A lightning climatology of the South-West Indian Ocean

The World Wide Lightning Location Network (WWLLN) data have been used to perform a lightning climatology in the South-West Indian Ocean (SWIO) region from 2005 to 2011. Maxima of lightning activity were found in the Maritime Continent and southwest of Sri Lanka (>50 fl km<sup>−2</sup> yr<sup>−1</sup>) but also over Madagascar and above the Great Lakes of East Africa (>10–20 fl km<sup>−2</sup> yr<sup>−1</sup>). Lightning flashes within tropical storms and tropical cyclones represent 50 % to 100 % of the total lightning activity in some oceanic areas of the SWIO (between 10° S and 20° S). <br><br> The SWIO is characterized by a wet season (November to April) and a dry season (May to October). As one could expect, lightning activity is more intense during the wet season as the Inter Tropical Convergence Zone (ITCZ) is present over all the basin. Flash density is higher over land in November–December–January with values reaching 3–4 fl km<sup>−2</sup> yr<sup>−1</sup> over Madagascar. During the dry season, lightning activity is quite rare between 10° S and 25° S. The Mascarene anticyclone has more influence on the SWIO resulting in shallower convection. Lightning activity is concentrated over ocean, east of South Africa and Madagascar. <br><br> A statistical analysis has shown that El Niño–Southern Oscillation mainly modulates the lightning activity up to 56.8% in the SWIO. The Indian Ocean Dipole has a significant contribution since ~49% of the variability is explained by this forcing in some regions. The Madden–Julian Oscillation did not show significative impact on the lightning activity in our study

Metallicity determination in gas-rich galaxies with semiempirical methods

A study of the precision of the semiempirical methods used in the determination of the chemical abundances in gas-rich galaxies is carried out. In order to do this the oxygen abundances of a total of 438 galaxies were determined using the electronic temperature, the $R_{23}$ and the P methods. The new calibration of the P method gives the smaller dispersion for the low and high metallicity regions, while the best numbers in the turnaround region are given by the $R_{23}$ method. We also found that the dispersion correlates with the metallicity. Finally, it can be said that all the semiempirical methods studied here are quite insensitive to metallicity with a value of $8.0\pm0.2$ dex for more than 50% of the total sample. \keywords{ISM: abundances; (ISM): H {\sc ii} regions}Comment: 26 pages, 9 figures and 2 tables. To appear at AJ, January 200

Transference Principles for Log-Sobolev and Spectral-Gap with Applications to Conservative Spin Systems

We obtain new principles for transferring log-Sobolev and Spectral-Gap inequalities from a source metric-measure space to a target one, when the curvature of the target space is bounded from below. As our main application, we obtain explicit estimates for the log-Sobolev and Spectral-Gap constants of various conservative spin system models, consisting of non-interacting and weakly-interacting particles, constrained to conserve the mean-spin. When the self-interaction is a perturbation of a strongly convex potential, this partially recovers and partially extends previous results of Caputo, Chafa\"{\i}, Grunewald, Landim, Lu, Menz, Otto, Panizo, Villani, Westdickenberg and Yau. When the self-interaction is only assumed to be (non-strongly) convex, as in the case of the two-sided exponential measure, we obtain sharp estimates on the system's spectral-gap as a function of the mean-spin, independently of the size of the system.Comment: 57 page

Probabilistic relational Hoare logics for computer-aided security proofs

International audienceNon

Moments of unconditional logarithmically concave vectors

We derive two-sided bounds for moments of linear combinations of coordinates od unconditional log-concave vectors. We also investigate how well moments of such combinations may be approximated by moments of Gaussian random variables.Comment: 14 page

Termination Casts: A Flexible Approach to Termination with General Recursion

This paper proposes a type-and-effect system called Teqt, which distinguishes terminating terms and total functions from possibly diverging terms and partial functions, for a lambda calculus with general recursion and equality types. The central idea is to include a primitive type-form "Terminates t", expressing that term t is terminating; and then allow terms t to be coerced from possibly diverging to total, using a proof of Terminates t. We call such coercions termination casts, and show how to implement terminating recursion using them. For the meta-theory of the system, we describe a translation from Teqt to a logical theory of termination for general recursive, simply typed functions. Every typing judgment of Teqt is translated to a theorem expressing the appropriate termination property of the computational part of the Teqt term.Comment: In Proceedings PAR 2010, arXiv:1012.455

A formally verified compiler back-end

This article describes the development and formal verification (proof of semantic preservation) of a compiler back-end from Cminor (a simple imperative intermediate language) to PowerPC assembly code, using the Coq proof assistant both for programming the compiler and for proving its correctness. Such a verified compiler is useful in the context of formal methods applied to the certification of critical software: the verification of the compiler guarantees that the safety properties proved on the source code hold for the executable compiled code as well

Towards a unified theory of Sobolev inequalities

We discuss our work on pointwise inequalities for the gradient which are connected with the isoperimetric profile associated to a given geometry. We show how they can be used to unify certain aspects of the theory of Sobolev inequalities. In particular, we discuss our recent papers on fractional order inequalities, Coulhon type inequalities, transference and dimensionless inequalities and our forthcoming work on sharp higher order Sobolev inequalities that can be obtained by iteration.Comment: 39 pages, made some changes to section 1