Differential Equations Seminar: Undergraduate Researchers
UMBC Undergraduate Math Students Present Virtually
Location
Mathematics/Psychology : 401
Date & Time
May 11, 2020, 11:00 am – 12:00 pm
Description
Speakers:
Michael Merkle (Advised by Dr. Hoffman)
Title: A Scaling Analysis for Discrete Elastic Rod Models
Abstract: Elastic rod configurations are understood to minimize the potential energy of the rod. There are both continuous and discrete models for elastic rods. In the Cosserat theory for elastic rods, the rod is a continuous framed curve that minimizes a strain energy functional. Here, we will first discretize the energy functional from the Cosserat theory to obtain a finite sum. We will then take the ratios of the variables in the resulting sum to the corresponding variables in the sum from a discrete model and compute their limits as the number of rod segments goes to infinity. From this, we will deduce a way to scale the stiffness parameters in the discrete model so that the energies converge to those from the continuous model as we partition the discrete rod into more segments.
Jeremy Rubin (Advised by Dr. Roy)
Title: Letting The LaxKAT out of the Bag: Packaging, Simulation, And Neuroimaging Data Analysis for a Powerful Kernel Test
Abstract: Biomedical research areas including genomics and neuroimaging often have a number of independent variables that is much greater than the sample size. The sequence kernel association test (KAT) and sum of scores tests can offer improved power in this feature setting; however, power is significantly reduced in the presence of a large number of unassociated independent variables. We propose the Linear Maximal KAT (LaxKAT), which maximizes the KAT test statistic over a subspace of linear kernels to increase power. A permutation testing scheme was used to estimate the null distribution of the LaxKAT statistic and perform hypothesis testing. Calculation of the LaxKAT was implemented using a combination of the R and C++ programming languages. We found that this test has power and controls the type I error for different sample sizes and signal distributions. It is expected that the LaxKAT will have competitive power relative to other high-dimensional testing procedures when applied to detect predictors of memory impairment in cortical thickness measurements from the Alzheimer’s Disease Neuroimaging Initiative study (ADNI).
Jessie Cooley (Advised by Dr. Peercy)
Title: Effects of the Geometry of Extracellular Space on Border Cell Activation Patterns
Abstract: Diffusion of chemoattractants from polar cells to their surrounding cells marks the beginning of the cell cluster migration in the egg chamber of Drosophila melanogaster, or fruit flies. A previous paper modeled the pattern of activation of surrounding border cells based off of the extracellular spaces caused by various positions of nurse cells. This project looks to recreate the model using Matlab and will aim to reproduce the findings of that paper. Furthermore, we also looked to expand on the model by then using a hexagonal cell formation in place of a rectangular one, to compare our results with this more biologically accurate arrangement of cells. In the future this will allow for further integration into the larger cell cluster migration model.
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