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 | Past Dissertations**

### Faculty Research

**Matt Biesecker**- Research Interests: Mathematical Modeling, Optimization, Calculus of Variations
- 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**- Research Interests: Dynamical Systems, Ergodic Theory
- Entropy and Volume Growth
- A Multiparameter Zero Density Subsequence Ergodic Theorem

**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

**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

**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

**Semhar Michael**- Research Interests: Computational Statistics with a focus on Finitemixture 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

**Cedric Neumann**- Research Interests: Applications of Statistics to the inference of sources of traces of evidence recovered from crime scenes (DNA, fingerprints, dust particles, etc.)
- Improving the Understanding and the Reliability of the Concept of "Sufficiency" in Friction ridge Examination
- Quantifying the weight of evidence from a forensic fingerprint comparison: a new paradigm

**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

**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**- 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**- 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

### Current Graduate Student Research

**Doug Armstrong**- working with Chris Saunders*Using Multi-State Markov Models to study Asian Carp Movement*

**Chad Birger**- working with Dan Schaal*Computational Ramsey Theory*

**Brandon Breitling**- working with Gemechis Djira*Mutual Information Pre-selection Compared to Step-wise Post-selection of Multiple Regression Model*

**Adam Buskirk**- working with Yunpeng Pan*Remote Sensing Data Mining for Extracting Data Center Site Characteristics*

**Nasir El Mesmari**- working with Yunpeng Pan*Combinatorial Optimization Approach to Familial Breast Cancer Attribution*

**Hari Lamitarey**- working with Yunpeng Pan*Support Vector Machines*

**Austin O'Brien**- working with Chris Saunders*Using Atypicalities to Find Abnormalities in Multi-Dimensional Data*

**Danica Ommen**- working with Chris Saunders*Convergence Properties of Different Computationally Efficient Approximations to the Weight of Forensic Evidence*

**Rajab Suliman**- working with Yunpeng Pan, Abu Farzan Mitul, Lal Mohammad and Qiquan Qiao*Modeling of bulk heterojunction polymer solar cell based on response surface methodology*

**Ameya Vaidya**- working with Gary Hatfield and Dennis Helder*Development Of Absolute Radiometric Calibration Model Using Pseudo Invariant Calibration Sites (PICS)*

**Daniel Vellek**- working with Tom Brandenburger*Competing Risk Survival Analysis: Credit Card Portfolio Application*

**Robert Vaselaar**- working with Jung-Han Kimn*Numerical Methods for the Dirac Equation Related to Neutrino Propagation*

**Matthew Whipple**- working with Xijin Ge*Understanding early embryo development through pathway analysis*

**Kang Ye**- working with Xijin Ge*Statistical pathway analysis in model plant Arabidopsis*

**William Young**- working with Gary Hatfield*Skellam Distribution*

### Past Dissertations

**Josie Wallin**(2010): Customer Segmentation Using Cluster Analysis on Student Loan Applications**Nathaniel Lutz**(2010): Reject Inference in Sub-Prime Credit**Larissa Peterson**(2010): Longitudinal Data Analysis of Bone Health During Lactation and Weaning**Adam Schmitz**(2010): Estimating Probabilities of Extreme Market Returns**Alfred Furth**(2010): A combination survival and time series model for predicting time to default**Liz Lane-Harvard**(2009): Disjunctive Rado numbers for the set of equations ax_1 + x_2 = x_3 and bx_1 + x_2 = x_3**Mike Bergwell**(2009): T-color selectivity Rado numbers**Thomas Brandenburger**(2009): A Markov multinomial regression model for predicting consumer credit risk**Nathan McClanahan**(2008): An algorithm for Excel Storage systems**Darren Row**(2008): Disjunctive Rado numbers for some cases of sets of generalized linear equations**Lynae Schoeneman**(2007): Two problems in Ramsey theory on the natural numbers**Joe Mousel**(2006): 2-color Rado numbers for the family of equations x(1) + x(2) + ... + x(m-1) + c = (m-1)x(m)**Brenda Johnson**(2004): Three-color Rado numbers for an inequality