Applications of Complex Networks

Francis Lau and Michael Tse

Many natural systems are not evenly distributing the workload among the constituent elements. Typically, in a system that is composed of interconnection of small units (cells or nodes), performance can be optimized by making a small of nodes work harder than the others. Usually when optimization is achieved, the workload distribution follows a power-law distribution. In this project, we try to mimick this natural power-law behavior of physical systems in engineering systems. Some success has been achieved in using such power-law property in coding systems. Specifically we have studied the LDPC decoding algorithm with a complex network node assignment that closely resembles a power-law distribution. The result is a more efficient algorithm requiring less connections of nodes for attaining the same performance.

Nonlinear Dynamics and the Human Cardiovascular System

Michael Small

Cardiac disease is a leading cause of death in much of the developed world. In Chinese traditional medicine, measurement of a patient's pulse is of primary importance in diagnosis of disease. The focus of this work is the application of nonlinear analysis methods; developed in the study of chaotic dynamics; to the characterization and classification of observed cardiac rhythms, and the eventual diagnosis of aberrant cardiovascular conditions. The ultimate aim of this avenue of research is the development of an expert system which can provide diagnosis and prognosis of a patient's physiological state based on non-invasive measurement of either pulse waveform or cardiac electrical potential.

Modeling SARS Propagation with Small-world Networks

Michael Small and Michael Tse

In the Spring of 2003, an epidemic outbreak of an unknown virus affected a few Asian cities (beginning in Guangzhou, propagating to Beijing, and spreading through Hong Kong to Vietnam, Toronto, Singapore and Taiwan), claiming the lives of hundreds and infecting thousands of people. In this project we attempt to model the propagation of the now called SARS virus in terms of small-world networks. The model has been found able to fit the Hong Kong data very well. Based on this model we are able to develop predictive software to aid the prediction and control of the propagation of this disease.

Nonlinear Systems and Time Series Analysis:

Complex Dynamics and Bifurcation in Cortical Synaptic Transmission

Michael Small and Michael Tse

Ingo Kleppe and Hugh Robinson (Cambridge)

This project aims to determine and develop optimal modeling regime for capturing deterministic patterns from multiple synaptic recordings, and to reliably extract qualitative dynamic information from representative models. We also study the bifurcation diagrams and develop quantitative descriptors to distinguish between synaptic behaviors. Our ultimate aim is to develop a deeper understanding of the mechanism underlying synaptic information coding and transmission in the cortex.

Recording of a nucleated patch (the soma of a neuron)

Power Electronics:

Power Factor Correction Converters (Award Winning)

Michael Tse and Martin Chow

Power electronics is an application-driven area and many useful ideas were generated from practical requirements. Circuit theory aspects of power electronics can enrich design and improve understanding, although not as rigorously pursued as in other circuits and systems areas. Our research in this area covers the basic work on applying circuit theoretic principles to analyze, model, synthesize and design power-factor-correction power converter circuits.

Bifurcation Behavior of Power Electronics

Michael Tse and S.C. Wong

Power electronics circuits and systems exhibits very rich nonlinear dynamics. Because nonlinear problems have no unique solution, every power electronic circuit is a distinct problem requiring independent investigation. This line of projects focuses on the nonlinear phenomena of power electronics circuits. So far, we have studied various bifurcation and chaotic behavior of PWM dc/dc converters, current-mode controlled converters, free-running converters, and parallel-connected converters. At present, we are actively studying the inter-connected systems such as those under a master-slave sharing control and central-limit control. Theoretical study of bifurcation in power electronics is also being studied, especially for the general switching systems.

Electronic Ballast Based on a Class E Converter Circuit

Michael Tse and S.C. Wong

Class E circuit has very high efficiency due to zero-voltage switching. Because of the low stress, the circuit can operate at a much higher frequency and the low-cost switch can be employed. This student project [Cheng Tze King (FYP student 2005/06)] has accomplished all the essential designs for powering a normal T8 fluorescent lamp.

Sliding-mode Control Application to Power Electronics

Y.M. Lai and S.C. Tan

Sliding-mode control represents simple robust solution to the control problem for switching converters. Yet, much work has been theoretical. In this project, practical design procedures are developed for the implementation of sliding-mode control as applied to switching dc/dc converters. In particular, we developed hysteresis-based and PWM-based sliding-mode controllers and derived systematic practical design rules.

Color Control and Power Supplies for LED Lights

S.C. Wong and Michael Tse

LEDs will become the main technology for the next generation lighting systems. Precision color control is an important technical problem that remains to be solved. We have developed an effective and low-cost procedure for color control of LEDs, without implementing sensors to the LEDs for feedback control.

Lifetime is an important issue for ballast design for LED applications. We have developed solutions to improve lifetime of power supplies so as to be compatible with the durable LEDs.

Driver Design for LED Lights: Getting More Light Out of the Same Watt (Award Winning)

Y.M. Lai, K.H. Loo, S.C. Tan and Michael Tse

A new driver technique has been proposed. The method gives about 20% more luminance with the same power.

The project won the GOLD MEDAL with JURY’S COMMENDATION at the International Exhibition of Inventions of Geneva in 2009.

LEDs developed in the group; being used in conference room

Communications:

Chaos-Based Communications

Francis Lau and Michael Tse

Chaos has been found useful for spread-spectrum communication. This is a relatively immature area. But as such, there is much room for basic research. Our group works on

1. performance evaluation methods

2. multiple access methods

3. optimal detection

4. channel equalisation

5. basic theory in waveform communication (led by Prof. Geza Kolumban)

Complex Network Approach to Modeling Traffic in Telephone Networks

Michael Tse, Francis Lau and Michael Small

Unlike classical traffic analysis where users are assumed to be connected uniformly, our proposed method employs a scale-free network to model the behavior of telephone users. Each user has a fixed set of acquaintances with whom the user may communicate, and the number of acquaintances follows a power-law distribution. We show that network traffic is greatly influenced by the user network behavior, and that network blocking (call failure) is generally more severe in the case of a scale-free user network. It is also shown that the carried traffic is practically limited by the scale-free property of the user network, rather than by the network capacity.

Complex Networks Applications in Art and Finance

Music, Finance, and Language

Michael Tse, Michael Small and Francis Lau

Research on complex networks has been a subject of rigorous theoretical research in the mathematics and physics research communities in the past decade. The many discoveries that human interactions, man-made and natural networks share a power-law degree distribution and small-world property have clearly indicated a high level of relevance of the study of complex networks with real-world applications. However, progress in applying the theoretical results to solving practical problems is still slow. In this project we apply results of complex networks research in real-world problems. The emphasis is on how complex networks would provide a new perspective on the way problems can be formulated, leading to possible new solution approaches. Examples in engineering, disease transmission, language, music and finance are given.

Additional resources:

Our recent work: “A Network Perspective of Stock Market”

Abstract: http://cktse.eie.polyu.edu.hk/stock/