Mathematical Sciences
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 inservice teachers, online learning and curriculum development.
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Modelling radicalization: how small violent fringe sects develop into large indoctrinated societies
(201708)We model radicalization in a society consisting of two competing religious, ethnic or political groups. Each of the \'sects\' is divided into moderate and radical factions, with intragroup transitions occurring either ... 
BatalinVilkovisky quantization and the algebraic index
(201709)Into a geometric setting, we import the physical interpretation of index theorems via semiclassical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization ... 
Accelerated Gibbs sampling of normal distributions using matrix splittings and polynomials
(201711)Standard Gibbs sampling applied to a multivariate normal distribution with a specified precision matrix is equivalent in fundamental ways to the Gauss Seidel iterative solution of linear equations in the precision matrix. ... 
The effects of interleukin2 on immune response regulation
(201702)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
(201701)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
(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 Cotranscribing RNA Polymerases
(201608)In fasttranscribing 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
(198801)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
(201608)"Model choice is usually an inevitable source of uncertainty in modelbased 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
(201611)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
(201701)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
(201002)Informationbased 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 overwinter within the ice column of a coastal Antarctic lake
(201103)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
(201203)Information Bottleneckbased 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
(201606)Synchronization and desynchronization is of great interest in the study of circadian rhythms, metabolic oscillations and timedependent 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
(201303)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 ProteinProtein Switching Networks with Fast Decay Rates
(201606)A significant conceptual difficulty in the use of switching systems to model regulatory networks is the presence of socalled "black walls" codimension 1 regions of phase space with a vector field pointing inward on both ... 
Advanced collegelevel students' categorization and use of mathematical definitions
(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
(200710)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 2SAT Solution Components and a Fitness Landscape
(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 2SAT formula. We show that, for the probability range where ...