In this work, I consider the possibility of using typicality-type arguments for understanding intractably complex damped-driven dynamical systems. By approximating such dynamics with appropriately constrained random process, I illustrate quantitative predictive power for some aspects of the motion. In particular, I argue that local dynamical stability, or exit rate, of a state is typically sufficient to predict steady-state probability in such systems -- circumventing the classic no-go theorems via our disorder approximation. I then focus on one consequence of this result: that the most likely long-time configurations should also be the dynamically stable ones. In a strongly-driven system, however, such stability may be hard to achieve, and therefore has interesting implications about the corresponding configurations: they must be well-adapted to the details of the driving forces, their dynamical robustness may be viewed in the context of self-healing, and depending on the drive, they can require substantial collective fine-tuning among the system's degrees of freedom. I confirm the emergence of such adapted states in several example systems, both in simulation and in experiment, and verify a quantitative agreement with the predicted scaling between their steady-state probability and local stability. I then explore several arguments and test-cases suggesting further generality of this framework. While it is not yet clear what the precise limits of applicability are for this approach, our results suggest that the intuition it builds can help with prediction and design in a broad class of complex dynamics.

In the context of this book, adaptation is taken to mean a feature of a system aimed at achieving the best possible performance, when mathematical models of the environment and the system itself are not fully available. This has applications ranging from theories of visual perception and the processing of information, to the more technical problems of friction compensation and adaptive classification of signals in fixed-weight recurrent neural networks. Largely devoted to the problems of adaptive regulation, tracking and identification, this book presents a unifying system-theoretic view on the problem of adaptation in dynamical systems. Special attention is given to systems with nonlinearly parameterized models of uncertainty. Concepts, methods and algorithms given in the text can be successfully employed in wider areas of science and technology. The detailed examples and background information make this book suitable for a wide range of researchers and graduates in cybernetics, mathematical modelling and neuroscience.

Discover a wide range of findings in quantitative complex system science that help us make sense of our complex world. Written at an introductory level, the book provides an accessible entry into this fascinating and vitally important subject.

Information theory and inference, taught together in this exciting textbook, lie at the heart of many important areas of modern technology - communication, signal processing, data mining, machine learning, pattern recognition, computational neuroscience, bioinformatics and cryptography. The book introduces theory in tandem with applications. Information theory is taught alongside practical communication systems such as arithmetic coding for data compression and sparse-graph codes for error-correction. Inference techniques, including message-passing algorithms, Monte Carlo methods and variational approximations, are developed alongside applications to clustering, convolutional codes, independent component analysis, and neural networks. Uniquely, the book covers state-of-the-art error-correcting codes, including low-density-parity-check codes, turbo codes, and digital fountain codes - the twenty-first-century standards for satellite communications, disk drives, and data broadcast. Richly illustrated, filled with worked examples and over 400 exercises, some with detailed solutions, the book is ideal for self-learning, and for undergraduate or graduate courses. It also provides an unparalleled entry point for professionals in areas as diverse as computational biology, financial engineering and machine learning.

The book presents nonlinear, chaotic and fractional dynamics, complex systems and networks, together with cutting-edge research on related topics. The fifteen chapters – written by leading scientists working in the areas of nonlinear, chaotic, and fractional dynamics, as well as complex systems and networks – offer an extensive overview of cutting-edge research on a range of topics, including fundamental and applied research. These include but are not limited to, aspects of synchronization in complex dynamical systems, universality features in systems with specific fractional dynamics, and chaotic scattering. As such, the book provides an excellent and timely snapshot of the current state of research, blending the insights and experiences of many prominent researchers.

Analyzes approaches to the study of complexity in the physical, biological, and social sciences.

Foundations of Computational Intelligence Volume 2: Approximation Reasoning: Theoretical Foundations and Applications Human reasoning usually is very approximate and involves various types of - certainties. Approximate reasoning is the computational modelling of any part of the process used by humans to reason about natural phenomena or to solve real world problems. The scope of this book includes fuzzy sets, Dempster-Shafer theory, multi-valued logic, probability, random sets, and rough set, near set and hybrid intelligent systems. Besides research articles and expository papers on t- ory and algorithms of approximation reasoning, papers on numerical experiments and real world applications were also encouraged. This Volume comprises of 12 chapters including an overview chapter providing an up-to-date and state-of-the research on the applications of Computational Intelligence techniques for - proximation reasoning. The Volume is divided into 2 parts: Part-I: Approximate Reasoning – Theoretical Foundations Part-II: Approximate Reasoning – Success Stories and Real World Applications Part I on Approximate Reasoning – Theoretical Foundations contains four ch- ters that describe several approaches of fuzzy and Para consistent annotated logic approximation reasoning. In Chapter 1, “Fuzzy Sets, Near Sets, and Rough Sets for Your Computational Intelligence Toolbox” by Peters considers how a user might utilize fuzzy sets, near sets, and rough sets, taken separately or taken together in hybridizations as part of a computational intelligence toolbox. In multi-criteria decision making, it is necessary to aggregate (combine) utility values corresponding to several criteria (parameters).