This fascinating work is devoted to the fundamental phenomenon in physics – synchronization that occurs in coupled non-linear dissipative oscillators. Examples of such systems range from mechanical clocks to population dynamics, from the human heart to neural networks. The main purpose of this book is to demonstrate that the complexity of synchronous patterns of real oscillating systems can be described in the framework of the general approach, and the authors study this phenomenon as applied to oscillations of different types, such as those with periodic, chaotic, noisy and noise-induced nature.
The first textbook that focuses purely on Synchronization - a fundamental challenge in Computer Science that is fast becoming a major performance and design issue for concurrent programming on modern architectures, and for the design of distributed systems.
The field of distributed algorithms revolves around efficiently solving synchronization tasks, such as leader election and consensus. We make contributions towards a better understanding of the complexity of central tasks in standard distributed models. In the population protocols model, we demonstrate how to solve majority and leader election efficiently, in time 0(log2 n), using 0(log n) states per node, for n nodes. Central to our algorithms is a new leaderless phase clock technique. We also prove tight lower bounds on the state complexity of solving these tasks. In shared memory, we prove that any nondeterministic solo terminating consensus algorithm for anonymous processes has to use [omega](n) read-write registers. Then, we show how to solve n-process wait-free consensus by combining synchronization instructions that would be considered “weak” according to Herlihy’s consensus hierarchy. This collapses the hierarchy when instructions can be applied to the same memory location, as is the case in all existing multicore processors. We suggest an alternative hierarchy and provide a practical universal construction using only “weak” instructions, that performs as well as the Compare-and-Swap-based solution. Space complexity of solving k-set agreement is a problem that highlights important gaps in our understanding and state-of-the-art methods. No general lower bound better than 2 is known. We introduce a new technique based on an indirect black-box application of Sperner’s Lemma through an algorithmic reduction to the impossibility of wait-free k-set agreement. We design a simulation such that for any protocol either the simulating processes solve wait-free k-set agreement (impossible), or they simulate an execution of that uses many registers. Finally, time complexity of leader election is a long-standing open problem. We give an algorithm with 0(log* k) time complexity in asynchronous message-passing system, for k participants.
This book constitutes the proceedings of the 23rd International Symposium on Fundamentals of Computation Theory, FCT 2021, held in Athens, Greece, in September 2021. The 30 full papers included in this volume were carefully reviewed and selected from 94 submissions. In addition, the book contains 2 invited talks. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.
The origin of the word synchronization is a greek root, meaning "to share the common time". The original meaning of synchronization has been maintained up to now in the colloquial use of this word, as agreement or correlation in time of different processes. Historically, the analysis of synchronization phenomena in the evolution of dynamical systems has been a subject of active investigation since the earlier days of physics. Recently, the search for synchronization has moved to chaotic systems. In this latter framework, the appearance of collective (synchronized) dynamics is, in general, not trivial. Indeed, a dynamical system is called chaotic whenever its evolution sensitively depends on the initial conditions. The above said implies that two trajectories emerging from two different closeby initial conditions separate exponentially in the course of the time. As a result, chaotic systems intrinsically defy synchronization, because even two identical systems starting from slightly different initial conditions would evolve in time in a unsynchronized manner (the differences in the systems' states would grow exponentially). This is a relevant practical problem, insofar as experimental initial conditions are never known perfectly. The setting of some collective (synchronized) behavior in coupled chaotic systems has therefore a great importance and interest.The subject of the present book is to summarize the recent discoveries involving the study of synchronization in coupled chaotic systems.Not always the word synchronization is taken as having the same colloquial meaning, and one needs to specify what synchrony means in all particular contexts in which we will describe its emergence.The book describes the complete synchronization phenomenon, both for low and for high dimensional situations, and illustrates possible applications in the field of communicating with chaos.Furthermore, the book summarizes the concepts of phase synchronization, lag synchronization, imperfect phase synchronization, and generalized synchronization, describing a general transition scenario between a hierarchy of different types of synchronization for chaotic oscillators.These concepts are extended to the case of structurally different systems, of uncoupled systems subjected to a common external source, of space extended nonlinearly evolving fields, and of dynamical units networking via a complex wiring of connections, giving thus a summary of all possible situations that are encountered in real life and in technology. - Technical, but not specialistic language - About 100 illustrative Figures - Full overview on synchronization phenomena - Review of the main tools and techniques used in the field - Paradigmatic examples and experiments illustrating the basic concepts - Full Reference to the main publications existing in the literature on the subject
The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory. Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find this text a valuable resource in terms of its unusually large collection of results and proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope.
This book brings together two emerging research areas: synchronization in coupled nonlinear systems and complex networks, and study conditions under which a complex network of dynamical systems synchronizes. While there are many texts that study synchronization in chaotic systems or properties of complex networks, there are few texts that consider the intersection of these two very active and interdisciplinary research areas. The main theme of this book is that synchronization conditions can be related to graph theoretical properties of the underlying coupling topology. The book introduces ideas from systems theory, linear algebra and graph theory and the synergy between them that are necessary to derive synchronization conditions. Many of the results, which have been obtained fairly recently and have until now not appeared in textbook form, are presented with complete proofs. This text is suitable for graduate-level study or for researchers who would like to be better acquainted with the latest research in this area. Sample Chapter(s). Chapter 1: Introduction (76 KB). Contents: Graphs, Networks, Laplacian Matrices and Algebraic Connectivity; Graph Models; Synchronization in Networks of Nonlinear Continuous-Time Dynamical Systems; Synchronization in Networks of Coupled Discrete-Time Systems; Synchronization in Network of Systems with Linear Dynamics; Agreement and Consensus Problems in Groups of Interacting Agents. Readership: Graduate students and researchers in physics, applied mathematics and engineering.
