The Mathematics and Statistics Department supports an active group of researchers with interests spanning a broad range. There is a strong emphasis on conducting research of regional significance, and on active involvement of both graduate and undergraduate students. Faculty members and graduate students are currently conducting research in the areas of bioinformatics, biostatistics, computational biology, computational engineering, financial analytics, forensic statistics, numerical analysis, quantitative genetics, Ramsey theory and statistics.

## Descriptions of some projects currently in progress.

**Faculty Research**** | ****Current Graduate Student Research**** | ****Recent Dissertations**

### Faculty Research

**Matt Biesecker**- 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

**Tom Brandenburger**- Research interests: predictive analytics, financial statistics
- A Credit Evolution ASMBI

**Kurt Cogswell**(Google Scholar Page)- Research interests: dynamical systems, Ergodic theory
- Entropy and Volume Growth
- A Multiparameter Zero Density Subsequence Ergodic Theorem

**Gemechis Djira**(Google Scholar Page)- 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

**Xijin Ge**(Google Scholar Page)- 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

**Jung-Han Kimn**(Google Scholar Page)- 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

**Semhar Michael**(Google Scholar Page)- Research interests: computational statistics with a focus on finite mixture modeling and model-based clustering
- Studying complexity of model-based clustering
- Semi-supervised model-based clustering with positive and negative constraints
- Recent developments in model-based clustering with applications

**Hossein Moradi**(Google Scholar Page)- 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

**Michael Puthawala**(Google Scholar Page)- 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

**Chris Saunders**(Google Scholar Page)- 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

**Dan Schaal**- 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

**Don Vestal**(Google Scholar Page)- 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
*x*_{1}+x_{2}+...+x_{m}+c=2x_{0}

**Sharon Vestal**(Google Scholar Page)- Research interests: analyzing and Improving student performance in calculus courses, abstract harmonic analysis and wavelet theory
- Orthonormal wavelets and shift invariant generalized multiresolution analyses
- What I Learned… by Using an Online Homework System in Calculus I

### Graduate Student Research

**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**Cole Rausch**- working with Michael Puthawala- Stability of Inverses of Relu Activation Layers in Deep Neural Networks

**William Ternes**- working with Michael Puthawala and Peter Cheng- Applications of Numerical PDE to Navier Stokes and fluid simulation

### Recent Theses and Dissertations

**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 x_{1}+ x_{2}+ x_{3}+ ... + 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 Multi-Class 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