Aspects of supergeometry in locally covariant quantum field theory

In questa tesi vengono presentati i piu recenti risultati relativi all'estensione della teoria dei campi localmente covariante a geometrie che permettano di descrivere teorie di campo supersimmetriche. In particolare, si mostra come la definizione assiomatica possa essere generalizzata, mettendo in evidenza le problematiche rilevanti e le tecniche utilizzate in letteratura per giungere ad una loro risoluzione. Dopo un'introduzione alle strutture matematiche di base, varieta Lorentziane e operatori Green-iperbolici, viene definita l'algebra delle osservabili per la teoria quantistica del campo scalare. Quindi, costruendo un funtore dalla categoria degli spazio-tempo globalmente iperbolici alla categoria delle *-algebre, lo stesso schema viene proposto per le teorie di campo bosoniche, purche definite da un operatore Green-iperbolico su uno spazio-tempo globalmente iperbolico. Si procede con lo studio delle supervarieta e alla definizione delle geometrie di background per le super teorie di campo: le strutture di super-Cartan. Associando canonicamente ad ognuna di esse uno spazio-tempo ridotto, si introduce la categoria delle strutture di super-Cartan (ghsCart) il cui spazio-tempo ridotto e globalmente iperbolico. Quindi, si mostra, in breve, come e possibile costruire un funtore da una sottocategoria di ghsCart alla categoria delle super *-algebre e si conclude presentando l'applicazione dei risultati esposti al caso delle strutture di super-Cartan in dimensione 2|2.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

Pseudo Focal Points Along Lorentzian Geodesics and Morse Index

Given a Lorentzian manifold (M,g), a geodesic gamma in M and a timelike Jacobi field Y along gamma, we introduce a special class of instants along gamma that we call Y-pseudo conjugate (or focal relatively to some initial orthogonal submanifold). We prove that the Y-pseudo conjugate instants form a finite set, and their number equals the Morse index of (a suitable restriction of) the index form. This gives a Riemannian-like Morse index theorem. As special cases of the theory, we will consider geodesics in stationary and static Lorentzian manifolds, where the Jacobi field Y is obtained as the restriction of a globally defined timelike Killing vector field.

Genericity of Nondegeneracy for Light Rays in Stationary Spacetimes

Given a Lorentzian manifold (M, g), an event p and an observer U in M, then p and U are light conjugate if there exists a lightlike geodesic gamma : [0, 1] -> M joining p and U whose endpoints are conjugate along gamma. Using functional analytical techniques, we prove that if one fixes p and U in a differentiable manifold M, then the set of stationary Lorentzian metrics in M for which p and U are not light conjugate is generic in a strong sense. The result is obtained by reduction to a Finsler geodesic problem via a second order Fermat principle for light rays, and using a transversality argument in an infinite dimensional Banach manifold setup.

A manifold approach to face recognition from low quality video across illumination and pose using implicit super-resolution

We consider the problem of matching a face in a low resolution query video sequence against a set of higher quality gallery sequences. This problem is of interest in many applications, such as law enforcement. Our main contribution is an extension of the recently proposed Generic Shape-Illumination Manifold (gSIM) framework. Specifically, (i) we show how super-resolution across pose and scale can be achieved implicitly, by off-line learning of subsampling artefacts; (ii) we use this result to propose an extension to the statistical model of the gSIM by compounding it with a hierarchy of subsampling models at multiple scales; and (iii) we describe an extensive empirical evaluation of the method on over 1300 video sequences – we first measure the degradation in performance of the original gSIM algorithm as query sequence resolution is decreased and then show that the proposed extension produces an error reduction in the mean recognition rate of over 50%.

Geometrical Lagrangian for a supersymmetric Yang-Mills theory on the group manifold

Perhaps one of the main features of Einstein's General Theory of Relativity is that spacetime is not flat itself but curved. Nowadays, however, many of the unifying theories like superstrings on even alternative gravity theories such as teleparalell geometric theories assume flat spacetime for their calculations. This article, an extended account of an earlier author's contribution, it is assumed a curved group manifold as a geometrical background from which a Lagrangian for a supersymmetric N = 2, d = 5 Yang-Mills - SYM, N = 2, d = 5 - is built up. The spacetime is a hypersurface embedded in this geometrical scenario, and the geometrical action here obtained can be readily coupled to the five-dimensional supergravity action. The essential idea that underlies this work has its roots in the Einstein-Cartan formulation of gravity and in the 'group manifold approach to gravity and supergravity theories'. The group SYM, N = 2, d = 5, turns out to be the direct product of supergravity and a general gauge group g: G = g circle times <(SU(2, 2/1))over bar>.

Partially Supervised Neighbor Embedding for Example-Based Image Super-Resolution

Neighbor embedding algorithm has been widely used in example-based super-resolution reconstruction from a single frame, which makes the assumption that neighbor patches embedded are contained in a single manifold. However, it is not always true for complicated texture structure. In this paper, we believe that textures may be contained in multiple manifolds, corresponding to classes. Under this assumption, we present a novel example-based image super-resolution reconstruction algorithm with clustering and supervised neighbor embedding (CSNE). First, a class predictor for low-resolution (LR) patches is learnt by an unsupervised Gaussian mixture model. Then by utilizing class label information of each patch, a supervised neighbor embedding is used to estimate high-resolution (HR) patches corresponding to LR patches. The experimental results show that the proposed method can achieve a better recovery of LR comparing with other simple schemes using neighbor embedding.

Braneworld remarks in Riemann-Cartan manifolds

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Warped Product CR-Submanifolds in Lorentzian para Sasakian Manifolds

2000 Mathematics Subject Classification: 53C15, 53C40, 53C42.

Service quality in Hong Kong : wet markets vs super markets

Purpose – The purpose of this paper is to determine consumer perceptions of service quality in wet markets and supermarkets in Hong Kong. Design/methodology/approach – A questionnaire was developed and distributed via a convenience sample to consumers in shopping malls in Causeway Bay, Mong Kok and Tsuen Wan. Findings – The study finds that supermarkets outperformed wet markets across all aspects of service quality as measured by SERVQUAL-P. Research limitations/implications – Implications suggest that wet market vendors are not providing the level of service quality demanded by their customers. In particular, findings suggest that wet market vendors need to improve the visual attractiveness of their stalls, work on making them look more professional and start using more modern equipment. Practical implications – Wet market vendors in conjunction with government representatives need to develop standards of service quality for wet markets across Hong Kong. This is imperative if the wet market model is to survive in what is a highly competitive food retailing industry. Without action, it appears that the supermarketization of the Hong Kong food retailing industry will continue unabated. Originality/value – This paper adds to a small but growing research stream examining service quality in the food retailing industry in Hong Kong. It provides empirical results that guide suggested actions for change.

Automatic tracking, super-resolution and recognition of human faces from surveillance video

Identifying an individual from surveillance video is a difficult, time consuming and labour intensive process. The proposed system aims to streamline this process by filtering out unwanted scenes and enhancing an individual's face through super-resolution. An automatic face recognition system is then used to identify the subject or present the human operator with likely matches from a database. A person tracker is used to speed up the subject detection and super-resolution process by tracking moving subjects and cropping a region of interest around the subject's face to reduce the number and size of the image frames to be super-resolved respectively. In this paper, experiments have been conducted to demonstrate how the optical flow super-resolution method used improves surveillance imagery for visual inspection as well as automatic face recognition on an Eigenface and Elastic Bunch Graph Matching system. The optical flow based method has also been benchmarked against the ``hallucination'' algorithm, interpolation methods and the original low-resolution images. Results show that both super-resolution algorithms improved recognition rates significantly. Although the hallucination method resulted in slightly higher recognition rates, the optical flow method produced less artifacts and more visually correct images suitable for human consumption.