Abstract:
In this paper we show that if $A$ is a subset of the primes with positive relative density $\delta$, then $A+A$ must have positive upper density $C_1\delta e^{-C_2(\log(1/\delta))^{2/3}(\log\log(1/\delta))^{1/3}}$ in $\mathbb{N}$. Our argument applies the techniques developed by Green and Green-Tao used to find arithmetic progressions in the primes, in combination with a result on sums of subsets of the multiplicative subgroup of the integers modulo $M$.

Abstract:
We extend two well-known results in additive number theory, S\'ark\"ozy's theorem on square differences in dense sets and a theorem of Green on long arithmetic progressions in sumsets, to subsets of random sets of asymptotic density 0. Our proofs rely on a restriction-type Fourier analytic argument of Green and Green-Tao.

Abstract:
We extend the best known bound on the largest subset of {1,2,...,N} with no square differences to the largest possible class of quadratic polynomials.

Abstract:
Suppose that A is a set of n real numbers, each at least 1 apart. Define the ``perturbed sum and product sets'' S and P to be the sums a + b + f(a,b) and products (a+g(a,b))(b+h(a,b)), where f, g, and h satisfy certain upper bounds in terms of the n, |a| and |b|. We develop almost best possible lower bounds on |P| + |S|, using the largest possible sizes of the ``perturbation parameters'' f(a,b), g(a,b) and h(a,b). Our proof uses Elekes's idea for bounding |A+A|+|A.A| from below, in combination with the Szemeredi-Trotter curve theorem (actually, a minor generalization of it) of Szekely, applied to certain polygonal arcs.

Abstract:
Using a slight modification of an argument of Croot, Ruzsa and Schoen we establish a quantitative result on the existence of a dilated copy of any given configuration of integer points in sparse difference sets. More precisely, given any configuration $\{v_1,...,v_\ell\}$ of vectors in $\mathbb{Z}^d$, we show that if $A\subset[1,N]^d$ with $|A|/N^d\geq C N^{-1/\ell}$, then there necessarily exists $r\ne0$ such that $\{rv_1, ...,rv_\ell\}\subseteq A-A$.

Abstract:
Observational bias against finding Milky Way (MW) dwarf galaxies at low Galactic latitudes (b < 20 deg) and at low surface brightnesses (fainter than 29 mag arcsec^-2, in the V-band) currently limits our understanding of the faintest limits of the galaxy luminosity function. This paper is a proof-of-concept that groups of two or more RR Lyrae stars reveal MW dwarf galaxies at d > 50 kpc in these unmined regions of parameter space, with only modest contamination from interloper groups when large halo structures are excluded. For example, a friends-of-friends (FOF) search with a linking length of 500 pc could reveal dwarf galaxies more luminous than M_V = -3.2 mag and with surface brightnesses as faint as 31 mag arcsec^-2 (or even fainter, depending on RR Lyrae specific frequency). Although existing public RR Lyrae catalogs are highly incomplete at d > 50 kpc and/or include <1% of the MW halo's volume, a FOF search reveals two known dwarfs (Bootes I and Sextans) and two dwarf candidate groups possibly worthy of follow-up. PanSTARRS 1 (PS1) may catalog RR Lyrae to 100 kpc which would include ~15% of predicted MW dwarf galaxies. Groups of PS1 RR Lyrae should therefore reveal very low surface brightness and low Galactic latitude dwarfs within its footprint, if they exist. With sensitivity to RR Lyrae to d >600 kpc, LSST is the only planned survey that will be both wide-field and deep enough to use RR Lyrae to definitively measure the Milky Way's dwarf galaxy census to extremely low surface brightnesses, and through the Galactic plane.

Abstract:
Retinitis pigmentosaRetinitis pigmentosa (RP) belongs to the group of pigmentary retinopathies, a generic name that covers all retinal dystrophies presented with a loss of photoreceptors and retinal pigment deposits. RP is a retinal degenerative disease characterized by pigment deposits predominant in the peripheral retina and by a relative sparing of the central retina. In most of the cases of RP, there is a primary degeneration of the photoreceptor rods, with secondary degeneration of cones. Thus, the typical RP is also described as a rod-cone dystrophy, photoreceptor rods being more affected than cones. This sequence of photoreceptor involvement explains why patients initially present with night blindness, and only in the later life would suffer visual impairment in diurnal conditions.？ Night blindness (nyctalopia) is the earliest symptom？ Photophobia appears later？ The visual acuity is preserved in early and mid stages？ Patchy losses of peripheral vision evolving to？ Ring shape scotoma, and eventually？ Tunnel vision？ Pigmentary deposits resembling bone spicules, initially in peripheral retina？ Attenuation of the retinal vessels？ Waxy pallor of the optic disc？ Various degrees of retinal atrophy？ Dramatic diminution in a- and b-wave's amplitudes？ Scotopic system (rods) predominates over photopic (cones) systemPrevalence of non syndromic RP is approximately 1/4,000 [1-5].RP is a long lasting disease that usually evolves over several decades. However, there are extreme cases with a rapid evolution over two decades or a slow progression that never leads to blindness. The disease course can be conveniently divided into three stages.In the early stage, night blindness is the main symptom. It may be present from the first years of life or may appear during the second decade, or even later. Mild night blindness is often ignored by the patients and becomes apparent in the teen age, at evening parties. At this stage, there may be peripheral visual field defects in dim ligh

Abstract:
this paper analyzes the way racism manipulates accusations of racism, and presents the effects of such discourses on discriminated individuals. it argues that, far from reducing sexist violence, the racist logic concealed by anti-sexism tends to reinforce it. our theses is based on data collected in a survey on experiences of racism, sexuality and hiv-infection risks management, carried out from 1997 to 2003, among 69 young males and females, aged 18-25 years, in france.

Abstract:
Décrire, comprendre et expliquer, selon la formule qui traduit l’entreprise sociologique, est ici illustrée à la lumière notamment de la théorie et des considérations de Pierre Bourdieu. Sur cette base, l’article cherche à cerner les enjeux que soulèvent ces trois ma tres mots dans l’élaboration de la connaissance sociologique con ue comme connaissance d’une connaissance . L’objet de l’analyse appara t dans cette perspective le c ur de ce chiasme épistémologique que représente l’édification de l’explication en sociologie. Describe, Understand, and Explain: Reflections and Illustrations in SociologyTo describe, understand, and explain, following the formula which expresses the purpose of the field of sociology, is here illustrated principally through the theories and approach of Pierre Bourdieu. On this basis, the article seeks to clarify the issues that these three key words raise in the process of developing sociological knowledge (the latter conceived of as the knowledge of how knowledge is constructed). In this perspective, the object of analysis appears to be the central epistemological opposition in Sociology constituted by the construction of theories on one hand and their explanation on the other. Describir, comprender y explicar. Reflexiones y ejemplos de la Sociología.Describir, comprender y explicar, según la fórmula que representa lo que es el proyecto sociológico, están aquí ilustrados muy particularmente a la luz de la teoría y de los comentarios de Pierre Bourdieu. El autor se focaliza en las apuestas que suscitan estos conceptos en la elaboración del conocimiento sociológico concebido este como el conocimiento de un conocimiento . El objeto del análisis aparece dentro de esta perspectiva como el nudo central del cruce epistemológico constituido por la edificación de la explicación en Sociología