**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