My interests are mainly in high-end computing and data mining. Of particular focus are statistical and other techniques for analyzing biological datasets including those related to gene sequences, gene expression, and protein folding. Another area is tools for high-end computing, including middleware, runtime, compiler, and algorithmic techniques for solving large scale computational and data-intensive problems.

Systems biology and biomedical systems modeling. The focus of my research program is the mathematical and computational analysis of cancer networks - especially those involved in the cell cycle, apoptosis, and associated signaling pathways. There are on-going collaborations with cancer research groups at the Ohio State University and Georgetown University Medical Centers. For more information, visit http://people.mbi.ohio-state.edu/baguda/AgudaLab/

Integrated Multiscale Modeling and Experimental Study of Thrombus Development: To prevent the loss of blood following a break in blood vessels, components in blood and the vessel wall interact rapidly to form a clot to limit hemorrhage. This hemostatic response is rapid since delayed clotting results in excessive bleeding. Furthermore, the process is regulated, since excessive and inappropriate clotting within a vessel (thrombosis) reduces the patency of blood flow. The biomedical importance of these processes is highlighted by the approximately 900,000 cases of venous thromboembolic disease resulting in approximately 300,000 deaths in the United States each year. The goal of this proposal is to better understand the regulation of thrombus development by addressing the question why a developing thrombus induced by injury to the vessel wall stops growing.

The main goal of this project is to develop and refine a three dimensional multiscale computational model of thrombogenesis to include the Protein C anticoagulant pathway, the fibrinolytic system, and the polymerized fibrin mesh generated by the coagulation system. The hypotheses generated by the model can then be tested in an experimental vascular injury model utilizing intravital, multiphoton microscopy. The high resolution microscopic images will be processed using newly developed algorithms to generate quantitative outputs and metrics of the internal clot structure that can be compared to the predictions of the simulation.

To achieve this goal we formed collaboration between Drs. Alber, Xu and Chen (Notre Dame) and Dr. Rosen (Indiana University School of Medicine) with additional support from Dr. Kenneth Mann (University of Vermont) and Dr. Susan Lord (UNC). A key component of the collaborative effort is close integration of the predictive simulations with in vivo venous injury protocols involving multiphoton intravital microscopy.

While, it is impractical to systematically vary the value of multiple hemostatic factors in in vivo experimental systems, such studies could readily be performed in silico using validated computational models of thrombogenesis. Thus, refined simulations of clot development will not only advance our basic understandings of thrombogenesis but likely have significant impact on the development of therapeutic and diagnostic strategies.

This research is supported by the NSF Grant DMS-0800612, Joint DMS/NIGMS Initiative to Support Research in the Area of Mathematical Biology.

1. Xu, Z., Chen, N., Shadden, S., Marsden, J.E., Kamocka, M.M., Rosen, E.D., and M.S. Alber, Study of Blood Flow Impact on Growth of Thrombi Using a Multiscale Model, Soft Matter 5, 769-779 (2009).
2. Xu, Z., Chen, N., , Kamocka, M.M., Rosen, E.D., and M.S. Alber, Multiscale Model of Thrombus Development, Journal of the Royal Society Interface 5, 705-722 (2008).
3. Lushnikov, P.P., Chen, N., and M.S. Alber, Macroscopic dynamics of biological cells interacting via chemotaxis and direct contact, Phys. Rev. E. 78, 061904 (2008).

Combined Computational and Experimental Study of Complex Interactions that Control Bacterial Motility Pattern Development: Modeling and simulation are becoming very important research tools in environmental microbiology and engineering. The most advanced of these efforts have focused on single levels or scales, e.g., genomic/proteomic, cellular and population. We are developing computational approaches to integrate models from micro-scales to macro-scales in a seamless fashion. Such multiscale models are essential for producing quantitative, predictive simulations of complex bacterial behaviors such as swarming. At the same time, integration between scales will lead to a much deeper understanding of the universal or generic features of biological phenomena and how simultaneous multiscale processes interact.

The long-term goal of this project is to develop a predictive and quantitative 3-dimensional (3D) multiscale modeling environment and computational Toolkit to study bacterial motility pattern development on different surfaces, which is essential to how bacteria function in real environments. Swarming describes a bacterial surface motility where communities of cells rapidly spread over surfaces. Swarm motility represents a community response to external stimuli. How do biological communities process information? Any question of this kind represents a multiscale problem where individuals sense information and act but it is poorly understood how these interactions are coordinated among large number of cells. Extensive study of this biological problem using predictive simulations involving millions of cells and requiring teraflop computing capabilities, will be a breakthrough in understanding complex natural interactions, connections, complex relations, and interdependencies in biology.

To achieve goals of this project a collaboration has been formed between Mark Alber, Zhiliang Xu, Departments of Mathematics and Physics, Joshua Shrout, Department of Civil Engineering and Geological Sciences, University of Notre Dame, and Matthew Leevy (Senior Personnel), Notre Dame Integrated Imaging Facility.

The ability to understand and predict complex interactions between biological organisms that respond to differences in their chemical and physical environment will transform our understanding of community behavior. P. aeruginosa and other swarming bacteria colonize water distribution systems, agricultural plants and animals, and many medically important surfaces including engineered materials used in joint replacement, medical imaging instruments, contact lenses, and catheters. Prevention of bacterial colonization is a very important method of preventing subsequent transfer and infection to humans.

This research is supported by the NSF Grants DMS-0719895 and CCF-0622940.

1. Wu, Y., Jiang, Y., Kaiser, D., and M. Alber, Bacteria perceive distant neighbors via repeated cell-cell contacts, Proc. Natl. Acad. Sci. USA USA 106 4 1222-1227 (2009) (featured in the Nature News, Heidi Ledford, Reversing helps bacterial swarms to spread, January 20th, 2009, doi:10.1038/news.2009.43).
2. Wu, Y., Jiang, Y., Kaiser, D., and M. Alber, Social Interactions in Myxobacterial Swarming, PLoS Computational Biology 3 12, e253 (2007).
3. Sozinova, O., Y. Jiang, D. Kaiser, and M. Alber, A Three-Dimensional Model of Fruiting Body Formation, Proc. Natl. Acad. Sci. USA 103 No.46, 17255-17259 (2006).

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, 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.

I am interested in the development, analysis and application of mathematical and computational techniques for understanding biological systems. In particular, much of my recent research to date has focussed on investigating the mechanisms underlying spatio-temporal patterning in developmental biology, along with the integration of domain growth, and I am also interested in modelling systems of coupled biological oscillators.

Oscillations in GnRH neurons. I am looking at systems of ODE's and PDE's for the concentration of ions and signaling proteins in excitatory cells. Included are such things as the endoplasmic reticulum, IP_3 and ryanodine receptors, Na-Ca exchangers, and other ion channels.

Genetic evolution and fitness landscapes. Several projects are envisioned that use either Markov chains or large systems of ODEs to model mutation and selection pressures, including the effects of "hypermutation genes".

Stochastic models for the action of molecular motors, such as kinesin traveling on microtubules.

The geometry and evolution of molecular surfaces for large bio-molecules. PDE methods are used to produce surfaces on which the Poisson-Boltzman equation is solved, with electrostatics contributing to the forces that drive changes in configuration.

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.

My research areas are anatomical, pharmacological, and physiological organization of the cerebellum including connections from the brainstem.

We are looking for a postdoctoral fellow to join a well-established, interdisciplinary collaboration among faculty in the physics, mathematics, neurology and physiology departments at the University of Michigan that is focused on developing quantitative models and methods to investigate the genesis of temporal lobe epilepsy (TLE). Mechanisms proposed to contribute to the development of spontaneous seizure activity following an initial brain insult in TLE include the modification of individual neuron function, changes in neuronal network architecture and differences in neurogenesis processes. In this project, the postdoctoral fellow will develop and analyze a large-scale biophysical network model of the dentate gyrus region of the hippocampus to investigate how experimentally observed changes in the intrinsic properties of the granule neurons and interneurons, that occur in TLE, interact with the experimentally observed changes in network structure, through pathologies of the neurogenesis process, to promote and sustain seizure activity. This project will train the postdoctoral fellow in interdisciplinary, collaborative research in the field of computational neuroscience. The fellow will gain valuable experience integrating results from experimental recordings into biophysically accurate neural network models and numerically analyzing how the experimentally observed pathologies affect network spatio-temporal activity.

Axonal transport is the mechanism by which proteins and membranous organelles move along nerve fibers from their site of synthesis in the nerve cell body. This movement is essential for the growth and survival of axons, and it continues throughout the life of the neuron. I am interested in using mathematical modeling to test specific hypotheses concerning the mechanism of axonal transport.

In the primate, the organization of systems for control of movement is remarkably similar to that of the human. From analysis of signals from neurons in multiple locations within the brain, the communication and coordination within neural networks is being deciphered. In my laboratory, students record for neurons in awake, behaving primates. Opportunities exist for neural network modeling among components of these circuits and analysis of neural influences within the circuits. Quantification of the strengths of connections between the brain and the muscles during movement is also required.

Research in the Bundschuh group revolves around the physical properties and interactions of biopolymers (largely nucleic acids but also some proteins) and statistical as well as algorithmic questions in biological sequence analysis. Current research includes projects on the thermodynamics and kinetics of RNA secondary structure, RNA editing, and protein sequence database searches.

I am interested in using mathematics to develop and analyse mathematical models that provide mechanistic insight into the behaviour of biomedical systems in normal and diseased states. General application areas of interest to me include the growth and treatment of solid tumours, wound healing, tissue engineering and stem cell biology. The mathematical techniques that I use range from nonlinear dynamics and asymptotic analysis to continuum mechanics and multiscale-hybrid modelling. Collaboration with experimentalists is extremely important to me in order to ensure that the models we develop are biologically meaningful and generate useful, testable predictions. For example, I am working with experimental colleagues in order to assess the feasibility of using genetically-engineered macrophages loaded with magnetic nano-particles to target the delivery of chemotherapy to hypoxic tumour regions. Other projects involve investigating how mutations in the Wnt signalling pathway influence the early stages of colorectal cancer and studying how biomechanical cross-talk between cancer and stromal cells (eg fibroblasts) may influence a tumour's development.

I have been working on runtime systems for data management and manipulation of very large databases, and hypergraph partitioning methods, with a particular focus on parallel computing applications. My current research focuses on runtime optimizations and systems software for efficient storage and processing of very large scientific datasets on disk-based storage clusters and in the grid environment.

Our group studies gene transcriptional regulation during animal development, using the microscopic nematode C. elegans as a research model. We are interested in understanding gene regulatory networks, and the gene regulatory logic responsible for complex biological processes. We are also interested in comparative genomics, and in understanding the molecular changes responsible for phenotypic differences between and within species.

Long Chen has been working on advanced numerical methods for partial differential equations (PDEs) that arise from scientific and engineering applications. The theme of my research is on the development, analysis, and applications of multilevel adaptive finite element methods. More precisely, I am interested in the mesh generation and optimization, mesh adaptation through local refinement, multi-grid method, super-convergence, and error estimate on adaptive finite element methods. Recently I am developing an efficient MATLAB software package for adaptive finite element method and high order finite volume method for elliptic equations.

My research area is Computational Systems Biology. In this area, I have been working on (1) modeling signaling pathways of pheromone response of yeast cells; (2) modeling feedback regulation in a cell lineage of the epithelium and cell stratification within the epithelium. Trained as a numerical analyst, I am also specialized in numerical partial differential equations. Most of my work is computational analysis of complex biological systems. Recently, I also work on stochastic models arising from yeast cell signaling pathway.

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).

My research in mathematical neuroscience uses tools from nonlinear dynamics and statistical physics to probe the fundamental mechanisms responsible for experimentally observed behaviour in a number of settings. My recent work has been concerned with developing a sound understanding of single neuron models and developing the tools to understand their dynamics at the network level. As an EPSRC Advanced Research Fellow (2002-2007) I developed theoretical work for the understanding of travelling waves and spatially structured activity in cortical and thalamic neural tissue. I am now actively engaged with experimentalists at Nottingham promoting the practical application of his work. Together with Prof. D Auer (Academic Radiology) I am working on the analysis of resting state brain activity (using combined EEG & functional MRI data), with Dr. C Sumner (MRC Institute of hearing research), I am studying mode-locked spike trains in responses of ventral cochlear nucleus chopper neurons to periodic stimuli, with Dr. R Mason (Electrophysiology), I am exploring the effect of cannabinoids on emergent neural network dynamics, and with Dr J. Peirce (Psychology) have just secured Wellcome Trust funding to develop feature based models of visual cortex. My other main research activity outside Nottingham is with Dr. Y. Timofeeva (Warwick) on a biophysically realistic model of branched dendritic tissue with active spines and the design principles by which dendritic machinery is used for information processing.

I am currently PI of the EPSRC funded UK Mathematical Neuroscience Network (http://mathneuronet.org.uk/), whose remit is to bring together experimental neuroscientists and mathematicians to tackle outstanding challenges in the neurosciences.

My primary research interest lies in understanding the dynamics and underlying processes of adaptive evolution. By using tractable experimental systems I aim to identify and integrate these processes at genotypic and phenotypic levels, and examine how they depend on genetic and environmental factors.

My approach uses experimental evolution - the lab based study of evolving populations. This approach is multi-disciplinary, incorporating molecular genetics, microbiology and ecology, as well as evolution. Experimental approaches examine evolution as it happens in the context of replicated and controlled studies. In the main, my work has used microbial systems. Advantages of these systems include: short generation times, large populations sizes, tractable genetics and the ability to store populations in a state of 'suspended animation' for subsequent study. These features make microbial systems powerful models with which to perform rigorous tests of ecological and evolutionary theories. The ability to perform evolution experiments in 'real-time' offers the possibility to design experiments to experimentally test theoretical predictions of evolutionary processes.

As an example of the application of experimental evolution to mathematical biology, a current project aims to identify and measure biological parameters that influence adaptation, and incorporate these parameters into computational and analytical models that track the predictability of repeated bouts of evolution. Predicting the dynamics of evolving populations has been a long-standing goal of biology. This ability would open new questions: How repeatable is evolution? How many mutations are required to reach a local fitness peak? How long should we expect a population to take to explore all available fitness peaks, and what intermediates is it likely to pass through during this exploration?

My mathematical-biosciences research interests are 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. I am developing the necessary mathematical tools principally within the field of spatial statistics. Another interest is in ecology, biosecurity, and the spread of invasive species. This involves using a combination of pde's, heirarchical spatio-temporal statistical models, and Bayesian inference.

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.

The Daniel Lab works on insect flight control and aerodynamics, including investigations of the underlying circuitry using tools from computational neuroscience.

My lab uses theoretical and computational approaches based on statistical physics to uncover basic mechanistic principles underlying our innate and adaptive immune response. Obtaining such mechanistic principles from experimental observations alone is often difficult because the pertinent processes include co-operative dynamic events with many participating components. A further complication that confounds intuition is stochastic fluctuations in these systems with small numbers of molecules. However, by synergistically integrating observations from experiments with transgenic animals, single molecule techniques and imaging studies with these theoretical and computational approaches we can provide system-level understanding into such complex systems. The mechanistic insight gained from such studies not only will help develop future experiments to unravel basic principles of our immune system, but may also help envision therapeutic strategies for infectious diseases and autoimmune disorders. More details can be found at the lab website,http://openwetware.org/wiki/User:Jayajit_Das

I am interested in applying mathematics to application problems, especially nonlinear wave phenomena. I use a wide array of mathematical methods, both analytical and numerical. The methods I use come from a variety of mathematical areas such as Integrable Systems and Solitons, Dynamical Systems, Hamiltonian Dynamics, Riemann Surfaces and Algebraic Geometry, Lie Algebras, Complex Variables, Asymptotics and Perturbation theory.Although I have not worked on biological problems thus far, the mathematical techniques I use are relevant for the study of pattern formation and the investigation of coherent structures, which often arise in biological applications.

German Enciso studies network architectures of complex biological systems. His research interests involve developing and studying models of biochemical processes which use available molecular data to describe overall dynamics and to provide useful ideas for the design of new experiments. This work involves the development of new mathematical theory.

My research is focused on ion channels in secretory cells, and the exploration of their role in regulating hormone secretion and gene expression. I am interested in the possibility that electrically-coupled endocrine cells function as synchronized coupled oscillators, wherein hormone secretion is tightly linked to Ca2+ influx through synchronized oscillating membrane potentials. Secretion may be optimized in glandular cells through modulation of waveform amplitude and frequency. Mathematical models of electrical activity in cellular networks can be tested using electrophysiological methods, including patch clamp.

I work on the development, analysis and application of mathematical and computational methods to biological problems, with a focus on problems in which stochastic effects and multiscale phenomena play a key role. The biological systems I have investigated to date include gene regulatory networks, bacterial and amoeboid chemotaxis, reaction-diffusion processes with applications to morphogenesis, pharmacological applications of chemisorption, cell-cycle modelling, social insect behaviour and ion channels. To understand the behaviour of these systems, I use a combination of mathematical and computational approaches that include partial differential equations, stochastic simulation algorithms, networks and data analysis.

Noisy oscillators: How does noise interact with rhythmic phenomena in the nervous system and other areas of biology? We use small noise expansion and the phase resetting curve of oscillators to understand how correlated inputs can affect the synchrony or both coupled and uncoupled oscillators. We also characterize what types of oscillators are optimal fro transmitting correlated inputs to correlated outputs.

Dynamics and phase resetting: The phase resetting curve (PRC) tells us how the timing of inputs shift the timing of oscillators. The shapse of these curves are important both in coupled and in forced systems and play a critical role in synchronization. In neurons, there are many currents which are subject to modulation and these currents can have a strong affect on the shape and sensitivity of the PRC. Uncorrelated noise and coupling to other oscillators also alter the shape of the PRC. We use nonlinear dynamics and simulations to study how these curves are changed.

Pattern formation in neural systems: This is fun stuff. I continue a long held interest in hallucinations and phosphenes as well as various types of pattern sensitive and reflex epilepsies. I am interested in mechanisms through which flickering light can induce geometric hallucinations as well as seizures in susceptible populations.

Waves and persistent states in neural systems: Due to the massive recurrent interactions between neurons, networks are able to sustain various types of persistent activity. By persistent, I mean activity that remains after a stimulus is removed. Working memory is believed to be such a state - a localized region of cortex remains active until the memory task is completed. We have several types of models involving combinations of multi-region interactions, multi-layer interactions and facilitation.

Another type of persistent activity comes in the form of propagating waves. These are observed in brain slices, cell cultures, and in vivo. We use spatial networks of neurons and singular perturbation theory to study propagation of activity in one- and two-dimensions.

Modeling the inflammatory response: Pathogens, damage, and other insults to the body can result in inflammation which can sometimes be worse than the original insult. We work closely with several people at UPMC developing models for the signalling pathways and responses of the innate immune system. We have applied these models to influenza, malaria, lung inflammation, necrotizing enterocolitis, and multiple organ dysfunction syndrome.

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.

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.

My research is primarily in the application of continuum modelling in cellular and physiological systems. One current focus is the micro-biofluidics of ciliate and flagellate flows, especially the biophysical basis of spermatozoa swimming, which is pursued with collaborators from the Reproductive Biology and Genetics at The University of Birmingham and The Centre for Human Reproductive Science, Birmingham Women's NHS Foundation Trust. Another area of current interest concerns ocular surface fluid dynamics and solute transport, especially in the context of "dry eye" with the collaboration of researchers from The Nuffield Laboratory of Ophthalmology, University of Oxford. I am also particularly interested in reaction diffusion models of oxygen and metabolite transport in skeletal and cardiac muscle, supporting research within The Centre for Cardiovascular Sciences, University of Birmingham.

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.

My research has focused generally on bifurcation theory and its applications and more recently on transitions from synchronous states in networks of differential equations. This work is motivated by central pattern generators for animal gaits, the orientation tuning structure of the primary visual cortex, and the discussion of motifs in biological networks.

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.

One of the interests of my lab is to establish the architecture of regulatory networks in higher eukaryotes, using plants (Arabidopsis and maize) as models. We utilize combinations of genome-wide RNA profiling (microarrays) coupled with chromatin immunoprecipitation (ChIP) and genome-widel location analyses (ChIP on chip) to determine where transcription factors bind in the genome and what genes they directly control. This information is then used to populate our databases on plant transcription factors and cis-regulatory elements, with the goal to visualize regulatory motifs. We also investigate how transcription factors with very similar DNA-binding domains acquire regulatory specificity, primarily by interacting with other cofactors.

I study the mathematical and computational modeling of free boundary flows arising in biomedical applications. My research interests include modeling of arterial blood flow and mitral valve function.

Patrick Guidotti's research is the areas of Nonlinear Partial Differential Equations and their Applications and in Applied Mathematics.

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.

I use a combination of mathematical modeling and experimental work, mainly with fish, to study the evolution of social behavior. Many behaviors, like cooperation or mating displays, only make sense if we consider the social context in which they occur. However, that social context emerges from social interactions that are also under selection. Therefore, social behavior is both a target and an agent of selection. Specific areas of research include: punishment and cooperation in cooperatively-breeding groups, including helping behavior and self-inhibition of growth and reproduction as responses to credible threats of punishment, direct benefits of cooperative behavior, cooperative syndromes (consistent individual differences in cooperation across contexts),the use of socially acquired information as a cause and consequence of group living and social influences on mating systems, foraging and territorial behavior.

My field is population dynamics, specifically of infectious diseases (but on and off I also work on stability of ecosystems). I am a biologist and a mathematician by university training and my PhD thesis (1992; title: R_0) was supervised by Odo Diekmann and Hans Metz. In my thesis we developed the next-generation theory to calculate the basic reproduction number for infectious diseases in heterogeneous populations, which has been in use ever since throughout the epidemic modelling field.

My group is called Theoretical Epidemiology and is part of the Faculty of Veterinary Medicine of Utrecht University in The Netherlands. The group consists of one professor (me), one associate professor, two assistant professors, two postdocs and six PhD students. Our work is divided approximately evenly between the development of new mathematical methods, using mathematics to study questions on human infections, and using mathematics to study questions on animal infections (farmed animals and wildlife). In 2000 Odo Diekmann and I published a textbook in mathematical epidemiology (Mathematical epidemiology of infectious diseases: model building, analysis and interpretation; Wiley). Currently we are finishing a new version of this book, much expanded in the direction of stochastic systems, together with Tom Britton (Stockholm). Recent work in the group has focussed on the interaction between different levels of biological integration in determining the dynamics of infectious agents. Within this focus, one large project is devoted to immuno-epidemiology (interaction between within-host dynamics of the immune reaction and between-host transmission), and one large project is devoted to infectious diseases in metapopulations (interaction within a local population coupled to spread between these local populations). An example of our work on the latter can be found in Nature in 2008 (Davis et al.), where we showed that percolation theory is relevant to explain epidemics of plague in vast metapopulations of rodents in Kazachstan.

Additional information: I am one of the editors-in-chief of a new journal called Epidemics; an editor of Mathematical Biosciences; and one of the editors of Proceedings of the Royal Society B. I mention this only to show that my activities, the problems to which I am exposed, and contacts are very much mixed between biology, mathematics and their interaction. In addition, my group is part of the recently established (virtual) Utrecht Centre for Infection Dynamics (UCID), where the people working in the field of infectious disease dynamics at the academic hospital of Utrecht (UMCU), at the mathematics department, at the Institute for Risk Asessment Sciences (IRAS), at the national centre for infectious disease control (Cib, RIVM), and in my group collaborate and exchange ideas and knowledge (including journal clubs, lectures, joint working sessions). Together with the above brief outline this adds to the fact that Utrecht provides a dynamic and stimulating environment for a postdoc. If I can be of service and interest then I gladly offer to be part of the mentoring program.

Most of my research has been in nonlinear dynamical systems, including simple stochastic ODEs, with applications in the physical and biological sciences and in engineering. My current work is driven by the question "How do neural spikes determine behavior?" I collaborate with biomechanicians and neuroscientists, focusing on mathematical models of legged locomotion, anguilliform swimming, decision making and other cognitive tasks.

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.

Partial Differential Equations (PDE) enjoyed a variety of applications in Engineering, Industry, Biology, and Math Finance. Many interesting physical processes can be modeled using PDEs. I am particularly interested in nonlinear PDE problems such as free boundary problems with PDE estimates. My recent interests include applications of mathematics to models in tumor growth, thermal runaways, etc.

My group is working on developing computational methods for modeling and understanding complex biological processes such as cancer progression and developmental biology. At the molecular level, we take machine learning and data mining approaches for identifying gene networks using microarray and massive parallel sequencing (MPS) data. Since the MPS technology (e.g., ChIP-seq, RNA-seq) are relatively new, we also develop new algorithms and software tools for analyzing and visualizing such data. At the cellular and tissue level, we develop new image analysis algorithms for reconstructing high resolution 3D models using large set of microscopy data (i.e., in the scale of terabytes). Our algorithms cover the entire image processing pipeline including image registration, segmentation, visualization and quantification. Finally, we extend the computational framework by integrating the molecular and imaging data with clinical information in translational applications.

As a group of genetic diseases, cancer presents some of the most challenging problems for basic scientists, clinical investigators, and practitioners. In order to design treatments that are capable of specifically targeting the invasive cancer cells that drive malignant tumor growth, it is necessary to understand the mechanisms by which these cells initiate angiogenesis, enhance their motility, relax adhesive cellular bonds and penetrate normal tissue. Due to the inherent complexity of the many interconnected physiological processes involved in tumor initiation, new blood vessel formation, and cell invasion, conventional experimental approaches alone are often unable to penetrate to the core of these issues. Further, given the multi-scaled pathophysiology involved, it is becoming ever so important for cancer research to make use of cross-disciplinary, systems science approaches, in which innovative computational cancer models play a central role. Our research is aimed at combining mathematical modeling, numerical simulation, and carefully designed experiments to develop a comprehensive and predictive framework for better understanding tumor development and for improving cancer treatment. Many of our mathematical models consist of both continuous (partial differential equations) and discrete (cell-based) approaches to capture the complexity of tumorigenesis. Our current research focuses on molecular pathways and cell-tissue interactions associated with tumor angiogenesis, causes and consequences of tumor heterogeneity, and cancer cell - endothelial cell cross talk during angiogenesis and invasion.

Research area: We are interested in phenotype-genotype correlation in complex and infectious diseases as well as the evolution and geographic spread of pathogens. It is through comparison that we identify functional regions of DNA, diagnose affected from unaffected individuals, or distinguish pathogenic from nonpathogenic organisms. To this end, the field of computational phylogenetics has much to offer for the understanding of complex and infectious diseases. An alignment of various organisms can identify regulatory regions conserved by evolution. Moreover, a phylogenetic tree search provides a complete accounting of candidate genes that changed between ancestors and descendants in patient populations or disease causing organisms.

We have ongoing work on:

• The evolution and spread of influenza (e.g. drug resistance, zoonosis, and reassortment).
• Quasispecies evolution of HIV at the mother/fetus interface.
• Evolution and spread of zoonotic coronaviruses.
• Networks of community and hospital acquired multi-drug resistant organisms from the viewpoints of the pathogens and the hosts (humans and animals).
• Models the spread of schistosomiasis-carrying snails as a result of dam construction.
• Evolution of microbial biofilms.
• Developing better approaches to track lineages of pathogens.

Oliver Jensen's research involves the application of continuum mechanics and mathematical modelling to topics in medicine and biology. He has particular interests in problems involving flow-structure interaction and interfacial forces in the cardiovascular and respiratory systems, such as cell adhesion in the microcirculation, surface-tension driven flows in lung airways and instabilities in flows through flexible vessels. Other areas of interest include the mechanics of cells and tissues (in both plants and animals) and transport in physiological systems.

My current research interests are in two areas: (a) characterization of signaling pathways induced by the activation of RET receptor tyrosine kinases in human cancers and clinical applications of the acquired information to improve medical care for patients with cancers of MEN 2 inherited cancer syndromes or papillary thyroid carcinoma; and (b) characterization and regulation of Na+/I- symporter(NIS) and its clinical applications in noninvasive tumor imaging in vivo and radioiodine therapy for human cancers by induced endogenous NIS expression or by NIS gene transfer to facilitate exogenous NIS expression.

Jorgensen's research focuses on such areas of mathematics that have found use in physics and in engineering: In physics, this includes quantum mechanics, quantum computing, relativity and quantum field theory. In engineering, signal and image processing, representation of signals, time-frequency analysis, wavelet representations and algorithms, and bit-quantization.

The journals where his research papers appeared in 2008 include general state-of-the-art mathematics journals, as well as specialized journals in applied mathematics, in approximation theory, and in mathematical physics.

I am interested in a number of areas of mathematical biology. My research focuses on the application of tools from dynamical systems and stochastic processes to understand patterned activity in networks of biological units. My main interest is neuroscience, and I work with several experimental neuroscientists in Houston who are experts in multiple electrode recordings. I am also interested in the dynamics of gene networks, and collaborate with other experimentalists working in this area. Therefore a postdoc working with me would be involved in a project that would involve an experimental component.

Nerve cells communicate by conducting electrical signals along slender cytoplasmic extensions known as axons. Animals have evolved two basic mechanisms for increasing axonal conduction velocity. One is to increase axonal diameter and the other is to insulate axons by a process called myelination, which is a tight spiral wrapping of the axons that is formed by myelinating cells. In vertebrates the growth of axon diameter is caused principally by the accumulation of space-filling cytoskeletal polymers called neurofilaments inside the axons, and this is regulated locally by chemical signals from the myelinating cells. It is known that neurofilaments are transported along axons and that they alternate between rapid movements and prolonged pauses. The proportion of the time that the neurofilaments spend pausing is likely to be a principal determinant of their residence time in axons. This is a collaborative experimental and modeling project involving a biologist at Ohio State University and a physicist at Ohio University. The central hypothesis to be tested is that myelinating cells control axonal caliber by regulating neurofilament pausing. A computational model will be developed that relates the moving and pausing behavior of neurofilaments to their distribution along axons. The model will be based on detailed kinetic parameters of neurofilament movement derived experimentally in cultured neurons and will be verified experimentally by fluorescence microscopy of neurofilament movement in myelinated axons in tissue culture. This research will generate a rigorous and quantitative framework that relates the size and shape of axons, which is a key influence on their electrical properties, to the moving and pausing behavior of their internal constituents.

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.

My research interests lie in the field of computational mathematics and its application to physical, medical and biological areas. Particularly, I am interested in wave motion, level set methods, computational anatomy, and inverse problems. For medical and biological applications, I am working on the structural study of human brains, automatic numerical extraction of ciliary muscle, cell differentiation, and general image processing techniques based on partial differential equations.

We use a combination of mathematical, computational and lab experimental approaches to explore evolutionary and ecological dynamics. Particular areas of interest include the evolution of cooperation, disease ecology and evolution, the evolution of cognition, and evolutionary feedback from niche construction.

Keyfitz works on the analysis of Hyperbolic Conservation Laws (CL) and conservation laws that change type. The term "conservation laws" refers to systems of quasilinear hyperbolic partial differential equations. Although such systems are of great importance in scientific and engineering applications -- for example, compressible flow, high-speed flow, climate modelling, elasticity -- establishing well- posedness results that generalize the linear theory has proceeded slowly. In more than one space dimension, the correct function spaces for solutions are not know. Keyfitz and co-workers are pursuing a program that has had some success in studying self-similar, or quasi-steady, solutions of multidimensional systems. For systems of physical interest -- such as the gas dynamics equations -- the self-similar systems change type, being hyperbolic for some states and of mixed (hyperbolic-elliptic) type for others.

Change of type in CL also occurs in a different context, that of unsteady flow. Here it arises in some models for complex flows (such as two-phase and porous medium flow), and also in some models for tumor growth in mathematical oncology. Here the issues are quite different, as the linearized equations are catastrophically ill-posed, and nonlinear effects can stabilize the solutions only in a limited sense -- which may nonetheless say something interesting about the models.

There are interesting analytical questions in change-of-type systems from both sources. Unsteady change of type also gives rise to a number of questions to do with modelling, including the addition of other spatial and temporal scales, and more and better physics.

Multiscale deterministic and stochastic modelling of biological processes, including bacterial populations (intercellular signalling, biofilm growth, biofuel generation), regenerative medicine (intracellular signalling, stem-cell differentiation, tissue engineering) and plant growth (gene regulatory networks, biomechanics). The scales in question are subcellular, cellular (including single-cell motility) and organ/tissue and there is interest in developing the relevant asymptotic methods as well as investigating specific biological applications.

Natalia Komarova is interested in mathematical research in life sciences. Her two main areas of interest are cancer modeling and the evolution and learning of natural languages. In cancer research, she has investigated the following questions important for understanding of cancer: What are cellular origins of cancer? What is the role of stem cells in carcinogenesis? How can we fight resistance to drug therapies? In the area of language, Natalia focuses on the evolutionary models of color categorization, as well as questions of language learning and change. She studies both stochastic and deterministic modeling, and uses a combination of analytic and numerical approaches to solve problems.

Nancy Kopell is interested in brain dynamics, especially the range of cortical rhythms associated with sensory processing, cognitive activities and motor planning. She collaborates on projects concerning the physiology of in vitro rhythms, the mechanisms of in vivo dynamics associated with attention and learning, and relationship of pathologies in rhythms to neurological diseases. She works mainly with biophysical representations of networks of neurons, using dynamical systems methods of analysis.

My research interests include mathematical ecology and disease dynamics.

My research interests are in the area of statistical genetics, with a focus on the development of statistical methods for inferring phylogenies from molecular data. My recent work in this area is focused on bridging the gap between traditional phylogenetic techniques and methodology used in population genetics analyses, primarily through the application of coalescent theory to species-level phylogenetic inference. I have also worked in other areas of statistical genetics, including microarray data analysis and linkage studies.

My research interests include data-intensive computing, where I have developed techniques, systems software, and middleware tools to provide support for storage, data management, and manipulation of very large scientific datasets. In particular, in high-performance computing area, I am interested in domain decomposition techniques for efficient distribution of data and computation in scientific and engineering applications on distributed-memory machines, and the application of parallel computing in scientific visualization.

This laboratory studies molecular mechanisms underlying Alzheimer's disease pathogenesis. One aspect of our program focuses on the discovery of small molecule ligands that bind and also block the formation of neurofibrillary lesions, which are comprised of proteinaceous filaments. We are interested in applying mathematical modeling in conjunction with inhibition kinetic data to clarify the mechanism of action of these ligands.

My research interests lie in the development and application of computational techniques for statistical inference for partially observed stochastic processes. My work so far can be broadly split into two main areas: the development of efficient Markov Chain Monte Carlo (MCMC) algorithms for missing data problems; and the application of these and alternative computational methods to answer important scientific questions in different areas.

Most of my current research interests involve applications of Bayesian statistics and especially parameter inference to a variety of problems, such as stochastic epidemic models for infectious diseases (e.g. healthcare-associated infections, Foot-and-Mouth, Avian Influenza); exploring the anatomical features of the human brain using diffusion-weighted magnetic resonance images; stochastic chemical kinetic models with applications in systems and synthetic biology; semi-parametric time series models; network traffic modelling. Finally, I have recently been very interested in how High Performance Computing (and in particular parallel programming) can help in obtaining efficient algorithms for the aforementioned problems. More information about my research can found here: http://www.maths.nottingham.ac.uk/~tk

Research program:

1. Cancer systems biology. This is a project joint with cancer biologists at the Wake Forest University School of Medicine and the laboratory of Vladimir Shulaev at VBI. There are two main components:
   • iron metabolism in healthy and malignant breast epithelial cells. The main focus is the construction of a dynamic mathematical model that elucidates the changes taking place as breast cancer progresses.
   • a metabolomics approach to breast cancer detection. The focus is the development and use of new mathematical tools for the analysis of mass spectrometry data from cell culture and blood plasma samples. As one example, we are exploring the use of persistent homology for this purpose.
2. Modeling tools for computational systems biology. Using tools from computer algebra and algebraic geometry, we are working on developing mathematical tools for the modeling and simulation of biological networks, in particular gene regulatory networks. This includes the development of modeling software.

Harold Layton uses mathematical modeling to better understand the physiology and pathophysiology of the mammalian kidney. His research is mostly directed to elucidating aspects of renal hemodynamic control and to gaining a better understanding of the urine concentrating mechanism in the mammalian inner medulla. Modeling by Layton and his collaborators ranges from the cellular level, to the level of the nephron (which is the functional unit of the kidney), to the level of interactions among large populations of nephrons. The work on renal hemodynamic control is of mathematical interest because of the wide variety of control mechanisms and dynamical behaviors that have been observed by physiologists. Moreover, understanding renal hemodynamics is fundamental to gaining a better understanding of the control of blood pressure, total body water content, and electrolyte balance. Future work in renal hemodynamics will focused on gaining a better understanding of disorders that arise from disease or as side effects of pharmacological interventions. Collaborator Leon Moore (Physiology and Biophysics, SUNY Stony Brook) provides indispensable assistance in modeling hemodynamics. The work on the concentrating mechanism involves interactions among renal tubules that are arranged in complicated, but highly structured, patterns. The principal goal of this work is to understand how the renal medulla can produce urines that have very high osmolalities, relative to blood plasma. It is surprising that much of the pertinent micro-anatomy of the medulla of the kidney is only now being described by collaborators Thomas Pannabecker and William Dantzler at the University of Arizona.

The models of hemodynamic control involve small systems of semilinear hyperbolic partial differential equations (PDEs) with time-delays, which are solved numerically, or which are linearized for analytical investigation. Models presently under development include more detailed representations of fluid Dynamics in renal vessels and tubules. Models for the concentrating mechanism involve large systems of coupled hyperbolic PDEs that describe tubular advection, transepithelial transport, and preferential interactions among specific populations of vessels and tubules. Model formulation and analysis is conducted in collaboration with Anita Layton (Duke University), who is an expert in the scientific computing. Publications arising from this research program can be viewed at http://fds.duke.edu/db/aas/math/faculty/layton/publications

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.

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.

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.

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.

John Lowengrub's research interests focus on computational mechanics applied to a variety of different problems at the macro-, micro- and nano- scales in fluid dynamics, materials science and biology. In fluid dynamics, I have most recently been interested in complex fluid flows involving multi-component lipid bi-layer membranes. In materials science, I have been most recently interested in the growth of thin films and the self-assembly of nanostructures such as quantum dots and wires. In biology, my interests have centered on modeling solid tumor growth and tumor-induced angiogenesis. My work is characterized by the development of nonlinear models, analysis of the models and the development of sophisticated numerical algorithms to simulate solutions of the models.

Biological function arises from the integration of processes acting across a range of temporal and spatial scales. My research aims at investigating how these processes interact within and across scales using the techniques of applied mathematics and numerical simulation. Particular application areas include pattern formation in early development, aspects of bacterial chemotaxis, cancer growth and wound healing. Further details can be found at http://people.maths.ox.ac.uk/~maini/

We use the vertebrate retina, which is part of the brain, as a model system for understanding brain function due to its easy accessibility and well-characterized inputs. My laboratory is currently pursuing two research objectives using electrophysiological, neurochemical, anatomical, and computational techniques. First, we are studying how a circadian (24-hour) clock, a type of biological oscillator, in the retina modulates cellular processes and chemical and electrical synaptic transmission to control adaptive state so that the retina can respond to visual images in both the day and night during which the ambient or background illumination changes by approximately 8 orders of magnitude. Second, we are studying the cellular, subcellular, and neural network mechanisms that underlie the computation of the direction of image motion in the retina. The neural coding of the direction of stimulus motion, which is a classic example of local neural computation, is a common feature of the nervous system.

I use a combination of models, field sampling, and laboratory experiments to understand population structure and dynamics and the adaptiveness of energetic and behavioral traits (mainly of fish) in changing environments.

Jonathan Mattingly works primarily is stochastic dynamics, stochastic modeling, and stochastic analysis. He is interested in both specific models and more general questions of pure stochastic analysis motivated by applied questions.

In general, he is interested in stochastic dynamical systems and there qualitative behavior. In the biological context, he has worked on a number of problems related to stochastic fluctuations in biochemical networks. He is currently interested in the properties of large chemical networks, and using ideas from averaging to obtain effective reduced dynamics, and the qualitative behavior of specific small dimensional networks of biological importance. Recently, he has also become interested in using random algorithms to analyses large genomic data sets.

He as also worked on a number issues in simulating stochastic differential equations. He has looked at long time simulations, higher order methods, and adaptive methods.

He as worked one the spread of randomness though stochastically forced PDEs showing how it moves from scale to scale. Examples he has consider are the stochastic Navier-Stokes equations, Stochastic reaction diffusion equations, and a chain of anharmonic oscillators. More generally he has worked on the ergodic theory of infinite dimensional Markov processes including stochastic delay equations. In this context he has developed the tools from Malliavin calculus to understand the smoothing properties of stochastic PDEs.

For more information and publication see \texttt{http://www.math.duke.edu/~jonm/}.

Victor Matveev's research is focused on the mathematical and computational modeling of synaptic neurotransmitter release, including activity-dependent changes in synaptic strength termed short-term synaptic plasticity. Since calcium influx through voltage-dependent calcium channels serves as the main trigger for neurotransmitter release, this line of research requires the modeling of intracellular calcium ion diffusion, which is also relevant in the investigation of other fundamental physiological processes such as muscle contraction. V. Matveev is particularly interested in the role that the endogenous calcium buffers (such as calbindin, parvalbumin, etc.) play in shaping spatio-temporal dynamics of cell calcium signals. To help in this modeling work, V. Matveev is developing a software modeling tool called Calcium Calculator (http://www.calciumcalculator.org). Finally, V. Matveev is also exploring the impact of short-term synaptic dynamics on the activity and information-processing properties of neuronal networks.

I am interested in stochastic chemical kinetics and the analysis of complex biochemical networks. An important part of my research focuses on the development of bioinformatics algorithms with special emphasis on data clustering and dimensionality reduction. Active collaborations with experimental biologists include: (a) the analysis of the binding sensitivity of radioligands required for whole brain imaging of neurofibrillary lesions at different stages of Alzheimer's disease (Dr. Jeff Kuret, OSU), and (b) the modeling of tubulogenesis in zebrafish embryos (Dr. Jeff Essner, Iowa State University).

Gin McCollum is a theoretical neurobiologist who mathematically formalizes logical structure found in sensorimotor behavior, both motor and perceptual, and in neuronal populations and pathways relating to sensorimotor function. She is a theoretical physicist by training who has worked in theoretical neurobiology since the late 1970's. She has collaborated with several experimental neurobiologists, including Lewis M. Nashner, Lee Robertson, Neal H. Barmack, and Richard A. Boyle, and supervised several mathematical postdoctoral projects, including those of Jan Holly, Patrick D. Roberts, and Douglas A. Hanes. A current topic of interest is the range of symmetry groups that guide sensorimotor function in the central vestibular system.

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 uses game-theoretic and dynamic modeling 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.

My research interests include demography, epidemics and immunology, applied mathematics and numerical analysis.

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.

Nadim studies the mechanisms underlying generation and its neuromodulation of oscillations in small networks. The Nadim lab does electrophysiology and imaging experiments and the data are used to build computer and mathematical models that describe cellular and synaptic mechanisms involved different aspects of network bursting oscillations. A current focus of the lab is the mechanisms underlying frequency-preference of neurons and synapses, the neuromodulation of the preferred frequencies and how preferred frequencies of network components interact to determine the network frequency and the activity phase of component neurons. In the Nadim lab you will have the opportunity to be trained in both experimental and modeling aspects of network rhythm generation.

I am interested in the statistical modeling of biological and medical data. In collaboration with neurologists, I have built models for sleep-wake duration processes, and MRI lesion counts from patients suffering from Relapsing Remitting Multiple Sclerosis. I have interest in modelling lupus relapse phenomenon and have developed renewal process based parametric models. This has led to substantial collaboration with OSU nephrologists over the past decade. I also work in the area of ordered data analysis (order statistics and record values) and clinical trial designs.

Claudia Neuhauser is interested in two areas of biology: ecology and genetics. In ecology, she investigates spatial stochastic processes to study the role of space in community dynamics. In genetics, her research focuses on how selection affects genealogies.

Qing Nie works in the areas of computational biology and systems biology with applications to regulatory networks, cell signaling, cell fate switches, stem cells, and morphogenesis.

My research interests include the study of complex systems using agent-based modeling. I have created a model of the immune system that can be used to study many different aspects of disease. My current focus for this project is the study of potential mechanisms for the idiopathic interstitial lung diseases. I also have a project that involves studying the Medical Intensive Care Unit using agent based modeling, for the purpose of finding ways to improve compliance with best practices. In addition I am interested in applying computational methods including Artificial Neural Network analysis to medical data for the purpose of discovering new associations between patient phenotype, gene expression and disease processes.

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.

My laboratory utilizes a combination of cellular, molecular, and behavioral approaches to examine the second messenger signaling and transcriptional pathways that regulate biological timing. Another area of research examines the cellular signaling events that couple changes in cytosolic calcium to transcriptionally-dependent forms of neuronal plasticity in the cortex and hippocampus.

My research is concerned with stochastic models for the spread of communicable diseases, and in particular the development of methods for statistical inference of data from outbreaks. Computational techniques such as Markov chain Monte Carlo methods and data imputation methods are an important feature of this work. Recent areas of application are (i) influenza and (ii) nosocomial pathogens, especially antibiotic-resistant pathogens such as MRSA, VRE etc.

My lab has a long-standing interest in understanding how signaling pathways elicit selective changes in gene transcription in mammalian cells. More recently, we have become interested in understanding interactions between signaling pathways locating the different cell types involved in these complex biological processes of cancer cell progression and normal cellular differentiation. For example, a breast tumor is composed not only of the epithelial-cell derived tumor cell, but also stromal cells, endothelial cells, and immune cells including macrophages, B-cells and T-cells. It is the interaction of these cell types through complex signaling networks that are likely to be important for tumor cell progression and metastasis and not just the action of individual signaling pathways within the epithelial tumor cell.

Major research interests include pattern formation in development, cell-based and continuum descriptions of cell and tissue movement, analysis of complex metabolic and gene-control networks, and mathematical models of tumor development.

My principal research interests are in the application of nonlinear mathematical models to problems in cell biology, in particular to cancer, angiogenesis (the growth of new blood vessels), developmental biology (both in animals and plants) and neuroscience. I also have an interest in ecology and immunology. I use a variety of mathematical approaches, including models for single cells, populations and tissues, and a range of tools for mathematical analysis and computer simulation. Much of this work is underpinned by multidisciplinary collaborations with life scientists, engineers, computer scientists and other mathematicians (e.g. projects on regenerative medicine and plant root growth, and the Interdisciplinary Angiogenesis Network, ANGIONET).

My research interests are broadly in the area of data mining, network analysis and bioinformatics. Sample projects currently underway include: motif extraction from structured data (e.g. proteins, drugs), mathematical modeling of shape and mining in the context of eye disease prognosis and longitudunal analysis, and the analysis of gene and protein interaction networks.

My research interests include systems biology of decision-making and bioinspired engineering design. In particular I study mathematical modeling and analysis of coordinated motion, social foraging, group choice, and task allocation for multiagent (animal or robot) systems. Methods include stability theory for distributed feedback systems, evolutionary game theory, and optimization. In coordinated motion in swarms of insects, cells, or robots we focus on video analysis methods for finding dynamical patterns and developing models, and stability analysis of group cohesion and guidance mechanisms. In cooperative choice by honey bees or groups of robots we study process stability, and choice behavior and evolutionary adaptation using computational models. In social foraging we use evolutionary game-theoretic and stability formulations to analyze the distribution of foragers across a landscape of food, robots across surveillance areas, or heat energy across areas in a multizone temperature control application.

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.

My work focuses on developing and analyzing models of biochemical signaling in excitable cell systems. Projects continue to be: 1) calcium waves in pyramidal cells as a signal of long term plasticity, 2) short and long term effects of cyclic-AMP and protein kinase A signaling in pancreatic beta cells for secretion potentiation and upregulation of beta cell mass, 3) ischemia based heterogeneity generating arrhythmias in a cardiac syncytium. Theoretical tools involve compartmental and spatial dynamical system models. Computational and analytical bifurcation and perturbation theory.

My current research interests include:

1. Survival analysis with concentration on Cox regression with free knot splines where knots are considered parameters.
2. Correlated data analysis with concentration on regression analysis of data from medical and biological sciences, using the concept of exchangeability and partial exchangeability.
3. Semiparametric regression with focus on semiparametric efficiency.
4. Robust statistics with foucs on robust regression with depth functions.
5. Semiparametric generalized linear models.

Cancer Systems Biology: Systems Biology of Cancer is the definition of our mixed experimental and theoretical approach to studying many aspects of cancer progression, including invasion, metastasis, resistance to drugs, effects of mutations. Rather than focusing on clarifying details of a molecular or genetic pathway, or specific effects of growth or differentiation factors or proteases or drugs, we try and combine these details into a global picture that specifies overall trends in growth and progression of specific cancer cells under distinct microenvironmental conditions. Thus, we build quantitative hypotheses that translate experimental observations or datasets into computer simulations based of several mathematical modeling techniques, including ordinary or partial differential equations, cellular automata, neural networks, immersed boundary method.

To test the hypotheses, we populate these models with datasets from in vitro or animal experiments, or from clinical material. The simulations make theoretical predictions on specific ways experimental variables may affect cancer progression. We then design and perform experiments to validate these predictions, and the outcome of the experimentation is used to evaluate the realism of computer simulations and possibly modify their underlying mathematics.

Our group is comprised of an interdisciplinary collection of scientists, including cell and molecular biologists, mathematicians, engineers, bioengineers, bioinformaticians and computational biologists. We thrive on continued personal exchange and looking at cancer research problems through the eyes of different disciplines.

Vanderbilt Integrative Cancer Biology Center (VICBC) http://vicbc.vanderbilt.edu/vicbc/: The VICBC is part of the Integrative Cancer Biology Program (ICBP) by the National Cancer Institute (NCI) and establishes a novel cross-disciplinary approach by assimilating data, experimental approaches, and technologies from several disciplines: Cancer Biology, Mathematics and Bioinformatics, Bioengineering, and Imaging Sciences. We also reach out to the community through our dedicated Outreach and Education program.

• Goal: Develop and validate a robust, predictive mathematical model of cancer invasion, parameterized and informed by state-of-the-art experiments.
• Outcome: Advance our understanding of the requisite parameters and processes in cancer invasion and metastasis.
• Expectation: Predict prognosis, optimize treatment (surgical, pharmacological, or otherwise) for various cancers, and guide the design of novel therapeutics.

Professor Reed works on a variety of problems in mathematical biology and analysis. The main focus of his work in recent years has been on cell metabolism. The goal is to understand how specific biochemical and gene-biochemical networks function. With his main biology collaborator, Fred Nijhout, and other collaborators, he studies one-carbon metabolism, glutathione metabolism, and insulin signaling. The group is interested in discovering the homeostatic mechanisms that enable the networks to accomplish tasks despite highly varying inputs due to diet and environmental factors and how these mechanisms fail under extreme environmental stress and in neoplastic transformations. Many of the group's papers can be seen at http://metabolism.math.duke.edu. Recently, Reed has been studying dopamine and serotonin metabolism in the brain in collaboration with Janet Best of Ohio State.

This work has given rise to a variety of new mathematical questions. How do stochastic fluctuations propagate through biochemical networks (see the Anderson papers on the website)? What structure of a network can one infer by changing inputs and observing outputs? How can one simplify networks in such a way that the mapping from input to output changes as little as possible?

Reed also studies mathematical questions in the structure and function of the auditory brainstem (see Mitchell, Reed, SIAM J. App. Math. 68, 720-737) and trains graduate students and postdocs in analysis (see Laurent, Rider, Reed, SIAM J. Analysis, {\bf 38}, 1-15.)

My laboratory studies intracellular trafficking of membranes and certain protein molecules(e.g., IgG) in cells and tissues. We are particularly interested in specialized microdomains of the plasma membrane known as caveolae. Caveolae are thought to be enriched in certain lipids (i.e., sphingolipids and cholesterol) and a number of proteins associated with signal transduction events including caveolin. In addition, we are interested in the cytoskeleton of cells and how these polymeric supermolecular assemblies regulate the intracellular movements as well as motility of cells.

We work in Mathematical and Computational Neuroscience. Our long term goal is to understand the basic dynamic and biophysical principles governing the generation of rhythmic activity in the hippocampus, the entorhinal cortex and other areas of the brain over a wide spectrum of interacting levels of organization, ranging from the subcellular, through the cellular to the network levels, and how all this contributes to the functional role of rhythmic oscillations in brain activity and behavior. We use biophysical (conductance-based) modeling, dynamical systems techniques (analysis) and simulations to investigate how rhythms emerge at a single cell and network levels, what are their dynamic properties, how and under what conditions a network can be the neural substrate of two (or more) different rhythms, and how the switch between these two rhythms occurs. We have ongoing collaborations with experimental labs both 'in vivo' and 'in vitro'.

My research areas include: molecular neuroanatomy of developing cerebellar circuits and synapses and developmental regulation of neurotransmission involving glutamate and GABA/benzodiazepine receptors. My more recent interest is in genomics.

I study dynamics of activity patterns in networks of neurons, including mathematical mechanisms underlying emergent activity and functional implications of neuronal activity. Recent applications of interest have been central pattern generators, underlying repetitive rhythmic behaviors such as respiration and locomotion, and Parkinson's disease.

The effective application of genomic information to drug discovery and therapy promises a revolution in the treatment and prevention of disease. Current databases - on gene expression, proteomics, polymorphisms, tissue banks, drug effects and toxicities, and clinical outcomes - expand exponentially. Yet, the enormous complexity of the data impedes our ability to extract key elements relevant to therapy. Our challenge is to develop a mathematical/statistical approach to the design and interpretation of complex data sets from laboratory experiments and clinical trials.

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.

My expertise is in differential equations, both ordinary and partial, and in bifurcation theory. For much of my career I have applied these techniques to physical problems such as fluid flow, elasticity, and especially granular flow. More recently I have turned to biological problems.

For more than a decade I have studied mathematical models in electrocardiology. The goal of such research is to understand how the normal rhythm of the heart can be disrupted and, in the worst case, lead to ventricular fibrillation and sudden cardiac death. The underlying mathematics involves systems of reaction-diffusion equations and their bifurcations. Realistic models have many equations and exceedingly complex geometry. One may say with confidence that this problem will continue to offer many challenges for many years to come. I am hoping that detailed understanding of simpler models will shed useful insight on the behavior of the full problem.

In the past few years I have collaborated with biologists in the Center for Systems Biology, a NIH-funded institute at Duke. Specifically, this includes:

• Metabolic pathways in yeast (with Paul Magwene)
• Turing patterns in synthenic gene circuits (with Lingchong You)
• Growth pattern in the plant, arabidopsis (with Philip Benfey)

Let me elaborate on the first of these, the most active, which I am pursuing with my student Kevin Gonzales. Under conditions of starvation (either carbon or nitrogen), yeast cells have several possible responses, especially sporulation ("let's give up for now and wait till conditions are better") and pseudohyphal growth ("let's see if it's any better over there"). The goal of our research is to understand the gene network in yeast that is responsible for choosing which behavior to execute.

Dr. Schnell is interested in investigating cellular physiology systems comprising many interacting components, where modeling and theory may aid in the identification of the key mechanisms underlying the behavior of the system as a whole. His research lies at the interface between mathematics, biophysical chemistry and physiology. Dr. Schnell is particularly interested in investigating the quality control production of insulin, self-organization principles of cellular organelles and discovering the reactions laws for modeling reactions inside the cells.

Tissue Injury and Repair, Inflammation, Oxygenation, and Redox.

The Setubal research group works primarily on bioinformatics for bacterial genome annotation and sequence analysis. New bacterial genomes continue to become available at a rapid pace thanks to new DNA sequencing technologies. Comparative genomics is one of the main beneficiaries of the increase in sequencing since it has become cheap enough to sequence several strains of the same species as well as species from phylogenetically under-represented groups. This presents exciting opportunities for bioinformaticians working on genome analyses. In addition to work related to specific genomes, current topics of interest include automated genome annotation, algorithms to help infer bacterial genome evolution, web-based infrastructure for genome annotation and analysis, and phage display sequence analysis. For more details please check http://staff.vbi.vt.edu/setubal or send an e-mail to me (setubal at vt dot edu).

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.

Research interests of Hal L. Smith include theoretical issues such as the theory of monotone dynamical systems and the theory of persistence (permanence) as well as the applications of these theories to dynamical systems arising in the biological sciences. More applied interests include modeling of biofilms, modeling microbial growth and competition in bioreactors such as the chemostat, modeling within-host disease and treatment, epidemic modeling, and host-virus models. My mathematical expertise lies in ordinary differential equations, dynamical systems, partial differential equations, nonlinear analysis and applied mathematics. My interest in stochastic systems is increasing.

In many problems modeled by partial differential equations the parameters are heterogeneous and vary on multiple scales. Moreover, the coefficients are typically not known exactly and it is convenient to model them in terms of multi-scale random fields. An important challenge is then to describe the complicated coupling between the properties of the random field and the solution of the differential equation. A main component of my research deals with problems of this type. Many problems in biology, physics and also the social sciences fall in the aforementioned category. My two main application areas are:

1) Waves in Random Media: A number of important physical phenomena involve waves propagating through heterogeneous media, such as sound waves in the ocean, seismic waves in the earth's crust, electromagnetic waves propagating through the atmosphere or ultrasound probing the human body. A good understanding of how waves interact with the heterogeneities is crucial in applications like wireless communication, medical imaging, reflection seismology, remote sensing, atmospheric laser beam propagation, underwater communication, nondestructive testing, ?ber optics, nano-technology, seismology, helio-seismology and astronomic imaging to name a few. The mathematical description of this interaction simultaneously leads to deep and interesting questions. Many of the applications mentioned above do not fully exploit the mathematical description of waves in random media, partly because of its complexity. Moreover, there are many open problems, particularly in the case with waves propagating in several spatial dimensions and in rough and long-range media. The general objective of my research in this area is to further the theory for waves in clutter, the clutter modeled as a random medium, and show how a description of random waves can contribute to various applications. A main application that I consider is imaging in the context of noise and clutter.

2) Mathematical Finance: Recently there has been a rapid development of quantitative methods used in finance. Sophisticated methods have been developed for pricing of complex financial derivatives and investments and also for assessing the associated risk. In the Black-Scholes theory for pricing of options the volatility plays a key role. The underlying model here is a geometrical Brownian motion and the (constant) volatility corresponds to the magnitude of the random fluctuations in the growth rate for the considered financial instrument, a stock or an index say. I consider in particular problems where such parameters are modeled in terms of multi-scale stochastic processes. In for instance the context of credit risk where there are many underlying entities or names and the correlation between them which is implicitly generated via common parameter processes may be important and is also a problem that I work on.

We are interested in understanding how humans and other animals use their neurons and muscles to move: either their whole body, as in locomotion, or parts of their body, as in playing a piano. Our goal is to obtain a simple and tractable, yet complete, theory of legged locomotion and sensorimotor control -- a theory that will reliably predict how an animal will act in a novel situation (say, humans hopping on the moon) and how the animal will respond to perturbations (say, stepping on a banana peel). We use a mixture of mathematics, modeling, computation, and experiments. More generally, we are also interested in large-scale numerical optimization, optimal control, friction micro-mechanics, muscle micro-mechanics (including cell biology), classical mechanics, optimality principles in biology and engineering, etc. Please stop by to chat. Or check us out at http://movement.osu.edu/

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.

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.

Horst Thieme is interested in the mathematical modeling and analysis of infectious diseases, in other words, of host-parasite ecosystems. A particular interest is in how the disease spread interplays with the underlying structures of the host and/or parasite population. Mathematical methods are taken from the areas of differential equations, dynamical systems (especially persistence theory), and operator semigroups.

My research interests are twofold. One part addresses the role of stochastic phenomena ("noise") in the nervous system. I work on mathematical problems at the intersection of dynamical systems and stochastic processes which are strongly motivated by direct collaboration with experimental neuroscientists. For example I am working with Christopher Wilson (CWRU's School of Medicine) to integrate experimental, computational and mathematical techniques for studying the generation of robust respiratory rhythms in the developing mammalian brainstem. An MBI postdoctoral fellow with interests in computational neuroscience, dynamical systems and stochastic processes would work with us as a team. The fellow would have the opportunity to work with data collected via cutting-edge dynamic clamp protocols based on field programmable gate array technology, while also developing computational models (in NEURON, Matlab or similar environments) to study the effects of noise and developmental factors on synchronized activity underlying stable breathing patterns in the brain stem. A fellow experienced with the mathematical analysis of stochastic processes would have the opportunity to apply her or his expertise to biological modeling problems with significant potential human health impact.

My second area of interest concerns the effects of noise on biochemical signaling networks. Fluctuations in local concentrations of signaling molecules limit the precision with which a cell (e.g. a Dictyostelium amoeba or a white blood cell) can move towards the direction of a chemoattractant source. Posing questions about the performance of such signaling systems leads to novel applications of information theory to cell biology. We use mathematical tools, such as direct monte carlo simulation of model signal transduction pathways, and conceptual tools from the theory of stochastic processes. And we collaborate with experimentalists developing microfluidics devices to measure the responses of living cells to custom spatiotemporal gradient signals. An MBI postdoctoral fellow with interests in computational cell biology or systems biology, dynamical systems and stochastic processes would have an opportunity to make a major impact in the nascent field of stochastic cell biology.

I am broadly interested in mathematical biology, particularly mathematical epidemiology. Much of my epidemiological research concerns waterborne diseases. Research projects can range from being data-driven to completely theoretical, and involve techniques from dynamical systems and statistics.

My research in applied and computational mathematics lies at the interface between rigorous applied analysis and physical or biological applications. Most of my work has been focused on the development of analytical and computational techniques for investigating nonlinear phenomena. Specifically, in studying the Navier-Stokes equations and other related nonlinear partial differential equations. Such equations arise as models in a wide range of applications in nonlinear science and engineering. The applications include, but are not limited to, fluid mechanics, geophysics, turbulence, chemical reactions, combustion theory, nonlinear fiber optics, lasers, elasticity, control theory, and biological models.

In order to make significant progress in understanding application areas one must deploy all possible approaches, whether analytical, computational or originating in the application areas themselves. A solid background in analysis with some experience in scientific computing are highly recommended. This is in addition to some background and interest in the specific area of application.

Research program: Computational Cell Biology

1. Modeling the cell cycle
   • Nonlinear ODE models of cell cycle regulation in budding yeast and fission yeast.
   • Modeling mammalian cell cycle controls using nonlinear ODEs and hybrid systems theory.
   • Modeling cell division and differentiation in alpha-proteobacteria.
   • Stochastic modeling of cell cycle control in single cells.
2. Modeling signaling systems
   • DNA damage checkpoint in yeast and mammalian cells.
   • Intrinsic pathway of programmed cell death in mammalian cells.
   • Cell differentiation during the innate immune response.
   • Other pathways: MAP kinase, Fas, Smad, Wnt, integrin & cadherin
3. Software tools
   • Model building, reaction motifs.
   • Simulation and comparison to experiments, parameter estimation.
   • Tools for bifurcation analysis.
   • Tools for stochastic simulation and hybrid modeling.

Research in Dr. Vandre's laboratory examines posttranslational modification of cytoskeletal proteins involved in regulating cell cycle progression, cell differentiation, and degeneration. Current studies include development of proteomic, RNS interference, and immunocytochemical approaches to examine the functional properties of cytoskeletal proteins and the mechanisms of action for new cancer chemotherapeutic agents.

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.

My current research activities in mathematical and computational biology include

1. embryonic wound healing
2. cell signaling, morphogen gradient formation, tissue patterning, and their multi-factor robustness
3. viral dynamics
4. cell mutation and abnormal cell growth

My laboratory is primarily interested in the generation and modulation of respiratory rhythm in the mammalian central nervous system. The questions we seek to answer are: How does the brain generate the drive for breathing? How are breathing patterns modulated by reflexes and chemosensation? What are the neural pathways involved in breathing? What are the biophysical properties of cells involved in breathing? How does respiratory drive change as we age?

We use electrophysiology techniques (extracellular single-unit recording, whole cell patch-clamp recording, and electrochemistry) and fluorescence imaging (calcium indicators, pH sensitive dyes) to explore the dynamic relationship between cells that are rhythmically active during breathing.Our chief animal model is the developing rat but we also use mice to explore genetic variability in the respiratory neural network. Recently we have embarked on a series of experiments designed to quantify how neurons and astrocytes communicate with each other to modulate respiration as we age.

Members of my laboratory are collaborating with Prof. Peter Thomas (CWRUMathematics) to develop integrated experimental, computational and mathematical investigations of robust respiratory rhythm generation. An MBI postdoctoral fellow with interests in computational neuroscience, dynamical systems and stochastic processes would work with us as a team.The fellow would have the opportunity to work with data collected via cutting-edge dynamic clamp protocols based on field programmable gate array technology, while also developing computational models (in NEURON, Matlab or similar environments) to study the effects of noise and developmental factors on synchronized activity underlying stable breathing patterns in the brain stem. A fellow experienced with the mathematical analysis of stochastic processes would have the opportunity to apply her or his expertise to biological modeling problems with significant potential human health impact. For details please contact cgw5@case.edu or pjthomas@case.edu.

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.

My research is in two areas. One is proving and computing effective front speeds of stochastic reaction-advection-diffusion equations in the large time regime. The problem is rooted in turbulent combustion and interfaces in random media. The other is studying iterative methods of statistical inversion problems, specifically independent component methods of source recovery and feature extraction via constrained gradient descent. Such methods are potentially useful to digital hearing devices (signal processing on hearing aids, cell phones).

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.

My research interests are high accuracy numerical methods for partial differential equations on complex domains, and their applications in computational biology. The numerical methods I am currently working on include Weighted ENO finite volume / finite difference methods, discontinuous Galerkin (DG) finite element methods, fast sweeping methods, and integrating factor methods for various nonlinear partial differential equations, such as time-dependent and static Hamilton-Jacobi equations, hyperbolic conservation laws, convection dominated equations, stiff reaction-diffusion equations. The applications in computational biology include computational analysis of morphogenesis in developmental biology, such as dorsal-ventral patterning during the zebrafish and Drosophila embryos development, skeletal pattern formation during the vertebrate limb development; computational analysis of neurogenesis in a regenerative neuro-epithelium. I am especially interested in computational modeling of biological systems on complex spatial domains.

1. Optical imaging (optical tomography and molecular imaging): Radiative transport equation based inverse
2. Possion-Boltzman equation for molecur dynamics and structures and functions of biomolecules.

Jasmine Zhou is interested in developing computational algorithms and statistical methods to perform integrative analysis of heterogeneous public genomics data in order to predict gene function, reconstruct regulatory networks, and to analyze genome- phenome associations. Research in her lab also includes the development of efficient algorithms and machine learning methods for pattern discovery across many massive biological networks.

My research program is in the area of applied computational mathematics with biological applications. I am interested in numerical methods for and computer simulations of fundamental mechanical and/or biological processes which involve incompressible viscous fluids and elastic deformable boundaries. There are two major components of my research program: development of numerical methods for fluid-flexible-structure-interaction problems including extension/improvement of the immersed boundary (IB) method, and applications of these methods to problems in life science/ biomedical engineering.

Currently I am working on 1) developing a 3D implicit IB method using the lattice Boltzmann approach with applications in problems of biomedical interest -- blood flows with transport and reacting constituents interacting with a compliant vessel wall covered by an endothelial surface layer underlie the initiation and development of atherosclerosis; and the interaction of air flow through the pharyngeal airway with the genioglossal muscle, a process involved in sleep apnea, i.e. a disorder characterized by repetitive collapse of the pharyngeal air way during sleep. 2) developing novel numerical methods for modeling and simulations of red blood cells interacting with flowing blood using the thin-shell theory and the Navier-Stokes equations.

My lab focuses on the structure and function relationship of cation channels. Some of these channels mediate calcium influx following the stimulation of phospholipase C and thus control calcium homeostasis inside the cells. These channels have different activation and inactivation kinetics and are modulated by a number of cellular factors. Our challenge is to model the changes of intracellular calcium concentrations as functions of channel activity under different physiological conditions. The proposed models will be tested using electrophysiological and calcium imaging techniques.