Mathematics and Statistics Research

Research interests: mathematical modeling, optimization, calculus of variations

• Kinetic Monte Carlo modeling on organic solar cells: Domain size, donor-acceptor ratio and thickness
• Optimization of virotherapy for cancer
• The inverse problem of the calculus of variations for systems of second-order partial differential equations in the plane

Google Scholar – Fred Boehm

Research interests: biostatistics, with a focus in statistical genetics

Frederick Boehm – GitHub

Google Scholar – Gemechis Djira

Research interests: simultaneous inferences, bioassays, longitudinal data analysis, statistical computing, Bayesian analysis, sequential methods

• Multiple comparisons of parametric models and in longitudinal studies (with Ramu Sudhagoni)
• Relative potency estimation in parallel-line assays

Google Scholar - Xijin Ge

Research interests: bioinformatics, genomics and cancer

• Interpreting expression profiles of cancers by genome-wide survey of breadth of expression in normal tissues
• The microarray quality control (MAQC)-II Study
• Reducing false positives in molecular pattern recognition

Google Scholar – Jung-Han Kimn

Research interests: efficient parallel algorithm based on domain decompositions: mathematical analysis and practical implementation

• A convergence theory for an overlapping Schwarz algorithm using discontinuous iterates
• Restricted overlapping balancing domain decomposition methods and restricted coarse problems for the Helmholtz problem
• Numerical implementation of overlapping balancing domain decomposition methods on unstructured meshes
• A numerical approach to space-time finite elements for the wave equation

Google Scholar – Semhar Michael

Research interests: computational statistics with a focus on finite mixture modeling and model-based clustering

• Studying complexity of model-based clustering
• Semisupervised model-based clustering with positive and negative constraints
• Recent developments in model-based clustering with applications

Google Scholar – Hossein Moradi

Research interests: big data, dimension reduction and variable selection, functional data analysis, multivariate statistics, spatial and spatiotemporal statistics

• Response envelopes for linear coregionalization models
• New parsimonious multivariate spatial model: Spatial envelope
• A Bayesian multivariate functional model with spatially varying coefficient approach for modeling hurricane track data
• Robust estimation and variable selection in sufficient dimension reduction

Google Scholar – Trang Nguyen

Research interests: optimization, optimal control and applications, machine learning and statistical learning

• Trang Nguyen – GitHub

Google Scholar – Michael Puthawala

Research interests:

• Machine learning: manifold learning, geometric learning, universality
• Math/applied math: inverse problems, scientific computing, optimal transport

• Deep invertible approximation of topologically rich maps between manifolds
• Universal joint approximation of manifolds and densities by simple injective flows
• Globally injective ReLU networks

Google Scholar – Chris Saunders

Research interests: forensic inference of source, statistical pattern recognition and approximation theory

• Construction and evaluation of classifiers for forensic document analysis
• Using automated comparisons to quantify handwriting individuality
• A novel application of quantile regression for identification of biomarkers exemplified by equine cartilage microarray data

Research interests: combinatorics, Ramsey theory on the real numbers

• A zero-sum theorem
• Disjunctive Rado numbers
• On a variation of Schur numbers
• Off-diagonal generalized Schur numbers

Google Scholar – Don Vestal

Research interests: number theory and combinatorics (especially Ramsey theory)

• Construction of weight two eigenforms via the generalized Dedekind eta function
• The discrete Rado number for x₁+x₂+...+x_m+c=2x₀

Google Scholar – Sharon Vestal

Research interests: analyzing and Improving student performance in calculus courses, abstract harmonic analysis and wavelet theory

• Orthonormal wavelets and shift invariant generalized multiresolution analyses
• Improving student success in Calculus 1 using a corequisite calculus 1 lab

• Vahid Hosseinzadeh – working with Michael Puthawala
  • The intersection of geometric deep learning and power systems stability
• Cole Patten – working with Michael Puthawala and Chris Saunders
  • Contrastive learning, with application to forensic identification of source
• Cole Rausch – working with Michael Puthawala
  • Stability of inverses of ReLU activation layers in deep neural networks

• Emma Brookman (M.S., 2025): Association Between Water Pollution and Other Environmental Factor Exposures with Preterm Births and Potential Subsequent Birth Defects
• Eleanor Cain (M.S., 2025): An Extension of the Spatiotemporal Change of Support Model to Skew-Gaussian Distributions
• Annamarie Dobbs (M.S., 2025): Thinking in Ink: How Notetaking Adapts in a Thinking Classroom
• Nathan Meyer (M.S., 2025): Developing Proportional Hazards Mixture Cure Models and Predicting Risk for Persons With End-Stage Kidney Disease
• Edwin Mutimba (M.S., 2025): Modeling Area Deprivation Index Using Non-Gaussian Fixed Rank Kriging
• Addy Smith (M.S., 2025): Exploring the Role of Clinical and Social Factors in Predicting All-Cause Mortality in End-Stage Kidney Disease Patients: A Machine Learning Framework
• Anthony Glackin (M.S., 2024): Rado Numbers for Two Systems of Linear Equations
• Cole Patten (M.S., 2024): Contrastive Learning, with Application to Forensic Identification of Source
• Cami Fuglsby (Ph.D., 2023): U-Statistics for Characterizing Forensic Sufficiency Studies
• Rachel Bergjord (M.S., 2023): Some 2-Color Rado Numbers For A Linear Equation With A Negative Constant
• Shi Wen Wong (M.S., 2023): A Study of the Local Deep Galerkin Method for the Modified Cahn Hilliard Equation
• Skylar Halverson (M.S., 2022): Totally Multicolored Rado Numbers For the Equation x₁ + x₂ + x₃ + ... + x_m-1 = x_m
• Stephanie Liebl (M.S., 2022): Using Deep Neural Networks to Analyze Precision Agriculture Data
• Rylee Sundermann (M.S., 2022): Efficient Numerical Optimization for Parallel Dynamic Optimal Power Flow Simulation Using Network Geometry
• Tessa Sundermann (M.S., 2022): The Efficacy of the South Dakota State University Summer Jacks LeaP Program
• Madeline Anne Ausdemore (Ph.D., 2021): Development of a Probabilistic Multiclass Model Selection Algorithm for High-Dimensional and Complex Data
• Nicholas Brown (Ph.D., 2021): Detailing the Connection Between a Family of Polar Graphs and Tremain Equiangular Tight Frames
• Jessie Hendricks (Ph.D., 2021): Development and Properties of the ROC-ABC Bayes Factor for the Quantification of the Weight of Forensic Evidence
• Paul May (Ph.D., 2021): Methods for High-Dimensional Spatial Data: Dimension Reduction and Covariance Approximation
• Rong Zhou (M.S., 2021): Comparison of Software Packages for Detecting Differentially Expressed Genes from Single-Sample Rna-Seq Data
• Abdelbaset Abdalla (Ph.D., 2019): Finite Mixture of Regression Models for Complex Survey Data
• Shaopeng Gu (M.S., 2019): Applying Machine Learning Algorithms for the Analysis of Biological Sequences and Medical Records
• Amanda Jensen (M.S., 2019): Using Social Network Analysis to Examine the Connections within a Noyce Community’s Facebook Group
• Nicholas Stegmeier (M.S., 2019): A Study of Several Applications of Parallel Computing in the Sciences Using PETSC