Mathematical Biology Seminar
Spring Semester, 2001
Wednesdays at 3:05pm in
JWB 208
Optimization, conflict, and territoriality in ants
What geometric visual hallucinations tell us about visual cortex
How natural selection achieves what is mathematically impossible
Computational Challenges in Biomolecular Design
Abstract: The prospect of engineering functional biomolecules from
scratch creates striking new opportunities for the field of applied
and computational mathematics. Using amino or nucleic acids as raw
materials, the challenge is to model, design, construct and characterize
molecular systems for a range of biomedical and technological applications.
To illustrate the diversity of the computational issues that arise, this
talk will focus on two problems from the field of protein design: a
discrete NP hard sequence selection problem and a continuum modeling
approach for electrostatic solvation.
How to tell time with a variable-speed clock
Membrane recycling and intracellular vesicle dynamics
The Mathematics of Eddy Correlation - Studying Biological
Processes with Atmospheric Measurements
Survival modeling in CF: Implications and surprises
The Origins and Consequences of Intrinsic Fluctuations in
Transcriptional Regulation
We develop stochastic models of transcriptional regulation. The
starting point for these investigations is the underlying master
equation for the process. Using small noise approximations, we
are able to derive an effective diffusion equation
that takes into account both number fluctuations and fluctuations
in the chemical state of the operator. A direct comparison with
Monte-Carlo simulations is used to verify the validity of the
approximations. The models are shown to undergo noise-induced
transition, which might be important for understanding regulatory
networks. This is joint work with Tom Kepler (Santa Fe Institute).
Population and evolutionary consequences of consuming a structured
resource
The difference between ischemia and hypoxia:
A mathematical study of volume shifts and ionic
concentration changes
How predation can slow, stop or reverse a prey invasion
Observations on Mount St. Helens indicate that the spread of
recolonizing lupin plants has been slowed due to the presence
of insect herbivores, and it is possible that the spread of lupins
could be reversed in the future by intense insect herbivory.
In this talk I will investigate mechanisms by which herbivory can
contain the spatial spread of recolonizing plants. The approach is
to analyse a series of predator-prey reaction-diffusion models and
spatially coupled ordinary differential equation models. The analysis
yields qualitative conditions on the functional response of the plant
to herbivory under which predation pressure can slow, stall or
reverse a spatial invasion of prey. Theoretical predictions will
be compared to the field data collected from Mount St. Helens.
Mathematical modelling of solid tumour growth and invasion
Mathematical modelling of tumour-induced angiogenesis; Capillary
networks, form, function and heterogeneity
Conformal maps, wavelets and the visual cortex
Selection of Twisted Scroll Waves in Excitable Media
The selection of shape and rotation frequency for scroll waves in
reaction-diffusion equations modeling excitable media is investigated.
For scrolls with uniform twist about straight filaments, asymptotic
methods are used to derive free-boundary equations at leading order
and at first order in the small parameter of the problem. Both orders
are directly validated against full solutions of the reaction-diffusion
equations. Using these two orders and with no adjustable parameters,
the shape and frequency of twisted scroll waves are correctly
predicted for most cases of physical interest. This work also sheds
new light on the Fife limit in models of excitable media and Keener's
work on the dynamics of scroll waves.
PAST SEMINARS:
Seminars for Fall Semester, 1998
Seminars for Spring Semester, 1999
For more information contact Fred Adler, 1-6848