Current Postdoctoral Fellows
Márcio is interested in understanding how macroscopic behavior arises from simpler multiple (more...)
Márcio is interested in understanding how macroscopic behavior arises from simpler multiple interactions over time and space. He's currently investigating biological phenomena, but his long-term goal is to expand his research to biological, social, economical or even political systems. Márcio's work involves a combination of both theoretical and computational models.
Noelle investigates the roles of plant-animal, plant-microbe, and plant-plant interactions in limiting (more...)
Noelle investigates the roles of plant-animal, plant-microbe, and plant-plant interactions in limiting populations and maintaining diversity in temperate and tropical ecosystems. Using statistical models to analyze experimental and observational data, she can quantify the relationship between plant attributes and plant interactions with their environment to enable prediction for unstudied species, gain insight into the mechanisms for species coexistence, and understand ecosystem responses to change. Using mathematical and computational approaches, Noelle is investigating processes occurring over multiple spatial and temporal scales in order to address questions of species coexistence. She is also working to develop stochastic spatial models and analytical approximations to examine the interacting effects of seed dispersal and natural enemy attack on plant spatial patterns and the influence of these local interactions on plant diversity.
Josh is excited about a variety of fields in the mathematical and physical sciences including but not (more...)
Josh is excited about a variety of fields in the mathematical and physical sciences including but not limited to inverse problems, PDEs, homogenization theory, statistical physics, computer vision, and stochastic processes. His prior research has focused on regularization techniques applicable to inverse problems and computer vision. He has also worked on modeling of neurophysiology using reaction-diffusion equations. Aside from mathematical neuroscience, he is particularly curious about cancer growth, quorum sensing, pattern formation, scar formation, and models of nutrient delivery in vascular networks. Somewhat tangentially, he also likes to explore methods for transit modeling and other practical problems related to civil engineering.
Kimberly's research focuses on developing a comprehensive nonlinear wave model for the governing (more...)
Kimberly's research focuses on developing a comprehensive nonlinear wave model for the governing physics of the transduction mechanism in the inner ear. This work requires a detailed analysis of the fluid-solid interaction dynamics of the cochlea, as well as the utilization of various perturbation methods and numerical techniques.
Wenrui applies numerical algebraic geometry methods and numerical partial differential equation methods to (more...)
Wenrui applies numerical algebraic geometry methods and numerical partial differential equation methods to mathematical problems arising in biology, such as tumor growth, blood coagulation, and deriving efficient numerical methods for large scale computing. The mathematical tools that he uses include PDEs, numerical algebraic geometry, bifurcation analysis, and computational methods.
My research integrates techniques from the fields of dynamical systems, stochastic processes and (more...)
My research integrates techniques from the fields of dynamical systems, stochastic processes and statistics to develop and analyze mathematical models motivated by questions in population ecology, infectious disease and immunology. I also pursue interesting mathematical questions that emerge from these applications.
Karly's research is focused on the spread and control of disease at a range of scales, from cells (more...)
Karly's research is focused on the spread and control of disease at a range of scales, from cells within a tumor to individuals and communities at the population level. She works in oncolytic virotherapy, the use of cancer-targeting viruses in the treatment of solid tumors, where she models spatial spread of viruses by cell-to-cell fusion as well as interactions of the tumor, virus, and immune response. Using analytical and numerical techniques, she analyzes the corresponding partial differential equation systems to investigate mathematical questions such as well-posedness and dynamical behavior as well as to gain clinical insights into tumor control. At the population level, Karly is interested in how the structure and seasonality of community and environmental networks affect the spread of infectious diseases such as cholera. Ordinary differential equations, dynamical systems, and graph theory are used to investigate disease dynamics.
Jae's research has focused on developing theories and models to understand biological rhythms. Basic (more...)
Jae's research has focused on developing theories and models to understand biological rhythms. Basic questions are: Is there an easier way to find hidden or unknown biochemical interactions? How do complex biochemical networks generate rhythms and control period? He has worked closely with several experimental groups in biology to develop new protocols to test model predictions.
Adrian is interested in the application of reaction-diffusion equations in theoretical ecology. Via (more...)
Adrian is interested in the application of reaction-diffusion equations in theoretical ecology. Via rigorous analysis of different reaction-diffusion models, his work attempts to gain a better understanding of the effects of spatial heterogeneity and non-random transport on the dynamics of biological processes. His current project studies the effects of different directed movements of populations along environmental gradients or along density dependent growth rate gradients, using a reaction-diffusion-advection model. The goal is to determine the relative advantage of such dispersal strategy in the context of the competing species model.
Kang-Ling is interested in ordinary differential equations and dynamical systems. She focuses on the (more...)
Kang-Ling is interested in ordinary differential equations and dynamical systems. She focuses on the dynamics for gene expressions of somitogenesis in zebrafish. During the development of embryo, the clock gene expression exhibits synchronous oscillation in the tail bud and a traveling wave pattern arises from the posterior to the anterior of the presomitic mesoderm. The oscillation slows to a stop and cells form into somites. In order to investigate these phenomena, we considered the mathematical models which depict the kinetics of the zebrafish segmentation clock genes subject to direct autorepression by their own products under time delay, and cell-to-cell interaction through Delta-Notch signaling. The theoretical and numerical results not only provide some criteria and parameter regimes observed in somitogenesis, but also present how delays affect the dynamics of these models. Kang-
Ling plans to perform similar methodologies to patch model in ecology to explore how delay affects the dynamics of the model and investigate the global dynamics of the model. She also plans to study the cancer immunoediting and attempt to construct
a pertinent model which fits experimental data to investigate the mechanism of how tumor cells escape from the immune system.
Analytic and computational analysis of biological models related to multi-stage stem cell lineages, tissue (more...)
Analytic and computational analysis of biological models related to multi-stage stem cell lineages, tissue growth and morphogen-mediated patterning. In my studies, ODEs, PDEs with moving boundary and stochastic simulations are used for modeling.
Leopold's interests are in mathematical image analysis, numerical analysis of partial differential (more...)
Leopold's interests are in mathematical image analysis, numerical analysis of partial differential equations, applied mathematics, and statistics. In his Ph. D. dissertation, he used finite difference and Galerkin methods to construct continuous piecewise polynomial approximations of the continuum TV-L2 image decomposition model. He plans to expand on this work to other total variation based image decomposition models. This includes the application of the stochastic Gillespie Algorithm to simulate ecosystems indicators within the Ecological Network Analysis framework. Currently, Leopold is collaborating with Julie Rushmore (Odum School of Ecology, University of Georgia) to study dynamics of the social network of the community of chimpanzees of the Kibale National Forest (Uganda, East Africa), and its impact on disease transmission in the community.
Jay's interests lie in stochastic processes and their application to biological problems. Although (more...)
Jay's interests lie in stochastic processes and their application to biological problems. Although his primary area of focus is cellular neurobiology, he has also done work in intracellular transport, gene regulation, and population dynamics. During his time at MBI, Jay intends to investigate the link between the collective network behavior and cellular processes within an individual neuron, understand better how cellular processes (such as gene regulation) contribute to synaptic plasticity, and develop new perturbation methods to analyze rare events in jump Markov processes.
Michael's research spans three spatial scales in the brain: from electrical activity of single cells (more...)
Michael's research spans three spatial scales in the brain: from electrical activity of single cells and small networks, through the dynamics of neural populations, to models of behavior and cognition. At the cellular level, Michael studies how spatial properties modulate neuronal spiking dynamics; at the population level, and how neural substrates interact across multiple brain regions to integrate attention and decision making. At the behavioral level, he studies the limitations of human multitasking abilities. By building and analyzing models that connect aspects of these levels, he seeks to understand how biophysical and computational properties of neurons enable and constrain network activity and, ultimately, produce behavior.
Michal’s research is focused on the development of statistical models and methods for comparative (more...)
Michal’s research is focused on the development of statistical models and methods for comparative analysis of sparse populations. Here, similarity is expressed both in terms of diversity, as well as overlap between communities. The main aim of the project is to provide tools for the statistical analysis of the immune system related, next generation sequencing data. The diversity analysis relies on information-theoretical concepts based on measures of entropy. In the study of overlap, notions associated with either measures of bivariate statistical dependence or geometrical relations between probability vectors are used. The crucial challenge is to establish methods which both: are robust to next generation sequencing errors and take into account low coverage of samples due to sparseness of populations. From this point of view the nonparametric approach is much more demanding than the more standard methods based on parametric models for count data. This approach was used to uncover relations between different (in terms of location and function) T-cell receptor populations in murine models.
Lucy's research is in mathematical neuroscience, with a focus on the development and analysis of (more...)
Lucy's research is in mathematical neuroscience, with a focus on the development and analysis of models that produce rhythmic motor patterns. She uses geometric singular perturbation theory, phase plane analysis, and other tools from dynamical systems theory to deduce the mechanisms responsible for oscillations in different networks. Her interest lies in understanding how features like network structure and sensory input collaborate to produce oscillatory behaviors. She is also interested in inferring the architecture of networks underlying distinct rhythms produced by shared muscles and motoneurons. Recordings from the central nervous system indicate that individual neurons participate in multiple behaviors, but for large systems like the vertebrate nervous system, this is insufficient to deduce the network structure responsible for rhythmicity. To approach this problem, Lucy constructed and simulated ODE models with different architectures for comparison with experimental results.
Marc has studied a variety of areas including: spatio-temporal modeling, gene regulatory networks, (more...)
Marc has studied a variety of areas including: spatio-temporal modeling, gene regulatory networks, negative feedback loops, intracellular signaling pathways, systems biology, and cancer modeling.
Joy's research has focused on mathematical models for geographic range shifts of plants and animals (more...)
Joy's research has focused on mathematical models for geographic range shifts of plants and animals under climate change. Math tools include deterministic and stochastic dynamical systems, integral operators, and PDEs.