Permutation Complexity in Dynamical Systems

Permutation Complexity in Dynamical Systems
Author: José Amigó
Publisher: Springer Science & Business Media
Total Pages: 260
Release: 2010-03-20
Genre: Science
ISBN: 3642040845

The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.

Nonlinear Optical Cavity Dynamics

Nonlinear Optical Cavity Dynamics
Author: Philippe Grelu
Publisher: John Wiley & Sons
Total Pages: 456
Release: 2015-12-23
Genre: Science
ISBN: 3527685812

By recirculating light in a nonlinear propagation medium, the nonlinear optical cavity allows for countless options of light transformation and manipulation. In passive media, optical bistability and frequency conversion are central figures. In active media, laser light can be generated with versatile underlying dynamics. Emphasizing on ultrafast dynamics, the vital arena for the information technology, the soliton is a common conceptual keyword, thriving into its modern developments with the closely related denominations of dissipative solitons and cavity solitons. Recent technological breakthroughs in optical cavities, from micro-resonators to ultra-long fiber cavities, have entitled the exploration of nonlinear optical dynamics over unprecedented spatial and temporal orders of magnitude. By gathering key contributions by renowned experts, this book aims at bridging the gap between recent research topics with a view to foster cross-fertilization between research areas and stimulating creative optical engineering design.

Developments in Language Theory

Developments in Language Theory
Author: Igor Potapov
Publisher: Springer
Total Pages: 459
Release: 2015-07-17
Genre: Computers
ISBN: 3319215000

This book constitutes the proceedings of the 19th International Conference on Developments in Language Theory, DLT 2015, held in Liverpool, UK. The 31 papers presented together with 5 invited talks were carefully reviewed and selected from 54 submissions. Its scope is very general and includes, among others, the following topics and areas: combinatorial and algebraic properties of words and languages, grammars, acceptors and transducers for strings, trees, graphs, arrays, algebraic theories for automata and languages, codes, efficient text algorithms, symbolic dynamics, decision problems, relationships to complexity theory and logic, picture description and analysis, polyominoes and bidimensional patterns, cryptography, concurrency, cellular automata, bio-inspired computing, and quantum computing.

Mathematics of Complexity and Dynamical Systems

Mathematics of Complexity and Dynamical Systems
Author: Robert A. Meyers
Publisher: Springer Science & Business Media
Total Pages: 1885
Release: 2011-10-05
Genre: Mathematics
ISBN: 1461418054

Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.

Signal Processing Techniques for Computational Health Informatics

Signal Processing Techniques for Computational Health Informatics
Author: Md Atiqur Rahman Ahad
Publisher: Springer Nature
Total Pages: 347
Release: 2020-10-07
Genre: Technology & Engineering
ISBN: 3030549321

This book focuses on signal processing techniques used in computational health informatics. As computational health informatics is the interdisciplinary study of the design, development, adoption and application of information and technology-based innovations, specifically, computational techniques that are relevant in health care, the book covers a comprehensive and representative range of signal processing techniques used in biomedical applications, including: bio-signal origin and dynamics, sensors used for data acquisition, artefact and noise removal techniques, feature extraction techniques in the time, frequency, time–frequency and complexity domain, and image processing techniques in different image modalities. Moreover, it includes an extensive discussion of security and privacy challenges, opportunities and future directions for computational health informatics in the big data age, and addresses the incorporation of recent techniques from the areas of artificial intelligence, deep learning and human–computer interaction. The systematic analysis of the state-of-the-art techniques covered here helps to further our understanding of the physiological processes involved and expandour capabilities in medical diagnosis and prognosis. In closing, the book, the first of its kind, blends state-of-the-art theory and practices of signal processing techniques inthe health informatics domain with real-world case studies building on those theories. As a result, it can be used as a text for health informatics courses to provide medics with cutting-edge signal processing techniques, or to introducehealth professionals who are already serving in this sector to some of the most exciting computational ideas that paved the way for the development of computational health informatics.

Concepts and Recent Advances in Generalized Information Measures and Statistics

Concepts and Recent Advances in Generalized Information Measures and Statistics
Author: Andres M. Kowalski, Raul D. Rossignoli and Evaldo M. F. Curado
Publisher: Bentham Science Publishers
Total Pages: 432
Release: 2013-12-13
Genre: Science
ISBN: 1608057607

Since the introduction of the information measure widely known as Shannon entropy, quantifiers based on information theory and concepts such as entropic forms and statistical complexities have proven to be useful in diverse scientific research fields. This book contains introductory tutorials suitable for the general reader, together with chapters dedicated to the basic concepts of the most frequently employed information measures or quantifiers and their recent applications to different areas, including physics, biology, medicine, economics, communication and social sciences. As these quantifiers are powerful tools for the study of general time and data series independently of their sources, this book will be useful to all those doing research connected with information analysis. The tutorials in this volume are written at a broadly accessible level and readers will have the opportunity to acquire the knowledge necessary to use the information theory tools in their field of interest.

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors

Nonlinear Dynamics and Entropy of Complex Systems with Hidden and Self-excited Attractors
Author: Christos Volos
Publisher: MDPI
Total Pages: 290
Release: 2019-05-03
Genre: Technology & Engineering
ISBN: 3038978981

In recent years, entropy has been used as a measure of the degree of chaos in dynamical systems. Thus, it is important to study entropy in nonlinear systems. Moreover, there has been increasing interest in the last few years regarding the novel classification of nonlinear dynamical systems including two kinds of attractors: self-excited attractors and hidden attractors. The localization of self-excited attractors by applying a standard computational procedure is straightforward. In systems with hidden attractors, however, a specific computational procedure must be developed, since equilibrium points do not help in the localization of hidden attractors. Some examples of this kind of system are chaotic dynamical systems with no equilibrium points; with only stable equilibria, curves of equilibria, and surfaces of equilibria; and with non-hyperbolic equilibria. There is evidence that hidden attractors play a vital role in various fields ranging from phase-locked loops, oscillators, describing convective fluid motion, drilling systems, information theory, cryptography, and multilevel DC/DC converters. This Special Issue is a collection of the latest scientific trends on the advanced topics of dynamics, entropy, fractional order calculus, and applications in complex systems with self-excited attractors and hidden attractors.

Nonlinear Systems

Nonlinear Systems
Author:
Publisher: BoD – Books on Demand
Total Pages: 288
Release: 2020-05-13
Genre: Mathematics
ISBN: 1789854717

The editors of this book have incorporated contributions from a diverse group of leading researchers in the field of nonlinear systems. To enrich the scope of the content, this book contains a valuable selection of works on fractional differential equations.The book aims to provide an overview of the current knowledge on nonlinear systems and some aspects of fractional calculus. The main subject areas are divided into two theoretical and applied sections. Nonlinear systems are useful for researchers in mathematics, applied mathematics, and physics, as well as graduate students who are studying these systems with reference to their theory and application. This book is also an ideal complement to the specific literature on engineering, biology, health science, and other applied science areas. The opportunity given by IntechOpen to offer this book under the open access system contributes to disseminating the field of nonlinear systems to a wide range of researchers.

Complexity in Economic and Social Systems

Complexity in Economic and Social Systems
Author: Stanisław Drożdż
Publisher: MDPI
Total Pages: 534
Release: 2021-05-11
Genre: Business & Economics
ISBN: 3036507949

There is no term that better describes the essential features of human society than complexity. On various levels, from the decision-making processes of individuals, through to the interactions between individuals leading to the spontaneous formation of groups and social hierarchies, up to the collective, herding processes that reshape whole societies, all these features share the property of irreducibility, i.e., they require a holistic, multi-level approach formed by researchers from different disciplines. This Special Issue aims to collect research studies that, by exploiting the latest advances in physics, economics, complex networks, and data science, make a step towards understanding these economic and social systems. The majority of submissions are devoted to financial market analysis and modeling, including the stock and cryptocurrency markets in the COVID-19 pandemic, systemic risk quantification and control, wealth condensation, the innovation-related performance of companies, and more. Looking more at societies, there are papers that deal with regional development, land speculation, and the-fake news-fighting strategies, the issues which are of central interest in contemporary society. On top of this, one of the contributions proposes a new, improved complexity measure.

Time Series Analysis and Forecasting

Time Series Analysis and Forecasting
Author: Ignacio Rojas
Publisher: Springer
Total Pages: 383
Release: 2016-05-30
Genre: Business & Economics
ISBN: 3319287257

This volume presents selected peer-reviewed contributions from The International Work-Conference on Time Series, ITISE 2015, held in Granada, Spain, July 1-3, 2015. It discusses topics in time series analysis and forecasting, advanced methods and online learning in time series, high-dimensional and complex/big data time series as well as forecasting in real problems. The International Work-Conferences on Time Series (ITISE) provide a forum for scientists, engineers, educators and students to discuss the latest ideas and implementations in the foundations, theory, models and applications in the field of time series analysis and forecasting. It focuses on interdisciplinary and multidisciplinary research encompassing the disciplines of computer science, mathematics, statistics and econometrics.