Mathematical Biology Group

Research:

Emerging research within the Department of Mathematical Sciences in Biology is interdisciplinary with ongoing collaborations in the areas of Neuroscience, Systems Physiology and Evolutionary Genetics. The related mathematical research is in ordinary and partial differential equations as well as dynamical systems, perturbation analysis and scientific computation.

People:

Faculty:

Donald A. French has two ongoing collaborations in Neuroscience. He is building a computational model of the synchronized bursting in networks of cultured cortical neurons with Eric Gruenstein. He is also investigating ion channel distributions in olfactory cilia with Steve Kleene. (french@math.uc.edu)

Sookkyung Lim uses scientific computation to study aortic aneurysms and motile behavior of bacteria such as E. Coli (limsk@math.uc.edu).

Tony Leung looks at predator-prey partial differential equation models. (Anthony.Leung@UC.EDU)

Steve Pelikan works on the genetics and geometry (spatial structure)of small populations and estimating the origins of hybrids in collaboration with Steve Rogstadt from Biology. He has also done research in Bioinformatics at P & G. (Steve.Pelikan@UC.Edu)

Graduate Students:

Zeynep Teymuroglu finished her thesis integro-differential equation models for the spread of alcohol abuse. She graduated in June 2008.

Jiyeon Oh finished her PhD thesis under Dr. French in May 2005. Her research was on exponential Euler approximation techniques in Neuroscience.

Dorjsuren Badamdorj finished his thesis in August 2006. The research was on the determination of CNG and Cl(Ca) channel distributions in olfactory cilia using computational and analytical techniques. He now has a visiting position at the University of Delaware.

Mauricio Osorio is working on meshfree numerical methods for fluids problems with immersed structures.

Kristen Fox is a new student.

Longla Martial is a new student.

Undergraduates:

Sabrina Blakeman was a WISE/REU undergraduate in the Summer of 2003. She worked on parameter search techniques in Neuroscience.
The Department of Mathematical Sciences also has a strong statistics program and many of the researchers have interests in the biosciences. Both Seongho Song and Xiaodong Lin have already published in biology journals.

Math Biology Seminar:

Talks this Spring quarter (2009) will be from 3-4 PM in Braunstein 312 unless otherwise noted.

Friday, April 10th: Professor Anthony Leung will speak on techniques for optimization problems. (Department of Mathematical Sciences at University of Cincinnati) will speak on ???.
Friday, May 29th: Professor Hem Raj Joshi, Department of Mathematics at Xavier University will speak on ???.

We have had six talks so far this year. They were by Don French (Integro-differential equations models for the spread of alcoholism), Sookkyung Lim (Immersed boundary methods), Mauricio Osorio (Meshfree numerical methods), Dong Qian (Discontinuous Galerkin methods), Kumar Vemganti (Modeling errors) and David Rogers (Bayesian methods).

Last year we had several distinguished speakers; they were Nick Cogan, Steven Cox and Jim Keener .

Two years ago (2006-7) we had a wide range of interdisciplinary talks including ones by Tom Beck (Chemistry) on the Realization of Ion Channel Pathways, Jeff Johnson (Biomedical Engineering) on Computational Neuroscience, Ruxandra Dima (Chemistry) on Computational Biocheminformatics, George Stan (Chemistry) on Computational biophysical chemistry and bioinformatics, Frank Pinski (Physics) on Free Energy Landscapes, and Shaaban Abdallah (Aerospace Engineering) .

PhD in Mathematics with emphasis in Mathematical Biology

PhD graduate students interested in doing PhD research in Mathematical Biology need to fulfill the usual requirements for a PhD in mathematics (see the department handbook at the graduate studies webpage for details). Their curriculum would have an emphasis in applied mathematics and biology. Their research would typically be interdisciplinary with at least one faculty member from a biology or related department involved.

Publications

DA French and T Lewis, Weak coupling analysis rectifying gap junctions (in preparation).
A. Leung and X. Hou, Traveling waves solutions for a competitive reaction-diffusion system and their asymptotics, to appear in Nonlinear Analysis, Real World Appl.
D Edwards and DA French, Perturbation derivation of ligand-gated ion channel distributions arising in olfaction experimentation (accepted by J. Math. Biology).
A. Leung, X. Hou and Y. Li, Exclusive traveling waves for competitive reaction-diffusion systems and their stabilities, J. Math. Analysis and Applications, 338 (2008), 902-924.
DA French and CW Groetsch, Numerical Approximation of Solutions of a Constrained Integral Equation Arising in Olfaction Experimentation, J. of Physics: Conference Series 73, (2007), 1-10.
S Lim and C Peskin, Bent and twisted rod in fluid, in preparation.
S Lim, A Friedman, and Subha Raman, Mathematical modeling of aortic aneurysms, in preparation.
E Jung and S Lim, A three-dimensional mathematical model of valveless pumping, submitted to Bulletin of Mathematical Biology (2005).
DA French and E Gruenstein, An Integrate-and-Fire Model for Synchronized Bursting in a Network of Cultured Cortical Neurons, J. Comp. Neurosci., 21 (2006), 227-241.
R. Flannery, DA French and S.J. Kleene, Clustering of CNG channels in the cilia of frog olfactory receptor neurons, Biophys. J., 91 (2006), 179-188.
DA French, R Flannery, C.W Groetsch, W Krantz, and S Kleene, Identification of CNG channel distributions in frog olfactory cilia, Math. Comp. Modelling, 43 (2006), 945-956.
J Oh and DA French, Error Analysis of a Specialized Numerical Method for Mathematical Models in Neuroscience, Math. Comp. Model. 43 (2006), 945-956.
S Lim and CS Peskin, Simulations of the whirling instability by the immersed boundary method, SIAM Journal on Scientific Computing, Vol. 25, No. 6, pp. 2066-2083 (2004).
H Lim, S Pelikan and S Rogstad, Genetic diversity among populations and size classes of buckeyses Aesculus: Hippocastanaceae examined with multilocus VNTR DNA probes Plant Systematics and Evolution.
S Pelikan and S Rogstad, Estimating heterozygosity with multilocus probes, Molecular Biology and Evolution.
DA French, Identification of a free energy functional in an integro-differential equation model for neuronal activity, Appl. Math. Lett., 17 (2004), 1047-1051.
S Lim and CS Peskin, Subcritical bifurcation of a rotating elastic filament in a viscous fluid by the immersed boundary method, Proceedings of the Second MIT Conference on Computational Fluid and Solid Mechanics, pp. 1409-1412 (2003).
A Leung and B Villa, Bifurcation of reaction-diffusion systems related to epidemics, (with B. Villa), Proceedings of Nonlinear Diff. Eq. in honor of A. Lazer, Electronic J. of Diff. Eqs, Conference 5, 2000.
A Leung and B Villa, Bifurcation of reaction-diffusion systems, application to epidemics of many species, J. Math. Anal. Appl., 244 (2000), 542-563.