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 Impact of an automated hand hygiene monitoring system and additional promotional activities on hand hygiene performance rates and healthcare-associated infections(2019-07) Boyce, John M.; Laughman, Jennifer A.; Ader, Michael H.; Wagner, Pamela T.; Parker, Albert E.; Arbogast, James W.Objective: Determine the impact of an automated hand hygiene monitoring system (AHHMS) plus complementary strategies on hand hygiene performance rates and healthcare-associated infections (HAIs). Design: Retrospective, nonrandomized, observational, quasi-experimental study. Setting: Single, 93-bed nonprofit hospital. Methods: Hand hygiene compliance rates were estimated using direct observations. An AHHMS, installed on 4 nursing units in a sequential manner, determined hand hygiene performance rates, expressed as the number of hand hygiene events performed upon entering and exiting patient rooms divided by the number of room entries and exits. Additional strategies implemented to improve hand hygiene included goal setting, hospital leadership support, feeding AHHMS data back to healthcare personnel, and use of Toyota Kata performance improvement methods. HAIs were defined using National Healthcare Safety Network criteria. Results: Hand hygiene compliance rates generated by direct observation were substantially higher than performance rates generated by the AHHMS. Installation of the AHHMS without supplementary activities did not yield sustained improvement in hand hygiene performance rates. Implementing several supplementary strategies resulted in a statistically significant 85% increase in hand hygiene performance rates (P < .0001). The incidence density of non–Clostridioies difficile HAIs decreased by 56% (P = .0841), while C. difficile infections increased by 60% (P = .0533) driven by 2 of the 4 study units. Conclusion: Implementation of an AHHMS, when combined with several supplementary strategies as part of a multimodal program, resulted in significantly improved hand hygiene performance rates. Reductions in non–C. difficile HAIs occurred but were not statistically significant.Item Randomized controlled trial evaluating the antimicrobial efficacy of chlorhexidine gluconate and para-chloro-meta-xylenol handwash formulations in real-world doses(2019-06) Arbogast, James W.; Bowersock, Lisa B.; Parker, Albert E.; Macinga, D. R.Chlorhexidine gluconate-based soaps have become the gold standard for handwashing in critical care settings and para-chloro-meta-xylenol is an effective alternative antibacterial active ingredient. This study benchmarked 2 novel foaming handwashes, compared to a bland soap for antimicrobial effectiveness using the health care personnel handwash method at realistic soap doses (0.9 mL and 2.0 mL). To our knowledge, this is the first published efficacy study on realistic soap doses. Both soaps met Food and Drug Administration success criteria.Item Quorum sensing inhibition as a promising method to control biofilm growth in metalworking fluids(2019-04) Ozcan, Safiye S.; Dieser, Markus; Parker, Albert E.; Balasubramanian, Narayanaganesh; Foreman, Christine M.Microbial contamination in metalworking systems is a critical problem. This study determined the microbial communities in metalworking fluids (MWFs) from two machining shops and investigated the effect of quorum sensing inhibition (QSI) on biofilm growth. In both operations, biofilm-associated and planktonic microbial communities were dominated by Pseudomonadales (60.2–99.7%). Rapid recolonization was observed even after dumping spent MWFs and meticulous cleaning. Using Pseudomonas aeruginosa PAO1 as a model biofilm organism, patulin (40 µM) and furanone C-30 (75 µM) were identified as effective QSI agents. Both agents had a substantially higher efficacy compared to α-amylase (extracellular polymeric substance degrading enzyme) and reduced biofilm formation by 63% and 76%, respectively, in MWF when compared to untreated controls. Reduced production of putatively identified homoserine lactones and quinoline in MWF treated with QS inhibitors support the effect of QSI on biofilm formation. The results highlight the effectiveness of QSI as a potential strategy to eradicate biofilms in MWFs.Item Dynamic processing of DOM: Insight from exometabolomics, fluorescence spectroscopy, and mass spectrometry(2018-06) Smith, Heidi J.; Tigges, Michelle M.; D'Andrilli, Juliana; Parker, Albert E.; Bothner, Brian; Foreman, Christine M.Dissolved organic matter (DOM) in freshwater environments is an important source of organic carbon, supporting bacterial respiration. Frozen environments cover vast expanses of our planet, with glaciers and ice-sheets storing upwards of 6 petagrams of organic carbon. It is generally believed that DOM liberated from ice stimulates downstream environments. If true, glacial DOM is an important component of global carbon cycling. However, coupling the release of DOM to microbial activity is challenging due to the molecular complexity of DOM and the metabolic connectivity within microbial communities. Using a single environmentally relevant organism, we demonstrate that processing of compositionally diverse DOM occurs, but, even though glacially derived DOM is chemically labile, it is unable to support sustained respiration. In view of projected changes in glacier DOM export, these findings imply that biogeochemical impacts on downstream environments will depend on the reactivity and heterogeneity of liberated DOM, as well as the timescale.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 Accelerated Gibbs sampling of normal distributions using matrix splittings and polynomials(2017-11) Fox, Colin; Parker, Albert E.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. Specifically, the iteration operators, the conditions under which convergence occurs, and geometric convergence factors (and rates) are identical. These results hold for arbitrary matrix splittings from classical iterative methods in numerical linear algebra giving easy access to mature results in that field, including existing convergence results for antithetic-variable Gibbs sampling, REGS sampling, and generalizations. Hence, efficient deterministic stationary relaxation schemes lead to efficient generalizations of Gibbs sampling. The technique of polynomial acceleration that significantly improves the convergence rate of an iterative solver derived from a symmetric matrix splitting may be applied to accelerate the equivalent generalized Gibbs sampler. Identicality of error polynomials guarantees convergence of the inhomogeneous Markov chain, while equality of convergence factors ensures that the optimal solver leads to the optimal sampler. Numerical examples are presented, including a Chebyshev accelerated SSOR Gibbs sampler applied to a stylized demonstration of low-level Bayesian image reconstruction in a large 3-dimensional linear inverse problem.Item Micropatterned Endotracheal Tubes Reduce Secretion-Related Lumen Occlusion(2016-12) Mann, Ethan E.; Magin, Chelsea M.; Mettetal, M. Ryan; May, Rhea M.; Henry, MiKayla M.; DeLoid, Heather; Prater, Justin; Sullivan, Lauren; Thomas, John G.; Twite, Mark D.; Parker, Albert E.; Brennan, Anthony B.; Reddy, Shravanthi T.Tracheal intubation disrupts physiological homeostasis of secretion production and clearance, resulting in secretion accumulation within endotracheal tubes (ETTs). Novel in vitro and in vivo models were developed to specifically recapitulate the clinical manifestations of ETT occlusion. The novel Sharklet™ micropatterned ETT was evaluated, using these models, for the ability to reduce the accumulation of both bacterial biofilm and airway mucus compared to a standard care ETT. Novel ETTs with micropattern on the inner and outer surfaces were placed adjacent to standard care ETTs in in vitro biofilm and airway patency (AP) models. The primary outcome for the biofilm model was to compare commercially-available ETTs (standard care and silver-coated) to micropatterned for quantity of biofilm accumulation. The AP model's primary outcome was to evaluate accumulation of artificial airway mucus. A 24-h ovine mechanical ventilation model evaluated the primary outcome of relative quantity of airway secretion accumulation in the ETTs tested. The secondary outcome was measuring the effect of secretion accumulation in the ETTs on airway resistance. Micropatterned ETTs significantly reduced biofilm by 71% (p = 0.016) compared to smooth ETTs. Moreover, micropatterned ETTs reduced lumen occlusion, in the AP model, as measured by cross-sectional area, in distal (85%, p = 0.005), middle (84%, p = 0.001) and proximal (81%, p = 0.002) sections compared to standard care ETTs. Micropatterned ETTs reduced the volume of secretion accumulation in a sheep model of occlusion by 61% (p < 0.001) after 24 h of mechanical ventilation. Importantly, micropatterned ETTs reduced the rise in ventilation peak inspiratory pressures over time by as much as 49% (p = 0.005) compared to standard care ETTs. Micropatterned ETTs, demonstrated here to reduce bacterial contamination and mucus occlusion, will have the capacity to limit complications occurring during mechanical ventilation and ultimately improve patient care.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 The mathematical structure of information bottleneck methods(2012-03) Gedeon, Tomas; Parker, Albert E.; Dimitrov, Alexander G.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 compressed representations is by annealing a parameter. In this manuscript we present a common framework for the study of annealing in information distortion problems. We identify features that should be common to any annealing optimization problem. The main mathematical tools that we use come from the analysis of dynamical systems in the presence of symmetry (equivariant bifurcation theory). Through the compression problem, we make connections to the world of combinatorial optimization and pattern recognition. The two approaches use very different vocabularies and consider different problems to be “interesting†. We provide an initial link, through the Normalized Cut Problem, where the two disciplines can exchange tools and ideas.