Wednesday, November 29, 2006, 3:30pm
Location: MEC 339
Connections Between Mathematics and Biology
Carl Cowen (Dean of the School of Science at IUPUI, and President of the Mathematical Association of America)
Dr. Rita Colwell, a research microbiologist and former Director of the National Science Foundation, regards the mathematical sciences as the backbone for US Scientific and Engineering research. Many scholars see the next few decades as a time of intensive progress in the biological sciences. Dr. Colwell sees mathematics as being an integral part of the progress in biology, not a traditional view, but a forward looking one.

In this talk, Carl Cowen will outline some of the research areas in the emerging collaborations between mathematical and biological scientists. In addition, Cowen, who began his study of the mathematics of neuroscience in 2002-03 at the Mathematical Biosciences Institute at Ohio State University, and who worked in 2003-04 as a junior post-doc in the lab of Prof. Christie Sahley in the Purdue University Biology Department, will illustrate the connection between mathematics and neuroscience with a discussion of the Pulfrich phenomenon, an experiment that helps illuminate how the brain processes visual images. There are few mathematical or biological prerequisites for this discussion. (The talk should be very accessible to undergraduates in the sciences.)

Sunday, November 12, 2006, 4:00pm
Maury 209
Good News Everyone! Mathematical Morsels from "The Simpsons" and "Futurama"
Sarah Greenwald (Appalachian State University)
Lecture for general audience.
[Visit the webpage for this talk]

Thursday, November 9, 2006, 4:00pm
Kerchof 317
Spatial Moment Equations for the Dynamics of Ecological Systems and the Evolution of Dispersal Shape
Ben Bolker (University of Florida)
Understanding the dynamics of biological populations in continuous, heterogeneous landscapes continues to challenge population biologists one challenge is developing analytically tractable models that incorporate spatial variability. I apply one such class of models, to analyze the evolution of dispersal how does the shape of dispersal (the distribution of the distance that offspring move from their parents) respond to changes in landscape variability? If time permits, I will discuss strategies for estimating dispersal distributions and other spatial parameters from observational data.

(Refreshments precede the talk at 3:30 in Kerchof 314)

Thursday, October 12, 2006, 4:00pm
Kerchof 317
Modeling and Analyzing DNA Melting Transitions for Molecular Diagnostics
Bob Palais (Utah)
DNA undergoes a sharp phase transition from its double-helical state when it is heated. New fluorescent dyes can detect small sequence dependent differences in this process without expensive fluorescently labeled probes well enough to completely genotype samples in a PCR capillary tube quickly, non-destructively and without risk of contamination. We will discuss some of the theoretical and analytical methods involved in this technique, including nearest-neighbor thermodynamic models, background fluorescence filtering, and optimized mixing for quantitative heteroduplex analysis. The technology is currently being applied to determine living related donor transplant compatibility.
(Refreshments precede the talk at 3:30 in Kerchof 314)

Thursday, September 21, 2006, 4:00pm
Kerchof 317
Evolutionary Dynamics and the Problem of Cooperation
Christoph Hauert (Harvard)

Evolutionary dynamics in finite populations reflects a balance between Darwinian selection and random drift. For a long time population structures were assumed to leave this balance unaffected provided that the individuals' fitness is frequency independent, i.e., both mutants and residents have fixed fitness values. This result indeed holds for a certain (large) class of population structures or graphs. However, other structures can tilt the balance to the extend that either selection is eliminated and drift rules or drift is eliminated and only selection matters.

In nature, fitness is generally frequency depended, i.e., is affected by interactions with other members of the population. The most important case refers to the evolution of cooperation under Darwinian selection and represents a major challenge in evolutionary biology and behavioral ecology. The essence of the evolutionary conundrum is captured by social dilemmas where cooperators provide a benefit to the group at some cost, while defectors attempt to exploit the group by reaping the benefits without bearing the costs of cooperation. The most prominent game theoretical models to study this problem are the Prisoner's Dilemma (PD) and the Snowdrift game (SD). In the PD cooperators are doomed if interactions occur randomly but in structured populations, they may form clusters and thereby reduce exploitation by defectors. This results in stable co-existence of cooperators and defectors and has lead to the general belief that space is beneficial for cooperation. Interestingly, however, when relaxing the social dilemma and considering the SD, this no longer holds. Due to the less stringent conditions, cooperators persist in random interactions but spatial structure often tends to be deleterious and may even eliminate cooperation altogether.

In many biological situations it is more appropriate to consider a continuous range of cooperative investment levels instead of two a priori fixed strategic types. This situation can be analyzed using the framework of adaptive dynamics. The continuous SD exhibits rich dynamics but most importantly provides an intriguing natural explanation for phenotypic diversification and the evolutionary origin of cooperators and defectors. It turns out that selection may not always favor equal contributions but rather promotes states where two distinct types co-exist--those that fully cooperate and those that exploit. In the context of human societies and cultural evolution this could be termed the 'Tragedy of the Commune' because differences in contributions to a communal enterprise have significant potential for conflicts on the basis of accepted notions of fairness.

(Refreshments precede the talk at 3:30 in Kerchof 314)

Monday, April 17, 2006, 3:30pm
Maury 115
Biological Control System for Rhythmic Movements
Ted Iwasaki (UVa, Department of Mechanical & Aerospace Engineering )
Rhythmic body motions observed in animal locomotion such as walking, swimming, flying, etc., are known to be controlled by neuronal circuits called central pattern generators (CPGs). Such biological control systems based on CPGs may provide a new paradigm for feedback control theory to achieve oscillations (rather than regulations) in a robust, adaptive, and autonomous manner. The first part of this talk focuses on our hypothesis CPGs are energy efficient controllers that cooperate with biomechanical and environmental constraints through sensory feedback. In particular, CPGs tend to induce natural rhythmic motion of the body, achieving entrainment to a mechanical resonance. We consider a simple proof-of-concept example consisting of a pendulum and a CPG model, obtain evidence to support the hypothesis, and uncover the dynamical mechanism underlying the resonance entrainment. The latter part of this talk focuses on the design of (artificial) CPGs to be used as a controller in the feedback loop. We have developed two methods for designing CPGs with prescribed oscillation profile (frequency,amplitude,phase). One approach is based on the interconnection of simple neuron models with circulant connectivity architectures. It is proved that every generic trajectory converges exactly to a limit cycle with the prescribed profile, provided the desired phases are rational. The other approach is based on the multivariable harmonic balance, where the CPG design is essentially reduced to an eigenvalue/eigenvector problem in terms of the neuronal connectivity matrix. This method is approximate in nature, but has been verified to work well through numerical examples. An advantage over the exact circulant approach is the ability to impose a structural constraint on the interconnections. These results form a basis for developing a feedback control theory to achieve natural rhythmic motions.

Monday, April 10, 2006, 4:00pm
Clark 108
Living in the Variable World: Tales from Ecology, Evolution, and Epidemiology
Sebastian Schreiber (William and Mary)
Plants, animals, and viruses live in heterogeneous environments that can fundamentally influence their population dynamics. Using mathematical models, I will discuss how spatial, temporal, and individual heterogeneities influence the persistence of populations, the evolution of dispersal, and the dynamics of disease outbreaks.

Wednesday, March 15, 2006, 3:30pm
Physics 210
Mathematical Algorithms for Side Chain Placement in Protein Structure Prediction
Troy Siemers (VMI)
A brief background in protein structure will be given followed by the statement of the side chain placement problem. Several of the mathematical algorithms that have been used to attack this problem will be introduced and described.

Tuesday, February 21, 2006, 4:00pm
Cabell Hall 215
Accepting Biomathematics: The Needs, the Dilemmas, and the Consequences
Raina Robeva (Sweet Briar College)
As contemporary characterization of biological systems reaches unparalleled level of detail, virtually any advance in the life sciences requires sophisticated mathematical approaches. Modeling of biological systems is evolving into an important partner of experimental work. As a result, there is a rapidly increasing demand for people with training in the field of biomathematics. The talk will focus on some of the challenges faced by mathematicians interested in research in biomathematics and in teaching courses in the field. The speaker will also share successes, problems, and key questions raised in the context of teaching an experimental undergraduate course in Mathematical Biology at Sweet Briar College using projects from ongoing medical research studies. The course, designed for an undergraduate audience of students with minimal background in calculus and statistics, has been created jointly by faculty from Sweet Briar College and the UVA School of Medicine with funding from the NSF and the NIH.