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Percolation in Spatial Networks
Percolation theory is a well studied process utilized by networks theory to understand the resilience of networks under random or targeted attacks. Despite their importance, spatial networks have been less studied under the percolation process compared to the extensively studied non-spatial networks. In this Element, the authors will discuss the developments and challenges in the study of percolation in spatial networks ranging from the classical nearest neighbors lattice structures, through more generalized spatial structures such as networks with a distribution of edge lengths or community structure, and up to spatial networks of networks.
Multilayer Network Science
Networks are convenient mathematical models to represent the structure of complex systems, from cells to societies. In the last decade, multilayer network science – the branch of the field dealing with units interacting in multiple distinct ways, simultaneously – was demonstrated to be an effective modeling and analytical framework for a wide spectrum of empirical systems, from biopolymers networks (such as interactome and metabolomes) to neuronal networks (such as connectomes), from social networks to urban and transportation networks. In this Element, a decade after one of the most seminal papers on this topic, the authors review the most salient features of multilayer network science, covering both theoretical aspects and direct applications to real-world coupled/interdependent systems, from the point of view of multilayer structure, dynamics and function. The authors discuss potential frontiers for this topic and the corresponding challenges in the field for the next future.
Gillespie Algorithms for Stochastic Multiagent Dynamics in Populations and Networks
Many multiagent dynamics can be modeled as a stochastic process in which the agents in the system change their state over time in interaction with each other. The Gillespie algorithms are popular algorithms that exactly simulate such stochastic multiagent dynamics when each state change is driven by a discrete event, the dynamics is defined in continuous time, and the stochastic law of event occurrence is governed by independent Poisson processes. The first main part of this volume provides a tutorial on the Gillespie algorithms focusing on simulation of social multiagent dynamics occurring in populations and networks. The authors clarify why one should use the continuous-time models and the Gillespie algorithms in many cases, instead of easier-to-understand discrete-time models. The remainder of the Element reviews recent extensions of the Gillespie algorithms aiming to add more reality to the model (i.e., non-Poissonian cases) or to speed up the simulations. This title is also available as open access on Cambridge Core.
Fractional Order Systems and Applications in Engineering
Fractional Order Systems and Applications in Engineering presents the use of fractional calculus (calculus of non-integer order) in the description and modelling of systems and in a range of control design and practical applications. The book covers the fundamentals of fractional calculus together with some analytical and numerical techniques, and provides MATLAB® codes for the simulation of fractional-order control (FOC) systems. The use of fractional calculus can improve and generalize well-established control methods and strategies. Many different FOC schemes are presented for control and dynamic systems problems. These extend to the challenging control engineering design problems of rob...
Boolean Networks as Predictive Models of Emergent Biological Behaviors
Interacting biological systems at all organizational levels display emergent behavior. Modeling these systems is made challenging by the number and variety of biological components and interactions – from molecules in gene regulatory networks to species in ecological networks – and the often-incomplete state of system knowledge, such as the unknown values of kinetic parameters for biochemical reactions. Boolean networks have emerged as a powerful tool for modeling these systems. This Element provides a methodological overview of Boolean network models of biological systems. After a brief introduction, the authors describe the process of building, analyzing, and validating a Boolean model. They then present the use of the model to make predictions about the system's response to perturbations and about how to control its behavior. The Element emphasizes the interplay between structural and dynamical properties of Boolean networks and illustrates them in three case studies from disparate levels of biological organization.
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