Mathematical Sciences
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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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Item Surface micropattern reduces colonization and medical device-associated infections(2017-11) Xu, Binjie; Wei, Qiuhua; Mettetal, M. Ryan; Han, Jie; Rau, Lindsey; Tie, Jinfeng; May, Rhea M.; Pathe, Eric T.; Reddy, Shravanthi T.; Sullivan, Lauren; Parker, Albert E.; Maul, Donald H.; Brennan, Anthony B.; Mann, Ethan E.PURPOSE: Surface microtopography offers a promising approach for infection control. The goal of this study was to provide evidence that micropatterned surfaces significantly reduce the potential risk of medical device-associated infections. METHODOLOGY: Micropatterned and smooth surfaces were challenged in vitro against the colonization and transference of two representative bacterial pathogens - Staphylococcus aureus and Pseudomonas aeruginosa. A percutaneous rat model was used to assess the effectiveness of the micropattern against device-associated S. aureus infections. After the percutaneous insertion of silicone rods into (healthy or immunocompromised) rats, their backs were inoculated with S. aureus. The bacterial burdens were determined in tissues under the rods and in the spleens. RESULTS: The micropatterns reduced adherence by S. aureus (92.3 and 90.5 % reduction for flat and cylindrical surfaces, respectively), while P. aeruginosa colonization was limited by 99.9 % (flat) and 95.5 % (cylindrical). The micropatterned surfaces restricted transference by 95.1 % for S. aureus and 94.9 % for P. aeruginosa, compared to smooth surfaces. Rats with micropatterned devices had substantially fewer S. aureus in subcutaneous tissues (91 %) and spleens (88 %) compared to those with smooth ones. In a follow-up study, immunocompromised rats with micropatterned devices had significantly lower bacterial burdens on devices (99.5 and 99.9 % reduction on external and internal segments, respectively), as well as in subcutaneous tissues (97.8 %) and spleens (90.7 %) compared to those with smooth devices. CONCLUSION: Micropatterned surfaces exhibited significantly reduced colonization and transference in vitro, as well as lower bacterial burdens in animal models. These results indicate that introducing this micropattern onto surfaces has high potential to reduce medical device-associated infections. KEYWORDS: hospital-acquired infections; infections; medical devices; micropatternsItem Who Goes in and Out of the Hospital Patient Room?(2017-06) Arbogast, James W.; Quinn, Jeff; Clark, Tracy; Moore, Lori; Thompson, Maria; Wagner, Pamela; Young, Elizabeth; Parker, Albert E.BACKGROUND: The objective of this study was to determine what percentage of entries and exits (E/E) in and out of the patient room should be attributed to healthcare workers (HCWs) in a wide variety of hospital units. This is a critical question for hospitals considering an automated monitoring system (AMS) to measure hand hygiene performance (HHP) as a complement to data from visual observation. HCWs often implicate others and do not perceive a need to change their HH behavior because they are convinced that visitors, patients, and others are responsible for very low HHP data. METHODS: Events (defined as patient room E/E) were observed and recorded by nurses not employed by the hospital. Observations were made in US and Canadian hospital units including emergency, ICU, medical surgical, oncology, and pediatrics. Observers classified events by: HCWs (e.g., nursing staff, aides, doctors, EVS, etc.), patients plus visitors, and other (e.g., clergy, hospice workers). Logistic regression was used to determine who was responsible for the most E/E events by category of individuals. RESULTS: Observers recorded a total of 14,876 E/E events in 29 units of 16 hospitals with units varying in size from 10 to 41 beds. 84.3% of all E/E were attributed to HCWs; 15.0% were from patients plus visitors and 0.7% from others. The odds are 6 to 1 that an E/E into a patient room is by a HCW (P < .0005). Pediatric units had the lowest percentage of HCWs E/E (76.7% total) CONCLUSIONS: This study demonstrates HCWs account for the greatest proportion of hospitalized patient room E/E. Further, the data show that others share a very small percentage of room E/E countering the argument that those individuals are responsible for the low unit HHP measured by AMS. This study demonstrates that other categories of individuals are not a deterrent to increasing unit-level HHP.Item On the intrinsic dimensionality of chemical structure space(1988-01) Veith, D.; Greenwood, B.; Hunter, R. S.; Niemi, G. J.; Regal, R. R.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 "lead" structures with known chemical behavior. Chemical properties and recreation rates can be can be estimated from suitable homologs 1,2. Moreover, the safety of untested chemicals is often evaluated by comparing the chemical toanalogous structures for which toxicological data are available. Despite the widespread use of terms such as "homolog" and "analogs" in research, chemical similarity has evaded quantitative interpretation from a perspective where all chemicals are considered simultaneously. One reason is that chemical similarity is inherently a multivariate problem or, in other words, chemicals are simultaneously similar and different from many perspectives. We have approached chemical similarity by attempting to define a structure space in which all chemicals can be identified. Because there are so many potentially important variables, multivariate tools are necessary to reduce the dimensionality of this problem. When this is accomplished, we need to comprehend what this space means and what can be predicted from it . This paper is one of the first attempts to define chemical structure space for a large universe of chemicals.Item Symmetry breaking clusters in soft clustering decoding of neural codes(2010-02) Parker, Albert E.; Dimitrov, Alexander G.; Gedeon, TomasInformation-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 ensemble quantitatively, while making few assumptions about the nature of either the code or of relevant stimulus features. The neural codebook is derived by quantizing sensory stimuli and neural responses into a small set of clusters, and optimizing the quantization to minimize an information distortion function. The method of annealing has been used to solve the corresponding high-dimensional nonlinear optimization problem. The annealing solutions undergo a series of bifurcations, which we study using bifurcation theory in the presence of symmetries. In this contribution we describe these symmetry breaking bifurcations in detail, and indicate some of the consequences of the form of the bifurcations. In particular, we show that the annealing solutions break symmetry at pitchfork bifurcations, and that subcritical branches can exist. Thus, at a subcritical bifurcation, there are local information distortion solutions which are not found by the method of annealing. Since the annealing procedure is guaranteed to converge to a local solution eventually, the subcritical branch must turn and become optimal at some later saddle-node bifurcation, which we have shown occur generically for this class of problems. This implies that the rate distortion curve, while convex for noninformation-based distortion measures, is not convex for information-based distortion methods.Item When a habitat freezes solid: Microorganisms over-winter within the ice column of a coastal Antarctic lake(2011-03) Foreman, Christine M.; Dieser, Markus; Greenwood, Mark C.; Cory, R. M.; Laybourn-Parry, Johanna; Lisle, John T.; Jaros, C.; Miller, P. L.; Chin, Yu-Ping; McKnight, Diane M.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 throughout the year encounter severe environmental changes between seasons. In an attempt to bridge this gap, we collected ice core samples from Pony Lake in early November 2004 when the lake was frozen solid to its base, providing an archive for the biological and chemical processes that occurred during winter freezeup. The ice contained bacteria and virus-like particles, while flagellated algae and ciliates over-wintered in the form of inactive cysts and spores. Both bacteria and algae were metabolically active in the ice core melt water. Bacterial production ranged from 1.8 to 37.9 μg C L−1 day−1. Upon encountering favorable growth conditions in the melt water, primary production ranged from 51 to 931 μg C L−1 day−1. Because of the strong H2S odor and the presence of closely related anaerobic organisms assigned to Pony Lake bacterial 16S rRNA gene clones, we hypothesize that the microbial assemblage was strongly affected by oxygen gradients, which ultimately restricted the majority of phylotypes to distinct strata within the ice column. This study provides evidence that the microbial community over-winters in the ice column of Pony Lake and returns to a highly active metabolic state when spring melt is initiated.