Kumer Pial Das

From Inquiry-Based Learning to Student Research in an Undergraduate Mathematics Program

Abstract As an extension to various sponsored summer undergraduate research programs, academic year research for undergraduate students is becoming popular. Mathematics faculty around the country are getting involved with this type of research and administrators are encouraging this effort. Since 2007, we have been conducting academic year research at Lamar University. This study describes our academic year research program and some of its benefits.

Further Results for the Joint Distribution of the Surplus Immediately Before and After Ruin Under Force of Interest

This article studies the joint distribution of the surplus immediately before ruin and the deficit at ruin under constant force of interest. A Laplace transformation technique has been used to establish an explicit expression for the joint distribution function with zero initial reserve. Numerical computation using this alternative expression is quick and easy in the case of exponential, gamma, and Pareto claim sizes. Moreover, a numerical method has been developed to efficiently approximate the joint distribution in case of nonzero initial reserve.

Dimension reduction of gene expression data

DNA methylation of specific dinucleotides has been shown to be strongly linked with tissue age. The goal of this research is to explore different analysis techniques for microarray data in order to create a more effective predictor of age from DNA methylation level. Specifically, this study compares elastic net regression models to principal component regression, supervised principal component regression, Y-aware principal component regression, and partial least squares regression models and their ability to predict tissue age based on DNA methylation levels. It has been found that the elastic net model performs better than latent variable models when considering less than ten principal components for each method, but Y-aware principal component regression predicts more accurately (with a reasonably low testing RMSE) and captures more of the desired structure when the number of principal components increases to 20. Coding limitations inhibited forming conclusive results about the performance of supervised principal component regression as the number of components increases.

Modeling Extreme Hurricane Damage Using the Generalized Pareto Distribution

SYNOPTIC ABSTRACT Extreme value distributions are used to understand and model natural calamities, man-made catastrophes and financial collapses. Extreme value theory has been developed to study the frequency of such events and to construct a predictive model so that one can attempt to forecast the frequency of a disaster and the amount of damage from such a disaster. In this study, hurricane damage in the United States from 1900 to 2012 has been studied. The aim of the article is threefold. First, to normalize hurricane damage and fit an appropriate model for the normalized damage data. Secondly, to predict the maximum economic damage from a hurricane in the future by using the concept of return period. Finally, to quantify the uncertainty in the inference of extreme return levels of hurricane losses by using a simulated hurricane series, generated by bootstrap sampling. Normalized hurricane damage data are found to follow a generalized Pareto distribution. It is demonstrated that the standard deviation and coefficient of variation increase with the return period, which indicates an increase in uncertainty with model extrapolation.