Introduction to focus issue: dynamics in systems biology

The methods of nonlinear systems form an extensive toolbox for the study of biology, and systems biology provides a rich source of motivation for the development of new mathematical techniques and the furthering of understanding of dynamical systems. This Focus Issue collects together a large variety of work which highlights the complementary nature of these two fields, showing what each has to offer the other. While a wide range of subjects is covered, the papers often have common themes such as "rhythms and oscillations," "networks and graph theory," and "switches and decision making." There is a particular emphasis on the links between experimental data and modeling and mathematical analysis.     

Introduction to the focus issue on granular materials

In a review paper [H. M. Jaeger, S. R. Nagel, and R. P. Behringer, "Granular solids, liquids and gases," Rev. Mod. Phys. 68, 1259-1273 (1996)] a few years ago, we wrote about granular material as a distinctive form of matter that exhibits behavior rather different from that of ordinary solids, liquids, or gases. We traced this distinction to three characteristic properties. First, the individual particles making up a granular material are typically large so that thermal energy is irrelevant compared to gravitational energy. Consequently, concepts from equilibrium statistical mechanics are often not applicable. Second, the interactions between particles are frictional and can be mobilized to different degrees depending on the preparation history, giving rise to memory effects, i.e., a static pile will remember how it was formed. Third, when particles collide they do so inelastically so that a "gas" of particles will slow down and come to rest in clumps. In the intervening years, the research on granular matter has progressed rapidly and this may be a good time to ask what we have learned since that article was written. In this spirit, the present special issue of the journal Chaos assembles a spectrum of papers discussing recent developments in the field. (c) 1999 American Institute of Physics.     

Introduction to focus issue: design and control of self-organization in distributed active systems

Spatiotemporal self-organization is found in a wide range of distributed dynamical systems. The coupling of the active elements in these systems may be local or global or within a network, and the interactions may be diffusive or nondiffusive in nature. The articles in this focus issue describe biological and chemical systems designed to exhibit spatiotemporal dynamics and the control of such dynamics through feedback methods.     

Introduction to focus issue: mixed mode oscillations: experiment, computation, and analysis

Mixed mode oscillations (MMOs) occur when a dynamical system switches between fast and slow motion and small and large amplitude. MMOs appear in a variety of systems in nature, and may be simple or complex. This focus issue presents a series of articles on theoretical, numerical, and experimental aspects of MMOs. The applications cover physical, chemical, and biological systems.     

Introduction to Focus Issue: synchronization and cascading processes in complex networks

The study of collective dynamics in complex networks has emerged as a next frontier in the science of networks. This Focus Issue presents the latest developments on this exciting front, focusing in particular on synchronous and cascading dynamics, which are ubiquitous forms of network dynamics found in a wide range of physical, biological, social, and technological systems.     

Introduction to focus issue: intrinsic and designed computation: information processing in dynamical systems--beyond the digital hegemony

How dynamical systems store and process information is a fundamental question that touches a remarkably wide set of contemporary issues: from the breakdown of Moore's scaling laws--that predicted the inexorable improvement in digital circuitry--to basic philosophical problems of pattern in the natural world. It is a question that also returns one to the earliest days of the foundations of dynamical systems theory, probability theory, mathematical logic, communication theory, and theoretical computer science. We introduce the broad and rather eclectic set of articles in this Focus Issue that highlights a range of current challenges in computing and dynamical systems.     

Introduction to focus issue on "randomness, structure, and causality: measures of complexity from theory to applications"

We introduce the contributions to this Focus Issue and describe their origin in a recent Santa Fe Institute workshop.     

Introduction: optimization in networks

The recent surge in the network modeling of complex systems has set the stage for a new era in the study of fundamental and applied aspects of optimization in collective behavior. This Focus Issue presents an extended view of the state of the art in this field and includes articles from a large variety of domains in which optimization manifests itself, including physical, biological, social, and technological networked systems.     

Quasi-coarse-grained dynamics: modelling of metallic materials at mesoscales

A computationally efficient modelling method called quasi-coarse-grained dynamics (QCGD) is developed to expand the capabilities of molecular dynamics (MD) simulations to model behaviour of metallic materials at the mesoscales. This mesoscale method is based on solving the equations of motion for a chosen set of representative atoms from an atomistic microstructure and using scaling relationships for the atomic-scale interatomic potentials in MD simulations to define the interactions between representative atoms. The scaling relationships retain the atomic-scale degrees of freedom and therefore energetics of the representative atoms as would be predicted in MD simulations. The total energetics of the system is retained by scaling the energetics and the atomic-scale degrees of freedom of these representative atoms to account for the missing atoms in the microstructure. This scaling of the energetics renders improved time steps for the QCGD simulations. The success of the QCGD method is demonstrated by the prediction of the structural energetics, high-temperature thermodynamics, deformation behaviour of interfaces, phase transformation behaviour, plastic deformation behaviour, heat generation during plastic deformation, as well as the wave propagation behaviour, as would be predicted using MD simulations for a reduced number of representative atoms. The reduced number of atoms and the improved time steps enables the modelling of metallic materials at the mesoscale in extreme environments.     

Editorial for focus issue on microwave photonics

<正>Microwave photonic components and subsystems can replace or complement their electronic counterparts with a net gain in functionality,bandwidth,size,mass,complexity,and cost,facilitating the innovative implementation of radio frequency(RF)systems due to broad bandwidth,low loss,light weight,flat frequency response,favorable isolation,and immunity to electromagnetic interference(EMI)provided by photonic technologies.Much attention has been recently paid to this area,     

A generalized approach to complex networks

This work describes how the formalization of complex network concepts in terms of discrete mathematics, especially mathematical morphology, allows a series of generalizations and important results ranging from new measurements of the network topology to new network growth models. First, the concepts of node degree and clustering coefficient are extended in order to characterize not only specific nodes, but any generic subnetwork. Second, the consideration of distance transform and rings are used to further extend those concepts in order to obtain a signature, instead of a single scalar measurement, ranging from the single node to whole graph scales. The enhanced discriminative potential of such extended measurements is illustrated with respect to the identification of correspondence between nodes in two complex networks, namely a protein-protein interaction network and a perturbed version of it.     

Paths to synchronization on complex networks

The understanding of emergent collective phenomena in natural and social systems has driven the interest of scientists from different disciplines during decades. Among these phenomena, the synchronization of a set of interacting individuals or units has been intensively studied because of its ubiquity in the natural world. In this Letter, we show how for fixed coupling strengths local patterns of synchronization emerge differently in homogeneous and heterogeneous complex networks, driving the process towards a certain global synchronization degree following different paths. The dependence of the dynamics on the coupling strength and on the topology is unveiled. This study provides a new perspective and tools to understand this emerging phenomena.     

Dynamics-driven evolution to structural heterogeneity in complex networks

The mutual influence of dynamics and structure is a central issue in complex systems. In this paper we study by simulation slow evolution of network under the feedback of a local-majority-rule opinion process. If performance-enhancing local mutations have higher chances of getting integrated into its structure, the system can evolve into a highly heterogeneous small-world with a global hub (whose connectivity is proportional to the network size), strong local connection correlations and power-law-like degree distribution. Networks with better dynamical performance are achieved if structural evolution occurs much slower than the network dynamics. Structural heterogeneity of many biological and social dynamical systems may also be driven by various dynamics-structure coupling mechanisms.     

Optimal traffic networks topology: A complex networks perspective

We investigate and analyse an optimal traffic network structure for resisting traffic congestion with different volumes of traffic. For this aim, we introduce a cost function and user-equilibrium assignment (UE) which ensures the flow balance on traffic systems. Our finding is that an optimal network is strongly dependent on the total system flow. And the random network is most desirable when the system flow is small. But for the larger volume of traffic, the network with power-law degree distribution is the optimal one. Further study indicates, for scale-free networks, that the degree distribution exponent has large effects on the congestion of traffic network. Therefore, the volume of traffic and characteristic of network determine the optimal network structure so as to minimize the side-effect produced by traffic congestion.