Session Index
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Faculty Session 1
9:40--11:20
Speakers: Lindsay Dever, Atilla Sit, Nour Hawila, Yevgeniy Galperin, Cristina Bacuta
Faculty Session 2
9:40--10:20
Speakers: Dr. Sanju Vaidya, Myung Soon Song
Faculty Session 1
9:40, Lindsay Dever (Bryn Mawr College)
Distribution of Holonomy on Compact Hyperbolic 3-Manifolds
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Chebyshev’s bias states that although the prime numbers are equidistributed between equivalence classes of 1 mod 4 and 3 mod 4, there is a bias towards primes 3 mod 4. On hyperbolic 3-manifolds, the “prime” geodesics are parametrized by their length and holonomy, which measures the twist in the geodesic. It turns out that for geodesics of increasing lengths, holonomy is equidistributed throughout the circle; it is equally likely to land in any interval of a given size. In this talk, I’ll introduce compact hyperbolic 3-manifolds and present new results on the distribution of holonomy, including equidistribution in shrinking intervals and bias in the distribution of holonomy.
Close Abstract10:00, Atilla Sit (University of the Sciences)
Singular Value Decomposition
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Singular value decomposition (SVD) is one of the most useful methods in linear algebra with many applications in science, engineering, and statistics. It is defined for all matrices$-$rectangular or square$-$unlike the more commonly used spectral decomposition in linear algebra. It generalizes the eigendecomposition of a square matrix to any $m\times n$ matrix by factorizing it into the product of three matrices, where the one in the middle is a diagonal matrix containing the singular values. We introduce the SVD method, show examples of calculating the SVD, and demonstrate some applications.
Close Abstract10:20, Nour Hawila (Penn State University, Department of Biostatistics & Bioinformatics)
Introducing Bayesian Inference with the Taxicab Problem
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The taxi problem goes by many names in the literature including the Schrödinger problem, the German tank problem, the racing car problem, the horse-racing problem, and the taxicab problem. The basic problem goes like this: Suppose taxicabs in a certain city are numbered 1 to N, and one such taxicab is randomly selected, say number 1729. Based on this information, we wish to infer the total number of taxicabs, N, there are in the city. We present a non-Bayesian and Bayesian approach to dealing with this problem that uncovers a wealth of statistical inference although we are dealing with a single data value. We provide reasonable assumptions on the potential number of taxicabs that leads to a Bayesian inference that combines the observed data with the additional assumptions into a coherent estimate of N.
Close Abstract10:40, Yevgeniy Galperin (East Stroudsburg University of PA)
An Image Processing Tour of College Mathematics
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We discuss the use of basic and advance image processing methods to provide meaningful context for reviewing key topics of the college mathematics curriculum, to help students gain confidence in using concepts and techniques of applied mathematics, to increase student awareness of recent developments in mathematical sciences, and to help students prepare for graduate studies.
Close Abstract11:00, Cristina Bacuta (University of Delaware)
Adjusting to in person instruction and assessment after three semesters online
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The return to in person calculus instruction challenges both students and instructors this semester. We will present some strategies adopted to support our students’ learning and catching up with prerequisite material in a multivariable calculus course at the University of Delaware.
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Faculty Session 2
9:40, Dr. Sanju Vaidya (Mercy College, NY)
Bounds for Vulnerability Measures of Graphs
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In the last forty years, Graph Theory has provided many powerful tools for modeling and analysis of communication networks. In this study, the vertices correspond to the processors of the networks and the edges correspond to the links among the processors. Various vulnerability measures of graphs are crucial in assessing the stability and reliability of the communication networks. The main research question is how to compute bounds for various vulnerability measures for graphs. In this presentation, we will compute bounds for vulnerability measures, Closeness and Generalized Closeness, for graphs and we will describe graphs which attain the bounds. Moreover, we will establish bounds involving Zagreb indices for triangle and quadrangle free graphs.
Close Abstract10:00, Myung Soon Song (Kutztown University of Pennsylvania)
Variable Selection Using a Metaheuristic Method
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Variable selection is one of the very popular topics from regression models. Besides many conventional approaches, some metaheuristic approaches from the realm of optimization including, but are not limited to, GA (Genetic Algorithm) or SA (simulated annealing) have been suggested so far. These methods have a considerable advantage over the conventional methods when dealing with a variety of problems, but how to fine-tune parameters is very challenging. In this research, a parameter-free approach called Jaya will be suggested and explored. Many methods such as GA, TBO (Teaching Based Optimization), and Jaya will be compared to one another with a real-world dataset and a simulated dataset. The impact of using local search will also be analyzed. This is a follow-up to what we presented at EPaDel Fall 2020.
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