A renormalization approach for the 2D Anderson model at the band edge: Scaling of the localization volume

We study the localization volumes $V$ (participation ratio) of electronic wave functions in the 2d-Anderson model with diagonal disorder. Using a renormalization procedure, we show that at the band edges, i.e. for energies $E\approx \pm 4$, $V$ is inversely proportional to the variance \var of the site potentials. Using scaling arguments, we show that in the neighborhood of $E=\pm 4$, $V$ scales as V=\var^{-1}g((4-\ve E\ve)/\var) with the scaling function $g(x)$. Numerical simulations confirm this scaling ansatz

Pore opening effects and transport diffusion in the Knudsen regime in comparison to self- (or tracer-) diffusion

We study molecular diffusion in linear nanopores with different types of roughness in the so-called Knudsen regime. Knudsen diffusion represents the limiting case of molecular diffusion in pores, where mutual encounters of the molecules within the free pore space may be neglected and the time of flight between subsequent collisions with the pore walls significantly exceeds the interaction time between the pore wall and the molecules. We present an extension of a commonly used procedure to calculate transport diffusion coefficients. Our results show that using this extension, the coefficients of self- and transport diffusion in the Knudsen regime are equal for all regarded systems, which improves previous literature data.Comment: 5 pages, 7 figure

The Confidential Inquiry into premature deaths of people with intellectual disabilities in the UK: a population-based study

SummaryBackgroundThe Confidential Inquiry into premature deaths of people with intellectual disabilities in England was commissioned to provide evidence about contributory factors to avoidable and premature deaths in this population.MethodsThe population-based Confidential Inquiry reviewed the deaths of people with intellectual disabilities aged 4 years and older who had been registered with a general practitioner in one of five Primary Care Trust areas of southwest England, who died between June 1, 2010, and May 31, 2012. A network of health, social-care, and voluntary-sector services; community contacts; and statutory agencies notified the Confidential Inquiry of all deaths of people with intellectual disabilities and provided core data. The Office for National Statistics provided data about the coding of individual cause of death certificates. Deaths were described as avoidable (preventable or amenable), according to Office for National Statistics definitions. Contributory factors to deaths were identified and quantified by the case investigator, verified by a local review panel meeting, and agreed by the Confidential Inquiry overview panel. Contributory factors were grouped into four domains: intrinsic to the individual, within the family and environment, care provision, and service provision. The deaths of a comparator group of people without intellectual disabilities but much the same in age, sex, and cause of death and registered at the same general practices as those with intellectual disabilities were also investigated.FindingsThe Confidential Inquiry reviewed the deaths of 247 people with intellectual disabilities. Nearly a quarter (22%, 54) of people with intellectual disabilities were younger than 50 years when they died, and the median age at death was 64 years (IQR 52–75). The median age at death of male individuals with intellectual disabilities was 65 years (IQR 54–76), 13 years younger than the median age at death of male individuals in the general population of England and Wales (78 years). The median age at death of female individuals with intellectual disabilities was 63 years (IQR 54–75), 20 years younger than the median age at death for female individuals in the general population (83 years). Avoidable deaths from causes amenable to change by good quality health care were more common in people with intellectual disabilities (37%, 90 of 244) than in the general population of England and Wales (13%). Contributory factors to premature deaths in a subset of people with intellectual disabilities compared with a comparator group of people without intellectual disabilities included problems in advanced care planning (p=0·0003), adherence to the Mental Capacity Act (p=0·0008), living in inappropriate accommodation (p<0·0001), adjusting care as needs changed (p=0·009), and carers not feeling listened to (p=0·006).InterpretationThe Confidential Inquiry provides evidence of the substantial contribution of factors relating to the provision of care and health services to the health disparities between people with and without intellectual disabilities. It is imperative to examine care and service provision for this population as potentially contributory factors to their deaths—factors that can largely be ameliorated.FundingDepartment of Health for England

The Geometric Maximum Traveling Salesman Problem

We consider the traveling salesman problem when the cities are points in R^d for some fixed d and distances are computed according to geometric distances, determined by some norm. We show that for any polyhedral norm, the problem of finding a tour of maximum length can be solved in polynomial time. If arithmetic operations are assumed to take unit time, our algorithms run in time O(n^{f-2} log n), where f is the number of facets of the polyhedron determining the polyhedral norm. Thus for example we have O(n^2 log n) algorithms for the cases of points in the plane under the Rectilinear and Sup norms. This is in contrast to the fact that finding a minimum length tour in each case is NP-hard. Our approach can be extended to the more general case of quasi-norms with not necessarily symmetric unit ball, where we get a complexity of O(n^{2f-2} log n). For the special case of two-dimensional metrics with f=4 (which includes the Rectilinear and Sup norms), we present a simple algorithm with O(n) running time. The algorithm does not use any indirect addressing, so its running time remains valid even in comparison based models in which sorting requires Omega(n \log n) time. The basic mechanism of the algorithm provides some intuition on why polyhedral norms allow fast algorithms. Complementing the results on simplicity for polyhedral norms, we prove that for the case of Euclidean distances in R^d for d>2, the Maximum TSP is NP-hard. This sheds new light on the well-studied difficulties of Euclidean distances.Comment: 24 pages, 6 figures; revised to appear in Journal of the ACM. (clarified some minor points, fixed typos

A new paradigm for medium-range severe weather forecasts: probabilistic random forest-based predictions

Historical observations of severe weather and simulated severe weather environments (i.e., features) from the Global Ensemble Forecast System v12 (GEFSv12) Reforecast Dataset (GEFS/R) are used in conjunction to train and test random forest (RF) machine learning (ML) models to probabilistically forecast severe weather out to days 4--8. RFs are trained with 9 years of the GEFS/R and severe weather reports to establish statistical relationships. Feature engineering is briefly explored to examine alternative methods for gathering features around observed events, including simplifying features using spatial averaging and increasing the GEFS/R ensemble size with time-lagging. Validated RF models are tested with ~1.5 years of real-time forecast output from the operational GEFSv12 ensemble and are evaluated alongside expert human-generated outlooks from the Storm Prediction Center (SPC). Both RF-based forecasts and SPC outlooks are skillful with respect to climatology at days 4 and 5 with degrading skill thereafter. The RF-based forecasts exhibit tendencies to underforecast severe weather events, but they tend to be well-calibrated at lower probability thresholds. Spatially averaging predictors during RF training allows for prior-day thermodynamic and kinematic environments to generate skillful forecasts, while time-lagging acts to expand the forecast areas, increasing resolution but decreasing objective skill. The results highlight the utility of ML-generated products to aid SPC forecast operations into the medium range

Robertson-Walker fluid sources endowed with rotation characterised by quadratic terms in angular velocity parameter

Einstein's equations for a Robertson-Walker fluid source endowed with rotation Einstein's equations for a Robertson-Walker fluid source endowed with rotation are presented upto and including quadratic terms in angular velocity parameter. A family of analytic solutions are obtained for the case in which the source angular velocity is purely time-dependent. A subclass of solutions is presented which merge smoothly to homogeneous rotating and non-rotating central sources. The particular solution for dust endowed with rotation is presented. In all cases explicit expressions, depending sinusoidally on polar angle, are given for the density and internal supporting pressure of the rotating source. In addition to the non-zero axial velocity of the fluid particles it is shown that there is also a radial component of velocity which vanishes only at the poles. The velocity four-vector has a zero component between poles

Design of the Spitzer Space Telescope Heritage Archive

It is predicted that Spitzer Space Telescope’s cryogen will run out in April 2009, and the final reprocessing for the cryogenic mission is scheduled to end in April 2011, at which time the Spitzer archive will be transferred to the NASA/IPAC Infrared Science Archive (IRSA) for long-term curation. The Spitzer Science Center (SSC) and IRSA are collaborating to design and deploy the Spitzer Heritage Archive (SHA), which will supersede the current Spitzer archive. It will initially contain the raw and final reprocessed cryogenic science products, and will eventually incorporate the final products from the Warm mission. The SHA will be accompanied by tools deemed necessary to extract the full science content of the archive and by comprehensive documentation