Perfect Simulation of M/G/cM/G/c Queues

In this paper we describe a perfect simulation algorithm for the stable $M/G/c$ queue. Sigman (2011: Exact Simulation of the Stationary Distribution of the FIFO M/G/c Queue. Journal of Applied Probability, 48A, 209--213) showed how to build a dominated CFTP algorithm for perfect simulation of the super-stable $M/G/c$ queue operating under First Come First Served discipline, with dominating process provided by the corresponding $M/G/1$ queue (using Wolff's sample path monotonicity, which applies when service durations are coupled in order of initiation of service), and exploiting the fact that the workload process for the $M/G/1$ queue remains the same under different queueing disciplines, in particular under the Processor Sharing discipline, for which a dynamic reversibility property holds. We generalize Sigman's construction to the stable case by comparing the $M/G/c$ queue to a copy run under Random Assignment. This allows us to produce a naive perfect simulation algorithm based on running the dominating process back to the time it first empties. We also construct a more efficient algorithm that uses sandwiching by lower and upper processes constructed as coupled $M/G/c$ queues started respectively from the empty state and the state of the $M/G/c$ queue under Random Assignment. A careful analysis shows that appropriate ordering relationships can still be maintained, so long as service durations continue to be coupled in order of initiation of service. We summarize statistical checks of simulation output, and demonstrate that the mean run-time is finite so long as the second moment of the service duration distribution is finite.Comment: 28 pages, 5 figure

Optimal co-adapted coupling for the symmetric random walk on the hypercube

Let X and Y be two simple symmetric continuous-time random walks on the vertices of the n-dimensional hypercube, Z2n. We consider the class of co-adapted couplings of these processes, and describe an intuitive coupling which is shown to be the fastest in this class

State-dependent Foster-Lyapunov criteria for subgeometric convergence of Markov chains

We consider a form of state-dependent drift condition for a general Markov chain, whereby the chain subsampled at some deterministic time satisfies a geometric Foster-Lyapunov condition. We present sufficient criteria for such a drift condition to exist, and use these to partially answer a question posed by Connor & Kendall (2007) concerning the existence of so-called 'tame' Markov chains. Furthermore, we show that our 'subsampled drift condition' implies the existence of finite moments for the return time to a small set.Comment: 20 pages, LaTeX: paper reduced in lengt

Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod n

We analyse a random walk on the ring of integers mod $n$, which at each time point can make an additive `step' or a multiplicative `jump'. When the probability of making a jump tends to zero as an appropriate power of $n$ we prove the existence of a total variation pre-cutoff for this walk. In addition, we show that the process obtained by subsampling our walk at jump times exhibits a true cutoff, with mixing time dependent on whether the step distribution has zero mean

Insights into the pathological basis of dementia from population-based neuropathology studies

The epidemiological neuropathology perspective of population and community-based studies allows unbiased assessment of the prevalence of various pathologies and their relationships to late-life dementia. In addition, this approach provides complementary insights to conventional case–control studies, which tend to be more representative of a younger clinical cohort. The Cognitive Function and Ageing Study (CFAS) is a longitudinal study of cognitive impairment and frailty in the general United Kingdom population. In this review, we provide an overview of the major findings from CFAS, alongside other studies, which have demonstrated a high prevalence of pathology in the ageing brain, particularly Alzheimer's disease neuropathological change and vascular pathology. Increasing burdens of these pathologies are the major correlates of dementia, especially neurofibrillary tangles, but there is substantial overlap in pathology between those with and without dementia, particularly at intermediate burdens of pathology and also at the oldest ages. Furthermore, additional pathologies such as limbic-predominant age-related TDP-43 encephalopathy, ageing-related tau astrogliopathy and primary age-related tauopathies contribute to late-life dementia. Findings from ageing population-representative studies have implications for the understanding of dementia pathology in the community. The high prevalence of pathology and variable relationship to dementia status has implications for disease definition and indicate a role for modulating factors on cognitive outcome. The complexity of late-life dementia, with mixed pathologies, indicates a need for a better understanding of these processes across the life-course to direct the best research for reducing risk in later life of avoidable clinical dementia syndromes

QFMatch: multidimensional flow and mass cytometry samples alignment

Part of the flow/mass cytometry data analysis process is aligning (matching) cell subsets between relevant samples. Current methods address this cluster-matching problem in ways that are either computationally expensive, affected by the curse of dimensionality, or fail when population patterns significantly vary between samples. Here, we introduce a quadratic form (QF)-based cluster matching algorithm (QFMatch) that is computationally efficient and accommodates cases where population locations differ significantly (or even disappear or appear) from sample to sample. We demonstrate the effectiveness of QFMatch by evaluating sample datasets from immunology studies. The algorithm is based on a novel multivariate extension of the quadratic form distance for the comparison of flow cytometry data sets. We show that this QF distance has attractive computational and statistical properties that make it well suited for analysis tasks that involve the comparison of flow/mass cytometry samples

Earth Mover’s Distance (EMD): A True Metric for Comparing Biomarker Expression Levels in Cell Populations

Changes in the frequencies of cell subsets that (co)express characteristic biomarkers, or levels of the biomarkers on the subsets, are widely used as indices of drug response, disease prognosis, stem cell reconstitution, etc. However, although the currently available computational “gating” tools accurately reveal subset frequencies and marker expression levels, they fail to enable statistically reliable judgements as to whether these frequencies and expression levels differ significantly between/among subject groups. Here we introduce flow cytometry data analysis pipeline which includes the Earth Mover’s Distance (EMD) metric as solution to this problem. Well known as an informative quantitative measure of differences between distributions, we present three exemplary studies showing that EMD 1) reveals clinically-relevant shifts in two markers on blood basophils responding to an offending allergen; 2) shows that ablative tumor radiation induces significant changes in the murine colon cancer tumor microenvironment; and, 3) ranks immunological differences in mouse peritoneal cavity cells harvested from three genetically distinct mouse strains

Dementia in the older population is associated with neocortex content of serum amyloid P component.

Despite many reported associations, the direct cause of neurodegeneration responsible for cognitive loss in Alzheimer's disease and some other common dementias is not known. The normal human plasma protein, serum amyloid P component, a constituent of all human fibrillar amyloid deposits and present on most neurofibrillary tangles, is cytotoxic for cerebral neurones in vitro and in experimental animals in vivo. The neocortical content of serum amyloid P component was immunoassayed in 157 subjects aged 65 or more with known dementia status at death, in the large scale, population-representative, brain donor cohort of the Cognitive Function and Ageing Study, which avoids the biases inherent in studies of predefined clinico-pathological groups. The serum amyloid P component values were significantly higher in individuals with dementia, independent of serum albumin content measured as a control for plasma in the cortex samples. The odds ratio for dementia at death in the high serum amyloid P component tertile was 5.24 (95% confidence interval 1.79-15.29) and was independent of Braak tangle stages and Thal amyloid-β phases of neuropathological severity. The strong and specific association of higher brain content of serum amyloid P component with dementia, independent of neuropathology, is consistent with a pathogenetic role in dementia.NIH

Identifying cell enriched miRNAs in kidney injury and repair

Small noncoding RNAs, miRNAs (miRNAs), are emerging as important modulators in the pathogenesis of kidney disease, with potential as biomarkers of kidney disease onset, progression, or therapeutic efficacy. Bulk tissue small RNA-sequencing (sRNA-Seq) and microarrays are widely used to identify dysregulated miRNA expression but are limited by the lack of precision regarding the cellular origin of the miRNA. In this study, we performed cell-specific sRNA-Seq on tubular cells, endothelial cells, PDGFR-β+ cells, and macrophages isolated from injured and repairing kidneys in the murine reversible unilateral ureteric obstruction model. We devised an unbiased bioinformatics pipeline to define the miRNA enrichment within these cell populations, constructing a miRNA catalog of injury and repair. Our analysis revealed that a significant proportion of cell-specific miRNAs in healthy animals were no longer specific following injury. We then applied this knowledge of the relative cell specificity of miRNAs to deconvolute bulk miRNA expression profiles in the renal cortex in murine models and human kidney disease. Finally, we used our data-driven approach to rationally select macrophage-enriched miR-16-5p and miR-18a-5p and demonstrate that they are promising urinary biomarkers of acute kidney injury in renal transplant recipients