In this paper, we investigate the bifurcations of solutions to a class of degenerate constrained optimization problems. This study was motivated by the Information Bottleneck and Information Distortion problems, which have been used to successfully cluster data in many different applications. In the problems we discuss in this paper, the distortion function is not a linear function of the quantizer. This leads to a challenging annealing optimization problem, which we recast as a fixed-point dynamics problem of a gradient flow of a related dynamical system. The gradient system possesses an SN symmetry due to its invariance in relabeling representative classes. Its flow hence passes through a series of bifurcations with specific symmetry breaks. Here, we show that the dynamical system related to the Information Bottleneck problem has an additional spurious symmetry that requires more-challenging analysis of the symmetry-breaking bifurcation. For the Information Bottleneck, we determine that when bifurcations occur, they are only of pitchfork type, and we give conditions that determine the stability of the bifurcating branches. We relate the existence of subcritical bifurcations to the existence of first-order phase transitions in the corresponding distortion function as a function of the annealing parameter, and provide criteria with which to detect such transitions.
Hand hygiene product usage characteristics by food employees when hand sanitizers are made available are not well understood. To investigate hand hygiene product usage in casual dining and quick-service restaurants, we placed automated monitoring soap and sanitizer dispensers side-by-side at handwash sinks used by food employees in seven restaurants. Dispenses were monitored, and multiple dispenses that occurred within 60 s of each other were considered a single hand hygiene event. This resulted in 186,998 events during the study (149,779 soap only, 21 985 sanitizer only, and 15,234 regimen [defined as soap followed by sanitizer at the same sink within 60 s]) over 15,447 days of use. Soap was the most frequently used hand hygiene method by food employees in both restaurant types. Regimen use, despite being the preferred hand hygiene method by both restaurant chains, was the least used hand hygiene method. When pooled over restaurant types, the median daily usage for soap was statistically significantly highest of all methods at 23.5 dispenses per sink per day (p < 0.0001), the sanitizer median daily usage was 4.27 dispenses per sink per day, and regimen use was statistically significantly lowest of all methods at 4.02 dispenses per sink per day (p < 0.0001). When hand hygiene event types were pooled, casual dining restaurants had similar median hand hygiene event rates (11.4 dispenses per sink per day) compared to quick-service restaurants (11.9 dispenses per sink per day; p = 0.890). The number of events by sink location varied, with sinks located at a warewash station having the highest number of events (19.3 dispenses per sink per day; p < 0.0001), while sinks located by a ready-to-eat food preparation area had the lowest number of events (6.8 dispenses per sink per day; p < 0.0001). These data provide robust baseline benchmarks for future hand hygiene intervention studies in these settings.
We review reproducibility results for methods that test antimicrobial efficacy against biofilms, spores and bacteria dried onto a surface. Our review, that included test results for Pseudomonas aeruginosa, Salmonella choleraesuis and Bacillus subtilis, suggests that the level of reproducibility depends on the efficacy of the antimicrobial agent being tested for each microbe and microbial environment. To determine the reproducibility of a method, several laboratories must independently test the same antimicrobial agent using the method. Little variability among the efficacy results suggests good reproducibility. Such reproducibility assessments currently are hampered by the absence of an objective process for deciding whether the variability is sufficiently small. We present a quantitative decision process that objectively determines whether any method that assesses antimicrobial efficacy is reproducible. Because the perception of acceptable reproducibility may differ among stakeholders, the decision process is governed by a stakeholder's specifications that necessarily includes the efficacy of the agents to be tested.
Three dimensional confocal scanning laser microscope images offer dramatic visualizations of the action of living biofilms before and after interventions. Here we use confocal microscopy to study the effect of a treatment over time that causes a biofilm to swell and contract due to osmotic pressure changes. From these data, our goal is to reconstruct biofilm surfaces, to estimate the effect of the treatment on the biofilm's volume, and to quantify the related uncertainties. We formulate the associated massive linear Bayesian inverse problem and then solve it using iterative samplers from large multivariate Gaussians that exploit well-established polynomial acceleration techniques from numerical linear algebra. Because of a general equivalence with linear solvers, these polynomial accelerated iterative samplers have known convergence rates, stopping criteria, and perform well in finite precision. An explicit algorithm is provided, for the first time, for an iterative sampler that is accelerated by the synergistic implementation of preconditioned conjugate gradient and Chebyshev polynomials.
