Project Abstracts

These scholars give seminars, workshops and some public lectures. IRMACS facilities will be used to collaborate locally, to participate internationally in distributed seminars, and to establish a strong web presence. Research projects include: Mathematics and WWI; Ancient Greek and Medieval Islamic Mathematics; Visualization and the Historical Use of Diagrams in Mathematics; Canada and the International Mathematical Community; and the History of Differential and Integral Equations.

ICURS blends expert knowledge in government departments with leading edge theory and research in universities. Its goal is to work thematically across the disciplines of criminology, computing science, geography, economics, and applied mathematics to make advances in understanding and modeling of the complex urban environment, and with these models better understand how to improve approaches to crime reduction and the use of informatics in criminological research.

More and more sequences of expressed antibody genes are being examined in patients with specific diseases. Based on these sequences, researchers have observed distinct patterns of V-gene usage and somatic mutation. For example, specific types of somatic mutations are characteristic of autoimmune diseases, whereas HIV-1 infection may be characterized by the use of certain families of V-Genes.

This more sophisticated and statistically sound understanding of the patterns of V-gene usage and somatic mutation is critical to both vaccine development and understanding autoimmune diseases.

Students in this program come from diverse backgrounds in the applied and natural sciences and it is felt that only through frequent interaction with each other will these students truly be able to benefit from their interdisciplinary knowledge. However, currently the students in this funded program have no "home". There has therefore been a strong endorsement by the Director of this program, Steven Jones (BCGSC and adjunct of MBB), the SFU co-Director of this program, David Baillie (MBB), and members of the program committee, that these students be housed in the IRMACS facility as "regular" members. It is hoped that a bioinformatics core centered around this program and located in IRMACS will benefit greatly from interaction with other researchers in this interdisciplinary facility. These students, with their own interdisciplinary background will also hopefully benefit other researchers in the facility, and may help stimulate further collaborations within different research groups at SFU.

There are applications of Ramsey Theory to number theory, geometry, topology, set theory, logic, ergodic theory, information theory, and theoretical computer science. (A recent survey article on applications of Ramsey Theory has a bibliography of 252 items.)

Two of the largest branches of Ramsey Theory start with either ‘Ramsey's Theorem’ on the one hand, or ‘van der Waerden's Theorem on Arithmetic Progressions’ on the other. These two branches sometimes overlap, but a great number of results can be placed on one branch or the other.

We are working on problems that grow out of van der Waerden's Theorem, the simplest form of which is the following statement: For every positive integer k there exists a smallest positive integer w = w(k) such that if {1, 2, ?, w} is partitioned into two parts, in any way whatsoever, then at least one of the parts contains a k-term arithmetic progression, that is, a subset of the form {a, a+d, a+2d, ?, a+(k-1)d}.

The only known values of w(k) are w(1)=1, w(2)=3, w(3)=9, w(4)=35, w(5)=178.

In 1999, Ron Graham gave Timothy Gowers a ‘reward’ of 1000 USD for showing that w(k) < 2^2^2^2^2^(k+9). (The notation here is x^y = x y, and x^y^z = x^(y^z), so Gowers's bound is an exponential tower with 6 levels.) This bound, which may seem large, is tiny compared to the previous best known bounds. Gowers received a Fields Medal in 1998.

The true rate of growth of the function w(k) is one of the holy grails of Ramsey Theory, and Ron Graham now offers 1000 USD for a proof that w(k) < 2^(k^2).

We are interested in variations on van der Waerden's theorem in which one restricts the type of partitions allowed (a weakening of van der Waerden's theorem), or one restricts the allowable set of ?d?s? in the sets {a, a+d, a+2d, ?, a+(k-1)d} (a strengthening of van der Waerden's theorem), or combinations of these and other variations. Here one is interested in establishing the existence of some function w?(k) analogous to the function w(k) above, and/or upper and lower bounds on the function w?(k). One may also replace the set of arithmetic progressions by a smaller or larger or completely different set. Of course, one may also partition the underlying possibly infinite set into more than 2 sets, and even into infinitely many sets.

Number theory has historically been motivated by the study of properties of integers and solutions to equations in integers, but now iincludes many other aspects, each with its own flavour and viewpoints. Broadly speaking, these can be divided into Analytic, Algebraic, Diophantine, and Geometric aspects of Number Theory. Research in Number theory today often involves knowledge and expertise from areas such as Algebra, Algebraic Geometry, Analysis, Combinatorics, Probability Theory, Representation Theory, Topology. Connections to appplicable fields include Coding Theory and Cryptography.

At Simon Fraser University, we have a strong group in Number Theory which covers the spectrum of Number Theory. Together with the groups at the University of British Columbia and the University of Washington at Seattle, we form one of the largest groups of Number Theory Researchers in North America.

We maintain two active research seminars with UBC and UW which keep abreast of current developments in Number Theory. These are the SFU - UBC Number Theory Seminar and Pacific Northwest Number Theory Seminar. We also run a regular SFU Number Theory Study Seminar.

Our members are also active participants in the programs and initiatives of the PIMS and MITACS.

Electroencephalography (EEG) measures on-going changes in voltage potentials distributed over the scalp resulting from brain activity. These data sets are extremely low frequency (ELF 3-30Hz) to super low frequency (SLF 30-300Hz) manifestations of the electromagnetic or biopotential field generated through various aspects of metabolic brain activity in individuals. Various aspects of cognition and learning have been correlated with various amplitude and phase characteristics in frequency bands such as theta (4-7Hz; e.g., memory) alpha (8-12 Hz; sensorimotor), beta (12-30Hz; e.g., anxiety and concentration), and gamma (30-150Hz; e.g., consciousness)

Traditionally, educational research into cognition and learning has been restricted to audiovisual methods that only capture overt bewhavioural data. EEG data affords educational research the opportunity to correlate these traditional data sets with observations concerning brain and brain behaviour. Current audiovisual methods used for observing overt behaviour leave such discernments, as afforded by EEG in the study of cognition and learning, to matters for speculation. Consequently, there has been a proliferation of cognitive models in education research with no viable means for substantiating, refuting or refining them.

Fortunately, there have been dramatic improvements in EEG acquisition technologies and signal processing techniques, and more cost effective accessibility to them. With improved means for observing brain activity at hand, the time is ripe to integrate these methods and techniques into educational research. Integrating EEG with traditional audiovisual methods in educational research, however, requires analysis and interpretatioon of high-volume multi-channel data sets recorded over extended periods of time, co-acquired, time-synchronized, and integrated with audiovisual data sets. These long duration EEG data sets are single-trail data sets, as learning events are not typically replicable in a manner that would enable summation to improve signal to noise. Another reason for not summing such data sets, as is standard fare for event-related potential (ERP) studies in psychology, is to preserve valuable phase change information that mounting evidence has been associating with cognition and learning.

This project aims first to decompose these large data sets into characteristic frequency bands, which have been shown to in various ways with various aspects of cognitive function. There are at least three different methods available for this purpose: 1) sliding window fast fourier transforms (FFT); 2) complex demodulation; and 3) wavelet analysis. The initial focus will be on the sliding FFT, with eventual exploration of the efficacy of the other methods. These time-frequency data are then, in turn, digitally rendered as video files, and integrated in a time-synchronous manner with audiovisual bahavioural data. Theinitial focus here is on rendering and displaying time-frequency data for single channels, with eventual incorporation of most complete multi-channel montages. The initial objective will be to implement the time-frequency spectral decomposition and subsequent video display in batch mode.

Other aspects of this project include refining the parameters and layout EEG spectral analysis and visualization for optimal time-synchronization and integration with traditional audiovisual data sets. Future work will include: 1) adapting the batch mode processing in a manner amenable to interactive analysis and visualization; 2) adapting the interactive analysis in a manner amenable to real-time analysis and visualization for neurofeedback purposes.

The MoCSSy program brings together researchers with extensive expertise in criminology, health science, urban dynamics, computer science, and mathematical modelling. The unifying theme of this project is the modelling of the complex dynamics that drive the linked epidemiologies of crime, disease, homelessness and other social ills in urban neighborhoods. The MoCSSy program’s goals are to

• Generate a modelling and visualization toolset that will be applied to elevate the knowledge and understanding of urban complex systems to an unprecedented level.

• Develop a new generation of researchers who understand the complex dynamics of urban systems.

Simon Fraser University has elected to support the MoCSSy program through CTEF funding. This funding provides the chance to create a program that will attract and train a new generation of researchers who will understand the complex dynamics of urban systems.

An important goal is the development of methods for mapping disease or mortality rates of occurrence of events. This is important for epidemiological research to suggest factors which may be linked to mortality, and in health policy where the maps provide an overall description of mortality and are used to allocate health funding. The strength of the methods developed is that they take into account the spatial arrangement of the regions and any correlations which exist because of such configuration. They isolate time trends which manifest at the broad regional level as well as the small-area level thus permitting overall provincial and localized policy impact. Briefly, the research group considers methods for mixture models where the population consists of two or more subsets behaving differently and where spatial clustering is evident both in the placement of the population mixtures and their evolution over time in a Markov framework.

One special case of spatial mixture models arises when mapping rare disease rates where the usual Poisson spatial mixture distribution is mixed with a point mass at zero, so some regions are in a sense resistant. Apart from health studies, these projects find application at the Canadian Forestry Service, mapping vegetation species abundance and diversity and in studies to curb attacks of white pine weevil and certain weeds. The focus is on robust methods, handling different types of random effects arising in a hierarchical structure, design of clinical studies for monitoring recurrent events, zero-heavy data analysis, mixture models, state-space models and disease mapping and surveillance.

Part of the research is funded by the Canadian Forestry Service and is interdisciplinary in that it involves researchers from statistics, geomatics and ecology. This work concerns the development of methods for Markov mixture models and for mapping species abundance and diversity for forest management and conservation in coastal BC. The major part is funded from the GEOIDE NCE and involves researchers in geography, geomatics, epidemiology and statistics. This GEOIDE grant describes and compares revascularization intervention and mortality/morbidity profiles of patients suffering from acute myocardial infarction between 1991 and 2001 in Quebec. One specific aim is to identify whether the diffusion of practice guidelines by the Canadian Cardiology Society (e.g. C.J. Cardiology 1995; 1(6): 477-86) can explain differences in profiles.

In collaboration with partners in Canada and abroad, we will address decisions made by analysts, communication with field workers and coordination with government policy makers to insure that accurate and timely decisions are made throughout the chain of command.

For students this will provide fundingto participate in this cross-border collaboration on VA and interaction science, to work with their counterparts in the US and internationally.

For our Canadian industry partners this will provide transfer of knowledge from our interaction science and visual analytics research, opportunities to hire highly qualified students, international collaboration on the development of the next generation of VA applications from the best labs across the globe, and valuable contacts with potential clients for Canadian technology and consulting services brokered through our US and international government and industry partners.

Research and development at SFU's Software Technology Lab aim at bridging the gap between formal and empirical approaches by improving the practicability of applying formal methods and computational tools to challenging problems in high level design of distributed, embedded and mobile systems in a variety of application contexts. Beyond classical systems design, we also engage in interdisciplinary and cross-disciplinary research in computational criminology, distributed information fusion, public safety and security, and social networks.

Investigators often use statistical methods to infer haplotypes of unknown phase and treat the resulting reconstructions as known in subsequent association analyses. This two-stage strategy ignores uncertainty in haplotype reconstructions and can therefore lead to biased estimates of associations, overly optimistic assessments of precision, and potential errors in interpretation. The proposed research develops improved biostatistical methods that account for haplotype uncertainty in analyzing these disease associations. The new techniques will reduce inaccuracies associated with previous methods and will be applied to data from ongoing studies with collaborators. The analytic tools that are being developed should enable researchers to better evaluate genetic and environmental risks for conditions such as diabetes, cancer and asthma, and find the underlying genes. The knowledge gained can help with devising more effective treatment and prevention strategies for these conditions.

In many applications of optimization, one is forced to optimize a problem with no particular structure to exploit. As such, advanced methods like the “Simplex Method” or “Interior Point Methods” cannot be applied. In such cases, one is forced to resort to using nonsmooth optimization methods on the problem. In this project we explore methods of advancing nonsmooth optimization algorithms, and apply such algorithms to a variety of real-world problems.

Progress in understanding the properties of magnetic nanostructures and spintronics requires a thorough analysis of the structural and magnetic properties and spin dependent electron transport at metal/metal, metal/oxide, metal/semiconductor interfaces. In our effort we have tried to employ high quality crystalline epitaxial systems where one can compare experimental results with theoretical models allowing one to reach a better understanding of the underlying physical principles.

Research interest has shifted increasingly from the static to the dynamic properties of magnetic multilayers. This is motivated by the fact that the switching time of magnetic hybrid multilayers. This is motivated by the fact that the switching time of magnetic hybrid multilayers used in mass data storage devices and magnetic random access memories (MRAM) is a real technological issue. It is currently of considerable interest to acquire a thorough understanding of the spin dynamics in the nano-second time regime. My group is involved in spin dynamics of magnetic nanostructures.

1. Spin current studies: The precessing magnetization acts as a peristaltic spin pump which transports the spin momentum away from the ferro magnet (FM). It is important to realize that one can create the transport of spin momentum without using electrical current. In magnetic bi-layers the second FM absorbs the spin current acting as a spin sink, and that allows one to transport spin information with the net electric charge. This represents a new approach to spintronics. Currently, we are working on detection of spin currents using magneto-optics.

2. Two magnon scattering by spin density waves: We are able to enhance the relaxation rates significantly by employment of a self assembled network of crystalline defects. This work is carried out on crystalline magnetic multilayers using Molecular Beam Epitaxy system. A self-assembled network of crystalline defects is achieved by using crystalline lattice mismatch between the films and variable chemical stochiometery. This materials modifications are attractive to memory elements employed in spintronics applications.

3. Spin dynamics at large precessional angles: The non-local damping depends on the angle of magnetization precession. The non-local spin transport is going to be used at SPL using a high power microwave system with a dielectric ‘puck cavity’ and coplanar wavequides using intense magnetic pulses. Collaborations in this area include: Profs. J. Stohr, H. Siegmann, Stanford U and scientists from Stanford U., Lawrence Berkeley National Lab, Seagate and IBM. 30 GeV electronic pulses of 2-10 ps duration and 5um in diameter created by the Stanford Linear Accelator Center (SLAC) provide high intensity (several T) magnetic pulses for magnetization reversal studies of a new generation of ultrahigh density (>100 Gbits/in2) magnetic memory media.

Almost 30 years ago, Ronald Graham proved that for any permutation of N there is a monotone arithmetic process of length 3 and that there is a permutation of N with no monotone arithmetic progressions of length 5. It is still an open question if there are permutations that avoid monotone arithmetic progressions of length 4. We will use the standard Ramsey Theory methods together with extensive calculations and computer modeling to try to resolve the problem.

Wearable systems (sometimes incorporated into garments, shoes, costume jewellery, or “bandaids”) facilitate noninvasive and unobtrusive monitoring of individuals over extended periods of time. Such systems generally rely on wireless, miniature transmitters with adequate memory capacity to temporarily store data from sensors, than upload/transmit that data to a database server via a secure high reliability receiver link (radio, optical, induction) often through a LAN or Internet connection.

New techniques for short range radio communication unencumbered by regulatory restrictions (viz, wideband spread spectrum) enable wireless monitoring of ambulatory subjects both in home care and hospital that is relatively immune to interference. The following specific aims are addressed in this research:

1. Development and study of new generation, generically applicable biosensors. Reliable biosensor design, test, and packaging, emphasizing motion tolerance, stability control of a sensed monitoring signal, modular system architecture for easy modification/expandability, and user-friendly packaging.

2. Research methods for the integration of low-power digital radio. Wearable digital radio communication integrated with wearable monitors based on these biosensors. Ultra low-power and fault tolerant solutions will be proposed.

3. Investigate new algorithms optimized for rapid yet robust biosignal processing. The overarching goal of this project is to create solutions that will optimize lifetime wellness of a person, thereby enhancing quality of life, permit independent living as long as possible, provide real-time support and advice as an electronic “health companion”, and (eventually) reduce the overall life cycle cost of health and medical care.

This interdisciplinary project involves bioengineering at the interface between human physiology, sensors, telemedicine, wireless communication, biocompatible materials and packaging, microsystem design focused on low-power and fault-tolerance, combined with computer science research in ubiquitous computing, clinical research and psychosocial study.

Current Projects:

1. The structure of q-ary linear codes of minimum distance 4 and 5.

These are the smallest cases for which the problem of finding optimal codes remains unsolved (except when q=2 and d=4). These codes admit a simple geometric characterization in terms of point sets in finite projective spaces and their study provides an interesting link between algebra, combinatorics and geometry. One possible approach to finding good codes is to refine the minimum distance condition to a more detailed measure, such as studying the size and structure of the set of words of minimum weight. These codes are applied in digital communication (detecting and correcting errors ccurring during data storage/transmission) and in the design of statistical experiments.

2. The determination of the asymptotic maximum merit factor of binary sequences.

This is one of the fundamental problems of digital communication, studied since the 1950s. In equivalent guise it is an old unsolved problem in complex analysis. Extensive computational exploration has recently shed new light on this problem.

3. The structure of Golay complementary sequences.

These sequences have a long history of application to digital communication, most recently as a means of controlling power in wireless multicarrier transmission. The recent discovery of a connection between these sequences and Reed-Muller codes produces practical coding schemes for wireless transmission having powerful algebraic error-correction and tight power control.

The success of biological organisms in solving problems encountered in their environments is attributed to the process of natural selection, the rigors of this process ensuring the efficacy of the results. Biological systems represent the fruits of optimization through trial-and-error that has been in progress over billions of years, and the 1.7 million species that have been catalogued so far can be seen as a vast resource for inspiration of scientists and engineers. Biomimetics tries to extract concepts from biological systems that will allow the design of better, novel solutions, not merely imitating organisms’ characteristics but distilling aspects that can be applied effectively from complex integrated systems. Problems that biological systems face are often similar to those faced by engineers. Given the effectiveness with which some of these have been overcome, biologically inspired concepts should be considered seriously when designing new solutions. Although humans have been being inspired by nature for a long time, this process has been on an ad hoc basis. With the continuing emergency of biomimetics as a distinct scientific discipline, the systematic search for biomimetic solutions to particular problems is an increasingly important focus. Adaptability, autonomy, miniaturization, holistic design, reliability, robustness, self-repair, self-replication are the main traits that can be found in many biological organisms that are of particular interest in space systems design, with its particular requirements and constraints. In this project the basis for a biomimetic design process that is generally applicable, comprehensive and systematic in the search for solutions is investigated.

The biomimetic process, which is developed in the framework of this project, is applied in the design of different robotic systems of scientific and industrial interests. For instance, a strong interdisciplinary research program dedicated to providing scientific and engineering leadership in the development of robust and energy efficient bio-inspired climbing robotic systems will be developed. Applications may be categorized under four key areas: 1) Servicing (e.g., maintenance of skyscrapers, ships’ hulls, nuclear plants, etc.); 2) Rescue (e.g., during fire, earthquakes, landslide, etc.); 3) security (e.g., surveillance, inspection and military operations in premises and natural harsh environments, etc.); 4) Space (e.g., planetary exploration, Intra-Vehicular Activities, Extra-Vehicular Activities, etc.). Evolutionary examples will be used to design and develop engineered systems based on the principles of climbing in nature. So far the research performed in this field has demonstrated the value of the biomimetic approach, but current bio-inspired climbing prototypes lack both robustness and agaility. The research will focus on the synthesis of a robust and energy efficient climbing mechanism, which relies on the use of biomimetic attaching systems (e.g., gecko adhesive) previously investigated by the author. The current goal is to design a mechanism that enables the development of robotic systems capable of moving on both horizontal and inclined surfaces, as well as transferring between surfaces with differing gradients. During the scope of this project, the interaction between the mechanism and the adhering surface will be investigated. In order to maximize contact surface area, the research will focus on the design of an underactuated system capable of complying with both surface roughness and geometry. The kinematics, stiffness and dynamics of the synthesized mechanism will be investigated in order to optimize its design. Reliability is the paramount concern for climbing systems, as falls generally cause unacceptable damage. Therefore, the robotic system will be designed to prevent adhesion failure. Miniaturized tactile and acceleration sensors will be considered for monitoring and controlling the interaction of the mechanism with the surface.

This IRMACS working group serves as the focal point for several independent research efforts at SFU with common theme of the mathematics of fluids and continuum materials. The participants, comprising both research efforts at SFU with common theme of the mathematics of fluids and continuum materials. The participants, comprising both established researchers and students, will be enriched by the proximity to the broader SFU research community who all profit from the rising technologies of visualization, high-performance computing and computer graphics.

Current Projects

1. Flow dynamics of the midlatitude atmosphere. Active projects involve collaborations with computational scientists at Texas A&M, and meteorologists at NCAR Boulder and the University of Washington.

2. Heat transport in turbulent convection. Active projects involve collaborations with applied mathematicians at the University of Michigan.

3. Variational analysis of microphase separation of diblock copolymers. Active projects involve collaborations with mathematicians at New York University and the Universität Bonn.

Our objectives are to document the diversity of principles, interpretations, and actions arising in response to IP issues in cultural heritage; to analyze the many implications of these situations; to generate more robust theoretical understandings as well as norms of best practices; and to make these findings available to stakeholders to develop and refine their own theories, principles, policies and practices. Led by George Nicholas, this international collaboration of archaeologists, lawyers, anthropologists, Indigenous organizations, ethicists, information scientists, and heritage experts requests funds to expedite an integrated research agenda comprised of the creation of a comprehensive KnowledgeBase, focused inquiry and analysis by Topical Working Groups, and a program of field-based Case Study Research, which will combine to yield significant theoretical insights, valuable tools for practitioners, and evidence-based policy recommendations.

Our team consists of 50 senior and junior scholars from archaeology, law ethics, anthropology, Indigenous studies, and public policy from 9 Canadian and 18 other universities from 6 countries, with additional specialists fro mthe fields of heritage management, cultural tourism, information services, IP law and heritage policy. Together we will compile an accessible knowledge base on IP and cultural heritage, conduct 20 strategically chosen case studies employing a community-based participatory research methodology, and explore the implications of this empirical data for theory and policy in our topical working groups and publications. Twenty-five confirmed partners - ranging from First Nationals, professional associations and heritage institutes to national agencies and international NGOs specializing in IP policy - will collaborate on case study research and review and disseminate findings. Our methodology, networking and dissemination strategies ensure that results will be mobalized and accessible to key stakeholders and the public. Close to one-quarter of our budget supports student research and training, including 42 one-year graduate fellowships and 24 internships, offering unique interdisciplinary training opportunities in cultural heritage scholarship, policy, law and practice.

Our international collaboration will proactively address critical issues that promise to intensify in the coming decade. Parks Canada, the World Intellectual Property Organization and the UN Permanent Forum for Indigenous Issues are among those calling for empirically grounded research on IP issues to inform their policies. Members of our research team have long stood at the forefront of these initiatives in Canada and worldwide. We have assembled the expertise and resources required to address complex IP issues that increasingly affect research relationships, scholarship, and Indigenous knowledge systems and to equip diverse stakeholders to better understand and deal with these rapidly emerging concerns. This project also builds upon Canada’s global leadership in developing paradigms for ethical research and the negotiation of culturally based rights. The collaborations developed here will catalyze valuable theoretical insights, policy development, and long-term research relationships among an international cadre of multidisciplinary scholars and stakeholders for years to come.

The Clockwork Girl

Sean O'Reilly

Luximation is completing a stereoscopic 3D-CGI animated feature film entitled The Clockwork Girl, which tells the story of a nameless robot girl given the gift of life from her creator. While exploring the wonders of an ordinary world she meets an amazing mutant boy and they share a friendship that must overcome their warring families. Animated films are by their nature interdisciplinary, and the production aims to leverage the resources of the IRMACS Centre to bring the various components of animated film production together – using computers to composite, render and bring the CGI-animation to life as well as incorporate performance, sound design, traditional
filmmaking techniques and traditional art practices.

With the advent of microbial whole-genome sequencing, there has been some renewed optimism that genomic knowledge will speed the development of new antimicrobials, vaccines and diagnostics. Some success stories have been reported to date, however these have been extensive/costly endeavors involving significant laboratory requirements. This is largely due to the fact that the existing computational screens for identifying potential drug targets and vaccine components are not accurate enough.

Our recently funded CTEF project on combating infectious diseases aims to improve the effectiveness of genomic approaches for anti infective drug discovery through a technology driven, interdisciplinary methodology. The project aims to develop more accurate and faster bioinformatics algorithms and tools for identifying anti-infective drug targets, candidate drugs and potential vaccines. Our interdisciplinary team, composed of PIs Cenk Sahinalp and Fiona Brinkman and 8 other investigators, will capitalize on SFU’s unique strengths in computational, physical, chemical and biological sciences to discover potential new therapeutic targets and test them first in silico and then in the laboratory. Our program will provide an environment for trainees from the basic and applied sciences to learn career skills relevant to performing interesting interdisciplinary, team-based, internationally competitive research. With the ability to analyze many infectious disease-causing microbes in parallel, the computational methods we will develop could potentially have a wide impact on efforts to control multiple infectious diseases.

Complex systems are often controlled by many boolean (binary) variables, whose values are either "true" or "false". We would like to characterize how these variables affect a particular behaviour of the system, which itself is boolean. Suppose the behaviour is monotone in the sense that, given a setting of the variables that permits the behaviour, if additional variables are set to "true" the behaviour is still permitted. Then this behaviour is a monotone boolean function of the variables. Such a function is characterized uniquely by both the minimal sets of variables permitting the behaviour and the minimal sets of variables inhibiting the behaviour.

This situation is common in complex systems, such as those that comprise computational biology. As an example, a metabolic network can be characterized in its metabolites and reactions. In a steady state many of these reactions operate simultaneously. When some of these reactions are knocked out, various behaviours of the system will be blocked. We then have a boolean function which can be described either through elementary modes, i.e. minimal sets of reactions supporting the behaviour, or minimal cut sets blocking the behaviour.

Our goal is to develop efficient algorithms to enumerate these minimal sets, and to understand them both theoretically and computationally. We proceed from an oracle that evaluates the function. In the metabolic networks example mentioned above, this can be implemented as a simple linear program based on the stoichiometric matrix that records the number of metabolites produced and consumed by each reaction.

We are motivated in part by the novel algorithm of Fredman and Khachiyan which generates these forms with a surprisingly good worst-case complexity, but is not well understood in practice. These ideas also have an interesting connection to fundamental questions in computational geometry on describing polyhedra.

The research problems are interdisciplinary and require expertise in packet data networks (engineering and technology), statistical tools and analysis (applied mathematics), and data mining and visualization of large data sets (computing science).

Current Projects

1. Analysis of traffic traces and billing records from deployed wireless networks (E-Comm and Telus Mobility);

2. Use of analytical tools for traffic characterization and estimation of network performance;

3. Analysis and simulation of network protocols with active queue management schemes;

4. Application of control theory to modeling and analysis of network dynamics.