Crystal constructions in Number Theory

Weyl group multiple Dirichlet series and metaplectic Whittaker functions can be described in terms of crystal graphs. We present crystals as parameterized by Littelmann patterns and we give a survey of purely combinatorial constructions of prime power coefficients of Weyl group multiple Dirichlet series and metaplectic Whittaker functions using the language of crystal graphs. We explore how the branching structure of crystals manifests in these constructions, and how it allows access to some intricate objects in number theory and related open questions using tools of algebraic combinatorics

Metaplectic Ice

Spherical Whittaker functions on the metaplectic n-fold cover of GL(r+1) over a nonarchimedean local field containing n distinct n-th roots of unity may be expressed as the partition functions of statistical mechanical systems that are variants of the six-vertex model. If n=1 then in view of the Casselman-Shalika formula this fact is related to Tokuyama's deformation of the Weyl character formula. It is shown that various properties of these Whittaker functions may be expressed in terms of the commutativity of row transfer matrices for the system. Potentially these properties (which are already proved by other methods, but very nontrivial) are amenable to proof by the Yang-Baxter equation

A multiscale analysis of gene flow for the New England cottontail, an imperiled habitat specialist in a fragmented landscape

Landscape features of anthropogenic or natural origin can influence organisms\u27 dispersal patterns and the connectivity of populations. Understanding these relationships is of broad interest in ecology and evolutionary biology and provides key insights for habitat conservation planning at the landscape scale. This knowledge is germane to restoration efforts for the New England cottontail (Sylvilagus transitionalis), an early successional habitat specialist of conservation concern. We evaluated local population structure and measures of genetic diversity of a geographically isolated population of cottontails in the northeastern United States. We also conducted a multiscale landscape genetic analysis, in which we assessed genetic discontinuities relative to the landscape and developed several resistance models to test hypotheses about landscape features that promote or inhibit cottontail dispersal within and across the local populations. Bayesian clustering identified four genetically distinct populations, with very little migration among them, and additional substructure within one of those populations. These populations had private alleles, low genetic diversity, critically low effective population sizes (3.2-36.7), and evidence of recent genetic bottlenecks. Major highways and a river were found to limit cottontail dispersal and to separate populations. The habitat along roadsides, railroad beds, and utility corridors, on the other hand, was found to facilitate cottontail movement among patches. The relative importance of dispersal barriers and facilitators on gene flow varied among populations in relation to landscape composition, demonstrating the complexity and context dependency of factors influencing gene flow and highlighting the importance of replication and scale in landscape genetic studies. Our findings provide information for the design of restoration landscapes for the New England cottontail and also highlight the dual influence of roads, as both barriers and facilitators of dispersal for an early successional habitat specialist in a fragmented landscape

Obstructive sleep apnoea in obese adolescents and cardiometabolic risk markers

WHAT IS ALREADY KNOWN ABOUT THIS SUBJECT: In paediatric patients, obstructive sleep apnoea is associated with adiposity, especially visceral adiposity. In adults, obstructive sleep apnoea is also associated with a higher prevalence of cardiovascular disease and type 2 diabetes. There are limited and conflicting paediatric studies examining the association between obstructive sleep apnoea and biomarkers of risk for cardiovascular disease and type 2 diabetes in youth. WHAT THIS STUDY ADDS: Obstructive sleep apnoea is linked with greater cardiometabolic risk markers in obese adolescents. Fasting insulin and homeostasis model assessment-insulin resistance may be especially linked with obstructive sleep apnoea among obese male Hispanic adolescents. The relationship between obstructive sleep apnoea and cardiometabolic abnormalities in obese adolescents should be considered when evaluating patients found to have obstructive sleep apnoea. BACKGROUND: Paediatric studies examining the association between obstructive sleep apnoea (OSA) and insulin sensitivity/cardiometabolic risk are limited and conflicting. OBJECTIVE: This study aims to determine if cardiometabolic risk markers are increased among obese youth with obstructive sleep apnoea as compared with their equally obese peers without OSA. METHODS: We performed a retrospective analysis of 96 patients (age 14.2 ± 1.4 years) who underwent polysomnography for suspected OSA. Fasting lipids, glucose, insulin and haemoglobin A1 c (HbA1 c) were performed as part of routine clinical evaluation. Patients were categorized into two groups by degree of OSA as measured by the apnoea-hypopnoea index (AHI): none or mild OSA (AHI < 5) and moderate or severe OSA (AHI ≥ 5). RESULTS: Despite the similar degrees of obesity, patients with moderate or severe OSA had higher fasting insulin (P = 0.037) and homeostasis model assessment-insulin resistance (HOMA-IR [P = 0.0497]) as compared with those with mild or no OSA. After controlling for body mass index, there was a positive association between the AHI and log HOMA-IR (P = 0.005). There was a positive relationship between arousals plus awakenings during the polysomnography and fasting triglycerides. CONCLUSIONS: OSA is linked with greater cardiometabolic risk markers in obese youth

‘Scotland's different’: Narratives of Scotland's distinctiveness in the post-Brexit-vote era

While Scotland has been portrayed as an outlier in the context of Brexit, we know relatively little about how ordinary people in Scotland, including a growing migrant population, make sense of this (political and media) narrative. In order to address this gap, in this article I look at everyday narratives of Scotland's distinctiveness in the post-Brexit-vote era among the long-settled population and Polish – and to a lesser degree other European Union – migrants in the East End of Glasgow. By drawing upon scholarship on everyday nationalism and imagined communities, I explore discursive claims which romanticise Scotland as different and ‘welcoming’ of immigration and position it in binary opposition to England. How is Scotland produced as different in the context of Brexit? How are these stories used to re-imagine increasingly diverse Scottish society? In what ways are they being employed by migrant communities

Development of FTK architecture: a fast hardware track trigger for the ATLAS detector

The Fast Tracker (FTK) is a proposed upgrade to the ATLAS trigger system that will operate at full Level-1 output rates and provide high quality tracks reconstructed over the entire detector by the start of processing in Level-2. FTK solves the combinatorial challenge inherent to tracking by exploiting the massive parallelism of Associative Memories (AM) that can compare inner detector hits to millions of pre-calculated patterns simultaneously. The tracking problem within matched patterns is further simplified by using pre-computed linearized fitting constants and leveraging fast DSP's in modern commercial FPGA's. Overall, FTK is able to compute the helix parameters for all tracks in an event and apply quality cuts in approximately one millisecond. By employing a pipelined architecture, FTK is able to continuously operate at Level-1 rates without deadtime. The system design is defined and studied using ATLAS full simulation. Reconstruction quality is evaluated for single muon events with zero pileup, as well as WH events at the LHC design luminosity. FTK results are compared with the tracking capability of an offline algorithm.Comment: To be published in the proceedings of DPF-2009, Detroit, MI, July 2009, eConf C09072

The Evolution of FTK, a Real-Time Tracker for Hadron Collider Experiments

We describe the architecture evolution of the highly-parallel dedicated processor FTK, which is driven by the simulation of LHC events at high luminosity (1034 cm-2 s-1). FTK is able to provide precise on-line track reconstruction for future hadronic collider experiments. The processor, organized in a two-tiered pipelined architecture, execute very fast algorithms based on the use of a large bank of pre-stored patterns of trajectory points (first tier) in combination with full resolution track fitting to refine pattern recognition and to determine off-line quality track parameters. We describe here how the high luminosity simulation results have produced a new organization of the hardware inside the FTK processor core.Comment: 11th ICATPP conferenc

The Safety of EXPAREL ® (Bupivacaine Liposome Injectable Suspension) Administered by Peripheral Nerve Block in Rabbits and Dogs

A sustained-release DepoFoam injection formulation of bupivacaine (EXPAREL, 15 mg/mL) is currently being investigated for postsurgical analgesia via peripheral nerve block (PNB). Single-dose toxicology studies of EXPAREL (9, 18, and 30 mg/kg), bupivacaine solution (Bsol, 9 mg/kg), and saline injected around the brachial plexus nerve bundle were performed in rabbits and dogs. The endpoints included clinical pathology, pharmacokinetics, and histopathology evaluation on Day 3 and Day 15 (2/sex/group/period). EXPAREL resulted in a nearly 4-fold lower Cmax versus Bsol at the same dose. EXPAREL was well tolerated at doses up to 30 mg/kg. The only EXPAREL-related effect seen was minimal to mild granulomatous inflammation of adipose tissue around nerve roots (8 of 24 rabbits and 7 of 24 dogs) in the brachial plexus sites. The results indicate that EXPAREL was well tolerated in these models and did not produce nerve damage after PNB in rabbits and dogs