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This book explores the impact of nonlinearity on a broad range of areas, including time-honored fields such as biology, geometry, and topology, but also modern ones such as quantum mechanics, networks, metamaterials and artificial intelligence. The concept of nonlinearity is a universal feature in mathematics, physics, chemistry and biology, and is used to characterize systems whose behavior does not amount to a superposition of simple building blocks, but rather features complex and often chaotic patterns and phenomena. Each chapter of the book features a synopsis that not only recaps the recent progress in each field but also charts the challenges that lie ahead. This interdisciplinary book presents contributions from a diverse group of experts from various fields to provide an overview of each field’s past, present and future. It will appeal to both beginners and seasoned researchers in nonlinear science, numerous areas of physics (optics, quantum physics, biophysics), and applied mathematics (ODEs, PDEs, dynamical systems, machine learning) as well as engineering.
This book presents select, recent developments in nonlinear and complex systems reported at the 1st Online Conference on Nonlinear Dynamics and Complexity, held on November 23-25, 2020. It provides an exchange recent developments, discoveries, and progresses in Nonlinear Dynamics and Complexity. The collection presents fundamental and frontier theories and techniques for modern science and technology, stimulates more research interest for exploration of nonlinear science and complexity; and passes along new knowledge and insight to the next generation of engineers and technologists in a range of fields.
For almost ten years chaos and fractals have been enveloping many areas of mathematics and the natural sciences in their power, creativity and expanse. Reaching far beyond the traditional bounds of mathematics and science to the realms of popular culture, they have captured the attention and enthusiasm of a worldwide audience. The fourteen chapters of the book cover the central ideas and concepts, as well as many related topics including, the Mandelbrot Set, Julia Sets, Cellular Automata, L-Systems, Percolation and Strange Attractors, and each closes with the computer code for a central experiment. In the two appendices, Yuval Fisher discusses the details and ideas of fractal image compression, while Carl J.G. Evertsz and Benoit Mandelbrot introduce the foundations and implications of multifractals.
Written in Alwyn Scott’s inimitable style, one that readers will find both lucid and accessible, this masterwork elucidates the explosion of activity in nonlinear science in recent decades. The book explains the wide-ranging implications of nonlinear phenomena for future developments in many areas of modern science, including mathematics, physics, engineering, chemistry, biology, and neuroscience. Arguably as important as quantum theory, modern nonlinear science is essential for understanding the scientific developments of the twenty-first century.
This forward-looking Research Handbook showcases cutting-edge research on the relationship between international migration and digital technology. It sheds new light on the interlinkages between digitalisation and migration patterns and processes globally, capturing the latest research technologies and data sources. Featuring international migration in all facets from the migration of tech sector specialists through to refugee displacement, leading contributors offer strategic insights into the future of migration and mobility.
In a financial revolution, new determinants of performance arise and interest in the way performance is measured and communicated to stakeholders grows. This book presents a wide and accurate analysis of the impact that regulation, structural changes and new financial products have on the performance of markets and intermediaries.
The 2nd edition of this book provides novel topics and studyies in boundaries of networks and Big Data Systems.The central theme of this book is the extent to which the structure of the free dynamical boundaries of a system controls the evolution of the system as a whole. Applying three orthogonal types of thinking - mathematical, constructivist and morphological, it illustrates these concepts using applications to selected problems from the social and life sciences, as well as economics. In a broader context, it introduces and reviews some modern mathematical approaches to the science of complex systems. Standard modeling approaches (based on non-linear differential equations, dynamic systems, graph theory, cellular automata, stochastic processes, or information theory) are suitable for studying local problems. However they cannot simultaneously take into account all the different facets and phenomena of a complex system, and new approaches are required to solve the challenging problem of correlations between phenomena at different levels and hierarchies, their self-organization and memory-evolutive aspects, the growth of additional structures and are ultimately required to explain why and how such complex systems can display both robustness and flexibility. This graduate-level text addresses a broader interdisciplinary audience, keeping the mathematical level essentially uniform throughout the book, and involving only basic elements from calculus, algebra, geometry and systems theory.
Nowadays, graph theory is an important analysis tool in mathematics and computer science. Because of the inherent simplicity of graph theory, it can be used to model many different physical and abstract systems such as transportation and communication networks, models for business administration, political science, and psychology and so on. The purpose of this book is not only to present the latest state and development tendencies of graph theory, but to bring the reader far enough along the way to enable him to embark on the research problems of his own. Taking into account the large amount of knowledge about graph theory and practice presented in the book, it has two major parts: theoretical researches and applications. The book is also intended for both graduate and postgraduate students in fields such as mathematics, computer science, system sciences, biology, engineering, cybernetics, and social sciences, and as a reference for software professionals and practitioners.
When just a handful of economists predicted the 2008 financial crisis, people should wonder how so many well educated people with enormous datasets and computing power can be so wrong. In this short book Ionut Purica joins a growing number of economists who explore the failings of mainstream economics and propose solutions developed in other disciplines, such as sociology and evolutionary biology. While it might be premature to call for a revolution, Dr. Purica echoes John Maynard Keynes in believing that economic ideas are "dangerous for good or evil." In recent years evil seems to have had the upper hand. "Nonlinear Dynamics of Financial Crises" points to their ability to do good. Makes complex economics ideas accessible by carefully explaining technical terms and minimizing mathematics and equations Delivers easily-understood perspectives about the global economy by constructing broad assumptions and conclusions in the face of its infinitely complexity Challenges received economic ideas by focusing on human behavior and the roles it plays in easily-observable recent trends and events
Modern science has abstracted, as compensation for establishing rigorousness, the complexity of the real world, and has inclined toward oversimpli?ed ?ctitious n- ratives; as a result, a disjunction has emerged between the wisdom of science and reality. Re?ecting on this, we see the need for science to recover reality; can it reveal new avenues for thought and investigation of the complexity? The study of science is the pursuit of clarity and distinctness. Physics,after Galilei placed it in the realm of mathematics, has been trying to establish clearness by mathematical logic. While physics and mathematics, respectively, have different intellectual incentives, they have intersected in history on countless occasions and have woven a ?awless system of wisdom. The core of rigorous science is always made of mathematical logic; the laws of science cannot be represented without the language of mathematics. Conversely, it is undoubtedly dif?cult to stimulate ma- ematical intellect without a reference to the interests of science that are directed to the real world. However, various criticisms have been raised against the discourses of sciences that explain the events of the real world as if they are “governed” by mathematical laws. Sciences, being combined with technologies, have permeated, in the form of technical rationalism, the domain of life, politics, and even the psychological world. The criticisms accuse seemingly logical scienti?c narratives of being responsible for widespread destruction and emergence of crises, unprecedented suffering of hum- ity.