue problems, the theory of indefinite inner product spaces, operator theory in Pontryagin and Krein spaces, and applications to mathematical physics. His works include studies on and applications of Schur analysis in the indefinite setting, where the factorization theorems put forward by Krein and Langer for generalized Schur functions, and by Dijksma-Langer-Luger-Shondin, play a key role. The contributions in this volume reflect Heinz Langer's chief research interests and will appeal to a broad readership whose work involves operator theory.

This book highlights the most important aspects of mathematical modeling, computer simulation, and control of medium-scale power systems. It discusses a number of practical examples based on Sri Lanka's power system, one characterized by comparatively high degrees of variability and uncertainty. Recently introduced concepts such as controlled disintegration to maintain grid stability are discussed and studied using simulations of practical scenarios. Power systems are complex, geographically distributed, dynamical systems with numerous interconnections between neighboring systems. Further, they often comprise a generation mix that includes hydro, thermal, combined cycle, and intermittent renewable plants, as well as considerably extended transmission lines. Hence, the detailed analysis of their transient behaviors in the presence of disturbances is both highly theory-intensive and challenging in practice. Effectively regulating and controlling power system behavior to ensure consistent service quality and transient stability requires the use of various schemes and systems. The book's initial chapters detail the fundamentals of power systems; in turn, system modeling and simulation results using Power Systems Computer Aided Design/Electromagnetic Transients including DC (PSCAD/EMTDC) software are presented and compared with available real-world data. Lastly, the book uses computer simulation studies under a variety of practical contingency scenarios to compare several under-frequency load-shedding schemes. Given the breadth and depth of its coverage, it offers a truly unique resource on the management of medium-scale power systems.

After a short introduction to the fundamentals, this book provides a detailed account of major advances in applying fractional calculus to dynamical systems. Fractional order dynamical systems currently continue to gain further importance in many areas of science and engineering. As with many other approaches to mathematical modeling, the first issue to be addressed is the need to couple a definition of the fractional differentiation or integration operator with the types of dynamical systems that are analyzed. As such, for the fundamentals the focus is on basic aspects of fractional calculus, in particular stability analysis, which is required to tackle synchronization in coupled fractional order systems, to understand the essence of estimators for related integer order systems, and to keep track of the interplay between synchronization and parameter observation. This serves as the common basis for the more advanced topics and applications presented in the subsequent chapters, which include an introduction to the 'Immersion and Invariance' (I&I) methodology, the masterslave synchronization scheme for partially known nonlinear fractional order systems, Fractional Algebraic Observability (FAO) and Fractional Generalized quasi-Synchronization (FGqS) to name but a few. This book is intended not only for applied mathematicians and theoretical physicists, but also for anyone in applied science dealing with complex nonlinear systems.

This book is a tribute to Professor Pedro Gil, who created the Department of Statistics, OR and TM at the University of Oviedo, and a former President of the Spanish Society of Statistics and OR (SEIO). In more than eighty original contributions, it illustrates the extent to which Mathematics can help manage uncertainty, a factor that is inherent to real life. Today it goes without saying that, in order to model experiments and systems and to analyze related outcomes and data, it is necessary to consider formal ideas and develop scientific approaches and techniques for dealing with uncertainty. Mathematics is crucial in this endeavor, as this book demonstrates. As Professor Pedro Gil highlighted twenty years ago, there are several well-known mathematical branches for this purpose, including Mathematics of chance (Probability and Statistics), Mathematics of communication (Information Theory), and Mathematics of imprecision (Fuzzy Sets Theory and others). These branches often intertwine, since different sources of uncertainty can coexist, and they are not exhaustive. While most of the papers presented here address the three aforementioned fields, some hail from other Mathematical disciplines such as Operations Research; others, in turn, put the spotlight on real-world studies and applications. The intended audience of this book is mainly statisticians, mathematicians and computer scientists, but practitioners in these areas will certainly also find the book a very interesting read.

This volume contains the proceedings of the XII Symposium of Probability and Stochastic Processes which took place at Universidad Autonoma de Yucatan in Merida, Mexico, on November 16-20, 2015. This meeting was the twelfth meeting in a series of ongoing biannual meetings aimed at showcasing the research of Mexican probabilists as well as promote new collaborations between the participants. The book features articles drawn from different research areas in probability and stochastic processes, such as: risk theory, limit theorems, stochastic partial differential equations, random trees, stochastic differential games, stochastic control, and coalescence. Two of the main manuscripts survey recent developments on stochastic control and scaling limits of Markov-branching trees, written by Kazutoshi Yamasaki and Benedicte Haas, respectively. The research-oriented manuscripts provide new advances in active research fields in Mexico. The wide selection of topics makes the book accessible to advanced graduate students and researchers in probability and stochastic processes.

This book focuses on theoretical aspects of dynamical systems in the broadest sense. It highlights novel and relevant results on mathematical and numerical problems that can be found in the fields of applied mathematics, physics, mechanics, engineering and the life sciences. The book consists of contributed research chapters addressing a diverse range of problems. The issues discussed include (among others): numerical-analytical algorithms for nonlinear optimal control problems on a large time interval; gravity waves in a reservoir with an uneven bottom; value distribution and growth of solutions for certain Painleve equations; optimal control of hybrid systems with sliding modes; a mathematical model of the two types of atrioventricular nodal reentrant tachycardia; non-conservative instability of cantilevered nanotubes using the Cell Discretization Method; dynamic analysis of a compliant tensegrity structure for use in a gripper application; and Jeffcott rotor bifurcation behavior using various models of hydrodynamic bearings.

This book focuses on approximations under the presence of ordinary and fractional smoothness, presenting both the univariate and multivariate cases. It also explores approximations under convexity and a new trend in approximation theory -approximation by sublinear operators with applications to max-product operators, which are nonlinear and rational providing very fast and flexible approximations. The results presented have applications in numerous areas of pure and applied mathematics, especially in approximation theory and numerical analysis in both ordinary and fractional senses. As such this book is suitable for researchers, graduate students, and seminars of the above disciplines, and is a must for all science and engineering libraries.

1. Lossless Coding.- 2.Universal Coding on Finite Alphabets.- 3.Universal Coding on Infinite Alphabets.- 4.Model Order Estimation.- Notation.- Index.

Winner of the Neumann Prize for the History of Mathematics.

In their second collaboration, biographers Jimmy Soni and Rob Goodman present the story of Claude Shannon—one of the foremost intellects of the twentieth century and the architect of the Information Age, whose insights stand behind every computer built, email sent, video streamed, and webpage loaded. Claude Shannon was a groundbreaking polymath, a brilliant tinkerer, and a digital pioneer. He constructed the first wearable computer, outfoxed Vegas casinos, and built juggling robots. He also wrote the seminal text of the digital revolution, which has been called “the Magna Carta of the Information Age.”

In this elegantly written, exhaustively researched biography, Soni and Goodman reveal Claude Shannon’s full story for the first time. With unique access to Shannon’s family and friends, A Mind at Play brings this singular innovator and always playful genius to life.

This book contains three well-written research tutorials that inform the graduate reader about the forefront of current research in multi-agent optimization. These tutorials cover topics that have not yet found their way in standard books and offer the reader the unique opportunity to be guided by major researchers in the respective fields. Multi-agent optimization, lying at the intersection of classical optimization, game theory, and variational inequality theory, is at the forefront of modern optimization and has recently undergone a dramatic development. It seems timely to provide an overview that describes in detail ongoing research and important trends. This book concentrates on Distributed Optimization over Networks; Differential Variational Inequalities; and Advanced Decomposition Algorithms for Multi-agent Systems. This book will appeal to both mathematicians and mathematically oriented engineers and will be the source of inspiration for PhD students and researchers.

With its intuitive yet rigorous approach to machine learning, this text provides students with the fundamental knowledge and practical tools needed to conduct research and build data-driven products. The authors prioritize geometric intuition and algorithmic thinking, and include detail on all the essential mathematical prerequisites, to offer a fresh and accessible way to learn. Practical applications are emphasized, with examples from disciplines including computer vision, natural language processing, economics, neuroscience, recommender systems, physics, and biology. Over 300 color illustrations are included and have been meticulously designed to enable an intuitive grasp of technical concepts, and over 100 in-depth coding exercises (in Python) provide a real understanding of crucial machine learning algorithms. A suite of online resources including sample code, data sets, interactive lecture slides, and a solutions manual are provided online, making this an ideal text both for graduate courses on machine learning and for individual reference and self-study.

This book offers a detailed investigation of breakdowns in traffic and transportation networks. It shows empirically that transitions from free flow to so-called synchronized flow, initiated by local disturbances at network bottlenecks, display a nucleation-type behavior: while small disturbances in free flow decay, larger ones grow further and lead to breakdowns at the bottlenecks. Further, it discusses in detail the significance of this nucleation effect for traffic and transportation theories, and the consequences this has for future automatic driving, traffic control, dynamic traffic assignment, and optimization in traffic and transportation networks. Starting from a large volume of field traffic data collected from various sources obtained solely through measurements in real world traffic, the author develops his insights, with an emphasis less on reviewing existing methodologies, models and theories, and more on providing a detailed analysis of empirical traffic data and drawing consequences regarding the minimum requirements for any traffic and transportation theories to be valid. The book - proves the empirical nucleation nature of traffic breakdown in networks - discusses the origin of the failure of classical traffic and transportation theories - shows that the three-phase theory is incommensurable with the classical traffic theories, and - explains why current state-of-the art dynamic traffic assignments tend to provoke heavy traffic congestion, making it a valuable reference resource for a wide audience of scientists and postgraduate students interested in the fundamental understanding of empirical traffic phenomena and related data-driven phenomenology, as well as for practitioners working in the fields of traffic and transportation engineering.

Nonlinear Dynamics, Volume 1. Proceedings of the 34th IMAC, A Conference and Exposition on Dynamics of Multiphysical Systems: From Active Materials to Vibroacoustics, 2016, the fi rst volume of ten from the Conference, brings together contributions to this important area of research and engineering. Th e collection presents early fi ndings and case studies on fundamental and applied aspects of Structural Dynamics, including papers on: * Nonlinear Oscillations * Nonlinear Modal Analysis * Nonlinear System Identifi cation * Nonlinear Modeling & Simulation * Nonlinearity in Practice * Nonlinearity in Multi-Physics Systems * Nonlinear Modes and Modal Interactions

This book introduces and discusses the analysis of interacting many-body complex systems exhibiting spontaneous synchronization from the perspective of nonequilibrium statistical physics. While such systems have been mostly studied using dynamical system theory, the book underlines the usefulness of the statistical physics approach to obtain insightful results in a number of representative dynamical settings. Although it is intractable to follow the dynamics of a particular initial condition, statistical physics allows to derive exact analytical results in the limit of an infinite number of interacting units. Chapter one discusses dynamical characterization of individual units of synchronizing systems as well as of their interaction and summarizes the relevant tools of statistical physics. The latter are then used in chapters two and three to discuss respectively synchronizing systems with either a first- or a second-order evolution in time. This book provides a timely introduction to the subject and is meant for the uninitiated as well as for experienced researchers working in areas of nonlinear dynamics and chaos, statistical physics, and complex systems.

This book introduces readers to essential tools for the measurement and analysis of information loss in signal processing systems. Employing a new information-theoretic systems theory, the book analyzes various systems in the signal processing engineer's toolbox: polynomials, quantizers, rectifiers, linear filters with and without quantization effects, principal components analysis, multirate systems, etc. The user benefit of signal processing is further highlighted with the concept of relevant information loss. Signal or data processing operates on the physical representation of information so that users can easily access and extract that information. However, a fundamental theorem in information theory-data processing inequality-states that deterministic processing always involves information loss. These measures form the basis of a new information-theoretic systems theory, which complements the currently prevailing approaches based on second-order statistics, such as the mean-squared error or error energy. This theory not only provides a deeper understanding but also extends the design space for the applied engineer with a wide range of methods rooted in information theory, adding to existing methods based on energy or quadratic representations.

Designed for those wishing to study mathematics beyond linear algebra but unready for abstract material, this "invitation" to the excitement of dynamical systems appeals to readers from a wide range of backgrounds. Rather than taking a theorem-proof-corollary-remark approach, it stresses geometry and intuition. Topics include both the classical theory of linear systems and the modern theory of nonlinear and chaotic systems as well as bifurcation, symbolic dynamics, fractals, and complex systems.
In addition to offering a unified presentation of continuous and discrete time systems, this treatment integrates computing comfortably into the text. Appendixes feature important background material, including a gentle introduction to differential equations and explanations of how to write MATLAB, Mathematica, and C programs to compute dynamical systems. Prerequisites for advanced undergraduates and graduate students include two semesters of calculus and one semester of linear algebra.