Decomposing the queue length distribution of processor-sharing models into queue lengths of permanent customer queues

We obtain a decomposition result for the steady state queue length distribution in egalitarian processor-sharing (PS) models. In particular, for an egalitarian PS queue with $K$ customer classes, we show that the marginal queue length distribution for class $k$ factorizes over the number of other customer types. The factorizing coefficients equal the queue length probabilities of a PS queue for type $k$ in isolation, in which the customers of the other types reside \textit{ permanently} in the system. Similarly, the (conditional) mean sojourn time for class $k$ can be obtained by conditioning on the number of permanent customers of the other types. The decomposition result implies linear relations between the marginal queue length probabilities, which also hold for other PS models such as the egalitarian processor-sharing models with state-dependent system capacity that only depends on the total number of customers in the system. Based on the exact decomposition result for egalitarian PS queues, we propose a similar decomposition for discriminatory processor-sharing (DPS) models, and numerically show that the approximation is accurate for moderate differences in service weights. \u

Integrating Complementary Medicine Into the Care of Childhood Cancer Survivors: A Brief Report on the Preliminary Framework and Implementation of an Educational Program

BackgroundExisting educational programs typically include limited information on traditional, complementary, and integrative medicine (TCIM) for survivors of childhood cancer.ObjectivesThis brief report presents the preliminary results of an educational program that aims to promote the safe and effective use of Chinese medicine (CM) among survivors in Hong Kong.MethodsSurvivors of childhood cancer, their caregivers, and oncology practitioners were invited to participate in a program that consists of two didactic seminars and a written educational booklet that disseminated information on the use of CM. A structured questionnaire was used to evaluate participants' receptivity toward and perceived relevance of the program. The Reach, Effectiveness, Adoption, Implementation, and Maintenance (RE-AIM) framework was used to discuss the impact of the intervention.ResultsReach: A total of 174 participants attended the seminars, and the seminar recording received over 380 views on social media platforms since April 2021. The hardcopy of the educational booklet was distributed to 43 recipients. The web-version of the booklet was sent to 67 participants and downloaded 143 times. Efficacy: The majority found that the content of the seminar useful (mean score = 5.04/6 points), especially the CM exercise (mean score = 4.88/6 points) and dietary advice (mean score = 4.99/6 points). Intention to adopt: The survivors (or their caregivers) reported that they would adopt advice on food therapies (83.3%) and traditional Chinese health exercises (55.6%) during survivorship.ConclusionThe preliminary data on patient preferences will be applied to further develop educational materials and to establish a TCIM referral network within the cancer survivor community

Pharmaceuticals in tap water: human health risk assessment and proposed monitoring framework in China

Background: Pharmaceuticals are known to contaminate tap water worldwide, but the relevant human health risks have not been assessed in China. Objectives: We monitored 32 pharmaceuticals in Chinese tap water and evaluated the life-long human health risks of exposure in order to provide information for future prioritization and risk management. Methods: We analyzed samples (n = 113) from 13 cities and compared detected concentrations with existing or newly-derived safety levels for assessing risk quotients (RQs) at different life stages, excluding the prenatal stage. Results: We detected 17 pharmaceuticals in 89% of samples, with most detectable concentrations (92%) at < 50 ng/L. Caffeine (median-maximum, nanograms per liter: 24.4-564), metronidazole (1.8-19.3), salicylic acid (16.6-41.2), clofibric acid (1.2-3.3), carbamazepine (1.3-6.7), and dimetridazole (6.9-14.7) were found in ≥ 20% of samples. Cities within the Yangtze River region and Guangzhou were regarded as contamination hot spots because of elevated levels and frequent positive detections. Of the 17 pharmaceuticals detected, 13 showed very low risk levels, but 4 (i.e., dimetridazole, thiamphenicol, sulfamethazine, and clarithromycin) were found to have at least one life-stage RQ ≥ 0.01, especially for the infant and child life stages, and should be considered of high priority for management. We propose an indicator-based monitoring framework for providing information for source identification, water treatment effectiveness, and water safety management in China. Conclusion: Chinese tap water is an additional route of human exposure to pharmaceuticals, particularly for dimetridazole, although the risk to human health is low based on current toxicity data. Pharmaceutical detection and application of the proposed monitoring framework can be used for water source protection and risk management in China and elsewhere

Canagliflozin and renal outcomes in type 2 diabetes and nephropathy

BACKGROUND Type 2 diabetes mellitus is the leading cause of kidney failure worldwide, but few effective long-term treatments are available. In cardiovascular trials of inhibitors of sodium–glucose cotransporter 2 (SGLT2), exploratory results have suggested that such drugs may improve renal outcomes in patients with type 2 diabetes. METHODS In this double-blind, randomized trial, we assigned patients with type 2 diabetes and albuminuric chronic kidney disease to receive canagliflozin, an oral SGLT2 inhibitor, at a dose of 100 mg daily or placebo. All the patients had an estimated glomerular filtration rate (GFR) of 30 to &lt;90 ml per minute per 1.73 m2 of body-surface area and albuminuria (ratio of albumin [mg] to creatinine [g], &gt;300 to 5000) and were treated with renin–angiotensin system blockade. The primary outcome was a composite of end-stage kidney disease (dialysis, transplantation, or a sustained estimated GFR of &lt;15 ml per minute per 1.73 m2), a doubling of the serum creatinine level, or death from renal or cardiovascular causes. Prespecified secondary outcomes were tested hierarchically. RESULTS The trial was stopped early after a planned interim analysis on the recommendation of the data and safety monitoring committee. At that time, 4401 patients had undergone randomization, with a median follow-up of 2.62 years. The relative risk of the primary outcome was 30% lower in the canagliflozin group than in the placebo group, with event rates of 43.2 and 61.2 per 1000 patient-years, respectively (hazard ratio, 0.70; 95% confidence interval [CI], 0.59 to 0.82; P=0.00001). The relative risk of the renal-specific composite of end-stage kidney disease, a doubling of the creatinine level, or death from renal causes was lower by 34% (hazard ratio, 0.66; 95% CI, 0.53 to 0.81; P&lt;0.001), and the relative risk of end-stage kidney disease was lower by 32% (hazard ratio, 0.68; 95% CI, 0.54 to 0.86; P=0.002). The canagliflozin group also had a lower risk of cardiovascular death, myocardial infarction, or stroke (hazard ratio, 0.80; 95% CI, 0.67 to 0.95; P=0.01) and hospitalization for heart failure (hazard ratio, 0.61; 95% CI, 0.47 to 0.80; P&lt;0.001). There were no significant differences in rates of amputation or fracture. CONCLUSIONS In patients with type 2 diabetes and kidney disease, the risk of kidney failure and cardiovascular events was lower in the canagliflozin group than in the placebo group at a median follow-up of 2.62 years

Robust estimation of bacterial cell count from optical density

Optical density (OD) is widely used to estimate the density of cells in liquid culture, but cannot be compared between instruments without a standardized calibration protocol and is challenging to relate to actual cell count. We address this with an interlaboratory study comparing three simple, low-cost, and highly accessible OD calibration protocols across 244 laboratories, applied to eight strains of constitutive GFP-expressing E. coli. Based on our results, we recommend calibrating OD to estimated cell count using serial dilution of silica microspheres, which produces highly precise calibration (95.5% of residuals &lt;1.2-fold), is easily assessed for quality control, also assesses instrument effective linear range, and can be combined with fluorescence calibration to obtain units of Molecules of Equivalent Fluorescein (MEFL) per cell, allowing direct comparison and data fusion with flow cytometry measurements: in our study, fluorescence per cell measurements showed only a 1.07-fold mean difference between plate reader and flow cytometry data

Slowdown in the M/M/1M/M/1 discriminatory processor-sharing queue

We consider a queue with multiple K job classes, Poisson arrivals, and exponentially distributed required service times in which a single processor serves according to the discriminatory processor-sharing (DPS) discipline. For this queue, we obtain the first and second moments of the slowdown, which is a measure for queueing fairness. We then provide numerical examples and discuss aspects of the slowdown in the DPS queue