Mathematics

Applied Graph Theory - Director Kim Factor

This laboratory applies graph theory and combinatorics to a variety of areas, as such as network traffic in power sources and the use of graph theory to determine protocols for biosurveillance with an emphasis in animal diseases. This is a continually growing and changing area with many opportunities.

Computational Algebra - Director Michael Slattery

Research in this area offers a rare cross-over between pure mathematics and computation. In the case of Dr. Slattery, it is concerned with designing and analyzing algorithms and data structures to compute information about groups. Two important computer algebra systems (CAS) used for group theory are GAP and MAGMA.

Graph Theory - Director John Engbers

This laboratory investigates extremal and probabilistic questions in graph theory and combinatorics, including graph coloring questions and games on graphs.  Some specific topics currently being studied include independent sets, vertex colorings, and alternating sign matrices.  


Computational Applied Mathematics

Applied and Computational Probability - Director Elaine Spiller

Randomness and nonlinearity are dominant features in many mathematical models. The interplay between the two often causes interesting behavior that we wish to understand and predict. Current projects include:

  1. Hazard Mapping - Devastation caused by pyroclastic (rapid, granular, volcanic) flows can be extreme for communities situated near volcanoes. We are devising methods to draw accurate hazard maps for use in civil protection and planning. Work is in collaboration with investigators at the State University of New York at Buffalo (math, volcanology), Duke University (statistics), and National Institute of Statistical Sciences. This project is supported by the NSF.

  2. Nonlinear Optics - In nonlinear, random systems interesting phenomena are often in the form of rare but important events. The performance of optical communication systems and mode-locked lasers is limited physically by noise, i.e., incoherent photons introduced during amplification. We seek to understand both how errors occur and how frequently they occur. Work is in collaboration with investigators at the State University of New York at Buffalo and Northwestern University.

  3. Data Assimilation - Data assimilation is a broad term for techniques that combine noisy observations with dynamic model based predictions. Our current work is in devising methods of data assimilation that work well in systems that are both nonlinear and high-dimensional. Work is in collaboration with investigators at the University of North Carolina at Chapel Hill (math, statistics) and University of California at Los Angeles (geosciences).

Elaine Spiller’s research work intersects with the Biomathematics group’s activities, but also interfaces with the Statistics group’s work.

Electrical Impedance Tomography - Director Sarah Hamilton

Electrical Impedance Tomography (EIT) is a non-invasive, portable, radiation-free, imaging modality used for monitoring hearth and lung function of patients in the ICU setting. The goal of EIT is to recover the internal structure of a body from electrical measurements taken at the surface. The conductivity and permittivity of biological tissues such as heart, lung, blood, and fat are different allowing a medical doctor to then use the EIT images for diagnostic/monitoring purposes. Additional applications include: detection and classification of breast tumors, stroke classification in brain imaging, non-destructive evaluation on concrete structures, detection of groundwater contamination, oil exploration and landmine detection. The reconstruction task is a highly ill-posed nonlinear inverse problem and requires the use of mathematical techniques from functional and complex analysis as well as computational skills. Traditional methods based on least squares minimization or linearization are not sufficient for static imaging applications (breast cancer, stroke). Our lab focuses on solving the full nonlinear problem directly (non-iteratively), in real-time, using any available information to improve the images.

GasDay Lab - Director Ron Brown, with Richard Povinelli, George Corliss, Tom Quinn, and others.

GasDay forecasts natural gas consumption for about 30 energy delivery companies all over the US. We build mathematical models, perform statistical analysis of data, develop software, deliver that software to customer utilities, prepare custom research reports, and provide on-going customer support. We function like a small business within the University. Each day, we provide forecasts for nearly 20% of the natural gas in the US for residential, industrial, and commercial uses.  We are a student centered learning project, a research project, and the technology transfer project.  Students do research and publish in the areas of mathematical modeling, data mining, statistical analysis, database design, computer systems architecture, and software engineering. GasDay supports 10 graduate students and 20+ undergraduate students.  Participating faculty come from MCCS, Engineering, and Business.


Biomathematics

Pulmonary Lab - Director Gary Krenz

Applies mathematical modeling to address basic science questions regarding nonrespiratory functions of the [mammalian] pulmonary circulation. Current projects include:

  1. Pulmonary disposition of quinones. The working hypothesis is that metabolic changes precede the remodeling that occurs in pulmonary hypertension. Quinones are used as probes to investigate changes in the pulmonary endothelium redox status/signaling. Work is in collaboration with Marquette Biomedical Engineering and Zablocki/Medical College of Wisconsin researchers.

  2. Structure/function studies of the pulmonary circulation. Investigation of how structural changes that result in several biological models of pulmonary hypertension (chronic hypoxia exposure, monocrotaline exposure, thoracic irradiation) impact upon the hemodynamic functioning of the pulmonary circulation. 1 Ph.D. student working on the impact of supernumerary vessel recruitment may have upon normal pulmonary function.

Bioinformatics Lab - Director Serdar Bozdag

This lab applies machine learning and algorithmic techniques to biologically motivated questions. Particularly, we are interested in building models of gene regulation from high-throughput biomedical datasets in tumor cells. Current projects include:

  1. Age-specific signatures of glioblastoma. Glioblastoma (GBM), one of the deadly types of brain cancer exhibits different survival rates among young and old patients. More specifically, old GBM patients survive significantly shorter than young GBM patients. In this project, we analyze high-throughput genomic, genetic, and epigenetic datasets of several hundreds of GBM patients to find age-specific signatures of GBM. Work in collaboration with Howard A. Fine at the NYU Cancer Institute.

  2. Modeling of gene regulation from high-throughput biological datasets. It is known that there are several factors that affect how genes are regulated in genomes. In this project, we apply machine learning tools that incorporate high-throughput heterogeneous genomic, genetic, epigenetic datasets to build models of gene regulation. Work in collaboration with Stefan Wuchty at the National Center for Biotechnology Information at NIH.

  3. Genomic analysis of stress response against arsenic in Caenorhabditis elegans. In this project, we apply FastMEDUSA on gene expression datasets of C. elegans that are exposed to different levels of arsenic. We aim to identify significant regulators in the stress response against arsenic in C. elegans. Work in collaboration with Dr. H. Nese Cinar at Food and Drug Administration.

  4. Significant regulators glioma stem cells (GSCs) in response to metformin treatment. Metformin is a drug that is being used to type 2 diabetes. We hypothesize that metformin might be used to treat some glioblastoma patients, too. In this project, we analyze time-series gene expression datasets of GSCs treated with metformin to identify significant regulatory differences between metformin-sensitive and metformin-resistant GSCs. Work in collaboration with Howard A. Fine at the NYU Cancer Institute.

  5. Significant pathways of gene regulation. In this project, we analyze gene regulatory models derived from FastMEDUSA to compute significantly overrepresented pathways that potentially play an important role in gene regulation.

Biomedical Imaging - Director Anne Clough

This laboratory designs, develops, and optimizes imaging systems and requisite experimental protocols and image analysis tools for investigating cardio-pulmonary physiology pathophysiology of small laboratory animals. Close collaboration with Prof. Krenz’s group as well as scientists and clinicians at Zablocki VA Medical Center and Medical College of Wisconsin. Ongoing funded projects include:

  1. Micro-Angiography Investigation of Pulmonary Hemodynamics - Following completion of this instrument, its hardware, experimental protocols, and image analysis tools are being modified to determine capillary flow, its regional distribution, and changes therein following lung injury or treatment in rats. Supported by NHLBI, Co-Investigator.

  2. Angiogenesis in the Bronchial Circulation using SPECT (single-photon emission computed-tomography) – Micro-CT and SPECT to monitor angiogenesis in the bronchial circulation of rats. Supported by NHLBI, Co-principal investigator.

  3. Micro-SPECT Hardware and Software Design – Construction of a flexible system for rapid, high-resolution imaging of small animals using radiopharmaceuticals targeted at specific molecular functions. Supported by the Keck Foundation.

  4. Redox Status of Lungs in Rats Exposed to Chronic Oxidative Stress with Micro-SPECT – Use molecular imaging radiopharmaceuticals and pharmacokinetic modeling to assess early lung injury. Supported by NHLBI, Co-Investigator.

  5. Reducing Patient Dose in Spiral and Conebeam CT – Simulations designed to determine optimal scanning parameters. Supported by NIBIB, Co-Investigator with U. of Iowa.


Statistics

Functional Magnetic Resonance Image Analysis - Director Daniel B. Rowe

The long-term goal of the Rowe Functional Magnetic Resonance Image Analysis Lab research efforts is to develop a unified mathematical model for functional magnetic resonance imaging (fMRI). This mathematical model is to include the fundamental physics of the nuclear magnetic resonance signal, the compensation for biological signals not of interest, the preprocessing of the MR images, the statistical modeling of complex-valued time series, and the statistically significant determination of focal brain activation. This mathematical model will extract the most information from the acquired data in the most efficient way possible. This unified model will contain important physiological information that may not be available by other means or is only available by more time-consuming elaborate means. This model will allow us to address important fundamental neuroscience questions with fMRI. The Rowe fMRI Analysis Lab's primary research efforts are focused on working deeper in the data acquisition and processing stream while expanding the unified model at each step.

High Dimensional Data - Director Mehdi Maadooliat

My primary research interests lie in the developments of the statistical models in high-dimensional data structures with application to biological sciences, including, but not limited to genomics and proteomics.

In particular my doctoral research focuses on the dimension reduction and the functional data analysis in non-Gaussian frameworks, which has been applied in the context of analysis of high-dimensional gene expression data; and the main focus of my research during the postdoctoral program, was on the modeling of the large spherical data structures with an application in protein structure prediction and classification. My current research interests include:

  • Bioinformatics
  • Machine Learning
  • Proteomics
  • Functional Data Analysis and Skewed Distributions
  • Nonparametric and Semiparametric Methods

Statistical Methods - Co-Directors Naveen Bansal and Hossein Hamedani

This group develops and applies new statistical methods in a variety of applications. Projects include Bayesian hypothesis testing using a decision theoretic approach. A doctoral student is developing a decision theoretic methodology for testing multiple and multi-sided hypotheses to produce more powerful test procedures. The idea is to incorporate prior information in order to produce more powerful tests which will have application in gene expression data analysis.