How Fast Can You Escape a Compact Polytope?

The Continuous Polytope Escape Problem (CPEP) asks whether every trajectory of a linear differential equation initialised within a convex polytope eventually escapes the polytope. We provide a polynomial-time algorithm to decide CPEP for compact polytopes. We also establish a quantitative uniform upper bound on the time required for every trajectory to escape the given polytope. In addition, we establish iteration bounds for termination of discrete linear loops via reduction to the continuous case

Error Rate of the Kane Quantum Computer CNOT Gate in the Presence of Dephasing

We study the error rate of CNOT operations in the Kane solid state quantum computer architecture. A spin Hamiltonian is used to describe the system. Dephasing is included as exponential decay of the off diagonal elements of the system's density matrix. Using available spin echo decay data, the CNOT error rate is estimated at approsimately 10^{-3}.Comment: New version includes substantial additional data and merges two old figures into one. (12 pages, 6 figures

Quadratic Volume Preserving Maps

We study quadratic, volume preserving diffeomorphisms whose inverse is also quadratic. Such maps generalize the Henon area preserving map and the family of symplectic quadratic maps studied by Moser. In particular, we investigate a family of quadratic volume preserving maps in three space for which we find a normal form and study invariant sets. We also give an alternative proof of a theorem by Moser classifying quadratic symplectic maps.Comment: Ams LaTeX file with 4 figures (figure 2 is gif, the others are ps

High Energy Hadron-Nucleus Cross Sections and Their Extrapolation to Cosmic Ray Energies

Old models of the scattering of composite systems based on the Glauber model of multiple diffraction are applied to hadron-nucleus scattering. We obtain an excellent fit with only two free parameters to the highest energy hadron-nucleus data available. Because of the quality of the fit and the simplicity of the model it is argued that it should continue to be reliable up to the highest cosmic ray energies. Logarithmic extrapolations of proton-proton and proton-antiproton data are used to calculate the proton-air cross sections at very high energy. Finally, it is observed that if the exponential behavior of the proton-antiproton diffraction peak continues into the few TeV energy range it will violate partial wave unitarity. We propose a simple modification that will guarantee unitarity throughout the cosmic ray energy region.Comment: 8 pages, 9 postscript figures. This manuscript replaces a partial manuscript incorrectly submitte

Ozone loss derived from balloon-borne tracer measurements and the SLIMCAT CTM

Balloon-borne measurements of CFC-11 (on flights of the DIRAC in situ gas chromatograph and the DESCARTES grab sampler), ClO and O3 were made during the 1999/2000 winter as part of the SOLVE-THESEO 2000 campaign. Here we present the CFC-11 data from nine flights and compare them first with data from other instruments which flew during the campaign and then with the vertical distributions calculated by the SLIMCAT 3-D CTM. We calculate ozone loss inside the Arctic vortex between late January and early March using the relation between CFC-11 and O3 measured on the flights, the peak ozone loss (1200 ppbv) occurs in the 440–470 K region in early March in reasonable agreement with other published empirical estimates. There is also a good agreement between ozone losses derived from three independent balloon tracer data sets used here. The magnitude and vertical distribution of the loss derived from the measurements is in good agreement with the loss calculated from SLIMCAT over Kiruna for the same days

Racial Inequities in the Delivery of Social Services

Data from a survey of registered social workers in Michigan indicate inequities in the delivery of social services. Providers serving non-whites tend to spend less time providing casework services and more time on providing welfare services than do providers serving whites. These interracial differences may be explained by income or employment auspice. The major racial inequity is apparent when providers serving primarily non-white clients are analyzed. White providers serving non-whites spend more time on welfare activities and less on casework services than do non-white providers serving non-whites. These differences cannot be explained by income or the providers\u27 education and experience. Such patterns of delivery raise issues for the profession and have implications for manpower needs, usage, and training. Research aimed at evaluating the consequences of these differences and programs to eliminate inequities should be of the highest priority

Migraine aura: retracting particle-like waves in weakly susceptible cortex

Cortical spreading depression (SD) has been suggested to underlie migraine aura. Despite a precise match in speed, the spatio-temporal patterns of SD and aura symptoms on the cortical surface ordinarily differ in aspects of size and shape. We show that this mismatch is reconciled by utilizing that both pattern types bifurcate from an instability point of generic reaction-diffusion models. To classify these spatio-temporal pattern we suggest a susceptibility scale having the value [sigma]=1 at the instability point. We predict that human cortex is only weakly susceptible to SD ([sigma]<1), and support this prediction by directly matching visual aura symptoms with anatomical landmarks using fMRI retinotopic mapping. We discuss the increased dynamical repertoire of cortical tissue close to [sigma]=1, in particular, the resulting implications on migraine pharmacology that is hitherto tested in the regime ([sigma]>>1), and potentially silent aura occurring below a second bifurcation point at [sigma]=0 on the susceptible scale

Improved Upper Limit on the Neutrino Mass from a Direct Kinematic Method by KATRIN.

We report on the neutrino mass measurement result from the first four-week science run of the Karlsruhe Tritium Neutrino experiment KATRIN in spring 2019. Beta-decay electrons from a high-purity gaseous molecular tritium source are energy analyzed by a high-resolution MAC-E filter. A fit of the integrated electron spectrum over a narrow interval around the kinematic end point at 18.57 keV gives an effective neutrino mass square value of (-1.0_{-1.1}^{+0.9})  eV^{2}. From this, we derive an upper limit of 1.1 eV (90% confidence level) on the absolute mass scale of neutrinos. This value coincides with the KATRIN sensitivity. It improves upon previous mass limits from kinematic measurements by almost a factor of 2 and provides model-independent input to cosmological studies of structure formation

'Who do "they" cheer for?' Cricket, diaspora, hybridity and divided loyalties amongst British Asians

This article explores the relationship between British Asians' sense of nationhood, citizenship, ethnicity and some of their manifestations in relation to sports fandom: specifically in terms of how cricket is used as a means of articulating diasporic British Asian identities. Norman Tebbit's 'cricket test' is at the forefront of this article to tease out the complexities of being British Asian in terms of supporting the English national cricket team. The first part of the article locates Tebbit's 'cricket test' within the wider discourse of multiculturalism. The analysis then moves to focus on the discourse of sports fandom and the concept of 'home team advantage' arguing that sports venues represent significant sites for nationalist and cultural expression due to their connection with national history. The article highlights how supporting 'Anyone but England', thereby rejecting ethnically exclusive notions of 'Englishness' and 'Britishness', continues to be a definer of British Asians' cultural identities. The final section situates these trends within the discourse of hybridity and argues that sporting allegiances are often separate from considerations of national identity and citizenship. Rather than placing British Asians in an either/or situation, viewing British 'Asianness' in hybrid terms enables them to celebrate their traditions and histories, whilst also being proud of their British citizenship. © The Author(s) 2011