IWCSN'08 Speakers Details (Title/Abstract)
Complex Networks Course
The Complex Networks Course will cover the following topics:
- Motivating Examples in Complex Networks
- Complex Network Models
- Topological Properties of Complex Networks
- Synchronisation Characterisitics and Properties of Complex Networks
- Flocking and Swarming Behaviour as a Complex Network
- Pinning Control of Complex Networks
- Case Studies in Complex Networks including Power Systems, The Internet, etc..
- Future Work and Unanswered Problems.
The Complex Networks Course will be presented by:
- Professor David Hill
- Professor Guanrong Chen
- Professor Xiaofan Wang
Professor Guanrong Chen
Title: Network Synchronizability Analysis: A Graph-Theory Approach
Abstract:
In this talk, we discuss how graph theory may be applied to the analysis of complex network synchronization and synchronizability.
First, we observe that in the study of network synchronizability, network structural parameters (e.g., average path-length, degree distribution, and betweenness centrality) have been the main concern in the past. We show by simple examples of regular symmetrical networks that these parameters may not be good to use — two networks with exactly the same such structural parameters can have very different synchronizabilities.
Then, we notice that another common perception is that a network with more edges should be easier to sync. However, we give several examples to show that generally adding new edges to a network can either increase or decrease the network synchronizability. Nevertheless, we will also show that for networks with disconnected complementary graphs, adding edges never decreases their synchronizabilities.
The most well-known result today is that the synchronizability of a general complex network relies on two major factors — one is the eigenvalues of the Laplace matrix and the other is the synchronized regions. In this regard, on the one hand we show some sharp and attainable bounds for the eigenratio of a network Laplace matrix, especially when the network has subgraphs of the cyclic, bipartite or product types; on the other hand we show that for any positive integer
n, one can always find a network with
n disconnected synchronized regions, where bounded and unbounded synchronized regions may coexist. Since a network with unbounded synchronized regions is easier to analyze, we show how to design a simple rank-1 inner-linking matrix to control the network synchronized regions to become unbounded. This suggests a way to design a controller to enhance the synchronizability by enlarging the synchronized region of a given complex network.
Professor Xiaofan Wang
Title: Some Recent Developments in Flocking Control with Virtual Leaders.
Abstract:
Flocking is the phenomenon in which a large number of agents, using only limited environmental information and simple rules, organize into a coordinated motion. Recently, there has been a surge of interests among control theorists in flocking control problems, partly due to the wide applications of flocking in many control areas including cooperative control of mobile robots and design of mobile sensor networks. In this talk, we will present some of our recent researches on flocking control with virtual leaders.
We revisit a flocking algorithm proposed by Olfati-Saber. We first show that, even when only a fraction of agents are informed, the Olfati-Saber flocking algorithm still enables all the informed agents to move with the desired constant velocity, and an uninformed agent to also move with the same desired velocity if it can be influenced by the informed agents from time to time during the evolution. Numerical simulation demonstrates that a very small group of the informed agents can cause most of the agents to move with the desired velocity and the larger the informed group is the bigger portion of agents will move with the desired velocity.
In the situation where the virtual leader travels with a varying velocity, we propose modification to the Olfati-Saber algorithm and show that the modified algorithm enables the asymptotic tracking of the virtual leader. That is, the position and velocity of the center of mass of all agents will converge exponentially to those of the virtual leader. The convergent rate is also given.
We investigate the problem of controlling a group of mobile autonomous agents to track multiple virtual leaders with varying velocities in the sense that agents with the same virtual leader attain the same velocity and track the corresponding leader. We propose a provably-stable flocking algorithm. Moreover, we show that the position and velocity of the center of the mass of all agents will exponentially converge to weighted average position and velocity of the virtual leaders.
The underlying topology of the network remaining connected frequently enough during the evolution is a basic assumption made in many previous works on coordinated control in a network of multi-agent systems to guarantee the stability of the coordinated motion. However, for a given set of initial conditions, this assumption is very difficult to verify. In particular, connectivity of the initial network can not guarantee connectivity of the network during the evolution. We propose a flocking algorithm with connectivity preserving. This protocol can enable the group to converge at the same position and move with the same velocity while preserving connectivity of the network during the evolution only if the initial network is connected. We investigate the flocking algorithm with a virtual leader and show that all agents can asymptotically attain the desired velocity even if only one agent in the team has access to the virtual leader.
Professor Jurgen Kurths
Title:
Abstract:
Dr Chai Wah Wu
Title: Localization of forcing sites to facilitate synchronization in systems coupled via a complex network.
Abstract:
A network of coupled dynamical systems can exhibit synchronous behavior. This effect can be enhanced by applying external forcing to a subset of systems. In this talk, we look at the conditions for this to occur and how the most effective sites to apply forcing depend on the network topology. In particular, we provide evidence to show that applying forcing to sites with a small average distance to all the sites enhances the network's ability to synchronize.
Professor Jun Zhao
Title: Synchronization of complex dynamical networks with switching topology: a switched system point of view
Abstract:
We study the synchronization problem for complex
dynamical networks with switching topology from a switched system
point of view. The synchronization problem is transformed into the
stability problem for time-varying switched systems. We address two
basic problems: synchronization under arbitrary switching topology,
and synchronization via design of switching within a pre-given
collection of topologies when synchronization can not be achieved by
using any topology alone in this collection. For the both problems,
we first establish synchronization criteria for general connection
topology. Then, under the condition of simultaneous
triangularization of the connection matrices, a common Lyapunov
function (for the first problem) and a single Lyapunov and multiple
Lyapunov functions (for the second problem) are systematically
constructed respectively by those of several lower-dimensional
dynamic systems. In order to achieve synchronization using multiple
Lyapunov functions, a stability condition and switching law design
method for time-varying switched systems are also presented, which
avoid the usual non-increasing condition.
Dr Markus Brede
Title: Enhancing synchronization in systems of non-identical Kuramoto oscillators
Abstract:
In this talk I present results about arrangements of symmetrically coupled non-identical
Kuramoto oscillators that optimize synchronization
properties. The systems synchronization properties are determined by the
coupling architecture and by correlations in the oscillator arrangement on the coupling
network. While the bulk of the recent literature focusses on the relation
between coupling topology and synchronization, I discuss the coevolution of oscillator
arrangement and coupling topology as the systems evolve towards larger degrees of
synchronization.
Crucially, if the total available coupling is large enough to allow for full
synchronization, optimal system arrangements are mainly characterized by strong
anti-correlations between adjacent oscillators.
The heterogeneity in the oscillator population further conditions
deviations of the optimal coupling network from those discussed as the most stable
coupling for identical oscillators via the eigenratio analysis. For example,
oscillators with native frequencies far off the mean require more coupling than
oscillators with native frequencies close to the average frequency, thus generating a
certain amount of heterogeneity in the degree distribution of the optimal coupling
networks.
Demonstrating that the oscillator placement on a network influences the
critical point and the critical exponents, the talk also discusses the influence of
correlations between adjacent oscillators on sparse networks on the synchronization
transition.
Dr Jin Fan
Title: Synchronization of the Kuramoto Model with Multi-Scale-Free Property
Abstract:
Collective synchronization of coupled dynamical systems is an interesting and important phenomenon. One of the most famous framework for the mathematical study of collective synchronization of complex networks is the so-called Kuramoto model. The traditional Kuramoto model assumes that all pairs of oscillators, having unimodal and symmetric distributed frequencies, are connected with the same coupling strength. In the past decades, by exploring many large databases of real-world networks, the scale-free feature has been widely observed in complex network. In general, a network is referred to as a scale-free network, only because its connectivity distribution is in a power-law form. However, besides this heterogeneity in the connectivity distribution, a wide range of heterogeneous properties appears in real-world networks, such as in the weights on connections and parameter in the dynamics of the nodes. We call a network as a multi-scale-free (MSF) network is it has several scale-free features.
Here, we extend investigation to a class of Kuramoto model with the MSF property. We considered the problem of synchronization in a system of coupled oscillators in complex networks for which the topology (connectivity), dynamics of oscillators (natural frequency) and weights on links all follow power-law distributions. We found that homogeneous networks, with homogeneous topology, dynamics of oscillators and weights, have better synchronizability than heterogeneous ones. Moreover, the synchronization when the network parameters are mutual correlated is also investigated. We discovered that connecting more links to the nodes far away from the average frequency, and intentionally assigning large weights on the links between different dynamics nodes, could improve the synchronization of the network.
Professor Michael Tse
Title: Applications of Nodes and Edges: From Science to Art to Finance
Abstract:
In the past decade, complex networks have attracted a great deal of
attention from researchers across a variety of disciplines including
mathematics, science, engineering and humanities. Certain classes of complex
problems, arisen from many different disciplines, have been analyzed from a
networking viewpoint. Results generated from such network based analyses
often yield new insights into the basic structure of the system under study
as well as the way in which the various subsystems interact. The basic
foundation of the analysis is that the system can be broken down into a
large number of basic units or subsystems which are interconnected with one
another, and specifically, the way in which connections are distributed over
the entire system plays an important role in determining the behavior of the
whole system. The basic units or subsystems can be identical or different.
Although a considerable amount of fundamental findings have been reported in
complex networks, such as the general scalefree and small-world properties
of networks arising from human interactions, man-made and natural networks,
the progress of applying complex network analysis to practical problems is
still relatively slow. In this talk we briefly review a few applications.
Our purpose is to show some possible pathways through which practical
problems may be tackled from a network viewpoint, yielding entirely new
insights into the problems. We will first present a brief overview of
networks, and present a few cases of problem formulation in terms of
networks, including telephone traffic analysis, disease transmission
dynamics, music composition and stock market fluctuation.
Professor Ljijjana Trajkovic
Title: Stability Analysis of TCP/RED Communication Algorithms
Abstract:
The Transmission Control Protocol (TCP) with Random Early Detection (RED) mechanism can be viewed as a feedback control system where TCP adjusts its sending rate depending on packet loss.
In this talk, we first describe a simple second-order discrete-time model for the TCP/RED algorithm and investigate bifurcations and chaos in a TCP/RED system with a single TCP connection.
The complex behavior observed in the system is attributed to a class of discontinuity-induced bifurcations observed in piecewise smooth systems.
It has been also observed that the TCP-RED system may exhibit instability and oscillatory behavior. The stability boundary of the TCP-RED system depends on various network parameters, making the adjustment of the RED gateway a difficult task. Based on a fluid-flow model, we formulate analytical conditions that describe the stable boundary of the RED gateway depending on the number of TCP connections. The proposed model accurately generates a stability boundary
surface in a four dimensionalspace, which facilitates the adjustment of parameters for stable operation of the RED gateway. The accuracy of the analytical results has been verified using the ns-2 network simulations.
The proposed control methods have been based on the analytical models that rely on statistical measurements of network parameters. Hence, stability of the TCP-RED system may be also analyzed using the detrended fluctuation analysis (DFA) method, which has been used for detecting long-range correlations in seemingly non-stationary noisy signals. The key indicator emanating from DFA is known as the scaling exponent. By examining the variations of the DFA scaling exponent when varying
system parameters, we were able to quantify the stability of the TCP-RED system in terms of system's characteristics.
Professor Phil Pollett
Title: Stochastic models for population networks.
Abstract:
A metapopulation is a population that is confined to a network of geographically separated habitat patches. Although the individual patches may suffer local extinction, recolonization can occur through dispersal of individuals from other patches. Empirical evidence suggests that a balance between migration and extinction is reached that enables metapopulations to persist for long periods, and there has been considerable interest in developing models that account for the persistence of the population network. Typically, these models do not account specifically for local patch dynamics, nor for the movement of individuals from one patch to another. In this talk I will review some standard stochastic network theory (which was developed largely in engineering contexts) that can be bought to bear on the analysis of metapopulation networks, and show how these more detailed models can be reconciled with the simpler models familiar to ecologists, namely presence-absence models (that record which patches are occupied) and patch-occupancy models (which merely count the number of occupied patches).
Professor Janet Wiles
Title: Complex Systems from DNA to development
Abstract:
Multiple levels of complexity link genotypes to phenotypes, from molecules to minds. Computational modelling is a generic way of studying complexity and provides a basis for exploring the computational properties of biological systems, abstracting over the myriad details of real biology. This talk describes a multi-level approach to modelling three levels of biological complexity: nucleotide sequences, genetic networks and ontogeny (development of an organism). The talk will discuss the role that these intermediate layers play in the complexity of biological systems and the software challenges inherent in such a project.
Professor Dragan Nesic
Title: Networked control systems: an emulation approach to controller design
Abstract:
Emerging control applications, such as drive-by-wire cars, often require
some control loops to be closed over a network. The network operates as
a serial communication channel that transmits signals from many sensors
and actuators in the control system and, possibly, some signals from
other unrelated users that are connected to the network. Motivation for
using this set-up comes from lower cost, ease of maintenance, great
flexibility, as well as low weight and volume. This motivates research
into the emerging class of Networked Control Systems (NCS). The main
issue in NCS is that the serial communication channel has many "nodes"
(groups of sensors and actuators) where only one node can transmit its
value at a time and, hence, access to the channel needs to be scheduled
in an appropriate manner for a proper operation of the system. The
network scheduling algorithm is referred to as a "protocol". We overview
our recent work on a design approach for NCS that resembles controller
emulation for sampled-data systems. In the first step, we design a
controller ignoring the network and, in the second step, we implement
the designed controller over the network with sufficiently fast
transmissions and a given protocol.
Professor Matt James
Title: Quantum Feedback Networks
Abstract:
As quantum technology emerges from the fundamental sciences into engineering, significant questions concerning complexity and networks are being encountered. In this talk I will discuss recent developments in quantum feedback systems, viewed from a networks perspective. I explain how quantum components can be interconnected by boson fields (e.g. optical beams) that serve as quantum 'wires'. This modelling framework provides foundations on which important questions of complexity can be posed. In addition to the many issues encountered in classical networks, quantum networks are based on the laws of quantum mechanics and so unique quantum features and problems, such as entanglement and decoherence, present significant challenge and opportunity.
Dr Jinhu Lu
Title:Topology Identification of Uncertain Complex Dynamical Networks
Abstract:
Complex networks are ubiquitous in the world. Most of real-world complex networks have various uncertain information, such as unknown or uncertain topological structure and node dynamics. The structure identification issue is, therefore, both of theoretical and practical importance for the uncertain complex dynamical networks. This talk initiates a novel approach for identifying the topological structures and the unknown parameters of the uncertain general complex networks with (or without) time delay. In particular, this approach is also effective for the uncertain complex dynamical networks with non-identical nodes. This is a joint work with Hui Liu, Junan Lu, and David Hill.
Dr Alex Kalloniatis
Title: From Boyd to Kuramoto: applying networked dynamical systems to military Command and Control
Abstract:
Military Command and Control (C2), the art and science of expressing the intent for a mission and managing the structures and processes to accomplish it, is embracing the insights of Complex Systems research. One of the outcomes of this is the concept of Network Centricity or Enablement, which is driving changes in many military organisations around the world. Though focused on the significance of complex networks in socio-technical organisations, little of the rich mathematics of complex dynamical systems has yet been applied in these developments. This paper reports on an approach being developed by the author based on the formalism of self-synchronisation on networks encapsulated in models such as that of Kuramoto. This model maps elegantly onto a simple conceptual model for C2, of USAF Colonel John Boyd, which encodes the C2 process as an Observe-Orient-Decide-Act (OODA) loop. In Boyd’s terms, combat involves “getting inside the enemy’s OODA loop”. The explicit aim of net-centricity, in contrast, is to enable self-synchronisation of appropriate clusters of individual OODA loops within a given military organisation seen as a whole, including its tactical, operational and strategic levels. This problem is of more than just military significance, but applies to any human organisation that has a strategic purpose and tactical interfaces with external competitors and clients. What organisational structure and distribution of time-cycles is appropriate given the competing aims of synchronising within the given organisation and being able to respond to changes in the external environment? A mathematical model, based on Kuramoto’s, that addresses this question is proposed and interpreted in the context of the dynamical systems literature.
