Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the tinal question. G. K. Chesterton. The Scandal oj Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics, However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches, It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related, Further. the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces, And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes, They draw upon widely different sections of mathematics.

Mathematical analyses and computational predictions of the behavior of complex systems are needed to effectively deal with weather and climate predictions, for example, and the optimal design of technical processes. Given the random nature of such systems and the recognized relevance of randomness, the equations used to describe such systems usually need to involve stochastics. The basic goal of this book is to introduce the mathematics and application of stochastic equations used for the modeling of complex systems. A first focus is on the introduction to different topics in mathematical analysis. A second focus is on the application of mathematical tools to the analysis of stochastic equations. A third focus is on the development and application of stochastic methods to simulate turbulent flows as seen in reality. This book is primarily oriented towards mathematics and engineering PhD students, young and experienced researchers, and professionals working in the area of stochastic differential equations and their applications. It contributes to a growing understanding of concepts and terminology used by mathematicians, engineers, and physicists in this relatively young and quickly expanding field.

This volume is devoted to original research results and survey articles reviewing recent developments in reduction for stochastic PDEs with multiscale as well as application to science and technology, and to present some future research direction. This volume includes a dozen chapters by leading experts in the area, with a broad audience in mind. It should be accessible to graduate students, junior researchers and other professionals who are interested in the subject. We also take this opportunity to celebrate the contributions of Professor Anthony J Roberts, an internationally leading figure on the occasion of his 60th years birthday in 2017.

The first part of the book provides a pedagogical introduction to the physics of complex systems driven far from equilibrium. In this part we discuss the basic concepts and theoretical techniques which are commonly used to study classical stochastic transport in systems of interacting driven particles. The analytical techniques include mean-field theories, matrix product ansatz, renormalization group, etc. and the numerical methods are mostly based on computer simulations. In the second part of the book these concepts and techniques are applied not only to vehicular traffic but also to transport and traffic-like phenomena in living systems ranging from collective movements of social insects (for example, ants) on trails to intracellular molecular motor transport. These demonstrate the conceptual unity of the fundamental principles underlying the apparent diversity of the systems and the utility of the theoretical toolbox of non-equilibrium statistical mechanics in interdisciplinary research far beyond the traditional disciplinary boundaries of physics. - Leading industry experts provide a broad overview of the interdisciplinary nature of physics - Presents unified descriptions of intracellular, ant, and vehicular traffic from a physics point of view - Applies theoretical methods in practical everyday situations - Reference and guide for physicists, engineers and graduate students

This book contains all invited contributions of an interdisciplinary workshop of the UNESCO working group on systems analysis of the European and North American region entitled "Stochastic Phenomena and Chaotic Behaviour in Complex Systems". The meeting was held at Hotel Winterthalerhof in Flattnitz, Karnten, Austria from June 6-10, 1983. This workshop brought together some 20 mathematicians, physicists, chemists, biologists, psychologists and economists from different European and American coun tries who share a common interest in the dynamics of complex systems and their ana lysis by mathematical techniques. The workshop in Flattnitz continued a series of meetings of the UNESCO working group on systems analysis which started in 1977 in Bucharest and was continued in Cambridge, U.K., 1981 and in Lyon, 1982. The title of the meeting was chosen in order to focus on one of the current problems of the analysis of dynamical systems. A deeper understanding of the vari ous sources of stochasticity is of primary importance for the interpretation of experimental observations. Chaotic dynamics plays a central role since it intro duces a stochastic element into deterministic systems.

Dynamical evolution over long time scales is a prominent feature of all the systems we intuitively think of as complex — for example, ecosystems, the brain or the economy. In physics, the term ageing is used for this type of slow change, occurring over time scales much longer than the patience, or indeed the lifetime, of the observer. The main focus of this book is on the stochastic processes which cause ageing, and the surprising fact that the ageing dynamics of systems which are very different at the microscopic level can be treated in similar ways.The first part of this book provides the necessary mathematical and computational tools and the second part describes the intuition needed to deal with these systems. Some of the first few chapters have been covered in several other books, but the emphasis and selection of the topics reflect both the authors' interests and the overall theme of the book. The second part contains an introduction to the scientific literature and deals in some detail with the description of complex phenomena of a physical and biological nature, for example, disordered magnetic materials, superconductors and glasses, models of co-evolution in ecosystems and even of ant behaviour. These heterogeneous topics are all dealt with in detail using similar analytical techniques.This book emphasizes the unity of complex dynamics and provides the tools needed to treat a large number of complex systems of current interest. The ideas and the approach to complex dynamics it presents have not appeared in book form until now./a

This monograph set presents a consistent and self-contained framework of stochastic dynamic systems with maximal possible completeness. Volume 1 presents the basic concepts, exact results, and asymptotic approximations of the theory of stochastic equations on the basis of the developed functional approach. This approach offers a possibility of both obtaining exact solutions to stochastic problems for a number of models of fluctuating parameters and constructing various asymptotic buildings. Ideas of statistical topography are used to discuss general issues of generating coherent structures from chaos with probability one, i.e., almost in every individual realization of random parameters. The general theory is illustrated with certain problems and applications of stochastic mathematical physics in various fields such as mechanics, hydrodynamics, magnetohydrodynamics, acoustics, optics, and radiophysics.

This unique volume introduces the reader to the mathematical language for complex systems and is ideal for students who are starting out in the study of stochastical dynamical systems. Unlike other books in the field it covers a broad array of stochastic and statistical methods.

These proceedings present the results of the Eleventh International Conference on Dependability and Complex Systems DepCoS-RELCOMEX which took place in a picturesque Brunów Palace in Poland from 27th June to 1st July, 2016. DepCoS-RELCOMEX is a series of international conferences organized annually by Department of Computer Engineering of Wrocław University of Science and Technology since 2006. The roots of the series go as far back as to the seventies of the previous century – the first RELCOMEX conference took place in 1977 – and now its main aim is to promote a multi-disciplinary approach to dependability problems in theory and engineering practice of complex systems. Complex systems, nowadays most often computer-based and distributed, are built upon a variety of technical, information, software and human resources. The challenges in their design, analysis and maintenance not only originate from the involved technical and organizational structures but also from the complexity of the information processes that must be efficiently executed in a diverse, often hostile operational environment. Traditional methods of reliability evaluation focused only on technical resources are usually insufficient in this context and more innovative, multidisciplinary methods of dependability analysis must be applied. The diversity of the topics which need to be considered is well illustrated by the selection of the submissions in these proceedings with their subjects ranging from mathematical models and design methodologies through software engineering and data security issues up to practical problems in technical, e.g. transportation, systems.