The supermarket model with bounded queue lengths in equilibrium

In the supermarket model, there are n queues, each with a single server. Customers arrive in a Poisson process with arrival rate λn , where λ=λ(n)∈(0,1) . Upon arrival, a customer selects d=d(n) servers uniformly at random, and joins the queue of a least-loaded server amongst those chosen. Service times are independent exponentially distributed random variables with mean 1. In this paper, we analyse the behaviour of the supermarket model in the regime where λ(n)=1−n−α and d(n)=⌊nβ⌋ , where α and β are fixed numbers in (0, 1]. For suitable pairs (α,β) , our results imply that, in equilibrium, with probability tending to 1 as n→∞ , the proportion of queues with length equal to k=⌈α/β⌉ is at least 1−2n−α+(k−1)β , and there are no longer queues. We further show that the process is rapidly mixing when started in a good state, and give bounds on the speed of mixing for more general initial conditions

Early mortality and primary causes of death in mothers of children with ID or ASD: a retrospective cohort study

INTRODUCTION: Mothers of children with intellectual disability or autism spectrum disorder (ASD) have poorer health than other mothers. Yet no research has explored whether this poorer health is reflected in mortality rates or whether certain causes of death are more likely. We aimed to calculate the hazard ratios for death and for the primary causes of death in mothers of children with intellectual disability or ASD compared to other mothers. METHODS: The study population comprised all mothers of live-born children in Western Australia from 1983-2005. We accessed state-wide databases which enabled us to link socio-demographic details, birth dates, diagnoses of intellectual disability or ASD in the children and dates and causes of death for all mothers who had died prior to 2011. Using Cox Regression with death by any cause and death by each of the three primary causes as the event of interest, we calculated hazard ratios for death for mothers of children intellectual disability or ASD compared to other mothers. RESULTS AND DISCUSSION: During the study period, mothers of children with intellectual disability or ASD had more than twice the risk of death. Mothers of children with intellectual disability were 40% more likely to die of cancer; 150% more likely to die of cardiovascular disease and nearly 200% more likely to die from misadventure than other mothers. Due to small numbers, only hazard ratios for cancer were calculated for mothers of children with ASD. These mothers were about 50% more likely to die from cancer than other mothers. Possible causes and implications of our results are discussed. CONCLUSION: Similar studies, pooling data from registries elsewhere, would improve our understanding of factors increasing the mortality of mothers of children with intellectual disability or ASD. This would allow the implementation of informed services and interventions to improve these mothers' longevity

Multiple search methods for similarity-based virtual screening: analysis of search overlap and precision

Background: Data fusion methods are widely used in virtual screening, and make the implicit assumption that the more often a molecule is retrieved in multiple similarity searches, the more likely it is to be active. This paper tests the correctness of this assumption. Results: Sets of 25 searches using either the same reference structure and 25 different similarity measures (similarity fusion) or 25 different reference structures and the same similarity measure (group fusion) show that large numbers of unique molecules are retrieved by just a single search, but that the numbers of unique molecules decrease very rapidly as more searches are considered. This rapid decrease is accompanied by a rapid increase in the fraction of those retrieved molecules that are active. There is an approximately log-log relationship between the numbers of different molecules retrieved and the number of searches carried out, and a rationale for this power-law behaviour is provided. Conclusions: Using multiple searches provides a simple way of increasing the precision of a similarity search, and thus provides a justification for the use of data fusion methods in virtual screening