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.

BIAS-CORRECTED MAXIMUM LIKELIHOOD ESTIMATION OF THE PARAMETERS OF THE WEIGHTED LINDLEY DISTRIBUTION

This report discusses the calculation of analytic second-order bias techniques for the maximum likelihood estimates (for short, MLEs) of the unknown parameters of the distribution in quality and reliability analysis. It is well-known that the MLEs are widely used to estimate the unknown parameters of the probability distributions due to their various desirable properties; for example, the MLEs are asymptotically unbiased, consistent, and asymptotically normal. However, many of these properties depend on an extremely large sample sizes. Those properties, such as unbiasedness, may not be valid for small or even moderate sample sizes, which are more practical in real data applications. Therefore, some bias-corrected techniques for the MLEs are desired in practice, especially when the sample size is small. Two commonly used popular techniques to reduce the bias of the MLEs, are ‘preventive’ and ‘corrective’ approaches. They both can reduce the bias of the MLEs to order O(n−2), whereas the ‘preventive’ approach does not have an explicit closed form expression. Consequently, we mainly focus on the ‘corrective’ approach in this report. To illustrate the importance of the bias-correction in practice, we apply the bias-corrected method to two popular lifetime distributions: the inverse Lindley distribution and the weighted Lindley distribution. Numerical studies based on the two distributions show that the considered bias-corrected technique is highly recommended over other commonly used estimators without bias-correction. Therefore, special attention should be paid when we estimate the unknown parameters of the probability distributions under the scenario in which the sample size is small or moderate.

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.

Autonomous formation flying: unified control and collision avoidance methods for close manoeuvring spacecraft

The idea of spacecraft formations, flying in tight configurations with maximum baselines of a few hundred meters in low-Earth orbits, has generated widespread interest over the last several years. Nevertheless, controlling the movement of spacecraft in formation poses difficulties, such as in-orbit high-computing demand and collision avoidance capabilities, which escalate as the number of units in the formation is increased and complicated nonlinear effects are imposed to the dynamics, together with uncertainty which may arise from the lack of knowledge of system parameters. These requirements have led to the need of reliable linear and nonlinear controllers in terms of relative and absolute dynamics. The objective of this thesis is, therefore, to introduce new control methods to allow spacecraft in formation, with circular/elliptical reference orbits, to efficiently execute safe autonomous manoeuvres. These controllers distinguish from the bulk of literature in that they merge guidance laws never applied before to spacecraft formation flying and collision avoidance capacities into a single control strategy. For this purpose, three control schemes are presented: linear optimal regulation, linear optimal estimation and adaptive nonlinear control. In general terms, the proposed control approaches command the dynamical performance of one or several followers with respect to a leader to asymptotically track a time-varying nominal trajectory (TVNT), while the threat of collision between the followers is reduced by repelling accelerations obtained from the collision avoidance scheme during the periods of closest proximity. Linear optimal regulation is achieved through a Riccati-based tracking controller. Within this control strategy, the controller provides guidance and tracking toward a desired TVNT, optimizing fuel consumption by Riccati procedure using a non-infinite cost function defined in terms of the desired TVNT, while repelling accelerations generated from the CAS will ensure evasive actions between the elements of the formation. The relative dynamics model, suitable for circular and eccentric low-Earth reference orbits, is based on the Tschauner and Hempel equations, and includes a control input and a nonlinear term corresponding to the CAS repelling accelerations. Linear optimal estimation is built on the forward-in-time separation principle. This controller encompasses two stages: regulation and estimation. The first stage requires the design of a full state feedback controller using the state vector reconstructed by means of the estimator. The second stage requires the design of an additional dynamical system, the estimator, to obtain the states which cannot be measured in order to approximately reconstruct the full state vector. Then, the separation principle states that an observer built for a known input can also be used to estimate the state of the system and to generate the control input. This allows the design of the observer and the feedback independently, by exploiting the advantages of linear quadratic regulator theory, in order to estimate the states of a dynamical system with model and sensor uncertainty. The relative dynamics is described with the linear system used in the previous controller, with a control input and nonlinearities entering via the repelling accelerations from the CAS during collision avoidance events. Moreover, sensor uncertainty is added to the control process by considering carrier-phase differential GPS (CDGPS) velocity measurement error. An adaptive control law capable of delivering superior closed-loop performance when compared to the certainty-equivalence (CE) adaptive controllers is finally presented. A novel noncertainty-equivalence controller based on the Immersion and Invariance paradigm for close-manoeuvring spacecraft formation flying in both circular and elliptical low-Earth reference orbits is introduced. The proposed control scheme achieves stabilization by immersing the plant dynamics into a target dynamical system (or manifold) that captures the desired dynamical behaviour. They key feature of this methodology is the addition of a new term to the classical certainty-equivalence control approach that, in conjunction with the parameter update law, is designed to achieve adaptive stabilization. This parameter has the ultimate task of shaping the manifold into which the adaptive system is immersed. The performance of the controller is proven stable via a Lyapunov-based analysis and Barbalat’s lemma. In order to evaluate the design of the controllers, test cases based on the physical and orbital features of the Prototype Research Instruments and Space Mission Technology Advancement (PRISMA) are implemented, extending the number of elements in the formation into scenarios with reconfigurations and on-orbit position switching in elliptical low-Earth reference orbits. An extensive analysis and comparison of the performance of the controllers in terms of total Δv and fuel consumption, with and without the effects of the CAS, is presented. These results show that the three proposed controllers allow the followers to asymptotically track the desired nominal trajectory and, additionally, those simulations including CAS show an effective decrease of collision risk during the performance of the manoeuvre.

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

Assessing the fit of unidimensional IRT models for binary data under model misspecification

Model misspecification affects the classical test statistics used to assess the fit of the Item Response Theory (IRT) models. Robust tests have been derived under model misspecification, as the Generalized Lagrange Multiplier and Hausman tests, but their use has not been largely explored in the IRT framework. In the first part of the thesis, we introduce the Generalized Lagrange Multiplier test to detect differential item response functioning in IRT models for binary data under model misspecification. By means of a simulation study and a real data analysis, we compare its performance with the classical Lagrange Multiplier test, computed using the Hessian and the cross-product matrix, and the Generalized Jackknife Score test. The power of these tests is computed empirically and asymptotically. The misspecifications considered are local dependence among items and non-normal distribution of the latent variable. The results highlight that, under mild model misspecification, all tests have good performance while, under strong model misspecification, the performance of the tests deteriorates. None of the tests considered show an overall superior performance than the others. In the second part of the thesis, we extend the Generalized Hausman test to detect non-normality of the latent variable distribution. To build the test, we consider a seminonparametric-IRT model, that assumes a more flexible latent variable distribution. By means of a simulation study and two real applications, we compare the performance of the Generalized Hausman test with the M2 limited information goodness-of-fit test and the Likelihood-Ratio test. Additionally, the information criteria are computed. The Generalized Hausman test has a better performance than the Likelihood-Ratio test in terms of Type I error rates and the M2 test in terms of power. The performance of the Generalized Hausman test and the information criteria deteriorates when the sample size is small and with a few items.