Card shuffling and diophantine approximation

The ``overlapping-cycles shuffle'' mixes a deck of $n$ cards by moving either the $n$th card or the $(n-k)$th card to the top of the deck, with probability half each. We determine the spectral gap for the location of a single card, which, as a function of $k$ and $n$, has surprising behavior. For example, suppose $k$ is the closest integer to $\alpha n$ for a fixed real $\alpha\in(0,1)$. Then for rational $\alpha$ the spectral gap is $\Theta(n^{-2})$, while for poorly approximable irrational numbers $\alpha$, such as the reciprocal of the golden ratio, the spectral gap is $\Theta(n^{-3/2})$.Comment: Published in at http://dx.doi.org/10.1214/07-AAP484 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org

Avoidance Coupling

We examine the question of whether a collection of random walks on a graph can be coupled so that they never collide. In particular, we show that on the complete graph on n vertices, with or without loops, there is a Markovian coupling keeping apart Omega(n/log n) random walks, taking turns to move in discrete time.Comment: 13 pages, 3 figure

Maternal Influenza Immunization and Reduced Likelihood of Prematurity and Small for Gestational Age Births: A Retrospective Cohort Study

In an analysis of surveillance data from the state of Georgia (US), Saad Omer and colleagues show an association between receipt of influenza vaccination among pregnant women and reduced risk of premature births

Embedding of Cortical Representations by the Superficial Patch System

Pyramidal cells in layers 2 and 3 of the neocortex of many species collectively form a clustered system of lateral axonal projections (the superficial patch system—Lund JS, Angelucci A, Bressloff PC. 2003. Anatomical substrates for functional columns in macaque monkey primary visual cortex. Cereb Cortex. 13:15-24. or daisy architecture—Douglas RJ, Martin KAC. 2004. Neuronal circuits of the neocortex. Annu Rev Neurosci. 27:419-451.), but the function performed by this general feature of the cortical architecture remains obscure. By comparing the spatial configuration of labeled patches with the configuration of responses to drifting grating stimuli, we found the spatial organizations both of the patch system and of the cortical response to be highly conserved between cat and monkey primary visual cortex. More importantly, the configuration of the superficial patch system is directly reflected in the arrangement of function across monkey primary visual cortex. Our results indicate a close relationship between the structure of the superficial patch system and cortical responses encoding a single value across the surface of visual cortex (self-consistent states). This relationship is consistent with the spontaneous emergence of orientation response-like activity patterns during ongoing cortical activity (Kenet T, Bibitchkov D, Tsodyks M, Grinvald A, Arieli A. 2003. Spontaneously emerging cortical representations of visual attributes. Nature. 425:954-956.). We conclude that the superficial patch system is the physical encoding of self-consistent cortical states, and that a set of concurrently labeled patches participate in a network of mutually consistent representations of cortical inpu

Lessons for COVID-19 vaccination from eight federal government direct communication evaluations

We discuss eight randomized evaluations intended to increase vaccination uptake conducted by the US General Services Administration’s Office of Evaluation Sciences (OES). These evaluations had a median sample size of 55,000, deployed a variety of behaviorally-informed direct communications, and used administrative data to measure vaccination uptake. The confidence interval from an internal meta-analysis shows changes in vaccination rates ranging from -0.004 to 0.394 percentage points. Two studies yielded statistically significant increases, of 0.59 and 0.16 percentage points. The other six were not statistically significant, although the studies were powered to detect effect sizes in line with published research. This work highlights the likely effects of government communications and demonstrates the value of conducting rapid evaluations to support COVID-19 vaccination efforts

HEPATITIS C VIRUS GENOTYPING IN CHRONIC HEPATITIS C PATIENTS

Chronic hepatitis C virus infection is a massive worldwide healthcare burden with estimated costs in the USA alone of over $5 billon per annum. The virus has a 9.5kb positive sense single-stranded RNA genome with striking heterogeneity between isolates, which has led to it being divided into 6 genotypes and more than 50 subtypes and many quasispecies that has been arisen due to the infidelity of the viral polymerase, which lacks of a proofreading function. The virus exists as a range of related but not identical species at the quasispecies. In each infected individual, HCV circulates as a quasispecies in which the population consists of a number of closely related but distinct genetic species. The distribution of the genotype might be influenced by the mode of transmission and racial group. The only current effective treatment is combination therapy with pegylated interferon plus ribavirin (peg-IFNα + RBV) for 24–48 weeks based for genotypes 1 and 4 is 48 weeks, whereas the treatment for genotypes 2 and 3 is completed in 24 weeks. It has proved effective in up to 50% of those infected with HCV genotype 1 and 4 and it varies with other genotypes. HCV genotype is consider to be a clinically important parameter for determining both; the potential response and the duration of treatment.

Computer aided characterization of early cancer in Barrett's esophagus on i-scan magnification imaging - Multicenter international study

BACKGROUND AND AIMS: We aimed to develop a computer aided characterization system that can support the diagnosis of dysplasia in Barrett's esophagus (BE) on magnification endoscopy. METHODS: Videos were collected in high-definition magnification white light and virtual chromoendoscopy with i-scan (Pentax Hoya, Japan) imaging in patients with dysplastic/ non-dysplastic BE (NDBE) from 4 centres. We trained a neural network with a Resnet101 architecture to classify frames as dysplastic or non-dysplastic. The network was tested on three different scenarios: high-quality still images, all available video frames and a selected sequence within each video. RESULTS: 57 different patients each with videos of magnification areas of BE (34 dysplasia, 23 NDBE) were included. Performance was evaluated using a leave-one-patient-out cross-validation methodology. 60,174 (39,347 dysplasia, 20,827 NDBE) magnification video frames were used to train the network. The testing set included 49,726 iscan-3/optical enhancement magnification frames. On 350 high-quality still images the network achieved a sensitivity of 94%, specificity of 86% and Area under the ROC (AUROC) of 96%. On all 49,726 available video frames the network achieved a sensitivity of 92%, specificity of 82% and AUROC of 95%. On a selected sequence of frames per case (total of 11,471 frames) we used an exponentially weighted moving average of classifications on consecutive frames to characterize dysplasia. The network achieved a sensitivity of 92%, specificity of 84% and AUROC of 96% The mean assessment speed per frame was 0.0135 seconds (SD, + 0.006) CONCLUSION: Our network can characterize BE dysplasia with high accuracy and speed on high-quality magnification images and sequence of video frames moving it towards real time automated diagnosis

A cell topography-based mechanism for ligand discrimination by the T cell receptor.

The T cell receptor (TCR) initiates the elimination of pathogens and tumors by T cells. To avoid damage to the host, the receptor must be capable of discriminating between wild-type and mutated self and nonself peptide ligands presented by host cells. Exactly how the TCR does this is unknown. In resting T cells, the TCR is largely unphosphorylated due to the dominance of phosphatases over the kinases expressed at the cell surface. However, when agonist peptides are presented to the TCR by major histocompatibility complex proteins expressed by antigen-presenting cells (APCs), very fast receptor triggering, i.e., TCR phosphorylation, occurs. Recent work suggests that this depends on the local exclusion of the phosphatases from regions of contact of the T cells with the APCs. Here, we developed and tested a quantitative treatment of receptor triggering reliant only on TCR dwell time in phosphatase-depleted cell contacts constrained in area by cell topography. Using the model and experimentally derived parameters, we found that ligand discrimination likely depends crucially on individual contacts being ∼200 nm in radius, matching the dimensions of the surface protrusions used by T cells to interrogate their targets. The model not only correctly predicted the relative signaling potencies of known agonists and nonagonists but also achieved this in the absence of kinetic proofreading. Our work provides a simple, quantitative, and predictive molecular framework for understanding why TCR triggering is so selective and fast and reveals that, for some receptors, cell topography likely influences signaling outcomes.This work was funded by The Wellcome Trust, the UK Medical Research Council, the UK Biotechnology and Biological Sciences Research Council and Cancer Research UK. We thank the Wolfson Imaging Centre, University of Oxford, for access to their microscope facility. We would like to thank the Wellcome Trust for the Sir Henry Dale Fellowship of R.A.F. (WT101609MA), the Royal Society for the University Research Fellowship of S.F.L. (UF120277) and acknowledge a GSK Professorship (D.K.). We are also grateful to Doug Tischer (UCSF, US) and Muaz Rushdi (Georgia Tech, US) for their critical comments on the manuscript