Red Sock Awards Recognize Best Snowbird Posters

By TBA
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Veronica Ciocanel

I am a fourth-year graduate student in the Division of Applied Math at Brown University, and I am interested in mathematical biology and dynamical systems. I work on understanding the dynamics of mRNA localization in frog egg cells with my advisor Bjӧrn Sandstede (Applied Math), in collaboration with Professor Kim Mowry (Molecular Biology). We use both continuous and discrete modeling approaches in order to understand the localization process, which is essential for the healthy development of the egg cell. More about my work and interests can be found on my website. In my spare time, I enjoy traveling and swing dancing.

The poster I presented at Snowbird was on “Modeling of mRNA Localization in Xenopus egg cells.” Xenopus is a species of frog and a model organism for many biological studies. The accumulation of messenger RNA at the bottom of the cell during egg cell development is called localization and is believed to depend on bidirectional movement by molecular motor proteins. This accumulation gives the cell an axis that is crucial for embryo development. We use discrete and continuous (partial differential equations) modeling approaches for mRNA populations that diffuse, move or are paused in the cell. Our simulations show that anchoring of mRNA may be essential for the localization process. We estimate the model parameters using fluorescence recovery data from the Mowry lab, and validate their values using approximate solutions of the PDE models.


Full size poster

Ryan Goh

I am a Ph.D. candidate in the School of Mathematics at the University of Minnesota. Under the advisement of Arnd Scheel, I use techniques from dynamical systems and functional analysis to study how patterns form in nature. I grew up in St. Charles, Illinois, a suburb of Chicago, and did my undergraduate work in math and physics at Michigan State University. Outside of mathematics, I enjoy reading, playing jazz piano and soccer.

My poster, “Front-Dynamics and Pattern Selection in the Wake of Triggered Instabilities,” studies how external mechanisms or stimuli can be used to control pattern-forming processes. Such “triggers” control dynamics in two generic ways corresponding to pushed and pulled fronts. The former is governed by oscillatory nonlinear interactions, leading to hysteresis and multi-stability, while the latter is governed by absolute spectra and interacts monotonically. Such phenomena can be studied, using heteroclinic bifurcation techniques, in prototypical examples in the complex Ginzburg-Landau and Cahn-Hilliard equations.


Full size poster

Lucas Lin

My name is Lucas Lin and I have just recently graduated from Thomas Jefferson High School for Science and Technology in Alexandria, Virginia and will be attending Stanford University this coming fall. I conducted the research through the help of Dr. Paul So and Dr. Ernest Barreto of George Mason University, who served as my mentors.

The work displayed on the poster builds on Dr. So and Dr. Barreto’s previous research on networks of theta neurons. Specifically, the goal of the present work was to use the developed analytical techniques applicable to the theta neuron to examine the patterns in macroscopic behavior describing a more realistic network of neurons that includes variation in coupling strength as well as diversity in neuron excitability. We mirrored the analytical approach of the previous study on classifying the macroscopic behavior of theta neurons with bifurcation analysis, which we performed by taking two-dimensional surface slices while varying a fourth parameter that describes coupling heterogeneity. The analysis demonstrated that heterogeneity in coupling strength increases the robustness of equilibrium states and increasing synaptic diversity suppresses the emergence of the collective rhythmic state and other more complex collective dynamics in the network.


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Glenn Young

I am beginning my sixth and final year in the University of Pittsburgh’s Department of Mathematics Ph.D. program. My advisors are Dr. Jonathan Rubin and Dr. Bard Ermentrout. I am interested in disease dynamics, both within and outside of the host. In addition to the work presented in this poster, I’ve worked on projects modeling the interaction of salmonella with the “good” bacteria found in the mammalian gut, and on the effect of vaccination on the spread of rotavirus in a human population. When not working, I enjoy running and soccer.

We study the interaction of two colliding bacterial populations in a one-dimensional nutrient gradient. When placed on opposite ends of a long channel with a one-dimensional nutrient gradient between them, two populations of E. coli will move up the gradient toward each other. Remarkably, the outcome of such experiments varies from trial to trial. In particular, the two populations will either collide and mix together to become one indistinguishable population, or they will both turn around and move away from one another just before colliding. We use a Keller-Segel model of bacterial chemotaxis to determine mechanisms by which each observed outcome may occur. Our analysis suggests that the observed experimental outcomes depend heavily on the amount of nutrient available to the bacterial populations, as well as on the diffusion rate of the nutrient. This work is with my advisors Dr. Jonathan Rubin and Dr. Bard Ermentrout, and with Dr. Hanna Salman of the Department of Physics and Astronomy at the University of Pittsburgh.


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