Mathematics

Title: Modeling Individual Reproductive Fitness using Resource Allocation leading to a Post-reproductive Life

Authors: Lane D’Alessandro, Allison Kolpas, Josh Auld

Abstract: Some species exhibit a post-reproductive period , where individuals stop reproducing before they die. This is often explained as kin interactions—individuals forego additional reproduction, in turn increasing the fitness of genetic relatives. Recent evidence suggests that post-reproductive periods are not restricted to species exhibiting kin interactions. We developed a fitness model to test the hypothesis that a post-reproductive period can evolve as a consequence of optimal resource allocation. In the model, resource allocation is plastic and divided into reproduction, growth, or inducible defenses. The survival function utilizes a modified Gompertz-Makeham law for mortality. The fecundity function is the product of the reproductive schedule and output.  The schedule utilizes a gamma distribution and the output is modeled linearly. Optimizing the fitness model yields the optimal resource allocation and resulting reproductive schedule. This allows us to understand the effects of phenotypic plasticity in life-history traits on the evolution of a post-reproductive period.

Title:  Finding Efficient and Accurate Ways to Solve Interface Problems

Presented by:  Cameron Campbell, Stacy Porten-Willson, Chuan Li

Abstract: Interface problems are a large class of problems that study the change of a physical quantity in Physics, Biology, Engineering or Materials, such as heat or electrostatic potential, as it propagates across a material interface. Due to the irregularly shaped interface, solutions to interface problems can only be found numerically. However, for the very same reason, classical numerical methods cannot deliver accurate estimations, or may fail entirely. A new numerical method is necessary for solving interface problems efficiently and accurately. In this project, we present our recent study of a well-tuned matched Alternative Direction Interface (ADI) method for solving two-dimensional interface problems with the most general of physical interface jump conditions. We also plan to present our recent improvements on the efficiency, accuracy, and stability of the proposed method.

Title:  Parallel computing the minimized molecular surface of marcromolecules and large complexes

Presented by: Ryan Moser, Chuan Li

Abstract: Constructing the molecular surface is the first crucial stage to produce accurate calculations of electrostatic potentials and energies for the molecules immersed in the water phase.  When the macromolecules and complexes consist of hundreds of thousands of charged atoms, three-dimensional surface construction becomes unbearably slow due to the high computational cost. In this project, we propose a novel grid-based computing scheme to generate the Minimized Molecular Surface (MMS) by effectively utilizing the computational power of multiple CPUs on a computing cluster via the Message Passing Interface (MPI) library. The resulting parallel code will be tested against its sequential version to demonstrate its efficiency and accuracy, and the code will be released to the computational biophysics society free-of-charge for academic usage.

Title:  Development of a Model of Dorsal Closure

Presented by: Ben Plumridge, Dr. Andreas Aristotelous

Abstract: A model, based on relevant previous work, is being developed that simulates the dorsal closure process, a stage of Drosophila embryogenesis. The apical side of the amnioserosa (a cell monolayer- wound like region on the surface of the embryo) is being represented through polygonal two dimensional representations of cells, with forces acting on their edges and nodes. Those forces are being regulated by the action of actin and myosin. The model is granular enough so various sub regions can be studied to the level of the individual cell. Various equations are being tested, describing the evolution of forces generated by the action of the actomyosin network, which itself might be biochemically driven. Eventually, the model may be used to understand mechanisms of dorsal closure that are not easily analyzed in the lab or produce simulation results that might drive new experiments.}