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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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 ... 
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 ... 
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 ... 
Hantavirus transmission in sylvan and peridomestic environment
(201004)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
(201203)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 HighCodimension Critical Transitions In Dynamical Systems Using Active Learning
(201305)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 ... 
Discontinuous Galerkin calculations for a nonlinear PDE model of DNA transcription with short, transient and frequent pausing
(201409)A discontinuous Galerkin finite element method is used to approximate solutions to a classical traffic flow PDE. This PDE is used to model the biological process of transcription; the process of transferring genetic ... 
Impact of a Comprehensive Workplace Hand Hygiene Program on Employer Health Care Insurance Claims and Costs, Absenteeism, and Employee Perceptions and Practices
(201606)The aim of this study was to determine the efficacy of a multimodal hand hygiene intervention program in reducing health care insurance claims for hygiene preventable infections (eg, cold and influenza), absenteeism, and ... 
Fostering Conceptual Understanding in Mathematical Statistics
(201512)In many undergraduate statistics programs, the twosemester calculusbased mathematical statistics sequence is the cornerstone of the curriculum. However, 10 years after the release of the Guidelines for the Assessment and ... 
Pathogen prevalence and abundance in honey bee colonies involved in almond pollination
(201603)Honey bees are important pollinators of agricultural crops. Since 2006, US beekeepers have experienced high annual honey bee colony losses, which may be attributed to multiple abiotic and biotic factors, including pathogens. ... 
Supporting Information for "Significance of trends toward earlier snowmelt runoff, Columbia and Missouri Basin headwaters, western United States"
(American Geophysical Union, 200708)This is auxiliary material for this article contains one text file, four tables, and three figures from the article "Significance of trends toward earlier snowmelt runoff, Columbia and Missouri Basin headwaters, western ... 
Significance of trends toward earlier snowmelt runoff, Columbia and Missouri Basin headwaters, western United States
(American Geophysical Union, 200708)We assess changes in runoff timing over the last 55 years at 21 gages unaffected by human influences, in the headwaters of the ColumbiaMissouri Rivers. Linear regression models and tests for significance that control for ... 
An examination of college mathematics majors' understandings of their own written definitions
(201603)This qualitative study of ten undergraduate mathematics majors examined students' abilities to write definitions and found that students at the advanced level of undergraduate mathematical study have difficulty creating ... 
Microbial community signature in Lake Coeur d'Alene: Association of environmental variables and toxic heavy metal phases
(201603)The water and sediments of Lake Coeur d'Alene in northern Idaho (USA) have been impacted by decades of mining operations within the Coeur d'Alene mining district. Using a multivariate statistical approach, correlations ...