Stochastics Lab

Keisha is a postdoc who was hired as part of the Southeast Center for Mathematics and Biology. We have been working in collaboration with Christine Payne and Nathan Reyens to study the behavior of lysosomes in vivo, in order to understand the impact, if any, that the presence of toxic titanium dioxide nanoparticles have on intracellular transport. She has developed a protocol for identifying switches in behavior and quantifying the percentage of time active. The work raises challenging questions in experimental design, namely in trying to identify the optimal frame rate for detecting switch rates and revealing other particle movement properties.

As a graduate student, Elizabeth is primarily advised by Craig Osenberg (Georgia, School of Ecology) and I served as co-advisor. After a postdoc at Eastern Carolina, the crew is back together with Adrian Stier to work on an NSF-funded project. She does field work in Mo’orea and back in the States she uses a combination of field studies and mathematical models to explore how coral occupants interact with their habitat to influence spatial patterns on reefs.

Veronica’s main line of research concerns the modeling, analysis, and simulation of intracellular transport and filament organization mechanisms. We collaborated on a theoretical paper on intracellular transport in which we studied a probabilistic perspective on calculating the long-term velocity and diffusivity of particles that switch among several biophysical states. We also recently published a paper on topological data analysis applied to filamentous networks. We studied the question of how to identify when a topological feature (like the formation of a ring channel) becomes “significant” enough to be considered distinct from noisy spurious features.

Swati studies ecology and evolution and applying mathematical modeling to understand genetics and population dynamics. While in the Stochastics Lab we studied how random epistatic interactions (the phenomena that multiple successive mutations have a nonlinear impact on expressed trait fitness) can evolve to store up and hide genetic variation until an environmental stress later reveals it.

Riley is our “honorary graduate student.” She has been working in the Stochastics Lab since the summer of her freshman year and has collaborated on no fewer than three projects. Her longest-running project has been to develop a “dashboard” of summary statistics that can be used convert paths into points in a lower-dimensional space that can then be separated into distinct regions. She has developed a large database of biologically realistic simulations and trained a machine learning algorithm that can identify the type of behavior the path is most likely to exemplify. Her honors thesis focuses on two specific types of motion and is a theoretical investigation into model selection between them. In a separate project, Riley led the generation of simulations for the topological data analysis project with Veronica Ciocanel.

Melanie was a Tulane undergraduate who returned to math after taking a gap year. In her dissertation work, Melanie studied switching behavior observed in experimental observations of various microparticles. In her first paper, she studied the movement of Herpes Simplex Virus virions moving in mucus in the presence of various concentrations of IgG antibodies. Using a combination of mathematical modeling and statistical anlaysis, she challenged a prevailing theory for how antibodies hindered the movement of the virions.

Initial position after graduation: Schlumberger, Research Scientist

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Darby’s dissertation work focused on models of intracellular transport, particularly with an eye on unexpected interactions between pairs of motors and on how to infer subtle motor properties from common in vitro experiments.

Postdoctoral Appointment: Sandia National Laboratory.

One of the central characteristics of microparticles fluctuating in viscoelastic fluids is that their behavior exhibits long-term memory. The correlation between spatial displacements at distinct times is often negative, and this anti-persistence accumlates in novel long-term behavior called subdiffusion. Along with several collaborators, we have shown that a stochastic integro-differential equation called the generalized Langevin equation (GLE) does a nice job of capturing essential aspects of subdiffusive particle behavior. Interestingly though, the long-term memory structure presented some very challenging theoretical issues. Hung studied well-posedness, asymptotic behavior, and local regularity for both the GLE and also an associated fluctuating fluid model.

Postdoctoral Appointments: Iowa State, Mathematics (with David Herzog); UCLA, Mathematics (with Georg Menz).

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Co-advised by Juliet Pulliam (Biology, Emerging Pathogens Institute). In her dissertation, Rebecca mixed mathematical modeling and data analysis to understand the early stages of epidemics and how the presence or absence of nearby resources can affect encounters among consumers.

Postdoctoral appointments: Florida, Biology with Derek Cummings; Georgia, Odum School of Ecology with Pej Rohani; and now After working with Derek Cummings and Pej Rohani, she is now at Penn State, Biology, working with Katriona Shea.

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Co-advised by Colette St Mary (Biology). In his dissertation, Vin studied how the distribution of mutation effect sizes and the spatial architecture of stem cells in colonic crypts affects the probability of an organism developing tumors over a natural lifespan.

Postdoctoral appointment: Yale, School of Public Health with Jeffrey Townsend.

Lianne is primarily advised by Craig Osenberg (Georgia, School of Ecology). She did her field work in Mo’orea, and her desktop work on phylogenetic trees. In her dissertation, she investigatied the evolution of coloniality and the growth dynamics of corals.

Postdoctoral appointments: USDA, Agricultural Research Service; Northeastern, Marine and Environmental Sciences

He studies how organisms acquire, share, process, and respond to information. Members of his lab use experiments, mathematics, and computational models to understand the rules organisms use to make decisions, how these decisions influences the rates of ecological interactions and the dynamics of ecosystems, and how ecosystem policy can account for organismal behavior.