|August 27, 2004|
|Laboratory for Industrial and Applied Mathematics|
Department of Mathematics ad Statistics
|Co-ordinators||Huaiping Zhu, LIAM, York University|
University of Ontario Institute of Technology
Friday, A Room N638 Ross Building
|10:00-10:10||Opening Remarks by Jianhong Wu|
|10:10-10:50||Hildebrando Munhoz Rodrigues,
University of Sao Paulo
Smooth Linearization in Infinite Dimensional Banach Spaces
|10:50-11:30||Pietro-Luciano Buono, University of Ontario
Institute of Technology
Linear and nonlinear unfoldings of delay-differential equations
|11:30-12:10||Yuming Chen, Wilfrid Laurier University
Global Asymptotic stability of delayed Cohen-Grossberg neural networks
|2:00-2:40||Jifa Jiang, University of Science and
Technology of China
|2:40-3:20||Greg Lewis, University of Ontario Institute
Bifurcations in models for large-scale geophysical fluids
|3:20-4:00||Xinfu Zou, University of Western Ontario
Dynamics in numerics: on two different difference schemes for ODEs.
|4:20-5:00||Dong Liang, York
|5:00-5:40||Yi Zhang, University of Waterloo
Stability of switched delay system
Prof. Waclaw Marzantowicz
Adam Mickiewicz University, Poland
Symmetry Breaking Solutions of Nonlinear Elliptic Systems
We consider nonlinear elliptic systems with Dirichlet boundary
condition on a bounded domain in R^n which is invariant with respect to
the action of some group G of orthogonal transformations. For every
subgroup K of G, we give a simple criterion for the existence of
infinitely many solutions which are K-invariant but not G-invariant. We
include a detailed discussion of the case N=3.
Dr. Xingfu Zou
Department of Applied Mathematics
University of Western Ontario
Impact of dispersion on dynamics of a discrete metapopulation model
We propose and analyze a discrete time model for metapopulation on
two patches with local logistic dynamics. The model carries a delay in the
dispersion terms to account for long distance dispersion. Our results on this
models shows that the impact of the dispersion on the global dynamics of the
metapopulation is complicated and interesting: it can affect
the existence of a positive equilibrium; it can either drive the metapopulation
to global extinction, or
prevent the metapopulation from global extinction
and stabilize a positive equilibrium; it can also destabilize a positive
equilibrium or a periodic orbit.
Dr. M. Efendiev
University of Stuttgart, Germany
Symmetry and Elliptic Attractors
We study the trajectory dynamical systems approach to study the
positive solutions of semilinear elliptic equations on unbounded domains.
The existence of the global attractor for the trajectory dynamical systems
associated with this problem is proved.The symmetrization and
stabilization properties of positive solutions are established.
Generalized Projective Clustering in High Dimensional Data
Subspace clustering is a useful technique in data mining for
identifying hidden patterns in high dimensional data. Generalized projective
clustering technique has been developed which able to construct
clusters in arbitrarily aligned subspace of lower dimensionality.
This talk will focus on ORCLUS(arbitrarily ORiented projected CLUSter
generation) algorithm and present some comparisons with other clustering
Dr. Nilima Nigam
Department of Mathematics and Statistics
Truncation techniques- the Good, the Bad, and the not-so-Ugly
In the computation of exterior scattering problems (acoustic,
electromagnetic or elastic) we run across a basic problem- how do we
truncate the infinite exterior region in order to compute? Mathematically,
this often reduces to the problem of computing a Dirichlet-to-Neumann
(DtN) map. This talk will introduce these ideas, and provide a brief
survey of truncation techniques, illustrated by means of a model problem.
A simple series can be used to construct this DtN map under special
circumstances, an idea exploited by Givoli and Keller.
I then describe a new perturbative method for constructing a DtN map on boundaries which are perturbations of simple geometries, allowing us to extend the ideas of Givoli and Keller. I end with some computational experiments.
This is joint work with Dave Nicholls, Univ. Notre Dame.
Dr. Massimiliano Giuli
University of L'Aquila, Italy
On spectral probems, arizing in theory of functional differential equations
This paper combines the effects on asset price dynamics of two groups of traders: feedback traders who mechanically respond to price changes and bounded rationality traders who learn from lagged values of prices and dividends. First, we find that in the weak limit, as the trade interval goes to zero, the asset price is described by a mean reverting process around the level given by the forecasted price. Second, we show how feedback trading and learning effects on asset price dynamics may explain the empirical finding of long run dependencies on dividend yields in financial time series.
Dr. Victor Vlasov
Moscow State University
On spectral probems, arizing in theory of functional differential equations
The Results about geometrical properties [ completeness and Riesz
basisness ] of the system of exponential solutions for functional
differential equations of neutral type will be presented. The results
about asymtotic behavior and sharp estimates of the solutions of above
mentioned equations will be also formulated
Dr. Weiguang Yao
Department of Mathematics and Statistics, York University
Delayed Stochastic Differential Model For Quiet Standing
Standing quietly appears for the eye as a simple matter of being inert or at rest. However precise measurements reveal that it actually involves complex dynamical motions, which are too small for the eye to see. Thus the simple act of standing is revealed to be a complex control problem, involving both physiological and psychological processes. The standing capability may be learned and it may be affected by disease. The study of quiet standing may also be possible to help diagnose some disease. This talk will introduce the experimental data analysis and some phenomenological models, and focus on our simple physiological model which turns out to be a delayed stochastic differential equation. The numerical simulation and Hopf bifurcation analysis on the model give us an interesting explanation how people stand stilly and easily.
ABOUT:Dr. Weiguang Yao
Centre for Infectious Disease Prevention and Control
Population and Public Health Branch
Heterogeneous transmission of infectious diseases,
and implications on transmission potential,
epidemic control efforts and interpretation of trends
An application of stochastic processes and statistical methods to
the case of the outbreaks of SARS
Of various quantitative measures for the transmission of infectious diseases, such as SARS,
much interests are in the following aspects. One is the transmission potential: when a new
agent invades a host population, what is the probability that it will become naturally extinct
before manifesting itself into a large outbreak. Once a major outbreak does happen, a major
concern is the effectiveness of control measures, such as isolation of symptomatic cases and
quarantine of exposed but not yet symptomatic cases. Once data are collected, trends
interpretation becomes essential. Most of the infectious disease models have an implicit
assumption that the transmission pattern is homogeneous, that all individuals follow similar
contact patterns and transmission probability per contact. In this presentation, the focus is on
transmission heterogeneity, as documented by super-spreading events in SARS outbreaks, and
how it affects the three aspects.
Stochastic models with random effects are applied to the contact frequency and probability of transmission by extension of the work by Crump and Mode (J. Appl. Math. Analis. Applic., 24, 25, 1968,1969) and Jagers (Skand. Akturarietidskift, 1969). Combined with statistical methods one can achieve the following results.
(1) Transmission heterogeneity makes it more difficult for an infectious agent to invade and establish itself in a host population, and start a major outbreak. Even when the basic reproductive number is greater than 1, the probability of the infection become naturally extinct (before becoming an outbreak) is always greater than that in homogeneous transmission settings when all other parameters are assumed the same. This may explain why approx. 30 countries reported SARS cases in spring 2003, but only very few cities reported major outbreaks.
(2) If a major outbreak does happen, transmission heterogeneity makes it more difficult to put the outbreak under control, than that in homogeneous transmission settings. Here "control" refers to isolation of symptomatic cases. In homogeneous transmission settings, average time to isolation needs to be shorter than average time to infection produced by infectious individuals as "race against time", both measured from onset of symptoms. This race becomes more difficult to win if there is heterogeneity. The isolation speed needs to be much faster. In high heterogeneous situations with large extra-Poisson variance, isolation alone may not be sufficient. Control measures must include "quarantine" of exposed but not yet infectious cases, through contact tracing.
(3) With further information on incubation period and published "epidemic curves" as trends by date of onset over time, combined with linked data by "who infects whom", such as that from Singapore, one can use statistical methods to establish trends by time of infection and pin-point the timing of the super-spreading events. This helps the interpretation of SARS trends over time in heterogeneous transmission settings, with the potential to evaluate successfulness of control measures implemented over time.
TIME: 2:30p.m.-3:30p.m., Wednesday, January 28, 2004
PLACE: N638 Ross
ABOUT: Ping Yan
Dr. Yan is a trained statistician from the Dept. of Statistics and Actuarial Sciences, University of Waterloo, and he is currently managing a modelling and projection section in the Population and Public Health Branch of Health Canada, and has been playing a major role in the modeling and analysis of infectious diseases related data in Canada. He is also a member of WHO study group, and a member of the MITACS infectious diseases modeling team.
Dynamically modeling disease outbreaks as they occur
A problem identified in the recent SARS outbreaks in Toronto was the absence of
useful models to help answer the questions that arose in choosing and executing the
governmental and health systemic [and societal] response. Indeed, that is a lack
affecting any outbreak of a new disease, or of a familiar one before it can be
We are developing "rough and ready" dynamic models to use in the event of an outbreak of a disease, in order to answer policy related questions in the heat of an ongoing infectious disease outbreak, starting before the disease is well characterized or the causal agent found, and continuing throughout the outbreak lifespan. Critical questions we aim at answering include whether to quarantine victims, isolate potential victims, vaccinate susceptible individuals [if a vaccine in available], setting the relative priority of finding vaccine or diagnostic test, among others.
We have model results for SARS and smallpox, and we need now to make the model more generic.
TIME: 2:30p.m.-3:30p.m., Wednesday, January 21, 2004
PLACE: N638 Ross
Dr. Troy Day
Department of Mathematics and Statistics, Department of Biology, Queen's University
A general theory for the evolutionary dynamics of virulence?
As witnessed during the recent outbreak of SARS, quarantine and other transmission-blocking disease control measures such as the use of surgical masks are primary tools for halting the spread of newly emerging infectious agents. Such interventions are clearly desirable from an epidemiological standpoint, but they can also have unintended evolutionary effects on the pathogen population. I will discuss a possible approach towards a general theory for determining how these control measures might be altered to minimize the risks associated with evolutionary change during the initial emergence of any new disease.
TIME: 2:30p.m.-3:30p.m., Wednesday, January 14, 2004
PLACE: N638 Ross
ABOUT: Dr. Troy Day
Department of Physics, University of Alberta
A Simple Cellular Automaton Model for Influenza A Viral Infections
Viral kinetics have been extensively studied in the past through the use of spatially homogeneous ordinary differential equations describing the time evolution of the diseased state. However, spatial characteristics such as localized populations of dead cells might adversely affect the spread of infection, similar to the manner in which a counter-fire can stop a forest fire from spreading. In order to investigate the influence of spatial heterogeneities on viral spread, a simple 2-D cellular automaton (CA) model of a viral infection has been developed. In this initial phase of the investigation, the CA model is validated against clinical immunological data for uncomplicated Influenza A infections. Our results will be shown and discussed.
TIME: 2:00p.m.-3:000p.m., Wednesday, January 7, 2004
PLACE: N638 Ross
ABOUT: Catherine Beauchemin