Computing Integer Powers in Floating-Point Arithmetic

We introduce two algorithms for accurately evaluating powers to a positive integer in floating-point arithmetic, assuming a fused multiply-add (fma) instruction is available. We show that our log-time algorithm always produce faithfully-rounded results, discuss the possibility of getting correctly rounded results, and show that results correctly rounded in double precision can be obtained if extended-precision is available with the possibility to round into double precision (with a single rounding).Comment: Laboratoire LIP : CNRS/ENS Lyon/INRIA/Universit\'e Lyon

Some new estimates on the spectral shift function associated with random Schr\"{o}dinger operators

We prove some new pointwise-in-energy bounds on the expectations of various spectral shift functions associated with random Schr\"{o}dinger operators in the continuum having Anderson-type random potentials in both finite-volume and infinite-volume. These estimates are a consequence of our new Wegner estimate for finite-volume random Schr\"{o}dinger operators. For lattice models, we also obtain a representation of the infinite-volume density of states in terms of a spectral shift function. For continuum models, the corresponding measure is absolutely continuous with respect to the density of states and agrees with it in certain cases. We present a variant of a new spectral averaging result and use it to prove a pointwise upper bound on the SSF for finite-rank perturbations.Comment: Some results were improved and some proofs simplifie

The impact of Marguerite Broquedis victory in JO 1912 on the women's image in sport

En 1912, Margarita Broquedis, la única mujer miembro del equipo de Francia, obtuvo la medalla de oro en los Juegos Olímpicos de Estocolmo. En esa época, el lugar de las mujeres en el deporte y la sociedad era objeto de debate. Aprovechando el centenario de los Juegos Olímpicos de Estocolmo, nos propusimos rescatar las circunstancias de aquella campeona olvidada a partir de las referencias y testimonios aparecidos en la prensa de la época. Margarita Broquedis reivindicó, gracias a su victoria olímpica, un estatus de deportista de alto nivel, adelantando un entrenamiento que desde su visión debía ser igual que el de los hombres. Fue preciso esperar un siglo para que el COI integrara la paridad Hombre/Mujer en su estatusIn 1912, Marguerite Broquedis is the tennis gold medal winner in simple ladies of Stockholm’s Olympic Games. She is the only woman member of the French team too. In this time, the place of the women as well in the society as in the sport is discussed. On the occasion of the centenary of Stockholm’s Olympic Games, it is not doubtless useless to redraw in broad outline the course of this forgotten champion of tennis. From articles and testimonies appeared in the press of time, it is a question here of showing how, in the history of the feminine tennis, Marguerite Broquedis claimed, due to its Olympic victory, sportswoman's status of high level, advancing a rigorous training which in her mind had to equal that of the men player

Leading Guard Digits in Finite-Precision Redundant Representations

Redundant number representations are generally used to allow constant time additions, based on the fact that only bounded carry-ripples take place. But, carries may ripple out into positions which may not be needed to represent the final value of the result and, thus, a certain amount of leading guard digits are needed to correctly determine the result. Also, when cancellation during subtractions occurs, there may be nonzero digits in positions not needed to represent the result of the calculation. It is shown here that, for normal redundant digit sets with radix greater than two, a single guard digit is sufficient to determine the value of such an arbitrary length prefix of leading nonzero digits. This is also the case for the unsigned carry-save representation, whereas two guard digits are sufficient, and may be necessary, for additions in the binary signed-digit and 2's complement carry-save representations. Thus, only the guard digits need to be retained during sequences of additions and subtractions. At suitable points, the guard digits may then be converted into a single digit, representing the complete prefix

Les apprentissages informels au sein des associations dans une société de connaissances en mutation

Atelier 22 : Travail social et bénévolatDerrière une vision classique du savoir dans l'accumulation de connaissances de type académique, se joue une mutation importante dans nos sociétés éducatives. Dans nos recherches, nous nous sommes intéressés à l'observation de parcours où les expériences de la vie quotidienne peuvent être porteuses de connaissances. Pour identifier ces processus d'apprentissage informel, nous avons " interrogé " des bénévoles au sein des associations sur leur parcours identitaire. Les récits recueillis et retranscrits ont fait l'objet d'une analyse de contenu à l'aide du logiciel d'analyse statistique Alceste. Ces observations mettent en évidence la richesse des apprentissages souvent informels dans les tiers lieux de la vie quotidienne, et des modes de transmission originaux au sein de réseaux sociaux électifs

Choosing Starting Values for certain Newton-Raphson Iterations

Adresse de la revue : http://www.elsevier.com/wps/find/journaldescription.cws_home/505625/description#descriptionWe aim at finding the best possible seed values when computing $a^{\frac1p}$ using the Newton-Raphson iteration in a given interval. A natural choice of the seed value would be the one that best approximates the expected result. It turns out that in most cases, the best seed value can be quite far from this natural choice. When we evaluate a monotone function $f(a)$ in the interval $[a_{\min},a_{\max}]$, by building the sequence $x_n$ defined by the Newton-Raphson iteration, the natural choice consists in choosing $x_0$ equal to the arithmetic mean of the endpoint values. This minimizes the maximum possible distance between $x_0$ and $f(a)$. And yet, if we perform $n$ iterations, what matters is to minimize the maximum possible distance between $x_n$ and $f(a)$. In several examples, the value of the best starting point varies rather significantly with the number of iterations

Parallel Hierarchical Affinity Propagation with MapReduce

The accelerated evolution and explosion of the Internet and social media is generating voluminous quantities of data (on zettabyte scales). Paramount amongst the desires to manipulate and extract actionable intelligence from vast big data volumes is the need for scalable, performance-conscious analytics algorithms. To directly address this need, we propose a novel MapReduce implementation of the exemplar-based clustering algorithm known as Affinity Propagation. Our parallelization strategy extends to the multilevel Hierarchical Affinity Propagation algorithm and enables tiered aggregation of unstructured data with minimal free parameters, in principle requiring only a similarity measure between data points. We detail the linear run-time complexity of our approach, overcoming the limiting quadratic complexity of the original algorithm. Experimental validation of our clustering methodology on a variety of synthetic and real data sets (e.g. images and point data) demonstrates our competitiveness against other state-of-the-art MapReduce clustering techniques

An optimal Wegner estimate and its application to the global continuity of the integrated density of states for random Schrödinger operators

This version corrects the proof of Theorem 3.1.We prove that the integrated density of states (IDS) of random Schrödinger operators with Anderson-type potentials on $L^2 (\R^d)$, for $d \geq1$, is locally Hölder continuous at all energies with the same Hölder exponent $0<\alpha\leq1$ as the conditional probability measure for the single-site random variable. As a special case, we prove that if the probability distribution is absolutely continuous with respect to Lebesgue measure with a bounded density, then the IDS is Lipschitz continuous at all energies. The single-site potential $u\in L_0^\infty (\R^d)$ must be nonnegative and compactly-supported. The unperturbed Hamiltonian must be periodic and satisfy a unique continuation principle. We also prove analogous continuity results for the IDS of random Anderson-type perturbations of the Landau Hamiltonian in two-dimensions. All of these results follow from a new Wegner estimate for local random Hamiltonians with rather general probability measures