Graphs with the strong Havel-Hakimi property

The Havel-Hakimi algorithm iteratively reduces the degree sequence of a graph to a list of zeroes. As shown by Favaron, Mah\'eo, and Sacl\'e, the number of zeroes produced, known as the residue, is a lower bound on the independence number of the graph. We say that a graph has the strong Havel-Hakimi property if in each of its induced subgraphs, deleting any vertex of maximum degree reduces the degree sequence in the same way that the Havel-Hakimi algorithm does. We characterize graphs having this property (which include all threshold and matrogenic graphs) in terms of minimal forbidden induced subgraphs. We further show that for these graphs the residue equals the independence number, and a natural greedy algorithm always produces a maximum independent set.Comment: 7 pages, 3 figure

Error Correction and de novo Genome Assembly of DNA Sequencing Data

The ability to obtain the genetic code of any species has caused a revolution in biological sciences. Current technologies are capable of sequencing short pieces of DNA with very high quality. These short pieces of DNA determint the sequence of bases in the genome of any species. This information is key in understanding many of the aspects of how life functions. The accuracy of sequencing is extremely important since the differences between individuals of the same species are caused by very few changes. All sequencing technologies make errors, and before the data can be used for downstream applications it is usually best to correct the errors first. I present an error correction program called RACER that is an error correction program that aims to correct substitution sequencing errors. There are many substitution error correction programs available for DNA sequencing technologies, so it is important for biologists to know which program is best to use for their sequencing technology. I present a comprehensive survey of substitution error correction programs for DNA sequencing data to address this issue. I also present two programs to evaluate the performance of error correcting programs. Since the current dominant platform in the market can only obtain small pieces of DNA, software is needed to assemble these pieces to determine the full sequence of the sampled genome. Current genome assembly programs are not capable of assembling the entire genome of most species due to the repetitive nature of genomes and the uneven coverage of the sampled genome. I present a genome assembly program called SAGE2 that improves upon the current state-of-the-art

Error Correction in Next Generation DNA Sequencing Data

Motivation: High throughput Next Generation Sequencing (NGS) technologies can sequence the genome of a species quickly and cheaply. Errors that are introduced by NGS technologies limit the full potential of the applications that rely on their data. Current techniques used to correct these errors are not sufficient, and a more efficient and accurate program is needed to correct errors. Results: We have designed and implemented RACER (Rapid Accurate Correction of Errors in Reads), an error correction program that targets the Illumina genome sequencer, which is currently the dominant NGS technology. RACER combines advanced data structures with an intricate analysis of data to achieve high performance. It has been implemented in C++ and OpenMP for parallelization. We have performed extensive testing on a variety of real data sets to compare RACER with the current leading programs. RACER performs better than all the current technologies in time, space, and accuracy. RACER corrects up to twice more errors than all other parallel programs, while being one order of magnitude faster. We hope RACER will become a very useful tool for many applications that use NGS data

Consumer Purchasing Behaviors and Attitudes toward Shopping at Public Markets

This paper identifies and empirically evaluates factors that explain the variations in consumers’ attitudes toward shopping at farmers markets in general and public markets in particular. The analysis draws on data from a telephone survey conducted in Jefferson County, Alabama. Logit model results point to several factors that seem to be strongly correlated with consumer purchasing behaviors and attitudes toward shopping at public markets, including income, education, age of household head, household size, and price and quality of produce. The insights gained from the study should help farmers increase the profitability of their operations and improve the likelihood that they will continue farming.Consumer/Household Economics,

The arithmetic of modular grids

A modular grid is a pair of sequences $(f_m)_m$ and $(g_n)_n$ of weakly holomorphic modular forms such that for almost all $m$ and $n$, the coefficient of $q^n$ in $f_m$ is the negative of the coefficient of $q^m$ in $g_n$. Zagier proved this coefficient duality in weights $1/2$ and $3/2$ in the Kohnen plus space, and such grids have appeared for Poincar\'{e} series, for modular forms of integral weight, and in many other situations. We give a general proof of coefficient duality for canonical row-reduced bases of spaces of weakly holomorphic modular forms of integral or half-integral weight for every group $\Gamma \subseteq {\text{SL}}_2(\mathbb{R})$ commensurable with ${\text{SL}}_2(\mathbb{Z})$. We construct bivariate generate functions that encode these modular forms, and study linear operations on the resulting modular grids.Comment: Revised versio