Elements in Structure and Dynamics of Complex Netw

Complex networks are typically not homogeneous, as they tend to display an array of structures at different scales. A feature that has attracted a lot of research is their modular organisation, i.e., networks may often be considered as being composed of certain building blocks, or modules. In this Element, the authors discuss a number of ways in which this idea of modularity can be conceptualised, focusing specifically on the interplay between modular network structure and dynamics taking place on a network. They discuss, in particular, how modular structure and symmetries may impact on network dynamics and, vice versa, how observations of such dynamics may be used to infer the modular structure. They also revisit several other notions of modularity that have been proposed for complex networks and show how these can be related to and interpreted from the point of view of dynamical processes on networks.

In many systems consisting of interacting subsystems, the complex interactions between elements can be represented using multilayer networks. However percolation, key to understanding connectivity and robustness, is not trivially generalised to multiple layers. This Element describes a generalisation of percolation to multilayer networks: weak multiplex percolation. A node belongs to a connected component if at least one of its neighbours in each layer is in this component. The authors fully describe the critical phenomena of this process. In two layers with finite second moments of the degree distributions the authors observe an unusual continuous transition with quadratic growth above the threshold. When the second moments diverge, the singularity is determined by the asymptotics of the degree distributions, creating a rich set of critical behaviours. In three or more layers the authors find a discontinuous hybrid transition which persists even in highly heterogeneous degree distribu

Real networks comprise from hundreds to millions of interacting elements and permeate all contexts, from technology to biology to society. All of them display non-trivial connectivity patterns, including the small-world phenomenon, making nodes to be separated by a small number of intermediate links. As a consequence, networks present an apparent lack of metric structure and are difficult to map. Yet, many networks have a hidden geometry that enables meaningful maps in the two-dimensional hyperbolic plane. The discovery of such hidden geometry and the understanding of its role have become fundamental questions in network science giving rise to the field of network geometry. This Element reviews fundamental models and methods for the geometric description of real networks with a focus on applications of real network maps, including decentralized routing protocols, geometric community detection, and the self-similar multiscale unfolding of networks by geometric renormalization.

Higher-order networks describe the many-body interactions of a large variety of complex systems, ranging from the the brain to collaboration networks. Simplicial complexes are generalized network structures which allow us to capture the combinatorial properties, the topology and the geometry of higher-order networks. Having been used extensively in quantum gravity to describe discrete or discretized space-time, simplicial complexes have only recently started becoming the representation of choice for capturing the underlying network topology and geometry of complex systems. This Element provides an in-depth introduction to the very hot topic of network theory, covering a wide range of subjects ranging from emergent hyperbolic geometry and topological data analysis to higher-order dynamics. This Elements aims to demonstrate that simplicial complexes provide a very general mathematical framework to reveal how higher-order dynamics depends on simplicial network topology and geometry.

Complex networks datasets often come with the problem of missing information: interactions data that have not been measured or discovered, may be affected by errors, or are simply hidden because of privacy issues. This Element provides an overview of the ideas, methods and techniques to deal with this problem and that together define the field of network reconstruction. Given the extent of the subject, the authors focus on the inference methods rooted in statistical physics and information theory. The discussion is organized according to the different scales of the reconstruction task, that is, whether the goal is to reconstruct the macroscopic structure of the network, to infer its mesoscale properties, or to predict the individual microscopic connections.

This volume details the importance of multiple experimental techniques and computational methods needed to obtain the comprehensive picture of protein complex structure, dynamics and assembly afforded

A landmark book that strives to provide both grand theory and practical application, innovatively describing the structure and dynamics of human ecosystems As the world faces ever more complex an

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 structu

This book covers the wide spectrum of system dynamics methodology for modeling and simulation of complex systems: systems thinking, causal diagrams, systems structure of stock and flow diagrams, param

This monograph is devoted to problems of propagation and stability of linear and nonlinear waves in continuous media with complex structure. It considers the different media, such as solid with caviti

This atlas provides a detailed insight into the complex structure and organization of cells and tissues, and highlights their specific functions as well as the dynamics of diverse intracellular proces

Understanding Complex Ecosystem Dynamics: A Systems and Engineering Perspective takes a fresh, interdisciplinary perspective on complex system dynamics, beginning with a discussion of relevant systems

This award-winning thesis investigates the mechanisms underlying cardiac arrhythmia development and termination from an entirely new perspective. By viewing the heart as a complex system, the author u

Robert Siegfried presents a framework for efficient agent-based modeling and simulation of complex systems. He compares different approaches for describing structure and dynamics of agent-based models

This book considers the technological and social evolutionary forces that shaped modern telecommunication technology, and contemplates how these forces may structure it in the future. It analyzes netw

This first systematic scientific reference in the area of micro and nanostructured biopolymer systems discusses in two volumes the morphology, structure, dynamics, properties and applications of all i

This volume considers experimental and theoretical dielectric studies of the structure and dynamics of complex systems. Complex systems constitute an almost universal class of materials including ass

This volume considers experimental and theoretical dielectric studies of the structure and dynamics of complex systems. Complex systems constitute an almost universal class of materials including ass

Models of Science Dynamics aims to capture the structure and evolution of science, the emerging arena in which scholars, science and the communication of science become themselves the basic objects of

The conference volume of the Bochumer Kolleg “Dynamics in the History of Religions between Asia and Europe” outlines the thesis that religion is not a homogeneous cultural phenomenon, but a dense netw

Sounding Out Food Quality is focused on sound science-based description of ultrasonic techniques that can be used to analyze the material properties, the structure, and the dynamics of soft materials

Mammalian spermatozoa have complex structures. The structure-function relationship of sperm has been studied from various viewpoints. Accumulated evidence has shown that the sperm components undergo s

This collection, with 17 carefully selected contributions on the field of complex dynamics and adjacent fields, helps people get an overview of the active field of complex dynamics in its current scop

This volume presents a comprehensive introduction into rigorous geometrical dynamics of complex systems of various natures. By "complex systems", in this book are meant high-dimensional nonlinear syst

In recent decades, the biosphere has become increasingly stressed, often beyond the point where the internal structure and function of ecosystems are sustained. We have experienced an intensified R

The book introduces the bioinformatics tools, databases and strategies for the translational research, focuses on the biomarker discovery based on integrative data analysis and systems biological netw

This book introduces readers to MesoBioNano (MBN) Explorer – a multi-purpose software package designed to model molecular systems at various levels of size and complexity. In addition, it presents a s

This book is the culmination of three years of research effort on a multidisciplinary project in which physicists, mathematicians, computer scientists and social scientists worked together to arrive a

This book focuses on structure-preserving numerical methods for flexible multibody dynamics, including nonlinear elastodynamics and geometrically exact models for beams and shells. It also deals with

Whereas the first volume deals with the fundamentals, this volume is dedicated to applications in various civil engineering problems, related to dynamic soil-structure interaction, machine foundation

Maritime transport is one of the most ancient supports to human interactions across history and it still supports more than 90% of world trade volumes today. The changing connectivity of maritime netw

Maritime transport is one of the most ancient supports to human interactions across history and it still supports more than 90% of world trade volumes today. The changing connectivity of maritime netw

An invaluable resource for computational biologists and researchers from other fields seeking an introduction to the topic, Chromatin: Structure, Dynamics, Regulation offers comprehensive coverage of