Causal structure of the entanglement renormalization ansatz

We show that the multiscale entanglement renormalization ansatz (MERA) can be reformulated in terms of a causality constraint on discrete quantum dynamics. This causal structure is that of de Sitter space with a flat space-like boundary, where the volume of a spacetime region corresponds to the number of variational parameters it contains. This result clarifies the nature of the ansatz, and suggests a generalization to quantum field theory. It also constitutes an independent justification of the connection between MERA and hyperbolic geometry which was proposed as a concrete implementation of the AdS-CFT correspondence.

Fundamental domains for proper affine actions of Coxeter groups in three dimensions

We study proper actions of groups $G \cong \Z/2\Z \ast \Z/2\Z \ast \Z/2\Z$ on affine space of three real dimensions. Since $G$ is nonsolvable, work of Fried and Goldman implies that it preserves a Lorentzian metric. A subgroup $\Gamma < G$ of index two acts freely, and $\R^3/\Gamma$ is a Margulis spacetime associated to a hyperbolic surface $\Sigma$. When $\Sigma$ is convex cocompact, work of Danciger, Gu{\'e}ritaud, and Kassel shows that the action of $\Gamma$ admits a polyhedral fundamental domain bounded by crooked planes. We consider under what circumstances the action of $G$ also admits a crooked fundamental domain. We show that it is possible to construct actions of $G$ that fail to admit crooked fundamental domains exactly when the extended mapping class group of $\Sigma$ fails to act transitively on the top-dimensional simplices of the arc complex of $\Sigma$. We also provide explicit descriptions of the moduli space of $G$ actions that admit crooked fundamental domains.

Analysis of the four wave mixing effect (FWM) in a dispersion decreasing fiber (DDF) for a WDM system

We did a numerical investigation of the propagation of short light pulses in the region of 1.55 mu m and the conversion efficiency (CE) for the four wave mixing generation (FWM) of ordinary and dispersion decreasing fibers for use in wavelength division multiplexing (WDM) systems, Our simulations studies three different profiles, linear, hyperbolic. and constant, One conclude that for all the profiles there is decrease of the conversion efficiency with the increase in the channel separation. The hyperbolic profile present a higher efficiency of around 1000 above in magnitude compared with the others profiles at 0.2 nm of channel separation. We calculate the conversion efficiency versus the fiber length for the three profiles. The conversion efficiency for the hyperbolic profile is higher when compared to the constant and linear profiles. The other interesting point of the hyperbolic profile is that the increase of the CE in the beginning of the fiber does not show my oscillation in the CE value (log eta), which was observed for the constant and linear profiles. For all the profiles there is an increase of the conversion efficiency with the increase of the pump power. The compression factor C-i for the generated FWM signal at omega(3) was measured along the DDF's and the constant profile fibers. One can conclude that with the use of decreasing dispersion profile (DDF) fibers one can have a control of the (CE) conversion efficiency and the compression factor of the four wave mixing (FWM) generation in WDM systems. (c) 2005 Elsevier B.V. All rights reserved.

Radiation from a D-dimensional collision of shock waves: two-dimensional reduction and Carter–Penrose diagram

We analyze the causal structure of the two-dimensional (2D) reduced background used in the perturbative treatment of a head-on collision of two D-dimensional Aichelburg–Sexl gravitational shock waves. After defining all causal boundaries, namely the future light-cone of the collision and the past light-cone of a future observer, we obtain characteristic coordinates using two independent methods. The first is a geometrical construction of the null rays which define the various light cones, using a parametric representation. The second is a transformation of the 2D reduced wave operator for the problem into a hyperbolic form. The characteristic coordinates are then compactified allowing us to represent all causal light rays in a conformal Carter–Penrose diagram. Our construction holds to all orders in perturbation theory. In particular, we can easily identify the singularities of the source functions and of the Green’s functions appearing in the perturbative expansion, at each order, which is crucial for a successful numerical evaluation of any higher order corrections using this method.

Desenvolvimento e estudo em microcanais de fluidos inovadores análogos ao sangue baseados em vesículas unilamelares gigantes

O escoamento sanguíneo é um dos temas de grande interesse para a comunidade científica. Assim, a busca de fluidos que sejam análogos ao sangue bem como o estudo do seu escoamento em microcanais, tal como acontece com o sangue nos capilares, continua a ser alvo de investigação. Numa primeira fase deste trabalho, procedeu-se ao desenvolvimento de um modelo inovador para produzir glóbulos vermelhos artificiais, constituído por Vesículas Unilamelares Gigantes, vulgarmente designadas Giant Unilamellar Vesicles (GUVs), com três concentrações diferentes. Pretende-se que estas vesículas tenham um comportamento reológico idêntico ao escoamento dos glóbulos vermelhos (GVs) em microcanais, permitindo assim proceder a vários estudos hemodinâmicos. No desenvolvimento destas vesículas, foi verificado que as mais adequadas são constituídas por uma mistura natural de lípidos e lecitina de soja. Foi realizado um estudo relativamente à sua concentração, onde se verificou que, com o aumento da quantidade da lecitina de soja nas soluções, a concentração de GUVs tende a aumentar. Foi também realizado um estudo relativo aos diâmetros dos GUVs para verificar se estes se aproximavam em termos de tamanho dos GVs, onde foi verificado que a maioria dos GUVs possuem diâmetros com dimensões entre os 5 e 7 μm, tal como os GVs. Foi ainda verificado que a solução com a menor concentração de lecitina de soja possui uma maior quantidade de GUVs com diâmetros entre os 5 e 7 μm. Na segunda fase, foi estudado experimentalmente o escoamento das três soluções de GUVs em microcanais hiperbólicos, com três caudais diferentes, com o objetivo de visualizar a Camada Livre de Células (CLC), determinar a deformação e estudar as velocidades destes. Foi verificado que existe a formação de CLC em todas as concentrações e que aumenta com o aumento do caudal. Relativamente à deformação, esta é bastante mais evidente na contração do microcanal onde a taxa deformação é máxima. Para o caso da velocidade, foi observado um aumento bastante significativo e linear da velocidade na região da contração do microcanal hiperbólico e uma velocidade baixa e aproximadamente constante a montante e jusante da contração. vi Por fim, foi também realizado o estudo reológico dos GUVs, de forma a investigar se estes têm uma viscosidade próxima do sangue. Foi verificado que os GUVs apresentam uma viscosidade inferior à do sangue total e que existe um ligeiro aumento da viscosidade dos GUVs com o aumento da sua concentração. Por último, também foi efetuada uma comparação da viscosidade da solução de GUVs com uma solução de 5% de Hematócrito (Hct) em soro fisiológico, onde foi verificado que ambas as viscosidades são muito próximas.

Rare sex or out of reach equilibrium? The dynamics of F-IS in partially clonal organisms

Background: Partially clonal organisms are very common in nature, yet the influence of partial asexuality on the temporal dynamics of genetic diversity remains poorly understood. Mathematical models accounting for clonality predict deviations only for extremely rare sex and only towards mean inbreeding coefficient (F-IS) over bar < 0. Yet in partially clonal species, both F-IS < 0 and F-IS > 0 are frequently observed also in populations where there is evidence for a significant amount of sexual reproduction. Here, we studied the joint effects of partial clonality, mutation and genetic drift with a state-and-time discrete Markov chain model to describe the dynamics of F-IS over time under increasing rates of clonality. Results: Results of the mathematical model and simulations show that partial clonality slows down the asymptotic convergence to F-IS = 0. Thus, although clonality alone does not lead to departures from Hardy-Weinberg expectations once reached the final equilibrium state, both negative and positive F-IS values can arise transiently even at intermediate rates of clonality. More importantly, such "transient" departures from Hardy Weinberg proportions may last long as clonality tunes up the temporal variation of F-IS and reduces its rate of change over time, leading to a hyperbolic increase of the maximal time needed to reach the final mean (F-IS,F-infinity) over bar value expected at equilibrium. Conclusion: Our results argue for a dynamical interpretation of F-IS in clonal populations. Negative values cannot be interpreted as unequivocal evidence for extremely scarce sex but also as intermediate rates of clonality in finite populations. Complementary observations (e.g. frequency distribution of multiloci genotypes, population history) or time series data may help to discriminate between different possible conclusions on the extent of clonality when mean (F-IS) over bar values deviating from zero and/or a large variation of F-IS over loci are observed.

Delay discounting in mild cognitive impairment

Introduction : Patients with mild cognitive impairme nt (MCI) may make suboptimal decisions particularly in complex situations, and thi s could be due to temporal discounting, the tendency to prefer immediate rewards over delayed but larger rewards. The present study proposes to evaluate intertemporal prefere nces in MCI patients as compared to healthy controls. Method : Fifty-five patients with MCI and 57 h ealthy controls underwent neuropsy- chological evaluation and a delay discounting questionnaire, which evaluates three para- meters: hyperbolic discounting ( k ), the percentage of choices for delayed and later rewards (%LL), and response consistency (Acc). Results : No significant differences were found in the delay discounting questionnaire between MC I patients and controls for the three reward sizes considered, small, medium, and large, using both k and %LL parameters. There were also no differences in the response consistency, Acc, between the two groups. Conclusions : Patients with MCI perform similarly to healthy controls in a delay discounting task. Memory deficits do not notably affect intertemporal preferences.

ADVERTISEMENT ALLOCATION AND TRUST MECHANISMS DESIGN IN SOCIAL NETWORKS

Social network sites (SNS), such as Facebook, Google+ and Twitter, have attracted hundreds of millions of users daily since their appearance. Within SNS, users connect to each other, express their identity, disseminate information and form cooperation by interacting with their connected peers. The increasing popularity and ubiquity of SNS usage and the invaluable user behaviors and connections give birth to many applications and business models. We look into several important problems within the social network ecosystem. The first one is the SNS advertisement allocation problem. The other two are related to trust mechanisms design in social network setting, including local trust inference and global trust evaluation. In SNS advertising, we study the problem of advertisement allocation from the ad platform's angle, and discuss its differences with the advertising model in the search engine setting. By leveraging the connection between social networks and hyperbolic geometry, we propose to solve the problem via approximation using hyperbolic embedding and convex optimization. A hyperbolic embedding method, \hcm, is designed for the SNS ad allocation problem, and several components are introduced to realize the optimization formulation. We show the advantages of our new approach in solving the problem compared to the baseline integer programming (IP) formulation. In studying the problem of trust mechanisms in social networks, we consider the existence of distrust (i.e. negative trust) relationships, and differentiate between the concept of local trust and global trust in social network setting. In the problem of local trust inference, we propose a 2-D trust model. Based on the model, we develop a semiring-based trust inference framework. In global trust evaluation, we consider a general setting with conflicting opinions, and propose a consensus-based approach to solve the complex problem in signed trust networks.

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 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.)

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