Windowed-Wigner Representations, Interferences and Operators

2010 Mathematics Subject Classification: 42B10, 47A07, 35S05.

Representation and parameterisation issues in genetic algorithms

A multi-chromosome GA (Multi-GA) was developed, based upon concepts from the natural world, allowing improved flexibility in a number of areas including representation, genetic operators, their parameter rates and real world multi-dimensional applications. A series of experiments were conducted, comparing the performance of the Multi-GA to a traditional GA on a number of recognised and increasingly complex test optimisation surfaces, with promising results. Further experiments demonstrated the Multi-GA's flexibility through the use of non-binary chromosome representations and its applicability to dynamic parameterisation. A number of alternative and new methods of dynamic parameterisation were investigated, in addition to a new non-binary 'Quotient crossover' mechanism. Finally, the Multi-GA was applied to two real world problems, demonstrating its ability to handle mixed type chromosomes within an individual, the limited use of a chromosome level fitness function, the introduction of new genetic operators for structural self-adaptation and its viability as a serious real world analysis tool. The first problem involved optimum placement of computers within a building, allowing the Multi-GA to use multiple chromosomes with different type representations and different operators in a single individual. The second problem, commonly associated with Geographical Information Systems (GIS), required a spatial analysis location of the optimum number and distribution of retail sites over two different population grids. In applying the Multi-GA, two new genetic operators (addition and deletion) were developed and explored, resulting in the definition of a mechanism for self-modification of genetic material within the Multi-GA structure and a study of this behaviour.

Positive-P and Wigner representations for quantum-optical systems with nonorthogonal modes

We generalize the basic concepts of the positive-P and Wigner representations to unstable quantum-optical systems that are based on nonorthogonal quasimodes. This lays the foundation for a quantum description of such systems, such as, for example an unstable cavity laser. We compare both representations by calculating the tunneling times for an unstable resonator optical parametric oscillator.

Explicit description of generic representations for quivers of type An or Dn

We describe explicitly a generic representation for Dynkin quivers of type An or Dn for any dimension vector.

On representations of finite type

Representations of the (infinite) canonical anticommutation relations and the associated operator algebra, the fermion algebra, are studied. A “coupling constant” (in (0,1]) is defined for primary states of “finite type” of that algebra. Primary, faithful states of finite type with arbitrary coupling are constructed and classified. Their physical significance for quantum thermodynamical systems at high temperatures is discussed. The scope of this study is broadened to include a large class of operator algebras sharing some of the structural properties of the fermion algebra.

Integral Representations of Generalized Mathieu Series Via Mittag-Leffler Type Functions

Mathematics Subject Classification: 33C05, 33C10, 33C20, 33C60, 33E12, 33E20, 40A30

Advancing Bag-of-visual-words Representations For Lesion Classification In Retinal Images.

Diabetic Retinopathy (DR) is a complication of diabetes that can lead to blindness if not readily discovered. Automated screening algorithms have the potential to improve identification of patients who need further medical attention. However, the identification of lesions must be accurate to be useful for clinical application. The bag-of-visual-words (BoVW) algorithm employs a maximum-margin classifier in a flexible framework that is able to detect the most common DR-related lesions such as microaneurysms, cotton-wool spots and hard exudates. BoVW allows to bypass the need for pre- and post-processing of the retinographic images, as well as the need of specific ad hoc techniques for identification of each type of lesion. An extensive evaluation of the BoVW model, using three large retinograph datasets (DR1, DR2 and Messidor) with different resolution and collected by different healthcare personnel, was performed. The results demonstrate that the BoVW classification approach can identify different lesions within an image without having to utilize different algorithms for each lesion reducing processing time and providing a more flexible diagnostic system. Our BoVW scheme is based on sparse low-level feature detection with a Speeded-Up Robust Features (SURF) local descriptor, and mid-level features based on semi-soft coding with max pooling. The best BoVW representation for retinal image classification was an area under the receiver operating characteristic curve (AUC-ROC) of 97.8% (exudates) and 93.5% (red lesions), applying a cross-dataset validation protocol. To assess the accuracy for detecting cases that require referral within one year, the sparse extraction technique associated with semi-soft coding and max pooling obtained an AUC of 94.2 ± 2.0%, outperforming current methods. Those results indicate that, for retinal image classification tasks in clinical practice, BoVW is equal and, in some instances, surpasses results obtained using dense detection (widely believed to be the best choice in many vision problems) for the low-level descriptors.

Quantum symmetries and the Weyl–Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.

Group theory and quasiprobability integrals of Wigner functions

The integral of the Wigner function of a quantum-mechanical system over a region or its boundary in the classical phase plane, is called a quasiprobability integral. Unlike a true probability integral, its value may lie outside the interval [0, 1]. It is characterized by a corresponding selfadjoint operator, to be called a region or contour operator as appropriate, which is determined by the characteristic function of that region or contour. The spectral problem is studied for commuting families of region and contour operators associated with concentric discs and circles of given radius a. Their respective eigenvalues are determined as functions of a, in terms of the Gauss-Laguerre polynomials. These polynomials provide a basis of vectors in a Hilbert space carrying the positive discrete series representation of the algebra su(1, 1) approximate to so(2, 1). The explicit relation between the spectra of operators associated with discs and circles with proportional radii, is given in terms of the discrete variable Meixner polynomials.

Transforming scientific information with everyday thinking: A social representations perspective

Cette thèse examine la circulation et l'intégration des informations scientifiques dans la pensée quotidienne d'après la théorie des représentations sociales (TRS). En tant qu'alternative aux approches traditionnelles de la communication de la science, les transformations survenant entre le discours scientifique et le discours de sens commun sont considérées comme adaptatives. Deux études sur la circulation des informations dans les media (études 1 et 2) montrent des variations dans les thèmes de discours exposés aux profanes, et parmi les discours de ceux-ci, en fonction de différentes sources. Ensuite, le processus d'ancrage dans le positionnement préalable envers la science est étudié, pour l'explication qu'il fournit de la réception et de la transmission d'informations scientifiques dans le sens commun. Les effets d'ancrage dans les attitudes et croyances préexistants sont reportés dans différents contextes de circulation des informations scientifiques (études 3 à 7), incluant des études de type corrélationnel, experimental et de terrain. Globalement, cette thèse procure des arguments en faveur de la pertinence de la TRS pour la recherche sur la communication de la science, et suggère des développements théoriques et méthodologiques pour ces deux domaines de recherche. Drawing on the social representations theory (SRT), this thesis examines the circulation and integration of scientific information into everyday thinking. As an alternative to the traditional approaches of science communication, it considers transformations between scientific and common-sense discourses as adaptive. Two studies, focused on the spreading of information into the media (Studies 1 and 2), show variations in the themes of discourses introduced to laypersons and in the themes among laypersons' discourses, according to different sources. Anchoring in prior positioning toward science is then studied for the explanation it provides on the reception and transmission of scientific information into common sense. Anchoring effects in prior attitudes and beliefs are reported in different contexts of circulation of scientific information (Studies 3 to 7) by using results from correlational, field, and experimental studies. Overall, this thesis provides arguments for the relevance of SRT in science communication research and suggests theoretical and methodological developments for both domains of research.

Dynamical systems of type (m,n) and their C*-algebras

Given positive integers n and m, we consider dynamical systems in which n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra we denote by Om;n, which in turn is obtained as a quotient of the well known Leavitt C*-algebra Lm;n, a process meant to transform the generating set of partial isometries of Lm;n into a tame set. Describing Om;n as the crossed-product of the universal (m; n) -dynamical system by a partial action of the free group Fm+n, we show that Om;n is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed-product, denoted Or m;n, is shown to be exact and non-nuclear. Still under the assumption that m; n &= 2, we prove that the partial action of Fm+n is topologically free and that Or m;n satisfies property (SP) (small projections). We also show that Or m;n admits no finite dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.

Petrou type-D perfect-fluid solutions in generalized Kerr-Schild form.

Generalized KerrSchild space-times for a perfect-fluid source are investigated. New Petrov type D perfect fluid solutions are obtained starting from conformally flat perfect-fluid metrics.

The emergence of parental and paternity leaves in Switzerland : a challenge to gendered representations and practices of parenthood?

The thesis addresses the issue of parenthood and gender equality in Switzerland through the emergence of parental leave policies. This is an original and relevant research topic, as Switzerland is one of the few industrialized countries that have not yet implemented a parental or paternity leave. I first describe the emergence of parental leave policies in the last ten to fifteen years in the political, media, and labor-market spheres. Secondly, adopting a gender and discursive theoretical approach, I analyze whether and to what extent this emergence challenged gendered representations and practices of parenthood. The multilevel and mixed-methods research design implies analyzing various data sets such as parliamentary interventions (N=23J and newspaper articles (N=579) on parental leave policies. A case study of a public administration which implemented a one-month paid paternity leave draws on register data of leave recipients (N=95) and in-depth interviews with fathers and managers (n=30). Results show that parental leave policies, especially in recent years, have been increasingly problematized in the three social spheres considered, as a result of political and institutional events. While there is a struggle over the definition of the legitimate leave type to implement [parental or paternity leave) in the political sphere, paternity leave has precedence in the media and labor-market spheres. Overall, this emergence contributes to making fatherhood visible in the public sphere, challenging albeit in a limited way gendered representations and practices of parenthood. Along with representations of involved fatherhood and change in gender relations, different roles and responsibilities are attributed to mothers and fathers, the latter being often defined as secondary, temporary and optional parents. Finally, I identify a common trend, namely the increasing importance of the economic aspects of parental leave policies with the consequence of sidelining their gender-equality potential. The dissertation contributes to the literature which analyzes the interconnections between the macro-, the meso- and the micro-levels of society in the constitution of gender relations and parenthood. It also provides useful tools for the analysis of the politics of parental leave policies in Switzerland and their effects for gender equality. - Cette thèse traite de la parentalité et de l'égalité de genre en Suisse à travers l'émergence des congés parentaux. Ce sujet de recherche est original et pertinent puisque la Suisse est à ce jour un des seuls pays industrialisés à ne pas avoir adopté de droit au congé parental ou paternité. Cette recherche décrit l'émergence des congés parentaux au cours des 10 à 15 dernières années dans les sphères politique, médiatique et du marché de l'emploi en Suisse. En combinant perspective de genre et analyse de discours, elle examine dans quelle mesure cette émergence remet en question les représentations et pratiques genrées de parentalité. Des méthodes de recherche mixtes sont employées pour analyser des interventions parlementaires (N=23) et des articles de presse (N=579) sur les congés parentaux. L'étude de cas d une entreprise publique qui a adopté un congé paternité payé d'un mois s'appuie sur des données de registre (N=95) et des entretiens semi-structurés avec des pères et des cadres (n=30). Les résultats indiquent que dans les trois sphères considérées, les congés parentaux ont reçu une attention croissante au cours de ces dernières années, en lien avec des événements politiques et institutionnels. Alors que dans la sphère politique il n'y a pas de consensus quant au type de congé considéré comme légitime (congé parental ou paternité), dans les sphères médiatique et du marché de l'emploi le congé paternité semble l'emporter. Dans l'ensemble, l'émergence des congés parentaux contribue à rendre la paternité plus visible dans l'espace public, remettant en question-bien que d'une manière limitée-les représentations genrées de la parentalité. En effet, d'une part l'image de pères impliqués et de rapports de genre plus égalitaires au sein de la famille est diffusée. D'autre part, mères et pères continuent à être associés à des rôles différents, les pères étant définis comme des parents secondaires et temporaires. Finalement, l'analyse révèle une tendance générale, soit l'importance croissante accordée aux aspects économiques des congés parentaux, avec pour conséquence la mise à l'écart de leur potentiel pour l'égalité de genre. Cette thèse contribue à la recherche sur les liens entre les niveaux macro- meso- et microsociaux dans la constitution des rapports de genre et de la parentalité. Elle propose également des outils pour analyser les politiques de congés parentaux en Suisse et leurs implications pour l'égalité de genre.

Wigner higher-order spectra: definition, properties, computation and application to transient signal analysis

The Wigner higher order moment spectra (WHOS)are defined as extensions of the Wigner-Ville distribution (WD)to higher order moment spectra domains. A general class oftime-frequency higher order moment spectra is also defined interms of arbitrary higher order moments of the signal as generalizations of the Cohen’s general class of time-frequency representations. The properties of the general class of time-frequency higher order moment spectra can be related to theproperties of WHOS which are, in fact, extensions of the properties of the WD. Discrete time and frequency Wigner higherorder moment spectra (DTF-WHOS) distributions are introduced for signal processing applications and are shown to beimplemented with two FFT-based algorithms. One applicationis presented where the Wigner bispectrum (WB), which is aWHOS in the third-order moment domain, is utilized for thedetection of transient signals embedded in noise. The WB iscompared with the WD in terms of simulation examples andanalysis of real sonar data. It is shown that better detectionschemes can be derived, in low signal-to-noise ratio, when theWB is applied.

A Type-Preserving Compiler from System F to Typed Assembly Language

L'utilisation des méthodes formelles est de plus en plus courante dans le développement logiciel, et les systèmes de types sont la méthode formelle qui a le plus de succès. L'avancement des méthodes formelles présente de nouveaux défis, ainsi que de nouvelles opportunités. L'un des défis est d'assurer qu'un compilateur préserve la sémantique des programmes, de sorte que les propriétés que l'on garantit à propos de son code source s'appliquent également au code exécutable. Cette thèse présente un compilateur qui traduit un langage fonctionnel d'ordre supérieur avec polymorphisme vers un langage assembleur typé, dont la propriété principale est que la préservation des types est vérifiée de manière automatisée, à l'aide d'annotations de types sur le code du compilateur. Notre compilateur implante les transformations de code essentielles pour un langage fonctionnel d'ordre supérieur, nommément une conversion CPS, une conversion des fermetures et une génération de code. Nous présentons les détails des représentation fortement typées des langages intermédiaires, et les contraintes qu'elles imposent sur l'implantation des transformations de code. Notre objectif est de garantir la préservation des types avec un minimum d'annotations, et sans compromettre les qualités générales de modularité et de lisibilité du code du compilateur. Cet objectif est atteint en grande partie dans le traitement des fonctionnalités de base du langage (les «types simples»), contrairement au traitement du polymorphisme qui demande encore un travail substantiel pour satisfaire la vérification de type.