A L\'evy input fluid queue with input and workload regulation

We consider a queuing model with the workload evolving between consecutive i.i.d.\ exponential timers $\{e_q^{(i)}\}_{i=1,2,...}$ according to a spectrally positive L\'evy process $Y_i(t)$ that is reflected at zero, and where the environment $i$ equals 0 or 1. When the exponential clock $e_q^{(i)}$ ends, the workload, as well as the L\'evy input process, are modified; this modification may depend on the current value of the workload, the maximum and the minimum workload observed during the previous cycle, and the environment $i$ of the L\'evy input process itself during the previous cycle. We analyse the steady-state workload distribution for this model. The main theme of the analysis is the systematic application of non-trivial functionals, derived within the framework of fluctuation theory of L\'evy processes, to workload and queuing models

Boundary driven zero-range processes in random media

The stationary states of boundary driven zero-range processes in random media with quenched disorder are examined, and the motion of a tagged particle is analyzed. For symmetric transition rates, also known as the random barrier model, the stationary state is found to be trivial in absence of boundary drive. Out of equilibrium, two further cases are distinguished according to the tail of the disorder distribution. For strong disorder, the fugacity profiles are found to be governed by the paths of normalized $\alpha$-stable subordinators. The expectations of integrated functions of the tagged particle position are calculated for three types of routes.Comment: 23 page

Plasma ACE2 predicts outcome of COVID-19 in hospitalized patients

AimsSevere acute respiratory syndrome coronavirus 2 (SARS-CoV-2) binds to angiotensin converting enzyme 2 (ACE2) enabling entrance of the virus into cells and causing the infection termed coronavirus disease of 2019 (COVID-19). Here, we investigate associations between plasma ACE2 and outcome of COVID-19.Methods and resultsThis analysis used data from a large longitudinal study of 306 COVID-19 positive patients and 78 COVID-19 negative patients (MGH Emergency Department COVID-19 Cohort). Comprehensive clinical data were collected on this cohort, including 28-day outcomes. The samples were run on the Olink® Explore 1536 platform which includes measurement of the ACE2 protein. High admission plasma ACE2 in COVID-19 patients was associated with increased maximal illness severity within 28 days with OR = 1.8, 95%-CI: 1.4-2.3 (P ConclusionThis study suggests that measuring plasma ACE2 is potentially valuable in predicting COVID-19 outcomes. Further, ACE2 could be a link between COVID-19 illness severity and its established risk factors hypertension, pre-existing heart disease and pre-existing kidney disease

Dynamic control of a single-server system with abandonments

In this paper, we discuss the dynamic server control in a two-class service system with abandonments. Two models are considered. In the first case, rewards are received upon service completion, and there are no abandonment costs (other than the lost opportunity to gain rewards). In the second, holding costs per customer per unit time are accrued, and each abandonment involves a fixed cost. Both cases are considered under the discounted or average reward/cost criterion. These are extensions of the classic scheduling question (without abandonments) where it is well known that simple priority rules hold. The contributions in this paper are twofold. First, we show that the classic c-μ rule does not hold in general. An added condition on the ordering of the abandonment rates is sufficient to recover the priority rule. Counterexamples show that this condition is not necessary, but when it is violated, significant loss can occur. In the reward case, we show that the decision involves an intuitive tradeoff between getting more rewards and avoiding idling. Secondly, we note that traditional solution techniques are not directly applicable. Since customers may leave in between services, an interchange argument cannot be applied. Since the abandonment rates are unbounded we cannot apply uniformization-and thus cannot use the usual discrete-time Markov decision process techniques. After formulating the problem as a continuous-time Markov decision process (CTMDP), we use sample path arguments in the reward case and a savvy use of truncation in the holding cost case to yield the results. As far as we know, this is the first time that either have been used in conjunction with the CTMDP to show structure in a queueing control problem. The insights made in each model are supported by a detailed numerical study. © 2010 Springer Science+Business Media, LLC

Surgically generated aerosol and mitigation strategies: combined use of irrigation, respirators and suction massively reduces particulate matter aerosol

Background Aerosol is a health risk to theatre staff. This laboratory study quantifies the reduction in particulate matter aerosol concentrations produced by electrocautery and drilling when using mitigation strategies such as irrigation, respirator filtration and suction in a lab environment to prepare for future work under live OR conditions. Methods We combined one aerosol-generating procedure (monopolar cutting or coagulating diathermy or high-speed diamond- or steel-tipped drilling of cadaveric porcine tissue) with one or multiple mitigation strategies (instrument irrigation, plume suction and filtration using an FFP3 respirator filter) and using an optical particle counter to measure particulate matter aerosol size and concentrations. Results Significant aerosol concentrations were observed during all aerosol-generating procedures with concentrations exceeding 3 × 106 particles per 100 ml. Considerable reductions in concentrations were observed with mitigation. In drilling, suction, FFP3 filtration and wash alone respectively reduced aerosol by 19.3–31.6%, 65.1–70.8% and 97.2 to > 99.9%. The greatest reduction (97.38 to > 99.9%) was observed when combining irrigation and filtration. Coagulating diathermy reduced concentrations by 88.0–96.6% relative to cutting, but produced larger particles. Suction alone, and suction with filtration reduced aerosol concentration by 41.0–49.6% and 88.9–97.4% respectively. No tested mitigation strategies returned aerosol concentrations to baseline. Conclusion Aerosol concentrations are significantly reduced through the combined use of filtration, suction and irrigation. Further research is required to characterise aerosol concentrations in the live OR and to find acceptable exposure limits, and in their absence, to find methods to further reduce exposure to theatre staff