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Applied and Computational Mathematics Seminar

Applied Math Seminar

Computing Exponentials of Essentially Non-negative Matrices with Entry-wise Accuracy
Speaker: Qiang Ye, University of Kentucky
Abstract:

A real square matrix is said to be essentially non-negative if all of its off-diagonal entries are non-negative. In this talk, I will present new perturbation results and algorithms that demonstrate that the exponential of an essentially non-negative matrix can be computed with entrywise relative accuracy.

Date:
-
Location:
POT 745

Applied Math Seminar


Learning Algorithms for Restricted Boltzmann Machines
Speaker: Devin Willmott, University of Kentucky
Abstract: Restricted Boltzmann machines (RBMs) have played a central role in the development of deep learning. In this talk, we will introduce the theoretical framework behind stochastic binary RBMs, give motivation and a derivation for the most commonly used RBM learning algorithm (contrastive divergence), and prove some analytic results related to its convergence properties.

Date:
-
Location:
POT 745

Applied Math Seminar

Speaker: David, Murrugarra, UKY
Title: Estimating Propensity Parameters using Google PageRank and Genetic Algorithms
Abstract: Stochastic Boolean networks, or more generally stochastic discrete networks, are an important class of computational models for molecular interaction networks.
The stochasticity stems from the updating schedule. The standard updating schedules include the synchronous update, where all the nodes are updated at the same time
and gives a deterministic dynamic, and the asynchronous update, where a random node is updated at each time step that gives a stochastic dynamics.
A more general stochastic setting considers propensity parameters for updating each node.  SDDS is a modeling framework that considers two propensity values for updating each node, one when the update has a positive impact on the variable, that is, when the update causes the variable to increase its value, and the other when the update is negative, that is, when the update causes it to decrease its value. This extension adds a complexity in parameter estimation of the propensity parameters. This talk presents a method for estimating the propensity parameters for SDDS. The method is based on adding noise to the system using the Google PageRank approach to make the system ergodic and thus guaranteeing the existence of a stationary distribution and then with the use of a genetic algorithm the propensity parameters are estimated.
 
Date:
-
Location:
POT 745

Applied Math Seminar--Master's Exam

Title:  My preferred proof of the Lefschetz fixed point theorem 

Abstract:   There are many different proofs of the Lefschetz fixed point theorem.  The most familiar approach uses simplicial approximation and is often a first example of the power of simplicial homology.  I'll talk about a very different proof that I find much more useful.  This proof requires more input, but it generalizes easily. 

Date:
-
Location:
145 Patterson Office Tower

Applied Math Seminar

Title:  Modeling Foot and Mouth Disease in cattle in northern Cameroon

Abstract:  Foot and Mouth Disease (FMD) is endemic in cattle in the Far North Region of Cameroon. While many cattle herds remain in a fixed location throughout the year, there are a small number of mobile herds that migrate depending on the season. These mobile herds share grazing space with many other cattle throughout the year, leading to increased disease transmission. In this talk I will present a multi-scale agent-based simulation model of FMD in northern Cameroon, focusing on the mathematical SIRS epidemic model running both inter- and intra-herd. Various parameters are determined by data from researchers on the ground while others are determined via in silico experimentation. The goal of the first phase of the project is to determine how each herd type contributes to the overall number of secondary infections. This model is a work in progress and the talk is meant to stimulate discussion about means of incorporating epidemic models in a multi-scale setting.

Date:
-
Location:
145 Patterson Office Tower
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