Mentors in the Mathematical Sciences
Dieter Armbruster, Department of Mathematics and Statistics, Arizona State University
Dieter Armbruster is interested in applied and industrial mathematics. Recent research related to the biological sciences include bifurcations and dynamical behavior in ecological systems, simulation, modeling , control and functionality of metabolic, genetic and signal transduction networks.
Steven M. Baer, Department of Mathematics and Statistics, Arizona State University
Steven M. Baer, PhD, works in the area of mathematical and computational neuroscience. The mathematical techniques he develops and employs in his research involve asymptotic/singular perturbation and numerical methods applied to the analysis of nonlinear ordinary and partial differential equation systems. The goal of his neuroscience research program is to develop mathematical and computational tools to obtain new insights into the electro-chemical properties of individual neurons and their networks. At the network level his primary goal is to unravel the biophysical mechanisms of learning in the brain by exploring models of synaptic plasticity. Another goal is to build a biophysically realistic continuum model of network activity in the retina.
Jonathan Bell, Department of Mathematics and Statistics, University of Maryland, Baltimore County
Richard Bertram, Department of Mathematics, Florida State University
Richard Bertram's research interests are in neuroscience and endocrinology. In particular, he is interested in the mechanisms for pulsatile hormone secretion from pituitary cells. Plausible mechanisms involve interactions between pituitary cells and the hypothalamus region of the brain. He is also interested in the mechanism for and coordination of insulin secretion from pancreatic islets. The insulin secreting cells within islets, called beta-cells, are electrically excitable like neurons, but are also controlled by a wide array of intracellular signaling pathways. He are interested in the interactions mediated by these pathways in conjunction with ion channels in the cell's membrane. Finally, Bertram is working on the quantification of and the neural mechanism for birdsong production in the male zebra finch. All of Bertram's projects are done with experimental collaborators.
Nick Cogan, Department of Mathematics, Florida State University
The underlying focus of Nick Cogan's research concerns the dynamics of various bacterial populations in flowing systems. There are several projects that he is currently focusing on. The first concerns the effect of external fluid flow on the disinfection, growth and material properties of biofilms which are the predominant mode of existence for natural bacteria. It is well known that biofilms are extremely tolerant to antibiotics and biocides. It is less clear what the mechanisms that generate this tolerance are. Moreover, it is not known how these mechanisms feed back to the material properties of the developing biofilm and to what extent this can enhance or degrade the effectiveness of biofilm removal. This project has lead to several other bacterial/biofluid projects including investigating the development of apparent patterns in bacterial veils which are formed in marine environments. The veil-forming bacteria exhibit a novel chemotactic strategy (run-and-reverse) that is distinct from run-and-tumble motility that is relatively well understood. Therefore one of the main tasks is to develop mathematical models that include enough biological realism to reflect current experiments, while introducing a mathematical framework that is as simple as possible. Cogan has several experimental collaborators and contacts that he regularly consults to ensure that he is using mathematics to explore biologically realistic and important problems. He employs a diverse set of mathematical tools including PDE analysis, perturbation theory, fluid dynamics and numerical methods (including boundary integral method, immersed boundary and standard finite-difference methods).
Noel Cressie, Department of Statistics, OSU
My biostatistical research interests are principally in disease mapping and its use in understanding the effect of regional-scale environmental impacts on human health. This overlaps considerably with the field of environmental epidemiology, and the mathematical tools are being developed principally within the field of spatial statistics. Another interest is in brain mapping using fMRI data, where spatial statistical models prove to be very useful in searching for areas of activation in the brain and in the presence of considerable noise in the data.
Sharon Crook, Department of Mathematics and Statistics, Arizona State University
My research uses mathematical models, analysis, and computer simulations to examine the dynamics of neurons and neuronal networks and to understand the mechanisms underlying plasticity in neuron or network behavior due to trauma, rehabilitation, learning or development. My research group also contributes to an international effort to create standards for describing models in neuroscience, NeuroML.
Bernard Deconinck, Applied Mathematics, University of Washington
My biostatistical research interests are principally in disease mapping and its use in understanding the effect of regional-scale environmental impacts on human health. This overlaps considerably with the field of environmental epidemiology, and the mathematical tools are being developed principally within the field of spatial statistics. Another interest is in brain mapping using fMRI data, where spatial statistical models prove to be very useful in searching for areas of activation in the brain and in the presence of considerable noise in the data.
Donald French, Department of Mathematical Sciences, University of Cincinnati
I look at a broad range of problems in applied mathematics, computation and numerical analysis. My background was in the error analysis of finite element methods for partial differential equations but in the past 10 years have focused on interdisciplinary problems especially in the biosciences. I use numerical and perturbation methods to examine neuronal networks and synchronization, inverse problems involving the ion channel distributions in olfactory cilia, and, more recently, biolfilm formation in urban pipe systems.
Avner Friedman, Department of Mathematics, OSU
My research areas are partial differential equations, control theory, and stochastic differential equations. I am particularly interested in nonlinear problems including free boundary problems. My recent interests are applications of mathematics to models in tumor growth, wound healing, and chemotaxis.
Anne Gelb, Department of Mathematics and Statistics, Arizona State University
Anne Gelb is interested in applying high order numerical methods to reconstruct medical images, specifically from MRI. Data from MRI is given as non-uniform Fourier coefficients. Currently images are reconstructed via FFT. Errors generated by noise, non-uniform data collection, and patient and machine motion are reduced by ad hoc filtering and density compensation techniques. However, no rigorous convergence analysis exists for how well these techniques work to generate accurate image reconstructions. We are interested in analyzing current techniques as well as creating more robust and accurate reconstruction methods. We use tools from Fourier spectral methods, numerical linear algebra, optimization, and edge detection.
Pavel Grinfeld, Department of Mathematics, Drexel University
My research areas are partial differential equations, control theory, and stochastic differential equations. I am particularly interested in nonlinear problems including free boundary problems. My recent interests are applications of mathematics to models in tumor growth, wound healing, and chemotaxis.
Yixin Guo, Department of Mathematics, Drexel University
Yixin is working on modeling Parkinson's disease (PD) and various brain stimulations. She has incorporated recording data from neurons of monkey brain into mathematical models. In collaboration with brain surgeons, she is going to use human data from Parkinson's patients to study the neural circuitry involved in PD. Another direction she is actively pursuing is traveling and standing patterns of population dynamics of neural networks.
Kathleen Hoffman, Department of Mathematics and Statistics, University of Maryland, Baltimore County
Jason Hsu, Department of Statistics, OSU
I am working in the area of statistics called Multiple Comparisons, where I develop statistical methodologies useful to the pharmaceutical industry and the FDA. For example, one of my current projects is to control for multiplicity in testing thousands of genes simultaneously in microarray gene expression experiments.
Winfried Just, Department of Mathematics, Ohio University
My research covers various aspects of dynamical systems models of biological networks, especially gene regulatory networks and neuronal networks. The dynamics of such networks can often be modeled either by systems of differential equations or, on a coarser level, by dynamical systems with a discrete state space. My recent research focuses on algorithms for discovering discrete dynamical systems models based on network data, on how the network architecture influences the expected dynamics of these models, and finding conditions under which coarse-grained discrete models will reliably describe aspects of the dynamics of the underlying systems of differential equations.
Yang Kuang, Department of Mathematics and Statistics, Arizona State University
My research interests include mathematical ecology and disease dynamics.
Mario Lauria, Department of Computer Science and Engineering, OSU
My research interests cover different aspects of PC cluster technology - architecture, system software, and applications. On the applications side, I am studying how novel applications pose new challenges to the designer of machines for high performance computation. Particularly interesting to me is the use of Computational Biology tools for data and compute intensive tasks such as genome assemblies, genome analysis and phylogenetic studies.
Stanley Lemeshow, College of Public Health, OSU
My research areas are in statistical modeling and sampling survey in medicine and epidemiology, such as estimating the probability of mortality of critically ill patients, including HIV/AIDS.
Sookkyung Lim, Department of Mathematical Sciences, University of Cincinnati
I use scientific computation to solve biological fluids problems with imbedded structures. In particular I work with the immersed boundary method study aortic aneurysms, valveless pumping, bacterial flagellar locomotion and, related to this motion, the rods in fluids.
Shili Lin, Department of Statistics, OSU
My research interests are in developing statistical and computational methods for linkage and association studies of complex diseases, for analysis of micro-array gene expression data, and more generally, for modeling and analyses of biological processes. I am particularly focused on the sort of data that render conventional methods infeasible. One such example is data from large families with complex relationships.
Yuan Lou, Department of Mathematics, OSU
My current research interests are: applications of partial differential equations to mathematical ecology; predator-prey, competition of multiple species, and cross-diffusion model; and migration and selection models in population genetics.
Georgi Medvedev, Department of Mathematics, Drexel University
Georgi is interested in dynamical mechanisms underlying regular and stochastic behavior in biophysical models of neurons and neuronal networks, spatio-temporal phenomena in neuronal networks, and the role of noise in shaping the patterns of neuronal activity.
Mike Mesterton-Gibbons, Department of Mathematics, Florida State University
Mike Mesterton-Gibbons uses game-theoretic and dynamic modelling to study behavior and group structure in complex social networks among all kinds of animals, including humans. A current focus is agent-based modelling to explore the effects on group emergence and stability of coalition formation, information sharing, inter-group migration and other aspects of interaction rules. Recent work is summarized in "Animal network phenomena: insights from triadic games" by Mike Mesterton-Gibbons and Tom N. Sherratt, about to appear in the journal Complexity.
Fabio Milner, Department of Mathematics and Statistics, Arizona State University
My research interests include demography, epidemics and immunology, applied mathematics and numerical analysis.
Yoichiro Mori, Department of Mathematics, University of Minnesota
Yoichiro Mori's primary research interests are in mathematical biology, scientific computing, applied and numerical analysis. He currently works on mathematical problems that arise in electrophysiology and on the numerical analysis of fluid-structure interaction problems.
Haikady Nagaraja, Department of Statistics, OSU
I am interested in the statistical modeling of biological data. In collaboration with a psychophysiologist and a cardiologist, I am working on the problem of modeling of the heart period data. Our work is providing new insights into the study of respiratory sinus arrhythmia and the sympathetic and parasympathetic nervous system. Another project, in collaboration with a neurologist, involves the modeling of sleep duration data and a study of its applications.
Duane Nykamp, Department of Mathematics, University of Minnesota
Duane Nykamp's current research interests include Mathematical neuroscience: Developing methods to characterize biological neural networks through analysis of single and multiple neuron recordings; Modeling the neural networks of the primary visual cortex; Developing efficient methods for neural network simulation.
Hans Othmer, Department of Mathematics, University of Minnesota
Major research interests include pattern formation in development, calcium dynamics in neural tissue, cell-based and continuum descriptions of cell and tissue movement, analysis of complex metabolic and gene-control networks, and mathematical models of tumor angiogenesis.
Srinivasan Parthasarathy, Department of Computer Science and Engineering, OSU
My research interests are broadly in the areas of data mining, machine learning and high performance computing especially as they apply to biological and biomedical domains. Sample projects currently underway include: protein structure analysis and drug motif discovery; shape modeling and mining in the context of eye disease detection; modeling and mining clinical trials data for the study of hepatoxicity effects; graph mining techniques in the context of protein protein interaction graphs; and probablistic and deterministic learning models for rational design problems such as protein crystallization trials.
Kevin M. Passino, Department of Electrical and Computer Engineering, OSU
My research interests include mathematical modeling and analysis of coordinated motion, social foraging, group choice, and task allocation for multiagent (animal or vehicle) systems. Methods include stability theory for distributed systems, evolutionary game theory, and optimization. Applications include honey bees, gray jays, multirobot systems, and multizone temperature control.
Dennis Pearl, Department of Statistics, OSU
My research areas are: the probabilistic modeling of biological phenomena and simulation-based estimation for high-dimensional models; and collaborative research with biological scientists including studies of the biological control of pests, laboratory markers of cancer prognosis, the analysis of nucleotide sequence data, and statistical phylogenetics.
Bradford Peercy, Department of Mathematics and Statistics, University of Maryland, Baltimore County
Tom Santner, Department of Statistics, OSU
My research interests are in the design of experiments and the analysis of discrete data. I am currently developing statistical methods for designing computer experiments to find better engineering designs of prosthetic devices and on a brain mapping project using functional magnetic resonance imaging. I am also interested in the efficient calculation of small sample confidence intervals in a variety of biostatistical applications.
Eric Shea-Brown, Applied Mathematics, University of Washington
My interests span a wide set of topics in mathematical neuroscience and biological dynamics. Current and recent projects focus on optimal signal processing and decision making in simple neural networks, the dynamics of neural populations in interval timing tasks, and correlations and reliability in simple neural circuits.
Saleh Tanveer, Department of Mathematics, OSU
My research areas in fluid dynamics include inviscid vortex dynamics, turbulence, bubble dynamics, and Hele-Shaw flow, and my research in crystal growth include directional solidification and dendritic growth. The mathematical techniques I have been using are partial differential equations in the complex plane, and integro-differential equations.
David Terman, Department of Mathematics, OSU
I am interested in the general areas of mathematical biology, computational neuroscience, and dynamical systems. In particular, I have developed and analyzed mathematical models for neuronal systems including models for sleep rhythms and the Parkinsonian tremor.
Joseph Verducci, Department of Statistics, OSU
I am interested in various applications of statistics to chemo-informatics. One project involves searching large databases of chemicals, first to organize compounds into groups of similar scaffold structure, and then identify key substructures of pharmacophors in the group that predicts specific types of biological activity. Another project is to refine high throughput toxicity screening methods based on chemical similarity to compounds tested in animal studies, and then construct optimal designs for intensive toxicity testing.
Doug Wolfe, Department of Statistics,OSU
My current research revolves primarily around the development of ranked set sampling techniques for a variety of problems. Because the cost of many biological and medical measurements can be substantial, this recently emerging methodology should be of tremendous benefit to research studies in these areas. I am very interested in exploring these possibilities in some biological/medical applications.
Abdul-Aziz Yakubu, Department of Mathematics, Howard University
My research encompasses theoretical investigations of nonlinear systems that arise in the diverse fields of ecology, population dynamics, epidemiology and demography. I am interested in a wide variety of equations that define dynamical systems, including difference equations, recursive formulas, matrix equations, ordinary and partial differential equations, and delay equations. My work focuses on asymptotic dynamics, i.e., stability analysis, bifurcation analysis, oscillations, periodic solutions (forced or unforced), aperiodic dynamics, and chaos.
I also maintain a research interest in the asymptotic dynamics of discrete-time systems defined by recursive formulas, and particularly systems of this type that arise in applications to fisheries. In collaboration with scientists at the North East Fisheries Science Center (NEFSC-NOAA), I study the implications of linkages among subpopulations to determine the stability and resilience of exploited species.
