Objetos de la Geometría algebraica clásica y Espacios anillados

La Geometría Algebraica Clásica puede ser definida como el estudio de las variedades cuasiafines y cuasiproyectivas sobre un campo k, y en particular, del problema de su clasificación salvo isomorfismos -- Estas variedades son, por definición, subconjuntos de los n-espacios afínes y de los n-espacios proyectivos -- Es útil tener a disposición una definición intrínseca de estos objetos, es decir, independiente de un espacio ambiente -- En este artículo se muestra como la noción de Espacio Anillado es la clave para formular estas definiciones y reformular el problema de clasificación

La musculature hyperbolique de la figure héroïque du film d'action américain des années 80

Le corps demeure un sujet d'études en vogue de nos jours. Une multitude d'articles et d'ouvrages abordent la représentation du corps au cinéma. Notre étude se concentre précisément sur le corps du héros du film d'action américain pendant la période classique des années 80. Il sera ainsi question de la musculature hyperbolique d’Arnold Schwarzenegger et de Sylvester Stallone. L'hypothèse de notre recherche est que la mise en scène du physique de l’acteur dans le film d’action demeure représentative de la conception héroïque de son époque. Premièrement, nous explorons la construction héroïque spécifique au film d'action classique. Nous posons que cette figure de héros américain évoque une glorification de la corporalité qui renvoie à la conception mythologique du héros occidental, celle-ci relative à notre imaginaire collectif. Une attention particulière sur la performance de Stallone dans son rôle de John Rambo servira pour appuyer notre réflexion. Deuxièmement, une analyse de la représentation du corps de Schwarzenegger dans ses premiers rôles nous permettra de vérifier à quel point le physique de cet acteur correspond à un nouveau paradigme, un nouveau modèle corporel pour incarner une figure héroïque au cinéma. Troisièmement, nous considérons le contexte socio-politique américain pendant les années 80 afin de constater l'influence de la société dans la construction d'une figure héroïque au cinéma. Une étude de la figure héroïque « reaganienne » sera développée en fonction de la comparaison de ces deux stars. Nous pourrons appréhender comment la représentation du corps dans le film d'action américain peut contribuer à la construction sociale du corps dans notre société occidentale contemporaine.

Mathematical models for cellular aggregation: the chemotactic instability and clustering formation

In this thesis we present a mathematical formulation of the interaction between microorganisms such as bacteria or amoebae and chemicals, often produced by the organisms themselves. This interaction is called chemotaxis and leads to cellular aggregation. We derive some models to describe chemotaxis. The first is the pioneristic Keller-Segel parabolic-parabolic model and it is derived by two different frameworks: a macroscopic perspective and a microscopic perspective, in which we start with a stochastic differential equation and we perform a mean-field approximation. This parabolic model may be generalized by the introduction of a degenerate diffusion parameter, which depends on the density itself via a power law. Then we derive a model for chemotaxis based on Cattaneo's law of heat propagation with finite speed, which is a hyperbolic model. The last model proposed here is a hydrodynamic model, which takes into account the inertia of the system by a friction force. In the limit of strong friction, the model reduces to the parabolic model, whereas in the limit of weak friction, we recover a hyperbolic model. Finally, we analyze the instability condition, which is the condition that leads to aggregation, and we describe the different kinds of aggregates we may obtain: the parabolic models lead to clusters or peaks whereas the hyperbolic models lead to the formation of network patterns or filaments. Moreover, we discuss the analogy between bacterial colonies and self gravitating systems by comparing the chemotactic collapse and the gravitational collapse (Jeans instability).

La musculature hyperbolique de la figure héroïque du film d'action américain des années 80

Le corps demeure un sujet d'études en vogue de nos jours. Une multitude d'articles et d'ouvrages abordent la représentation du corps au cinéma. Notre étude se concentre précisément sur le corps du héros du film d'action américain pendant la période classique des années 80. Il sera ainsi question de la musculature hyperbolique d’Arnold Schwarzenegger et de Sylvester Stallone. L'hypothèse de notre recherche est que la mise en scène du physique de l’acteur dans le film d’action demeure représentative de la conception héroïque de son époque. Premièrement, nous explorons la construction héroïque spécifique au film d'action classique. Nous posons que cette figure de héros américain évoque une glorification de la corporalité qui renvoie à la conception mythologique du héros occidental, celle-ci relative à notre imaginaire collectif. Une attention particulière sur la performance de Stallone dans son rôle de John Rambo servira pour appuyer notre réflexion. Deuxièmement, une analyse de la représentation du corps de Schwarzenegger dans ses premiers rôles nous permettra de vérifier à quel point le physique de cet acteur correspond à un nouveau paradigme, un nouveau modèle corporel pour incarner une figure héroïque au cinéma. Troisièmement, nous considérons le contexte socio-politique américain pendant les années 80 afin de constater l'influence de la société dans la construction d'une figure héroïque au cinéma. Une étude de la figure héroïque « reaganienne » sera développée en fonction de la comparaison de ces deux stars. Nous pourrons appréhender comment la représentation du corps dans le film d'action américain peut contribuer à la construction sociale du corps dans notre société occidentale contemporaine.

On continuous families of geometric Seifert conemanifold structures

In this paper, dedicated to Prof. Lou Kauffman, we determine the Thurston’s geometry possesed by any Seifert fibered conemanifold structure in a Seifert manifold with orbit space (Formula presented.) and no more than three exceptional fibers, whose singular set, composed by fibers, has at most three components which can include exceptional or general fibers (the total number of exceptional and singular fibers is less than or equal to three). We also give the method to obtain the holonomy of that structure. We apply these results to three families of Seifert manifolds, namely, spherical, Nil manifolds and manifolds obtained by Dehn surgery on a torus knot (Formula presented.). As a consequence we generalize to all torus knots the results obtained in [Geometric conemanifolds structures on (Formula presented.), the result of (Formula presented.) surgery in the left-handed trefoil knot (Formula presented.), J. Knot Theory Ramifications 24(12) (2015), Article ID: 1550057, 38pp., doi: 10.1142/S0218216515500571] for the case of the left handle trefoil knot. We associate a plot to each torus knot for the different geometries, in the spirit of Thurston.

Steroid induced neuroprotection of damaged photoreceptor cells

Retinitis Pigmentosa (RP) is the name given to a group of hereditary diseases causing progressive and degenerative blindness. RP affects over 1 in 4000 individuals, making it the most prevalent inherited retinal disease worldwide, yet currently there is no cure. In 2011, our group released a paper detailing the protective effects of the synthetic progestin ‘Norgestrel’. A common component of the female oral contraceptive pill, Norgestrel was shown to protect against retinal cell death in two distinct mouse models of retinal degeneration: in the Balb/c light damage model and the Pde6brd10 (rd10) model. Little was known of the molecular workings of this compound however and thus this study aimed to elucidate the protective manner in which Norgestrel worked. To this aim, the 661W cone photoreceptor-like cell line and ex vivo retinal explanting was utilised. We found that Norgestrel induces a increase in neuroprotective basic fibroblast growth factor (bFGF) with subsequent downstream actions on the inhibition of glycogen synthase kinase 3β. Progesterone receptor expression was subsequently characterised in the C57 and rd10 retinas and in the 661W cell line. Norgestrel caused nuclear trafficking of progesterone receptor membrane complex one (PGRMC1) in 661W cells and thus Norgestrel was hypothesised to work primarily through the actions of PGRMC1. This trafficking was shown to be responsible for the critical upregulation of bFGF and PGRMC1- Norgestrel binding was proven to cause a neuroprotective bFGF-mediated increase in intracellular calcium. The protective properties of Norgestrel were further studied in the rd10 mouse model of retinitis pigmentosa. Using non-invasive diet supplementation (80mg/kg), we showed that Norgestrel gave significant retinal protection out to postnatal day 40 (P40). Overactive microglia have previously been shown to potentiate photoreceptor cell loss in the degenerating rd10 retina and thus we focussed on Norgestrel-mediated changes in photoreceptor-microglial crosstalk. Norgestrel acted to dampen pro-inflammatory microglial cell reactivity, decreasing chemokine (MCP1, MCP3, MIP-1α, MIP-1β) and subsequent damaging cytokine (TNFα, Il-1β) production. Critically, Norgestrel up-regulated photoreceptor-microglial, fractalkine-CX3CR1 signalling 1000-fold in the P20 rd10 mouse. Known to prevent microglial activation, we hypothesise that Norgestrel acts as a vital anti-inflammatory in the diseased retina, driving fractalkine-CX3CR1 signalling to delay retinal degeneration. This study stands to highlight some of the neuroprotective mechanisms utilised by Norgestrel in the prevention of photoreceptor cell death. We identify for the first time, not only a pro-survival pathway activated directly in photoreceptor cells, but also a Norgestreldriven mediation of an otherwise damaging microglial cell response. All taken, these results form the beginning of a case to bring Norgestrel to clinical trials, as a potential therapeutic for the treatment of RP.

Homotheties and topology of tangent sphere bundles

We prove a Theorem on homotheties between two given tangent sphere bundles SrM of a Riemannian manifold (M,g) of dim ≥ 3, assuming different variable radius functions r and weighted Sasaki metrics induced by the conformal class of g. New examples are shown of manifolds with constant positive or with constant negative scalar curvature which are not Einstein. Recalling results on the associated almost complex structure I^G and symplectic structure ω^G on the manifold TM , generalizing the well-known structure of Sasaki by admitting weights and connections with torsion, we compute the Chern and the Stiefel-Whitney characteristic classes of the manifolds TM and SrM.

On a Limit of Perturbed Conservation Laws with Diffusion and Non-Positive Dispersion

We consider a conservation law perturbed by a linear diffusion and a general form of non-positive dispersion. We prove the convergence of the corresponding solution to the entropy weak solution of the hyperbolic conservation law.

Detection of Glass pattern configurations by the primary visual cortex

The neurons in the primary visual cortex that respond to the orientation of visual stimuli were discovered in the late 1950s (Hubel, D.H. & Wiesel, T.N. 1959. J. Physiol. 148:574-591) but how they achieve this response is poorly understood. Recently, experiments have demonstrated that the visual cortex may use the image processing techniques of cross or auto-correlation to detect the streaks in random dot patterns (Barlow, H. & Berry, D.L. 2010. Proc. R. Soc. B. 278: 2069-2075). These experiments made use of sinusoidally modulated random dot patterns and of the so-called Glass patterns - where randomly positioned dot pairs are oriented in a parallel configuration (Glass, L. 1969. Nature. 223: 578-580). The image processing used by the visual cortex could be inferred from how the threshold of detection of these patterns in the presence of random noise varied as a function of the dot density in the patterns. In the present study, the detection thresholds have been measured for other types of patterns including circular, hyperbolic, spiral and radial Glass patterns and an indication of the type of image processing (cross or auto-correlation) by the visual cortex is presented. As a result, it is hoped that this study will contribute to an understanding of what David Marr called the ‘computational goal’ of the primary visual cortex (Marr, D. 1982. Vision: A Computational Investigation into the Human Representation and Processing of Visual Information. New York: Freeman.)

Automorphisms of O'Grady's sixfolds

We study automorphisms of irreducible holomorphic symplectic (IHS) manifolds deformation equivalent to the O’Grady’s sixfold. We classify non-symplectic and symplectic automorphisms using lattice theoretic criterions related to the lattice structure of the second integral cohomology. Moreover we introduce the concept of induced automorphisms. There are two birational models for O'Grady's sixfolds, the first one introduced by O'Grady, which is the resolution of singularities of the Albanese fiber of a moduli space of sheaves on an abelian surface, the second one which concerns in the quotient of an Hilbert cube by a symplectic involution. We find criterions to know when an automorphism is induced with respect to these two different models, i.e. it comes from an automorphism of the abelian surface or of the Hilbert cube.

Numerical invariants for measurable cocycles

The theory of numerical invariants for representations can be generalized to measurable cocycles. This provides a natural notion of maximality for cocycles associated to complex hyperbolic lattices with values in groups of Hermitian type. Among maximal cocycles, the class of Zariski dense ones turns out to have a rigid behavior. An alternative implementation of numerical invariants can be given by using equivariant maps at the level of boundaries and by exploiting the Burger-Monod approach to bounded cohomology. Due to their crucial role in this theory, we prove existence results in two different contexts. Precisely, we construct boundary maps for non-elementary cocycles into the isometry group of CAT(0)-spaces of finite telescopic dimension and for Zariski dense cocycles into simple Lie groups. Then we approach numerical invariants. Our first goal is to study cocycles from complex hyperbolic lattices into the Hermitian group SU(p,q). Following the theory recently developed by Moraschini and Savini, we define the Toledo invariant by using the pullback along cocycles, also by involving boundary maps. For cocycles Γ × X → SU(p,q) with 1

New catalytic strategies for the manipulation of arenes

The aim of this Doctoral Thesis is the development of new catalytic synthetic methodologies in the context of the modern organic chemistry setting, with special focus on the use of cheap, sustainable catalytic materials. Specifically, during the course my PhD, I focused my research on two main distinct catalytic strategies, namely: the use of carbonaceous materials as catalysts (carbocatalysis) and nickel catalysis, also investigating a synergistic combination of the two. These methodologies were explored as means for the manipulation of (hetero)aromatic cores, representing ubiquitous, easily accessible and privileged scaffolds in medicinal or natural products chemistry. Both polar and radical reaction manifolds were engaged as complementary reactivities, capitalizing on metal- as well as organo-based activation modes. Particular attention has been devoted to addressing modern synthetic challenges or highly sought- after methodologies. Specifically, protocols for direct substitution of alcohols, dearomatization of arene nuclei, formation of C-S bonds, carbon dioxide fixation, C-C bond activation and fluoroalkylation were successfully achieved under carbo- or nickel catalyzed conditions.