New and Ongoing Research

TSU Computational Mathematics research group

Research interests of some members of the department include

• Dr. Bryant Wyatt – Particle Modeling
• Dr. Claudia Rodriguez – Mathematics Education
• Dr. Courtney Holland – Mathematics Education, Faculty Professional Development, and Postsecondary Teaching and Learning
• Dr. Jesse Crawford – Mathematical Statistics and Data Mining
• Dr. José Herrera-Diestra – Modeling Infectious Diseases
• Dr. Keith Emmert – Mathematical Biology
• Dr. Madhur Wyatt – Atrial Fibrillation Study
• Dr. Taylor Darwin – Mathematics Education
• Dr. Yao-Chi Yu – Clinical Data Mining and Machine Learning

Dr. Bryant Wyatt- Particle Modeling

Dr. Wyatt and his students work in a high performance computing lab doing Particle Modeling research. In the old days to run large N-body simulations you needed a CRAY supercomputer which cost tens of millions of dollars. Today with the advances Graphics Processing Units (GPUs) supercomputing can be done in your living room. The lab was built with a grant from Tarleton State University and donations from Mellanox Technology and NVIDIA. We are grateful for their support.

N-body Simulations of Late Lunar Forming Impacts

The Giant Impact Hypothesis is currently the most widely accepted explanation for the formation of the Earth-Moon system. Though this mode of formation is stated in text books it has never been modeled. Dr. Robin Canup (Associate Vice President at the Southwest Research Institute) made the problem popular when she was featured on the history channel. Researchers have been able to create impact models that produce a disk of debris around the earth with enough mass to create the moon. They have also created models that can start with a disk of debris around the earth and coalesce into a moon. But no one to date has been able to produce both from a single model. Brett and Justin were able to produce models using only a single GPU with very similar results to Dr. Canup’s.

Brett Hokr graduated from Tarleton in May 2011 and moved on to Texas A&M to work on his Ph.D. in Quantum Optics studying under Dr. Marlan Scully.

Justin Highland graduated from Tarleton December 2011 and will be joining the team down at Texas A&M in the fall of 2012.

We are still trying to create a single model that will produce the accretion disk from an impact that will then coalesce into a moon.

N-body Study of the Thermodynamic Properties of Water

Student: Travis Salzillo is working on a model of the water molecule and trying to check the validity of the model to known thermodynamic properties of water. Once we have an understanding of the models temperature we will study the phase changes of water using the model.

Travis is scheduled to graduate in May 2013 and hopes to continue his studies toward his Ph.D.

Particle Based Simulation of Oscillating String

Student: Robert Pierce is working on comparing a particle based model to a continuum based model. He is building a physical vibrating string apparatus that he can set the amount of tension. He can also find the mass per unit length of the string. Using these two parameters he will build a continuous model that he solves using partial differential equations and a discrete case which he will solve using particle modeling. He will then compare both back to the physical vibrating string.

Particle Modeling Optimization on a CUDA-enabled High-performance Cluster

Student: David Gibson is working on ways of optimizing different N-body problems to run most efficiently on a CUDA cluster.

Student: Eli Symm has just joined our group and is working on finding a problem to study.

Graduation parties on the Paluxy River at Wyatt’s in Glen Rose.

If you would like more information on our group drop us a line at wyatt@tarleton.edu

Dr. Claudia Rodriguez – Mathematics Education

Dr. Claudia Rodriguez’s research examines how universities can serve as catalysts for strengthening mathematics education and expanding STEM pathways through collaborative partnerships with schools and surrounding communities. Her work focuses on designing educational ecosystems that connect K–12 students, pre-service teachers, in-service teachers, and higher education institutions to improve mathematics instruction, increase college readiness, and support successful transitions into STEM fields. She is particularly interested in developing sustainable models that enhance mathematics learning opportunities for students in rural communities and first-generation college students.

Her scholarship integrates mathematics education, higher education policy, teacher preparation, and emerging technologies to identify innovative approaches that improve teaching and learning. Current projects include research on summer bridge programs, artificial intelligence as a tool for mathematics instruction and teacher professional learning, mathematics teacher preparation, and university-community partnerships. Through interdisciplinary collaboration, Dr. Rodriguez seeks to develop research-informed models that strengthen STEM education, support teacher development, and create lasting partnerships between universities, schools, and local communities.

Dr. Courtney Holland – Mathematics Education, Faculty Professional Development, and Postsecondary Teaching and Learning

Dr. Holland’s research focuses on professional development in undergraduate mathematics education, with an emphasis on understanding the factors that influence mathematics faculty participation in and implementation of evidence-based teaching practices. Her research has examined how professional identity, motivation, and faculty beliefs shape engagement in professional development and instructional decision-making. Using qualitative methodologies, she investigates strategies for designing meaningful and sustainable professional development that supports instructional improvement in collegiate mathematics.

Current and future research directions include faculty professional development in higher education, active learning in undergraduate mathematics, curriculum and course coordination, faculty mentoring, and the scholarship of teaching and learning in mathematics. Her work seeks to identify practices that support faculty growth while improving student engagement and success in collegiate mathematics courses.

Dr. Jesse Crawford – Multivariate Statistics, Data Science, Environmental Science, and Health Care Analytics

Dr. Crawford research has involved the study of multivariate normal distributions with covariance matrices determined by group symmetries and acyclic mixed graphs, including the generalization of canonical correlations to group symmetry models, and developing a likelihood ratio test for testing equality of natural parameters for generalized Riesz distributions. 

 He is currently working on a project sponsored by Blue Cross and Blue Shield of Texas under the Affordability Cures Initiative to minimize improper payments for health insurance claims.  Previous projects include ensemble models of climate variability, identification of nitrate contamination in water wells, SIR disease models in amphibian populations, development of general canonical correlations for group symmetry models, and likelihood ratio tests for generalized Riesz distributions.

Dr. José Herrera-Diestra – Modeling Infectious Diseases

Mobility-Informed Epidemic Surveillance and Forecasting

Human mobility plays a fundamental role in shaping how infectious diseases spread across communities. In this line of research, I investigate whether mobility patterns observed before an epidemic season can be used to anticipate where disease burden will be greatest. By combining large-scale mobility data, network science, statistical modeling, and machine learning, I develop methods to identify communities that may be at elevated risk before outbreaks occur.

Recent work has focused on influenza and respiratory syncytial virus (RSV), using mobility networks constructed from millions of movements between communities to predict hospitalization burden across Texas. This research aims to transform mobility data into practical tools for early warning, epidemic preparedness, and public health planning.

Key question: Can mobility data collected before an epidemic season be used to predict where disease burden will be highest?

Surveillance and Vaccination Strategies for Respiratory Diseases

Public health resources are often limited, making it essential to identify where surveillance and intervention efforts can have the greatest impact. My research explores how mobility networks, demographic information, and epidemiological models can be combined to improve the placement of surveillance systems and optimize vaccination strategies for respiratory diseases.

Current projects focus on identifying communities that could serve as effective sentinel locations for early outbreak detection and evaluating how vaccination resources can be allocated to reduce disease burden most efficiently. These studies integrate mathematical models with real-world mobility and hospitalization data to support evidence-based public health decision-making.

Key question: Can mobility networks improve the effectiveness of disease surveillance and vaccination programs?

Infectious Disease Importation Risk During Mass Gathering Events

Large international events create unique opportunities for infectious diseases to spread across countries through increased travel and population mixing. This research investigates how publicly available data can be used to estimate disease importation risk during mass gathering events, providing rapid and transparent assessments that can support preparedness efforts.

A recent project examines the 2026 FIFA World Cup, integrating international travel data, disease incidence estimates, and tournament schedules to evaluate the potential risk of importing infectious diseases into host cities. More broadly, this work seeks to develop scalable frameworks for assessing epidemic risk in highly connected global systems and to provide actionable information before more detailed proprietary datasets become available.

Key question: How can publicly available data be used to rapidly assess infectious disease importation risk during global events?

Social Vulnerability, Mobility, and Health Disparities

Communities do not experience epidemics equally. Differences in socioeconomic conditions, demographics, and mobility patterns can lead to substantial disparities in disease burden. My research examines how social vulnerability interacts with human mobility to influence the spatial distribution of infectious diseases.

Using data from Texas communities, I investigate how mobility reduction, network connectivity, and measures of social vulnerability contribute to differences in hospitalization rates and epidemic outcomes. This work aims to improve our understanding of why certain communities experience disproportionately severe impacts during outbreaks and how public health interventions can be targeted more effectively.

Key question: Why do some communities experience disproportionately higher disease burden than others?

Livestock Mobility Networks and Disease Surveillance

The movement of animals between farms creates transportation networks that can facilitate the spread of infectious diseases. In this line of research, I apply methods from network science and epidemiology to study livestock movement systems and evaluate their role in disease surveillance and outbreak risk.

Past work has examined cattle transportation networks and their ability to explain patterns of epidemic burden. Ongoing efforts explore how publicly available movement-network data can be used to support surveillance for emerging livestock diseases such as H5N1, particularly in situations where access to proprietary industry data is limited. These projects extend concepts developed in human epidemiology to agricultural systems and food security.

Key question: Can livestock transportation networks be used to identify high-risk locations and improve disease surveillance?

Mathematical Modeling of Infectious Diseases

Mathematical models provide a framework for understanding how infectious diseases spread through populations and how interventions can alter epidemic trajectories. My research develops and analyzes compartmental and metapopulation models that incorporate demographic structure, vaccination, climate effects, and human mobility.

Recent projects include age-structured models of influenza transmission calibrated to hospitalization data and simulations designed to evaluate the impact of vaccination strategies and surveillance systems. These models help bridge theoretical epidemiology and real-world public health applications by providing quantitative tools to evaluate competing intervention scenarios.

Key question: How can mathematical models help explain and predict epidemic dynamics?

Complex Systems and Network Dynamics

Many biological and social phenomena emerge from interactions among large numbers of interconnected individuals. My research in complex systems seeks to understand how local interactions generate large-scale collective behavior, drawing on tools from statistical physics, nonlinear dynamics, and network science.

This work includes studies of adaptive networks, social dynamics, opinion formation, collective behavior, and the interplay between network structure and dynamics. Although my recent research focuses primarily on epidemiological applications, these ideas continue to provide the theoretical foundation for many of the network-based approaches used throughout my work.

Key question: How do local interactions generate large-scale collective behavior in complex systems?

Dr. Keith Emmert – Mathematical Biology

Dr. Emmert research is focused on the development of new deterministic and stochastic epidemic models for the spread of disease in a structured host population. Past models have been included difference as well as differential equations with both fixed or periodic coefficients. I use theory as well as simulations to investigate the richness of the models.

Future directions in research include investigating the robustness of stability results, improved visualization techniques for bifurcations in higher dimensions, animal movement models, epidemic models that incorporate a spatial component, and population genetics. Parallel algorithms and genetic algorithms will most likely be of great use in exploring these new topics.

Dr. Madhur Wyatt – Atrial Fibrillation and Left Atrium Digital Twin

Interactive N-Body Digital Twin of the Left Atrium

The left atrium is the primary site of origin for atrial fibrillation (AF), the most common sustained cardiac arrhythmia. Dr. Wyatt’s research focuses on validating the interactive, GPU-accelerated N-body digital twin of the left atrium that simulates the electrical dynamics underlying AF and other atrial arrhythmias in near real-time. Unlike traditional simulation approaches that require offline computation, this model allows users to induce arrhythmias, adjust physiological parameters, and explore intervention strategies interactively — making it a powerful tool for both research and education.

Physiological Validation and Anatomically Realistic Modeling

Computational models are only as meaningful as their fidelity to real cardiac anatomy and physiology. A central component of Dr. Wyatt’s work involves validating model parameters against known electrophysiologic behavior and integrating anatomically realistic structures into the simulation framework. This includes building the Bachmann’s bundle component — a key inter-atrial conduction pathway — as a branching network of specialized myocytes, and identifying anatomical landmarks from clinical imaging to ground the model geometry in patient-realistic structure.

Virtual Catheter Ablation Strategy Exploration

Catheter ablation is a frontline therapeutic procedure for AF, yet outcomes remain variable and procedural planning is largely empirical. Dr. Wyatt’s research uses the left atrium digital twin to simulate ablation lesion placement and evaluate its effect on arrhythmia termination and recurrence within the model. This work aims to provide a computational testbed for comparing ablation strategies before clinical application, with potential implications for procedural training and pre-operative planning theoretically.

Undergraduate Mentorship in Physiology-Informed Simulation

Training the next generation of interdisciplinary researchers requires intentional mentorship at the interface of biology, mathematics, and computing. Dr. Wyatt supervises undergraduate students in designing and interpreting physiology-grounded simulation studies, guiding them from model development through conference presentations. Students mentored in our lab have presented at local, regional, and international conferences including the Heart Rhythm Society Conference, Nvidia’s GTC, Supercomputing, and the Texas Section MAA meeting.

Dr. Taylor Darwin – Mathematics Education

Dr. Taylor Darwin’s research examines how systems-level reform, data science, and emerging technologies can improve mathematics teaching and learning. Her work focuses on scaling increased opportunity across mathematics pathways, exploring AI-supported instruction and professional learning, and strengthening STEM opportunities for rural and underserved communities through collaborative partnerships. She is particularly interested in translating research into sustainable institutional practices that improve student success.

Current research projects include:

• Data science initiatives in undergraduate mathematics education.
• Exploring the use of artificial intelligence to support mathematics teaching, learning, and faculty professional development.
• Advancing systems-level change in mathematics education by supporting the implementation and scaling of corequisite mathematics initiatives to improve student success.
• Supporting rural STEM teachers and students through collaborative STEM education initiatives and university–school partnerships.

Dr. Yao-Chi Yu – Clinical Data Mining and Machine Learning

Dr. Yu’s research focuses on applying machine learning and data science techniques to clinical and health data. His work specializes in clinical Natural Language Processing (NLP), anomaly detection, reinforcement learning and control, and medical decision analytics to develop predictive models that inform medical decision-making and improve patient outcomes.

Predicting Chronic Disease Risk: Develop interpretable machine learning models that identify predictors of cardiovascular disease and cancer risk across U.S. and Taiwanese populations, based on dietary behavior and food marketing exposure.

Mayo Clinic Headache and Cerebrovascular Research: Use AI and machine learning to improve outcomes for patients with headaches and cerebrovascular disorders.

Predictive Health and BMI Trajectories: Explore dietary dynamics and BMI trajectories for the prevention of chronic conditions.