A simple tool for assessing the completeness in apparent magnitude of magnitude-redshift samples

A new tool is proposed for finding out the completeness limit in apparent magnitude of a magnitude-redshift sample. The technique, closely related to the statistical test proposed by Efron & Petrosian (1992), presents a real improvement compared to standard completeness tests. Namely, no a priori assumptions are required concerning the redshift space distribution of the sources. It means in particular that neither the clustering nor the evolution of the mean number density of the galaxies do affect the result of the search.Comment: 6 pages, 5 figures, to be published in MNRA

Formal Analysis of CRT-RSA Vigilant's Countermeasure Against the BellCoRe Attack: A Pledge for Formal Methods in the Field of Implementation Security

In our paper at PROOFS 2013, we formally studied a few known countermeasures to protect CRT-RSA against the BellCoRe fault injection attack. However, we left Vigilant's countermeasure and its alleged repaired version by Coron et al. as future work, because the arithmetical framework of our tool was not sufficiently powerful. In this paper we bridge this gap and then use the same methodology to formally study both versions of the countermeasure. We obtain surprising results, which we believe demonstrate the importance of formal analysis in the field of implementation security. Indeed, the original version of Vigilant's countermeasure is actually broken, but not as much as Coron et al. thought it was. As a consequence, the repaired version they proposed can be simplified. It can actually be simplified even further as two of the nine modular verifications happen to be unnecessary. Fortunately, we could formally prove the simplified repaired version to be resistant to the BellCoRe attack, which was considered a "challenging issue" by the authors of the countermeasure themselves.Comment: arXiv admin note: substantial text overlap with arXiv:1401.817

The Tully-Fisher relation : Correspondence between the Inverse and Direct approaches

In a previous paper, we have demonstrated the importance to define a statistical model describing the observed linear correlation between the absolute magnitude $M$ and the log line width distance indicator $p$ of galaxies (the Tully-Fisher relation). As long as the same statistical model is used during the calibration step of the relation and the step of the determination of the distances of galaxies, standard statistical methods such as the maximum likelihood technic permits us to derive bias free estimators of the distances of galaxies. However in practice, it is convenient to use a different statistical model for calibrating the Tully-Fisher relation (because of its robustness, the Inverse Tully-Fisher relation is prefered during this step) and for determining the distances of galaxies (the Direct Tully-Fisher relation is more accurate and robust in this case). Herein, we establish a correspondence between the Inverse and the Direct Tully-Fisher approaches. Assuming a gaussian luminosity function, we prove that the ITF and DTF models are in fact mathematically equivalent (i.e. they describe the same physical data distribution in the TF diagram). It thus turns out that as long as the calibration parameters are obtained for a given model, we can deduce the corresponding parameters of the other model. We present these formulae of correspondence and discuss their validitity for non-gaussian luminosity functions.Comment: 10 pages, uuencoded en compressed Postscript file, figures avaible under requests. To be published in A\&

On the 3D Velocity Reconstruction of Clusters of Galaxies

The problem of reconstruction of the 3D velocities of clusters of galaxies from the redshift distribution of galaxies of the cluster is formulated. Though numerical simulations show the impossibility of direct use of Ambartsumian's formula derived for the stellar systems because of the small number of objects in the clusters, an additional physical assumption on the form of the searched velocity distribution can lead to the possibility of obtaining the transverse velocity of the cluster. The accuracy of the proposed reconstruction procedure is estimated.Comment: to appear in Astrofizika, vol.40, 1997; LaTex, 4 pages, 1 figure, *.ps figure can be obtained from the author

On the motion of the Local Group and its substructures

The problem of the relative motion of the substructures of the Local Group of galaxies revealed via S-tree method, as well as of the velocity of the Local Group itself, is considered. The existence of statistically significant bulk flow of the Milky Way subsystem is shown via 3D reconstruction procedure, which uses the information on the radial velocities of the galaxies, but not on their distances. Once the bulk motion of substructures is estimated, in combination with the observed CMB dipole we also consider the mean velocity of the Local Group itself. Assigning the Local Group the mean motion of its main substructures we evaluate its peculiar velocity in Milky Way frame V(LG->MW)= (-7 \pm 303,-15 \pm 155 ,+177 \pm 144) or 178 km/s toward galactic coordinates l=245 and b=+85. Combined with CMB dipole V(MW->CMB), we obtain Local Group velocity in CMB frame: V(LG->CMB) = (-41\pm 303,-497\pm 155,445 \pm 144) or 668 km/s towards l=265 and b=42. This estimation is in good agreement, within 1 sigma level, with the estimation of Yahil et al (1977).Comment: To be published in MNRA

Cluster luminosity function and n^th ranked magnitude as a distance indicator

We define here a standard candle to determine the distance of clusters of galaxies and to investigate their peculiar velocities by using the n^{th} rank galaxy (magnitude m$_n$). We address the question of the universality of the luminosity function for a sample of 28 rich clusters of galaxies ($cz \simeq 20000 km/s$) in order to model the influence on $m_n$ of cluster richness. This luminosity function is found to be universal and the fit of a Schechter profile gives $\alpha = -1.50 \pm 0.11$ and $M_{bj}* = -19.91 \pm 0.21$ in the range [-21,-17]. The uncorrected distance indicator $m_n$ is more efficient for the first ranks n. With n=5, we have a dispersion of 0.61 magnitude for the (m$_n$,5log(cz)) relation. When we correct for the richness effect and subtract the background galaxies we reduce the uncertainty to 0.21 magnitude with n=15. Simulations show that a large part of this dispersion originates from the intrinsic scatter of the standard candle itself. These provide upper bounds on the amplitude $\sigma_v$ of cluster radial peculiar motions. At a confidence level of 90%, the dispersion is 0.13 magnitude and $\sigma_v$ is limited to 1200 km/s for our sample of clusters.Comment: 9 pages, 7 postscript figures, LateX A&A, accepted in A&

Wavelet Analysis of Inhomogeneous Data with Application to the Cosmic Velocity Field

In this article we give an account of a method of smoothing spatial inhomogeneous data sets by using wavelet reconstruction on a regular grid in an auxilliary space onto which the original data is mapped. In a previous paper by the present authors, we devised a method for inferring the velocity potential from the radial component of the cosmic velocity field assuming an ideal sampling. Unfortunately the sparseness of the real data as well as errors of measurement require us to first smooth the velocity field as observed on a 3-dimensional support (i.e. the galaxy positions) inhomogeneously distributed throughout the sampled volume. The wavelet formalism permits us to introduce a minimal smoothing procedure that is characterized by the variation in size of the smothing window function. Moreover the output smoothed radial velocity field can be shown to correspond to a well defined theoretical quantity as long as the spatial sampling support satisfies certain criteria. We argue also that one should be very cautious when comparing the velocity potential derived from such a smoothed radial component of the velocity field with related quantities derived from other studies (e.g : of the density field).Comment: 19 pages, Latex file, figures are avaible under requests, published in Inverse Problems, 11 (1995) 76

VfrLPL

Nous présentons un lexique syntaxique des verbes du français. La ressource contient 8800 entrées environ (soit 6700 verbes distincts), pour lesquels nous produisons les formes conjuguées, leurs formes phonétisées correspondantes ainsi qu'un indice sur leurs fréquences d'usage. Pour chacun des verbes est donné son auxiliaire, son caractère pronominal et les informations caractérisant sa transitivité. Durant la constitution de cette ressource, nous avons apporté un soin particulier à valider les entrées produites en croisant nos résultats avec d'autres ressources de référence.Nous mettons à la disposition de la communauté une version préliminaire du lexique, la ressource électronique VfrLPL1.0.xml, pour laquelle les fréquences d'usage n'ont pas été recalculées.Ce travail s'inscrit dans un programme mené au Laboratoire Parole et Langage depuis quelques années, visant au développement et à la maintenance d'une ressource lexicale fiable et couvrante pour le français

New definitions in the theory of Type 1 computable topological spaces

Motivated by the two remarks, that the study of computability based on the use of numberings -- Type 1 computability -- does not have to be restricted to countable sets equipped with onto numberings, and that computable topologies have been in part developed with the implicit hypothesis that the considered spaces should be computably separable, we propose new definitions for Type 1 computable topological spaces. We define computable topological spaces without making reference to a basis. Following Spreen, we show that the use of a formal inclusion relation should be systematized, and that it cannot be avoided if we want computable topological spaces to generalize computable metric spaces. We also compare different notions of effective bases. The first one, introduced by Nogina, is based on an effective version of the statement "a set $O$ is open if for any point in $O$, there is a basic set containing that point and contained in $O$''. The second one, associated to Lacombe, is based on an effective version of "a set $O$ is open if it can be written as a union of basic open sets''. We show that neither of these notions of basis is completely satisfactory: Nogina bases do not permit to define computable topologies unless we restrict our attention to countable sets, and the conditions associated to Lacombe bases are too restrictive, and they do not apply to metric spaces unless we add effective separability hypotheses. We define a new notion of basis, based on an effective version of the Nogina statement, but adding to it several classically empty conditions, expressed in terms of formal inclusion relations. Finally, we obtain a new version of the theorem of Moschovakis which states that the Lacombe and Nogina approaches coincide on countable recursive Polish spaces, but which applies to sets equipped with non-onto numberings, and with effective separability as a sole hypothesis.Comment: 50 pages, 2 figure