Speakers:

Sally Hoyt,

University of Tennessee, Knoxville

Kristen Joyner,

University of Tennessee, Knoxville

---

Speaker: Sally Hoyt

Title: GETT: a MAGMA-based General Tensor-Tensor Multiplication Algorithm

Abstract: Tensors are multidimensional arrays of numerical objects. Tensors and, specifically, tensor-tensor multiplication have many uses in mathematics, physics, and engineering, and are often used to accommodate the large amounts of data processed for machine learning applications and scientific simulations. MAGMA (Matrix Algebra on GPU and Multicore Architectures) is a numerical linear algebra library developed by the Innovative Computing Laboratory (ICL) at the University of Tennessee, Knoxville. It is designed to exploit the computing power of GPUs and multicore CPUs to deliver high performance in numerical linear algebra computations. Our goal was to develop an efficient general tensor-tensor multiplication (GETT) algorithm based on the existing MAGMA kernels. Our single-precision GETT implementation is an improved version of the function developed by the previous years’ REU RECSEM students, and it shows to be especially effective in handling higher-ranked tensors with smaller dimension sizes.

---

Speaker: Kristen Joyner

Title: Mathematically Modeling Disease Transmission in Long-Term Care Facilities

Abstract: Clostridioides difficile, also known as C. difficile, is a prevalent cause of infectious diarrhea in United States healthcare facilities. Spread through the fecal-oral route and primarily through contact with spores on contaminated surfaces, C. difficile can cause severe diarrhea, stomach pain, and colitis. Most individuals can mount an effective immune response, but older populations, immunocompromised individuals, and those taking antibiotics have an increased risk of being colonized by C. difficile. While extensive research has been conducted in hospital-based settings to improve understanding of the transmission of this bacteria, few studies apply mathematical models in the context of long-term care facilities. 

This work introduces a mathematical model using a system of ordinary differential equations to represent C. difficile transmission dynamics in assisted living facilities, with their interactive nature and high-risk factors. The equations include four resident classes (susceptible, colonized, diseased, and quarantined) and three pathogen environmental reservoirs (high-traffic areas, low-traffic areas, and healthcare worker hands) to simultaneously capture the movement between classes and track the number of spores on these environmental reservoirs, including how they contribute to disease spread. Data from the Emerging Infections Program at the Centers for Disease Control and Prevention was used for parameter estimations, and sensitivity analyses were performed to quantify the impact of varying these parameters and their impact on incidence. Mitigation strategies such as frequent disinfection, increased handwashing compliance, and a lower ratio between residents and healthcare workers had the greatest impact on reducing the incidence of C. difficile.