Mutation and selection in a large population

In this paper we study a large, but finite population, in which mutation and selection occur at a single genetic locus in a diploid organism. We provide theoretical results for the equilibrium allele frequencies, their variances and covariances and their equilibrium distribution, when the population size is larger than the reciprocal of the mean mutation rate. [[We are also able to infer that the equilibrium distribution of allele frequencies takes the form of a constrained multivariate Gaussian distribution.]] Our results provide a rapid way of obtaining useful information in the case of complex mutation and selection schemes when the population size is large. We present numerical simulations to test the applicability of our theoretical formulations. The results of these simulations are in very reasonable agreement with the theoretical predictions

Artin Group Presentations Arising from Cluster Algebras

In 2003, Fomin and Zelevinsky proved that finite type cluster algebras can be classified by Dynkin diagrams. Then in 2013, Barot and Marsh defined the presentation of a reflection group associated to a Dynkin diagram in terms of an edge-weighted, oriented graph, and proved that this group is invariant (up to isomorphism) under diagram mutations. In this paper, we extend Barot and Marsh's results to Artin group presentations, defining new generator relations and showing mutation-invariance for these presentations.Comment: 26 pages, 7 figures, comments are welcom

Developing Epistemological Values in Students using Microsoft Excel(R) as a Software-Based Support Tool

This thesis project addresses student epistemological values through technology and independent laboratories. The literature provides evidence that students show greater learning when they are prompted to reflect and develop these epistemological values (Davis, 2003 Demetriadis et al., 2011; Edelson & Kyza, 2005; Reiser & Sandoval, 2004). Furthermore, in conjunctions with research that supports prompting, other research advocates for the development and use of more modern technologies (Edelson & Kyza, 2005; Keengwe et al., 2008; Kuhn, 2001; Maddux, 1998). As such, my culmination project consists of two virtual “lab notebooks.” These notebooks are made using Microsoft Excel® and consist of several quasi-intelligent macros that not only provide instant feedback, but also help guide students through the experimental process in a way akin to inquiry. While a completed series of these notebooks would show more scaffolding as the year progressed, the two I have created represent a student’s first and last experience with these notebooks