This book offers a unified perspective on the study of complex systems for scholars of various disciplines, including mathematics, physics, computer science, biology, economics and social science. The contributions, written by leading scientists, cover a broad set of topics, including new approaches to data science, the connection between scaling limits and conformal field theories, and new ideas on the Legendre duality approach in statistical mechanics of disordered systems. The volume moreover explores results on extreme values of correlated random variables and their connection with the Riemann zeta functions, the relation between diffusion phenomena and complex systems, and the Brownian web, which appears as the universal scaling limit of several probabilistic models. Written for researchers from a broad range of scientific fields, this text examines a selection of recent developments in complex systems from a rigorous perspective.

This undergraduate text explores a variety of large-scale phenomena - global warming, ice ages, water, poverty - and uses these case studies as a motivation to explore nonlinear dynamics, power-law statistics, and complex systems. Although the detailed mathematical descriptions of these topics can be challenging, the consequences of a system being nonlinear, power-law, or complex are in fact quite accessible. This book blends a tutorial approach to the mathematical aspects of complex systems together with a complementary narrative on the global/ecological/societal implications of such systems. Nearly all engineering undergraduate courses focus on mathematics and systems which are small scale, linear, and Gaussian. Unfortunately there is not a single large-scale ecological or social phenomenon that is scalar, linear, and Gaussian. This book offers students insights to better understand the large-scale problems facing the world and to realize that these cannot be solved by a single, narrow academic field or perspective. Instead, the book seeks to emphasize understanding, concepts, and ideas, in a way that is mathematically rigorous, so that the concepts do not feel vague, but not so technical that the mathematics get in the way. The book is intended for undergraduate students in a technical domain such as engineering, computer science, physics, mathematics, and environmental studies.

This book is an introduction to the theory, practice, and implementation of the Lattice Boltzmann (LB) method, a powerful computational fluid dynamics method that is steadily gaining attention due to its simplicity, scalability, extensibility, and simple handling of complex geometries. The book contains chapters on the method's background, fundamental theory, advanced extensions, and implementation. To aid beginners, the most essential paragraphs in each chapter are highlighted, and the introductory chapters on various LB topics are front-loaded with special "in a nutshell" sections that condense the chapter's most important practical results. Together, these sections can be used to quickly get up and running with the method. Exercises are integrated throughout the text, and frequently asked questions about the method are dealt with in a special section at the beginning. In the book itself and through its web page, readers can find example codes showing how the LB method can be implemented efficiently on a variety of hardware platforms, including multi-core processors, clusters, and graphics processing units. Students and scientists learning and using the LB method will appreciate the wealth of clearly presented and structured information in this volume.

Arturo Carsetti According to molecular Biology, true invariance (life) can exist only within the framework of ongoing autonomous morphogenesis and vice versa. With respect to this secret dialectics, life and cognition appear as indissolubly interlinked. In this sense, for instance, the inner articulation of conceptual spaces appears to be linked to an inner functional development based on a continuous activity of selection and "anchorage" realised on semantic grounds. It is the work of "invention" and g- eration (in invariance), linked with the "rooting" of meaning, which determines the evolution, the leaps and punctuated equilibria, the conditions related to the unfo- ing of new modalities of invariance, an invariance which is never simple repetition and which springs on each occasion through deep-level processes of renewal and recovery. The selection perpetrated by meaning reveals its autonomy aboveall in its underpinning, in an objective way, the ongoing choice of these new modalities. As such it is not, then, concerned only with the game of "possibles," offering itself as a simple channel for pure chance, but with providing a channel for the articulation of the " le" in the humus of a semantic (and embodied) net in order to prepare the necessary conditionsfor a continuousrenewal and recoveryof original creativity. In effect, it is this autonomy in inventing new possible modules of incompressibility whichdeterminestheactualemergenceofnew(andtrue)creativity, whichalsotakes place through the "narration" of the effected construction.

This book presents the theory and practical applications of the Master equation approach, which provides a powerful general framework for model building in a variety of disciplines. The aim of the book is to not only highlight different mathematical solution methods, but also reveal their potential by means of practical examples. Part I of the book, which can be used as a toolbox, introduces selected statistical fundamentals and solution methods for the Master equation. In Part II and Part III, the Master equation approach is applied to important applications in the natural and social sciences. The case studies presented mainly hail from the social sciences, including urban and regional dynamics, population dynamics, dynamic decision theory, opinion formation and traffic dynamics; however, some applications from physics and chemistry are treated as well, underlining the interdisciplinary modelling potential of the Master equation approach. Drawing upon the author's extensive teaching and research experience and consulting work, the book offers a valuable guide for researchers, graduate students and professionals alike.

The main body of this book is devoted to statistical physics, whereas much less emphasis is given to thermodynamics. In particular, the idea is to present the most important outcomes of thermodynamics - most notably, the laws of thermodynamics - as conclusions from derivations in statistical physics. Special emphasis is on subjects that are vital to engineering education. These include, first of all, quantum statistics, like the Fermi-Dirac distribution, as well as diffusion processes, both of which are fundamental to a sound understanding of semiconductor devices. Another important issue for electrical engineering students is understanding of the mechanisms of noise generation and stochastic dynamics in physical systems, most notably in electric circuitry. Accordingly, the fluctuation-dissipation theorem of statistical mechanics, which is the theoretical basis for understanding thermal noise processes in systems, is presented from a signals-and-systems point of view, in a way that is readily accessible for engineering students and in relation with other courses in the electrical engineering curriculum, like courses on random processes.

This book addresses the processes of stochastic structure formation in two-dimensional geophysical fluid dynamics based on statistical analysis of Gaussian random fields, as well as stochastic structure formation in dynamic systems with parametric excitation of positive random fields f(r,t) described by partial differential equations. Further, the book considers two examples of stochastic structure formation in dynamic systems with parametric excitation in the presence of Gaussian pumping. In dynamic systems with parametric excitation in space and time, this type of structure formation either happens - or doesn't! However, if it occurs in space, then this almost always happens (exponentially quickly) in individual realizations with a unit probability. In the case considered, clustering of the field f(r,t) of any nature is a general feature of dynamic fields, and one may claim that structure formation is the Law of Nature for arbitrary random fields of such type. The study clarifies the conditions under which such structure formation takes place. To make the content more accessible, these conditions are described at a comparatively elementary mathematical level by employing ideas from statistical topography.

The book addresses the problem of calculation of d-dimensional integrals (conditional expectations) in filter problems. It develops new methods of deterministic numerical integration, which can be used to speed up and stabilize filter algorithms. With the help of these methods, better estimates and predictions of latent variables are made possible in the fields of economics, engineering and physics. The resulting procedures are tested within four detailed simulation studies.

This book offers an informal, easy-to-understand account of topics in modern physics and mathematics. The focus is, in particular, on statistical mechanics, soft matter, probability, chaos, complexity, and models, as well as their interplay. The book features 28 key entries and it is carefully structured so as to allow readers to pursue different paths that reflect their interests and priorities, thereby avoiding an excessively systematic presentation that might stifle interest. While the majority of the entries concern specific topics and arguments, some relate to important protagonists of science, highlighting and explaining their contributions. Advanced mathematics is avoided, and formulas are introduced in only a few cases. The book is a user-friendly tool that nevertheless avoids scientific compromise. It is of interest to all who seek a better grasp of the world that surrounds us and of the ideas that have changed our perceptions.

This book collects contributions to the XXIII international conference "Nonlinear dynamics of electronic systems". Topics range from non-linearity in electronic circuits to synchronisation effects in complex networks to biological systems, neural dynamics and the complex organisation of the brain. Resting on a solid mathematical basis, these investigations address highly interdisciplinary problems in physics, engineering, biology and biochemistry.

This book is based on many years of teaching statistical and thermal physics. It assumes no previous knowledge of thermodynamics, kinetic theory, or probability---the only prerequisites are an elementary knowledge of classical and modern physics, and of multivariable calculus. The first half of the book introduces the subject inductively but rigorously, proceeding from the concrete and specific to the abstract and general. In clear physical language the book explains the key concepts, such as temperature, heat, entropy, free energy, chemical potential, and distributions, both classical and quantum. The second half of the book applies these concepts to a wide variety of phenomena, including perfect gases, heat engines, and transport processes. Each chapter contains fully worked examples and real-world problems drawn from physics, astronomy, biology, chemistry, electronics, and mechanical engineering.

This book is a short, but complete, introduction to the Loewner equation and the SLEs, which are a family of random fractal curves, as well as the relevant background in probability and complex analysis. The connection to statistical physics is also developed in the text in an example case. The book is based on a course (with the same title) lectured by the author. First three chapters are devoted to the background material, but at the same time, give the reader a good understanding on the overview on the subject and on some aspects of conformal invariance. The chapter on the Loewner equation develops in detail the connection of growing hulls and the differential equation satisfied by families of conformal maps. The Schramm-Loewner evolutions are defined and their basic properties are studied in the following chapter, and the regularity properties of random curves as well as scaling limits of discrete random curves are investigated in the final chapter. The book is aimed at graduate students or researchers who want to learn the subject fairly quickly.

This book presents an introduction to Evolutionary Game Theory (EGT) which is an emerging field in the area of complex systems attracting the attention of researchers from disparate scientific communities. EGT allows one to represent and study several complex phenomena, such as the emergence of cooperation in social systems, the role of conformity in shaping the equilibrium of a population, and the dynamics in biological and ecological systems.Since EGT models belong to the area of complex systems, statistical physics constitutes a fundamental ingredient for investigating their behavior. At the same time, the complexity of some EGT models, such as those realized by means of agent-based methods, often require the implementation of numerical simulations. Therefore, beyond providing an introduction to EGT, this book gives a brief overview of the main statistical physics tools (such as phase transitions and the Ising model) and computational strategies for simulating evolutionary games (such as Monte Carlo algorithms on lattices). This book will appeal to students and researchers in this burgeoning field of complex systems.

Multilayer networks, in particular multilayer social networks, where users belong to and interact on different networks at the same time, are an active research area in social network analysis, computer science, and physics. These networks have traditionally been studied within these separate research communities, leading to the development of several independent models and methods to deal with the same set of problems. This book unifies and consolidates existing practical and theoretical knowledge on multilayer networks including data collection and analysis, modeling, and mining of multilayer social network systems, the evolution of interconnected social networks, and dynamic processes such as information spreading. A single real dataset is used to illustrate the concepts presented throughout the book, demonstrating both the practical utility and the potential shortcomings of the various methods. Researchers from all areas of network analysis will learn new aspects and future directions of this emerging field.

Thermal physics deals with collections of large numbers of particles - typically 10 to the 23rd power or so. Examples include the air in a balloon, the water in a lake, the electrons in a chunk of metal, and the photons given off by the sun. We can't possibly follow every detail of the motions of so many particles. So in thermal physics we assume that these motions are random, and we use the laws of probability to predict how the material as a whole ought to behave. Alternatively, we can measure the bulk properties of a material, and from these infer something about the particles it is made of. This book will give you a working understanding of thermal physics, assuming that you have already studied introductory physics and calculus. You will learn to apply the general laws of energy and entropy to engines, refrigerators, chemical reactions, phase transformations, and mixtures. You will also learn to use basic quantum physics and powerful statistical methods to predict in detail how temperature affects molecular speeds, vibrations of solids, electrical and magnetic behaviors, emission of light, and exotic low-temperature phenomena. The problems and worked examples explore applications not just within physics but also to engineering, chemistry, biology, geology, atmospheric science, astrophysics, cosmology, and everyday life.

This book systematically interprets and documents new, unifying principles and basic laws describing the most relevant aspects of hierarchy. To do so, it discusses recent experiments and models that are simple and realistic enough to reproduce the observations, and develops concepts for a better understanding of the complexity of systems consisting of many organisms. The book covers systems ranging from flocks of birds to groups of people. Although it focuses on hierarchical collective behavior in general, two aspects pop up in the majority of cases: collective motion and dynamically changing, partially directed networks (and the natural relation between the two). In addition, it offers a brief description of the most relevant definitions and concepts involved in the context of hierarchies, presenting both a review of the current literature and a number of new experimental and computational results in more detail. It is a valuable resource for students and scholars pursuing research on the structure of interactions within the collectives of animals and humans.

This book is an introduction to maximum-entropy models of random graphs with given topological properties and their applications. Its original contribution is the reformulation of many seemingly different problems in the study of both real networks and graph theory within the unified framework of maximum entropy. Particular emphasis is put on the detection of structural patterns in real networks, on the reconstruction of the properties of networks from partial information, and on the enumeration and sampling of graphs with given properties. After a first introductory chapter explaining the motivation, focus, aim and message of the book, chapter 2 introduces the formal construction of maximum-entropy ensembles of graphs with local topological constraints. Chapter 3 focuses on the problem of pattern detection in real networks and provides a powerful way to disentangle nontrivial higher-order structural features from those that can be traced back to simpler local constraints. Chapter 4 focuses on the problem of network reconstruction and introduces various advanced techniques to reliably infer the topology of a network from partial local information. Chapter 5 is devoted to the reformulation of certain "hard" combinatorial operations, such as the enumeration and unbiased sampling of graphs with given constraints, within a "softened" maximum-entropy framework. A final chapter offers various overarching remarks and take-home messages.By requiring no prior knowledge of network theory, the book targets a broad audience ranging from PhD students approaching these topics for the first time to senior researchers interested in the application of advanced network techniques to their field.

Important aspects of social networking analysis are covered in this work by combining experimental and theoretical research. A specific focus is devoted to emerging trends and the industry needs associated with utilizing data mining techniques. Some of the techniques covered include data mining advances in the discovery and analysis of communities, in the personalization of solitary activities (like searches) and social activities (like discovering potential friends), in the analysis of user behavior in open fora (like conventional sites, blogs and fora) and in commercial platforms (like e-auctions), and in the associated security and privacy-preservation challenges; as well as social network modeling, scalable, customizable social network infrastructure construction, and the identification and discovery of dynamic growth and evolution patterns using machine learning approaches or multi-agent based simulation. These topics will be of interest to practitioners and researchers alike in this dynamic and growing field.

This easy-to read book looks at the many ways in which diffusion bears on processes that involve dispersion, starting from the Brownian motion of molecules, covering the invasion of exotic plants, migration of populations, epidemics, and extending to the spreading of languages and ideas. Recently, there has been a growing interest in understanding migrations, diffusion and spreading outside the "hard" natural sciences of physics and chemistry, for example the spreading of plants introduced as a result of globalization. Another fascinating story is that of human migration in the distant past, i.e. the immigration of our ancestors who brought agriculture from the Near East, or the fast spread of the Palaeo-Indians into the Americas after the end of the Ice Age. Likewise, the spread of languages in the past, and even more so the current spread and retreat of languages will be described here in terms of diffusion. By understanding these principles, there is hope that some of the less common languages that are threatened by globalization can be saved. Another important implication discussed by the author concerns the outbreak of epidemics; these may be mitigated if we understand their spreading mechanism. Last but not least the spreading of ideas and innovations, a process which changes the world sometimes faster than we wish, can also be usefully described in this picture.

The lectures in this book provide graduate students and non-specialist researchers with a concise introduction to the concepts and formalism required to reduce the ten-dimensional string theories to the observable four-dimensional space-time - a procedure called string compactification. The text starts with a very brief introduction to string theory, first working out its massless spectrum and showing how the condition on the number of dimensions arises. It then dwells on the different possible internal manifolds, from the simplest to the most relevant phenomenologically, thereby showing that the most elegant description is through an extension of ordinary Riemannian geometry termed generalized geometry, which was first introduced by Hitchin. Last but not least, the authors review open problems in string phenomenology, such as the embedding of the Standard Model and obtaining de Sitter solutions.

The field of ultracold atomic physics has developed rapidly during the last two decades, and currently encompasses a broad range of topics in physics, with a variety of important applications in topics ranging from quantum computing and simulation to quantum metrology, and can be used to probe fundamental many-body effects such as superconductivity and superfluidity. Beginning with the underlying and including the most cutting-edge experimental developments, this textbook covers essential topics such as Bose-Einstein condensation of alkali atoms, studies of BEC-BCS crossover in degenerate Fermi gas, synthetic gauge fields and Hubbard models, and many-body localization and dynamical gauge fields. Key physical concepts, such as symmetry and universality highlight the connections between different systems, and theory is developed with plain derivations supported by experimental results. This self-contained and modern text will be invaluable for researchers, graduate students and advanced undergraduates studying cold atom physics, from both a theoretical and experimental perspective.

Learn classical thermodynamics alongside statistical mechanics with this fresh approach to the subjects. Molecular and macroscopic principles are explained in an integrated, side-by-side manner to give students a deep, intuitive understanding of thermodynamics and equip them to tackle future research topics that focus on the nanoscale. Entropy is introduced from the get-go, providing a clear explanation of how the classical laws connect to the molecular principles, and closing the gap between the atomic world and thermodynamics. Notation is streamlined throughout, with a focus on general concepts and simple models, for building basic physical intuition and gaining confidence in problem analysis and model development. Well over 400 guided end-of-chapter problems are included, addressing conceptual, fundamental, and applied skill sets. Numerous worked examples are also provided together with handy shaded boxes to emphasize key concepts, making this the complete teaching package for students in chemical engineering and the chemical sciences.

Gauge/gravity duality creates new links between quantum theory and gravity. It has led to new concepts in mathematics and physics, and provides new tools to solve problems in many areas of theoretical physics. This book is the first textbook on this important topic, enabling graduate students and researchers in string theory and particle, nuclear and condensed matter physics to get acquainted with the subject. Focusing on the fundamental aspects as well as on the applications, this textbook guides readers through a thorough explanation of the central concepts of gauge/gravity duality. For the AdS/CFT correspondence, it explains in detail how string theory provides the conjectured map. Generalisations to less symmetric cases of gauge/gravity duality and their applications are then presented, in particular to finite temperature and density, hydrodynamics, QCD-like theories, the quark-gluon plasma and condensed matter systems. The textbook features a large number of exercises, with solutions available online at www.cambridge.org/9781107010345.

Analyzing the phase transition from diffusive to localized behavior in a model of directed polymers in a random environment, this volume places particular emphasis on the localization phenomenon. The main questionis: What does the path of a random walk look like if rewards and penalties are spatially randomly distributed?This model, which provides a simplified version of stretched elastic chains pinned by random impurities, has attracted much research activity, but it (and its relatives) still holds many secrets, especially in high dimensions. It has non-gaussian scaling limits and it belongs to the so-called KPZ universality class when the space is one-dimensional. Adopting a Gibbsian approach, using general and powerful tools from probability theory, the discrete model is studied in full generality. Presenting the state-of-the art from different perspectives, and written in the form of a first course on the subject, this monograph is aimed at researchers in probability or statistical physics, but is also accessible to masters and Ph.D. students.

This book presents a detailed study of a system of interacting Brownian motions in one dimension. The interaction is point-like such that the n-th Brownian motion is reflected from the Brownian motion with label n-1. This model belongs to the Kardar-Parisi-Zhang (KPZ) universality class. In fact, because of the singular interaction, many universal properties can be established with rigor. They depend on the choice of initial conditions. Discussion addresses packed and periodic initial conditions (Chapter 5), stationary initial conditions (Chapter 6), and mixtures thereof (Chapter 7). The suitably scaled spatial process will be proven to converge to an Airy process in the long time limit. A chapter on determinantal random fields and another one on Airy processes are added to have the notes self-contained. These notes serve as an introduction to the KPZ universality class, illustrating the main concepts by means of a single model only. The notes will be of interest to readers from interacting diffusion processes and non-equilibrium statistical mechanics.