Non-Markovian homodyne-mediated feedback on a two-level atom: a quantum trajectory treatment

Quantum feedback can stabilize a two-level atom against decoherence (spontaneous emission), putting it into an arbitrary (specified) pure state. This requires perfect homodyne detection of the atomic emission, and instantaneous feedback. Inefficient detection was considered previously by two of us. Here we allow for a non-zero delay time tau in the feedback circuit. Because a two-level atom is a non-linear optical system, an analytical solution is not possible. However, quantum trajectories allow a simple numerical simulation of the resulting non-Markovian process. We find the effect of the time delay to be qualitatively similar to chat of inefficient detection. The solution of the non-Markovian quantum trajectory will not remain fixed, so that the time-averaged state will be mixed, not pure. In the case where one tries to stabilize the atom in the excited state, an approximate analytical solution to the quantum trajectory is possible. The result, that the purity (P = 2Tr[rho (2)] - 1) of the average state is given by P = 1 - 4y tau (where gamma is the spontaneous emission rate) is found to agree very well with the numerical results. (C) 2001 Elsevier Science B.V. All rights reserved.

Investment optimization in distribution network based on fuzzy outage parameters

This paper presents a methodology that aims to increase the probability of delivering power to any load point of the electrical distribution system by identifying new investments in distribution components. The methodology is based on statistical failure and repair data of the distribution power system components and it uses fuzzy-probabilistic modelling for system component outage parameters. Fuzzy membership functions of system component outage parameters are obtained by statistical records. A mixed integer non-linear optimization technique is developed to identify adequate investments in distribution networks components that allow increasing the availability level for any customer in the distribution system at minimum cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a real distribution network.

An Extension of Gompertzian Growth Dynamics Weibull and Frechet Models

In this work a new probabilistic and dynamical approach to an extension of the Gompertz law is proposed. A generalized family of probability density functions, designated by Beta* (p, q), which is proportional to the right hand side of the Tsoularis-Wallace model, is studied. In particular, for p = 2, the investigation is extended to the extreme value models of Weibull and Frechet type. These models, described by differential equations, are proportional to the hyper-Gompertz growth model. It is proved that the Beta* (2, q) densities are a power of betas mixture, and that its dynamics are determined by a non-linear coupling of probabilities. The dynamical analysis is performed using techniques of symbolic dynamics and the system complexity is measured using topological entropy. Generally, the natural history of a malignant tumour is reflected through bifurcation diagrams, in which are identified regions of regression, stability, bifurcation, chaos and terminus.

Funções penalidade para o tratamento das variáveis discretas do problema de fluxo de potência ótimo reativo

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Análise estática não linear de um edifício em betão armado

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia Civil

Dimensão do sector público e crescimento económico: uma relação não linear na União Europeia dos 15?

Os Estados-Membros da União Europeia têm tido a preocupação de reduzirem a dimensão da Administração Pública na economia, a par de a tornar muito mais eficiente de forma a promover o crescimento económico. Neste artigo analisam-se as relações entre a despesa pública e o crescimento económico em 14 Estados-Membros da União Europeia dos 15, com o objectivo de determinar a dimensão óptima das Administrações Públicas, tendo por base teórica a Curva de Armey. Os resultados, para o período 1965-2007, sugerem uma dimensão do sector público maximizadora do crescimento económico de 47,37% e 22,17% do PIB, quando avaliada pelas despesas públicas totais e o consumo público, respectivamente.

A calculadora gráfica na promoção da escrita matemática na aprendizagem de modelos contínuos não lineares: um estudo com alunos do 11.º ano de Matemática B

Relatório de estágio de mestrado em Ensino de Matemática no 3.º Ciclo do Ensino Básico e no Ensino Secundário

Local non-negative initial data scalar characterization of the Kerr solution

For any vacuum initial data set, we define a local, non-negative scalar quantity which vanishes at every point of the data hypersurface if and only if the data are Kerr initial data. Our scalar quantity only depends on the quantities used to construct the vacuum initial data set which are the Riemannian metric defined on the initial data hypersurface and a symmetric tensor which plays the role of the second fundamental form of the embedded initial data hypersurface. The dependency is algorithmic in the sense that given the initial data one can compute the scalar quantity by algebraic and differential manipulations, being thus suitable for an implementation in a numerical code. The scalar could also be useful in studies of the non-linear stability of the Kerr solution because it serves to measure the deviation of a vacuum initial data set from the Kerr initial data in a local and algorithmic way.

Effect of hormonal changes on corneal biomechanical properties and anterior segment ocular perameters

Dissertação de mestrado em Optometria Avançada

Equivalence of piecewise-linear approximation and Lagrangian relaxation for network revenue management

The network revenue management (RM) problem arises in airline, hotel, media,and other industries where the sale products use multiple resources. It can be formulatedas a stochastic dynamic program but the dynamic program is computationallyintractable because of an exponentially large state space, and a number of heuristicshave been proposed to approximate it. Notable amongst these -both for their revenueperformance, as well as their theoretically sound basis- are approximate dynamic programmingmethods that approximate the value function by basis functions (both affinefunctions as well as piecewise-linear functions have been proposed for network RM)and decomposition methods that relax the constraints of the dynamic program to solvesimpler dynamic programs (such as the Lagrangian relaxation methods). In this paperwe show that these two seemingly distinct approaches coincide for the network RMdynamic program, i.e., the piecewise-linear approximation method and the Lagrangianrelaxation method are one and the same.

SAT Modulo Linear Arithmetic for Solving Polynomial

Polynomial constraint solving plays a prominent role in several areas of hardware and software analysis and verification, e.g., termination proving, program invariant generation and hybrid system verification, to name a few. In this paper we propose a new method for solving non-linear constraints based on encoding the problem into an SMT problem considering only linear arithmetic. Unlike other existing methods, our method focuses on proving satisfiability of the constraints rather than on proving unsatisfiability, which is more relevant in several applications as we illustrate with several examples. Nevertheless, we also present new techniques based on the analysis of unsatisfiable cores that allow one to efficiently prove unsatisfiability too for a broad class of problems. The power of our approach is demonstrated by means of extensive experiments comparing our prototype with state-of-the-art tools on benchmarks taken both from the academic and the industrial world.

On the Selection of Non-Invasive Methods Based on Speech Analysis Oriented to Automatic Alzheimer Disease Diagnosis

The work presented here is part of a larger study to identify novel technologies and biomarkers for early Alzheimer disease (AD) detection and it focuses on evaluating the suitability of a new approach for early AD diagnosis by non-invasive methods. The purpose is to examine in a pilot study the potential of applying intelligent algorithms to speech features obtained from suspected patients in order to contribute to the improvement of diagnosis of AD and its degree of severity. In this sense, Artificial Neural Networks (ANN) have been used for the automatic classification of the two classes (AD and control subjects). Two human issues have been analyzed for feature selection: Spontaneous Speech and Emotional Response. Not only linear features but also non-linear ones, such as Fractal Dimension, have been explored. The approach is non invasive, low cost and without any side effects. Obtained experimental results were very satisfactory and promising for early diagnosis and classification of AD patients.

Dynamic models of energy allocation and investment

In dynamic models of energy allocation, assimilated energy is allocated to reproduction, somatic growth, maintenance or storage, and the allocation pattern can change with age. The expected evolutionary outcome is an optimal allocation pattern, but this depends on the environment experienced during the evolutionary process and on the fitness costs and benefits incurred by allocating resources in different ways. Here we review existing treatments which encompass some of the possibilities as regards constant or variable environments and their predictability or unpredictability, and the ways in which production rates and mortality rates depend on body size and composition and age and on the pattern of energy allocation. The optimal policy is to allocate resources where selection pressures are highest, and simultaneous allocation to several body subsystems and reproduction can be optimal if these pressures are equal. This may explain balanced growth commonly observed during ontogeny. Growth ceases at maturity in many models; factors favouring growth after maturity include non-linear trade-offs, variable season length, and production and mortality rates both increasing (or decreasing) functions of body size. We cannot yet say whether these are sufficient to account for the many known cases of growth after maturity and not all reasonable models have yet been explored. Factors favouring storage are also reviewed.

Update on the non-prewhitening model observer in computed tomography for the assessment of the adaptive statistical and model-based iterative reconstruction algorithms.

The state of the art to describe image quality in medical imaging is to assess the performance of an observer conducting a task of clinical interest. This can be done by using a model observer leading to a figure of merit such as the signal-to-noise ratio (SNR). Using the non-prewhitening (NPW) model observer, we objectively characterised the evolution of its figure of merit in various acquisition conditions. The NPW model observer usually requires the use of the modulation transfer function (MTF) as well as noise power spectra. However, although the computation of the MTF poses no problem when dealing with the traditional filtered back-projection (FBP) algorithm, this is not the case when using iterative reconstruction (IR) algorithms, such as adaptive statistical iterative reconstruction (ASIR) or model-based iterative reconstruction (MBIR). Given that the target transfer function (TTF) had already shown it could accurately express the system resolution even with non-linear algorithms, we decided to tune the NPW model observer, replacing the standard MTF by the TTF. It was estimated using a custom-made phantom containing cylindrical inserts surrounded by water. The contrast differences between the inserts and water were plotted for each acquisition condition. Then, mathematical transformations were performed leading to the TTF. As expected, the first results showed a dependency of the image contrast and noise levels on the TTF for both ASIR and MBIR. Moreover, FBP also proved to be dependent of the contrast and noise when using the lung kernel. Those results were then introduced in the NPW model observer. We observed an enhancement of SNR every time we switched from FBP to ASIR to MBIR. IR algorithms greatly improve image quality, especially in low-dose conditions. Based on our results, the use of MBIR could lead to further dose reduction in several clinical applications.

Brain surface non-rigid registration in auditory processing

Résumé: Le développement rapide de nouvelles technologies comme l'imagerie médicale a permis l'expansion des études sur les fonctions cérébrales. Le rôle principal des études fonctionnelles cérébrales est de comparer l'activation neuronale entre différents individus. Dans ce contexte, la variabilité anatomique de la taille et de la forme du cerveau pose un problème majeur. Les méthodes actuelles permettent les comparaisons interindividuelles par la normalisation des cerveaux en utilisant un cerveau standard. Les cerveaux standards les plus utilisés actuellement sont le cerveau de Talairach et le cerveau de l'Institut Neurologique de Montréal (MNI) (SPM99). Les méthodes de recalage qui utilisent le cerveau de Talairach, ou celui de MNI, ne sont pas suffisamment précises pour superposer les parties plus variables d'un cortex cérébral (p.ex., le néocortex ou la zone perisylvienne), ainsi que les régions qui ont une asymétrie très importante entre les deux hémisphères. Le but de ce projet est d'évaluer une nouvelle technique de traitement d'images basée sur le recalage non-rigide et utilisant les repères anatomiques. Tout d'abord, nous devons identifier et extraire les structures anatomiques (les repères anatomiques) dans le cerveau à déformer et celui de référence. La correspondance entre ces deux jeux de repères nous permet de déterminer en 3D la déformation appropriée. Pour les repères anatomiques, nous utilisons six points de contrôle qui sont situés : un sur le gyrus de Heschl, un sur la zone motrice de la main et le dernier sur la fissure sylvienne, bilatéralement. Evaluation de notre programme de recalage est accomplie sur les images d'IRM et d'IRMf de neuf sujets parmi dix-huit qui ont participés dans une étude précédente de Maeder et al. Le résultat sur les images anatomiques, IRM, montre le déplacement des repères anatomiques du cerveau à déformer à la position des repères anatomiques de cerveau de référence. La distance du cerveau à déformer par rapport au cerveau de référence diminue après le recalage. Le recalage des images fonctionnelles, IRMf, ne montre pas de variation significative. Le petit nombre de repères, six points de contrôle, n'est pas suffisant pour produire les modifications des cartes statistiques. Cette thèse ouvre la voie à une nouvelle technique de recalage du cortex cérébral dont la direction principale est le recalage de plusieurs points représentant un sillon cérébral. Abstract : The fast development of new technologies such as digital medical imaging brought to the expansion of brain functional studies. One of the methodolgical key issue in brain functional studies is to compare neuronal activation between individuals. In this context, the great variability of brain size and shape is a major problem. Current methods allow inter-individual comparisions by means of normalisation of subjects' brains in relation to a standard brain. A largerly used standard brains are the proportional grid of Talairach and Tournoux and the Montreal Neurological Insititute standard brain (SPM99). However, there is a lack of more precise methods for the superposition of more variable portions of the cerebral cortex (e.g, neocrotex and perisyvlian zone) and in brain regions highly asymmetric between the two cerebral hemipsheres (e.g. planum termporale). The aim of this thesis is to evaluate a new image processing technique based on non-linear model-based registration. Contrary to the intensity-based, model-based registration uses spatial and not intensitiy information to fit one image to another. We extract identifiable anatomical features (point landmarks) in both deforming and target images and by their correspondence we determine the appropriate deformation in 3D. As landmarks, we use six control points that are situated: one on the Heschl'y Gyrus, one on the motor hand area, and one on the sylvian fissure, bilaterally. The evaluation of this model-based approach is performed on MRI and fMRI images of nine of eighteen subjects participating in the Maeder et al. study. Results on anatomical, i.e. MRI, images, show the mouvement of the deforming brain control points to the location of the reference brain control points. The distance of the deforming brain to the reference brain is smallest after the registration compared to the distance before the registration. Registration of functional images, i.e fMRI, doesn't show a significant variation. The small number of registration landmarks, i.e. six, is obvious not sufficient to produce significant modification on the fMRI statistical maps. This thesis opens the way to a new computation technique for cortex registration in which the main directions will be improvement of the registation algorithm, using not only one point as landmark, but many points, representing one particular sulcus.