Mathematical research at MSU is focused primarily on related topics in pure and applied mathematics. Research programs complement each other and are often applied to problems in science and engineering. Research in statistics encompasses a broad range of theoretical and applied topics. Because the statisticians are actively engaged in interdisciplinary work, much of the statistical research is directed toward practical problems. Mathematics education faculty are active in both qualitative and quantitative experimental research areas. These include teacher preparation, coaching and mentoring for in-service teachers, online learning and curriculum development.

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Recent Submissions

  • The effects of interleukin-2 on immune response regulation 

    Waters, Ryan S.; Perry, Justin S. A.; Han, SunPil; Bielekova, Bibiana; Gedeon, Tomáš (2017-02)
    The immune system has many adaptive and dynamic components that are regulated to ensure appropriate, precise and rapid response to a foreign pathogen. A delayed or inadequate immune response can lead to prolonged disease, ...
  • Global Dynamics for Steep Nonlinearities in Two Dimensions 

    Gedeon, Tomáš; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstanin; Oka, Hiroe (2017-01)
    This paper discusses a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. We study switching models of regulatory networks. To each switching network we ...
  • Bioenergy and Breast Cancer: A report on tumor growth and metastasis 

    Running, Alice; Greenwood, Mark; Hildreth, Laura; Schmidt, Jade (2016)
    As many as 80% of the 296,000 women and 2,240 men diagnosed with breast cancer in the United States will seek out complementary and alternative medicine (CAM) treatments. One such therapy is Healing Touch (HT), recognized ...
  • A Mechanistic Model for Cooperative Behavior of Co-transcribing RNA Polymerases 

    Davis, Lisa; Gedeon, Tomáš; Heberling, Tamra; Gedeon, Jakub; Morgan, Charles (2016-08)
    In fast-transcribing prokaryotic genes, such as an rrn gene in Escherichia coli, many RNA polymerases (RNAPs) transcribe the DNA simultaneously. Active elongation of RNAPs is often interrupted by pauses, which has been ...
  • On the intrinsic dimensionality of chemical structure space 

    Veith, D.; Greenwood, B.; Hunter, R. S.; Niemi, G. J.; Regal, R. R. (1988-01)
    An important expectation in chemistry and pharmacology is that similar chemical structures have similar properties and behavior. New industrial chemicals, pesticides, and therapeutics are often sublte modifications of ...
  • Considerations for assessing model averaging of regression coefficients 

    Banner, Katharine Michelle; Higgs, Megan D. (2016-08)
    "Model choice is usually an inevitable source of uncertainty in model-based statistical analyses. While the focus of model choice was traditionally on methods for choosing a single model, methods to formally account for ...
  • Combinatorial Representation of Parameter Space for Switching Networks 

    Cummins, Bree; Harker, Shaun; Mischaikow, Konstantin; Mok, Kafung; Gedeon, Tomáš (2016-11)
    We describe the theoretical and computational framework for the Dynamic Signatures Generated by Regulatory Networks (DSGRN) database. The motivation stems from an urgent need to understand the global dynamics of biologically ...
  • Global dynamics for steep nonlinearities in two dimensions 

    Gedeon, Tomáš; Harker, Shaun; Kokubu, Hiroshi; Mischaikow, Konstantin; Oka, Hiroe (2017-01)
    This paper discusses a novel approach to obtaining mathematically rigorous results on the global dynamics of ordinary differential equations. We study switching models of regulatory networks. To each switching network we ...
  • Symmetry breaking clusters in soft clustering decoding of neural codes 

    Parker, Albert E.; Dimitrov, Alexander G.; Gedeon, Tomáš (2010-02)
    Information-based distortion methods have been used successfully in the analysis of neural coding problems. These approaches allow the discovery of neural symbols and the corresponding stimulus space of a neuron or neural ...
  • When a habitat freezes solid: Microorganisms over-winter within the ice column of a coastal Antarctic lake 

    Foreman, Christine M.; Dieser, Markus; Greenwood, Mark C.; Cory, R. M.; Laybourn-Parry, J.; Lisle, J. T.; Jaros, C.; Miller, P. L.; Chin, Y. P.; McKnight, Diane M. (2011-03)
    A major impediment to understanding the biology of microorganisms inhabiting Antarctic environments is the logistical constraint of conducting field work primarily during the summer season. However, organisms that persist ...
  • The mathematical structure of information bottleneck methods 

    Gedeon, Tomáš; Parker, Albert E.; Dimitrov, Alexander G. (2012-03)
    Information Bottleneck-based methods use mutual information as a distortion function in order to extract relevant details about the structure of a complex system by compression. One of the approaches used to generate optimal ...
  • Cyclic Feedback Systems with Quorum Sensing Coupling 

    Gedeon, Tomáš; Pernarowski, Mark; Wilander, Adam (2016-06)
    Synchronization and desynchronization is of great interest in the study of circadian rhythms, metabolic oscillations and time-dependent cell aggregate behaviors. Several recent studies examine synchronization and other ...
  • Physicochemical and biological dynamics in a coastal Antarctic lake as it transitions from frozen to open water 

    Dieser, Markus; Foreman, Christine M.; Jaros, C.; Lisle, J. T.; Greenwood, Mark C.; Laybourn-Parry, J.; Miller, P. L.; Chin, Y. P.; McKnight, Diane M. (2013-03)
    Pony Lake, at Cape Royds, Antarctica, is a shallow, eutrophic, coastal lake that freezes solid in the winter. Changes in Pony Lake's physicochemical parameters and microbial community were studied during the transition ...
  • Convergence Properties of Posttranslationally Modified Protein-Protein Switching Networks with Fast Decay Rates 

    Fan, G.; Cummins, Bree; Gedeon, Tomáš (2016-06)
    A significant conceptual difficulty in the use of switching systems to model regulatory networks is the presence of so-called "black walls" co-dimension 1 regions of phase space with a vector field pointing inward on both ...
  • Advanced college-level students' categorization and use of mathematical definitions 

    Dickerson, David S.; Pitman, Damien (2012)
    This qualitative study of five undergraduate mathematics majors found that some students, (even students at an advanced level of undergraduate mathematical study) have a mathematician’s perspective neither on the concept ...
  • Percolation on Fitness Landscapes: Effects of Correlation, Phenotype, and Incompatibilities 

    Gravner, Janko; Pitman, Damien; Gavrilets, Sergey (2007-10)
    We study how correlations in the random fitness assignment may affect the structure of fitness landscapes, in three classes of fitness models. The first is a phenotype space in which individuals are characterized by a large ...
  • Random 2-SAT Solution Components and a Fitness Landscape 

    Pitman, Damien (2011)
    We describe a limiting distribution for the number of connected components in the subgraph of the discrete cube induced by the satisfying assignments to a random 2-SAT formula. We show that, for the probability range where ...
  • Hantavirus transmission in sylvan and peridomestic environment 

    Gedeon, Tomáš; Bodelón, Clara; Kuenzi, Amy (2010-04)
    We developed a compartmental model for hantavirus infection in deer mice (Peromyscus maniculatus) with the goal of comparing relative importance of direct and indirect transmission in sylvan and peridomestic environments. ...
  • Using machine learning to predict catastrophes in dynamical systems 

    Berwald, Jesse; Gedeon, Tomáš; Sheppard, John (2012-03)
    Nonlinear dynamical systems, which include models of the Earth’s climate, financial markets and complex ecosystems, often undergo abrupt transitions that lead to radically different behavior. The ability to predict such ...
  • Predicting High-Codimension Critical Transitions In Dynamical Systems Using Active Learning 

    Spendlove, Kelly; Berwald, Jesse; Gedeon, Tomáš (2013-05)
    Complex dynamical systems, from those appearing in physiology and ecology to Earth system modelling, often experience critical transitions in their behaviour due to potentially minute changes in their parameters. While the ...

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