6,398 research outputs found
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 Ășnica mujer miembro del equipo de Francia,
obtuvo la medalla de oro en los Juegos OlĂmpicos de Estocolmo. En esa Ă©poca, el lugar de
las mujeres en el deporte y la sociedad era objeto de debate. Aprovechando el centenario de
los Juegos OlĂmpicos de Estocolmo, nos propusimos rescatar las circunstancias de aquella
campeona olvidada a partir de las referencias y testimonios aparecidos en la prensa de la
Ă©poca. Margarita Broquedis reivindicĂł, gracias a su victoria olĂmpica, un estatus de
deportista de alto nivel, adelantando un entrenamiento que desde su visiĂłn debĂa 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
Stockholmâs 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 Stockholmâs 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 bĂ©nĂ©volatDerriĂšre une vision classique du savoir dans l'accumulation de connaissances de type acadĂ©mique, se joue une mutation importante dans nos sociĂ©tĂ©s Ă©ducatives. Dans nos recherches, nous nous sommes intĂ©ressĂ©s Ă l'observation de parcours oĂč les expĂ©riences de la vie quotidienne peuvent ĂȘtre porteuses de connaissances. Pour identifier ces processus d'apprentissage informel, nous avons " interrogĂ© " des bĂ©nĂ©voles au sein des associations sur leur parcours identitaire. Les rĂ©cits recueillis et retranscrits ont fait l'objet d'une analyse de contenu Ă l'aide du logiciel d'analyse statistique Alceste. Ces observations mettent en Ă©vidence la richesse des apprentissages souvent informels dans les tiers lieux de la vie quotidienne, et des modes de transmission originaux au sein de rĂ©seaux sociaux Ă©lectifs
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 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 in the interval , by building the sequence defined by the Newton-Raphson iteration, the natural choice consists in choosing equal to the arithmetic mean of the endpoint values. This minimizes the maximum possible distance between and . And yet, if we perform iterations, what matters is to minimize the maximum possible distance between and . 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 , for , is locally Hölder continuous at all energies with the same Hölder exponent 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 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
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