1. Alie Falastein

Title: Connectivity Estimation in Neuronal Networks: The Hidden Node Problem

Abstract: The human brain is a complex system consisting of billions of neurons. The network connectivity of these neurons gives rise to a variety of dynamical behaviors and understanding it is key to describing the underlying evolution of the system. However, in our analysis of network connectivity we are often confronted with the problem of hidden nodes, or parts of the network that we are unable to observe but that are strongly influencing the network. Identifying these hidden nodes, and the parts of the network they are affecting, is key to understanding the network and making predictions of the future network state. We investigate this problem of connectivity estimation, in the presence of hidden nodes, in random networks of Fitzhugh-Nagumo neurons. Our hypothesis is that we can identify the presence of hidden nodes by detecting abnormalities in the estimated network connectivity. (Faculty mentor: M. Olufsen)

2. Conor Perks

Title: Poro-Visco-Elastic Models in Biomechanics: A Numerical Investigation 

Abstract: We consider fluid flow through a deformable porous biological medium where structural viscosity is incorporated in the solid component. Through a balance of linear momentum and mass, one can obtain systems of partial differential equations that describe how the solid displacement, discharge, velocity, pressure and stress within our domain evolve over space and time.  We numerically solve this system to analyze the behavior of the solution with respect to certain combinations of geometric and physical parameters as well as boundary data. With this, we can provide a sensitivity analysis for the system. In this respect, we work with the reduced 1D dimensionless system. We solve it numerically using the backward Euler method for discretization in time, and a hybrid finite element method for the discretization in space.  Then we numerically investigate the dependence of solution on boundary data and structural viscosity.(Faculty Mentor: L. Bociu and M. Noorman)

3. Jaye Sudweeks

Title: Localization of Gene Drives: The Locally Fixed Allele Approach

Abstract: Invasive rodents are a major problem on many islands, threatening native species. Current eradication attempts involve the use of rodenticides, but these can harm other species. Genetic approaches, such as introduction of a gene that reduces rodent fertility, offer an alternative that precisely targets the rodents. Gene drives, which involve super-Mendelian inheritance of a gene, are a method by which such a desirable gene can be introduced into and spread through a population. This spread, however, could have unintended consequences: escape of gene drive-bearing rodents from an island to the mainland could lead to elimination of rodents elsewhere, potentially eradicating the rodent species worldwide. A desirable safeguard would be to geographically localize a gene drive to a target location. We propose an approach—the Locally Fixed Allele approach—that achieves this aim by targeting an allele that is fixed on the target island but is not fixed in neighboring populations. In this presentation, we discuss the results of a model of the population dynamics and genetics of mice in an island-mainland system, after the release of a gene drive targeting a locally fixed island allele. We show that even when the island mice population is successfully suppressed, under no conditions is a drive that targets a locally fixed allele capable of suppressing the mainland mouse population in the long term. Thus, even if gene drive mice escape from the island to the mainland, the locally fixed allele approach limits the impact of the escape of a gene drive to the mainland. (Faculty mentor: A. Lloyd and F. Gould)