Formal Verification of a Geometry Algorithm: A Quest for Abstract Views and Symmetry in Coq Proofs

This extended abstract is about an effort to build a formal description of a triangulation algorithm starting with a naive description of the algorithm where triangles, edges, and triangulations are simply given as sets and the most complex notions are those of boundary and separating edges. When performing proofs about this algorithm, questions of symmetry appear and this exposition attempts to give an account of how these symmetries can be handled. All this work relies on formal developments made with Coq and the mathematical components library

Compton Scattering in Ultra-Strong Magnetic Fields: Numerical and Analytical Behavior in the Relativistic Regime

This paper explores the effects of strong magnetic fields on the Compton scattering of relativistic electrons. Recent studies of upscattering and energy loss by relativistic electrons that have used the non-relativistic, magnetic Thomson cross section for resonant scattering or the Klein-Nishina cross section for non-resonant scattering do not account for the relativistic quantum effects of strong fields ($> 4 \times 10^{12}$ G). We have derived a simplified expression for the exact QED scattering cross section for the broadly-applicable case where relativistic electrons move along the magnetic field. To facilitate applications to astrophysical models, we have also developed compact approximate expressions for both the differential and total polarization-dependent cross sections, with the latter representing well the exact total QED cross section even at the high fields believed to be present in environments near the stellar surfaces of Soft Gamma-Ray Repeaters and Anomalous X-Ray Pulsars. We find that strong magnetic fields significantly lower the Compton scattering cross section below and at the resonance, when the incident photon energy exceeds $m_ec^2$ in the electron rest frame. The cross section is strongly dependent on the polarization of the final scattered photon. Below the cyclotron fundamental, mostly photons of perpendicular polarization are produced in scatterings, a situation that also arises above this resonance for sub-critical fields. However, an interesting discovery is that for super-critical fields, a preponderance of photons of parallel polarization results from scatterings above the cyclotron fundamental. This characteristic is both a relativistic and magnetic effect not present in the Thomson or Klein-Nishina limits.Comment: AASTeX format, 31 pages included 7 embedded figures, accepted for publication in The Astrophysical Journa

Rapid cognitive decline, one-year institutional admission and one-year mortality: Analysis of the ability to predict and inter-tool agreement of four validated clinical frailty indexes in the safes cohort

Objectives: To evaluate the predictive ability of four clinical frailty indexes as regards one-year rapid cognitive decline (RCD — defined as the loss of at least 3 points on the MMSE score), and one-year institutional admission (IA) and mortality respectively; and to measure their agreement for identifying groups at risk of these severe outcomes. Design: One-year follow-up and multicentre study of old patients participating in the SAFEs cohort study. Setting: Nine university hospitals in France. Participants: 1,306 patients aged 75 or older (mean age 85±6 years; 65% female) hospitalized in medical divisions through an Emergency department. Measurements: Four frailty indexes (Winograd; Rockwood; Donini; and Schoevaerdts) reflecting the multidimensionality of the frailty concept, using an ordinal scoring system able to discriminate different grades of frailty, and constructed based on the accumulation of identified deficits after comprehensive geriatric assessment conducted during the first week of hospital stay, were used to categorize participants into three different grades of frailty: Gl — not frail; G2 — moderately frail; and G3 — severely frail. Comparisons between groups were performed using Fisher's exact test. Agreement between indexes was evaluated using Cohen's Kappa coefficient. Results: All patients were classified as frail by at least one of the four indexes. The Winograd and Rockwood indexes mainly classified subjects as G2 (85% and 96%), and the Donini and Schoevaerdts indexes mainly as G3 (71% and 67%). Among the SAFEs cohort population, 250, 1047 and 1,306 subjects were eligible for analyses of predictability for RCD, 1-year IA and 1-year mortality respectively. At 1 year, 84 subjects (34%) experienced RCD, 377 (36%) were admitted into an institutional setting, and 445 (34%) had died With the Rockwood index, all subjects who expenenced RCD were classified in G2; and in G2 and G3 when the Donini and Schoevaerdts indexes were used No significant difference was found between frailty grade and RCD, whereas frailty grade was significantly associated with an increased risk of IA and death, whatever the frailty index considered. Agreement between the different indexes of frailty was poor with Kappa coefficients ranging from −0.02 to 0.15. Conclusion: These findings confirm the poor clinimetric properties of these current indexes to measure frailty, underlining the fact that further work is needed to develop a better and more widely-accepted definition of frailty and therefore a better understanding of its pathophysiolog

Galactic populations of radio and gamma-ray pulsars in the polar cap model

We simulate the characteristics of the Galactic population of radio and $\gamma$-ray pulsars using Monte Carlo techniques. At birth, neutron stars are spatially distributed in the Galactic disk, with supernova-kick velocities, and randomly dispersed in age back to $10^9$ years. They are evolved in the Galactic gravitational potential to the present time. From a radio luminosity model, the radio flux is filtered through a selected set of radio-survey parameters. $\gamma$-ray luminosities are assigned using the features of recent polar cap acceleration models invoking space-charge-limited flow, and a pulsar death valley further attenuates the population of radio-loud pulsars. Assuming a simple emission geometry with aligned radio and $\gamma$-ray beams of 1 steradian solid angle, our model predicts that EGRET should have seen 7 radio-loud and 1 radio-quiet, $\gamma$-ray pulsars. With much improved sensitivity, GLAST, on the other hand, is expected to observe 76 radio-loud and 74 radio-quiet, $\gamma$-ray pulsars of which 7 would be identified as pulsed sources. We also explore the effect of magnetic field decay on the characteristics of the radio and $\gamma$-ray pulsar populations. Including magnetic field decay on a timescale of 5 Myr improves agreement with the radio pulsar population and increases the predicted number of GLAST detected pulsars to 90 radio-loud and 101 radio-quiet (9 pulsed) $\gamma$-ray pulsars. The lower flux threshold allows GLAST to detect $\gamma$-ray pulsars at larger distances than those observed by the radio surveys used in this study.Comment: 38 pages, 11 figures, accepted for publication v565 n1 Ap

Eight gamma-ray pulsars discovered in blind frequency searches of Fermi LAT data

We report the discovery of eight gamma-ray pulsars in blind frequency searches using the LAT, onboard the Fermi Gamma-ray Space Telescope. Five of the eight pulsars are young (tau_c10^36 erg/s), and located within the Galactic plane (|b|<3 deg). The remaining three are older, less energetic, and located off the plane. Five pulsars are associated with sources included in the LAT bright gamma-ray source list, but only one, PSR J1413-6205, is clearly associated with an EGRET source. PSR J1023-5746 has the smallest characteristic age (tau_c=4.6 kyr) and is the most energetic (Edot=1.1E37 erg/s) of all gamma-ray pulsars discovered so far in blind searches. PSRs J1957+5033 and J2055+25 have the largest characteristic ages (tau_c~1 Myr) and are the least energetic (Edot~5E33 erg/s) of the newly-discovered pulsars. We present the timing models, light curves, and detailed spectral parameters of the new pulsars. We used recent XMM observations to identify the counterpart of PSR J2055+25 as XMMU J205549.4+253959. In addition, publicly available archival Chandra X-ray data allowed us to identify the likely counterpart of PSR J1023-5746 as a faint, highly absorbed source, CXOU J102302.8-574606. The large X-ray absorption indicates that this could be among the most distant gamma-ray pulsars detected so far. PSR J1023-5746 is positionally coincident with the TeV source HESS J1023-575, located near the young stellar cluster Westerlund 2, while PSR J1954+2836 is coincident with a 4.3 sigma excess reported by Milagro at a median energy of 35 TeV. Deep radio follow-up observations of the eight pulsars resulted in no detections of pulsations and upper limits comparable to the faintest known radio pulsars, indicating that these can be included among the growing population of radio-quiet pulsars in our Galaxy being uncovered by the LAT, and currently numbering more than 20.Comment: Submitted to Ap

Magnetic fileds of coalescing neutron stars and the luminosity function of short gamma-ray burst

Coalescing neutron star binaries are believed to be the most reliable sources for ground-based detectors of gravitational waves and likely progenitors of short gamma-ray bursts. In the process of coalescence, magnetic fields of neutron stars can induce interesting observational manifestations and affect the form of gravitational wave signal. In this papaer we use the population synthesis method to model the expected distribution of neutron star magnetic fields during the coalescence under different assumptions on the initial parameters of neutron stars and their magnetic field evolution. We discuss possible elecotrmagnetic phenomena preceding the coalescence of magnetized neutron star binaries and the effect of magnetic field on the gravitational wave signal. We find that a log-normal (Gaussian in logarithms) distribution of the initial magnetic fields of neutron stars, which agrees with observed properties of radio pulsars, produces the distribution of the magnetic field energy during the coalescence that adequately describes the observed luminosity function of short gamma-ray bursts under different assumptions on the field evolution and initial parameters of neutron stars. This agreement lends further support to the model of coalescing neutron star binaries as progenitors of gamma-ray bursts.Comment: v.2, LATEX, 25 pages, inc. 7 ps figures, Astron. Lett., in press. Typos corrected, reference adde

Commodity risk assessment of Crataegus monogyna plants from the UK

The European Commission requested the EFSA Panel on Plant Health to prepare and deliver risk assessments for commodities listed in Commission Implementing Regulation (EU) 2018/2019 as 'High risk plants, plant products and other objects'. Taking into account the available scientific information, including the technical information provided by the applicant country, this Scientific Opinion covers the plant health risks posed by the following commodities: Crataegus monogyna bare root plants and rooted plants in pots imported into the EU from the UK. A list of pests potentially associated with the commodities was compiled. The relevance of any pest was assessed based on evidence following defined criteria. Only the quarantine pest Erwinia amylovora was selected for further evaluation. For E. amylovora the special requirements specified in the Commission Implementing Regulation (EU) 2019/2072 are fulfilled by the UK and no other pests for further evaluation were selected