A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. Johannesburg, 2015. / The AdS/CFT correspondence asserts a duality between non-Abelian gauge theories and quantum theories of gravity, established by the value of the gauge coupling . Gerard t'Hooft found that the large N0 limit in non-Abelian Yang-Mills gauge theories results in a planar diagram simpli cation of the topological expansion. In this dissertation, SU(2) gauge theories are written in terms of vector models (making use of collective eld theory to obtain an expression for the Jacobian), a saddle point analysis is performed, and the large N limit taken. Initially this procedure is done for gauge theories dimensionally reduced on T4 and R T3, and then attempted for the full eld theory (without dimensional reduction). In each case this results in an expression for the non-perturbative propagator. A nite volume must be imposed to obtain a gap equation for the full eld theory; directives for possible solutions to this di culty are discussed.

A dissertation submitted in ful llment of the requirements for the degree of Master of Science in the School of Computer Science and Applied Mathematics Faculty of Science August 15, 2017 / Facial expression recognition is one of the most common means of communication used for complementing spoken word. However, people have grown to master ways of ex- hibiting deceptive expressions. Hence, it is imperative to understand di erences in expressions mostly for security purposes among others. Traditional methods employ machine learning techniques in di erentiating real and fake expressions. However, this approach does not always work as human subjects can easily mimic real expressions with a bit of practice. This study presents an approach that evaluates the time related dis- tance that exists between eye actions and an exhibited expression. The approach gives insights on some of the most fundamental characteristics of expressions. The study fo- cuses on nding and understanding the temporal relationship that exists between eye blinks and smiles. It further looks at the relationship that exits between eye closure and pain expressions. The study incorporates active appearance models (AAM) for feature extraction and support vector machines (SVM) for classi cation. It tests extreme learn- ing machines (ELM) in both smile and pain studies, which in turn, attains excellent results than predominant algorithms like the SVM. The study shows that eye blinks are highly correlated with the beginning of a smile in posed smiles while eye blinks are highly correlated with the end of a smile in spontaneous smiles. A high correlation is observed between eye closure and pain in spontaneous pain expressions. Furthermore, this study brings about ideas that lead to potential applications such as lie detection systems, robust health care monitoring systems and enhanced animation design systems among others. / MT 2018

Este trabalho consiste em um estudo sobre a propriedade de hipoeliticidade global para campos vetoriais complexos não singulares no plano. As órbitas de Sussmann de um tal campo desempenham um papel fundamental nesta análise. Mostramos que se todas as órbitas são unidimensionais o campo não é globalmente hipoelítico. Quando o campo apresenta uma órbita bidimensional e ao menos uma órbita unidimensional mergulhada também foi demonstrado que este campo não é globalmente hipoelítico. No caso em que o plano é a única órbita, define-se, como em Hounie (1982), uma determinada relação de equivalência entre pontos em que o campo deixa de ser elítico. As classes de equivalência desta relação são homeomorfas a um ponto, a um intervalo compacto ou a uma semirreta. Se todas as classes de equivalência são compactas, o campo é globalmente hipoelítico. Caso haja uma classe de equivalência fechada e homeomorfa a uma semirreta, o campo não é globalmente hipoelítico. / This work is a study about global hypoellipticity for nonsingular complex vector fields in the plane. Sussmanns orbits play a fundamental role in this analysis. We show that if all the orbits are one-dimensional then the vector field is not globally hypoelliptic. When there exist a two-dimensional orbit and an embedded one-dimensional one then the vector field is not globally hypoelliptic. In the case when the plane is the only orbit, one defines, as in Hounie (1982), a certain equivalence relation between points where the vector field is not elliptic. The equivalence classes are homeomorphic to a single point, a compact interval or a ray. If all the equivalence classes are compact then the vector field is globally hypoelliptic. If there exists an equivalence class that is closed and homeomorphic to a ray then the vector field is not globally hypoelliptic.

Seja M um conjunto compacto e conexo do plano que seja a união dos subconjuntos conexos N e S. Seja Z_L=(X_L,Y_L) uma família a um parâmetro de campos vetoriais descontínuos, onde X_L está definida em N e Y_L em S. Ambos os campos X_L e Y_L, assim como as suas dependências em L, são suaves i. e. de classe C^\\infty; a descontinuidade acontece na fronteira comum entre N e S. O objetivo deste trabalho é estudar as bifurcações que ocorrem em certas famílias de campos vetoriais descontínuos seguindo as convenções de Filippov. Aplicando o método da regularização, introduzido por Sotomayor e Teixeira e posteriormente aprofundado por Sotomayor e Machado à família de campos vetoriais descontínuos Z_L obtemos uma família de campos vetoriais suaves que é próxima da família descontínua original. Usamos esta técnica de regularização para estudar, por comparação com os resultados clássicos da teoria suave, as bifurcações que ocorrem nas famílias de campos vetoriais descontínuos. Na literatura há uma lista de bifurcações de codimensão um, no contexto de Filippov, apresentada mais completamente, no artigo de Yu. A. Kuznetsov, A. Gragnani e S. Rinaldi, One-Parameter Bifurcations in Planar Filippov Systems, Int. Journal of Bifurcation and Chaos, vol. 13, No. 8: 2157--2188, (2003). Alguns dos casos dessa lista já eram conhecidos por Kozlova, Filippov e Machado. Neste trabalho nos propomos a estudar as bifurcações de alguns dos casos, apresentados no artigo de Kuznetsov et. al, através do método da regularização dessas famílias. Nesta Tese consubstanciamos matematicamente a seguinte conclusão: As bifurcações das famílias descontínuas analisadas ficam completamente conhecidas através das bifurcações apresentadas pelas respectivas famílias regularizadas, usando recursos da teoria clássica suave. / Let M be a connected and compact set of the plane which is the union of the connected subsets N and S. Let Z_L=(X_L,Y_L) be a one-parameter family of discontinuous vector fields, where X_L is defined on N and Y_L on S. The two fields X_L, Y_L and their dependences on L are smooths, i. e., are of C^\\infty class; the discontinuity happens in the common boundary of N and S. The objective of this work is to study the bifurcations which occurs in certains families of discontinuous vector fields following the conventions of Filippov. Applying the regularization method, introduced by Sotomayor and Teixeira, to the family of discontinuous vector fields Z_L we obtain a family of regular vector fields which is close to the original family of discontinuous vector fields. In the literature there is a list of codimension one bifurcation, in the Filippov sense, presented more completely, in the article of Yu. A. Kuznetsov, A. Gragnani e S. Rinaldi, One-Parameter Bifurcations in Planar Filippov Systems, Int. Journal of Bifurcation and Chaos, vol. 13, No. 8: 2157--2188, (2003). Some of those cases was already known by Kozlova, Filippov and Machado. In this work we propose to study the bifurcations of some of those cases, presented in the article of Kuznetsov et. al, by the method of regularization of those families. In this thesis we justify mathematically the following conclusion: The bifurcations of the analysed discontinuous families are completelly known by the bifurcations contained in the respective regularized families, using the methods of the classical theory of regular vector fields.

Seja M um conjunto compacto e conexo do plano que seja a união dos subconjuntos conexos N e S. Seja Z_L=(X_L,Y_L) uma família a um parâmetro de campos vetoriais descontínuos, onde X_L está definida em N e Y_L em S. Ambos os campos X_L e Y_L, assim como as suas dependências em L, são suaves i. e. de classe C^\\infty; a descontinuidade acontece na fronteira comum entre N e S. O objetivo deste trabalho é estudar as bifurcações que ocorrem em certas famílias de campos vetoriais descontínuos seguindo as convenções de Filippov. Aplicando o método da regularização, introduzido por Sotomayor e Teixeira e posteriormente aprofundado por Sotomayor e Machado à família de campos vetoriais descontínuos Z_L obtemos uma família de campos vetoriais suaves que é próxima da família descontínua original. Usamos esta técnica de regularização para estudar, por comparação com os resultados clássicos da teoria suave, as bifurcações que ocorrem nas famílias de campos vetoriais descontínuos. Na literatura há uma lista de bifurcações de codimensão um, no contexto de Filippov, apresentada mais completamente, no artigo de Yu. A. Kuznetsov, A. Gragnani e S. Rinaldi, One-Parameter Bifurcations in Planar Filippov Systems, Int. Journal of Bifurcation and Chaos, vol. 13, No. 8: 2157--2188, (2003). Alguns dos casos dessa lista já eram conhecidos por Kozlova, Filippov e Machado. Neste trabalho nos propomos a estudar as bifurcações de alguns dos casos, apresentados no artigo de Kuznetsov et. al, através do método da regularização dessas famílias. Nesta Tese consubstanciamos matematicamente a seguinte conclusão: As bifurcações das famílias descontínuas analisadas ficam completamente conhecidas através das bifurcações apresentadas pelas respectivas famílias regularizadas, usando recursos da teoria clássica suave. / Let M be a connected and compact set of the plane which is the union of the connected subsets N and S. Let Z_L=(X_L,Y_L) be a one-parameter family of discontinuous vector fields, where X_L is defined on N and Y_L on S. The two fields X_L, Y_L and their dependences on L are smooths, i. e., are of C^\\infty class; the discontinuity happens in the common boundary of N and S. The objective of this work is to study the bifurcations which occurs in certains families of discontinuous vector fields following the conventions of Filippov. Applying the regularization method, introduced by Sotomayor and Teixeira, to the family of discontinuous vector fields Z_L we obtain a family of regular vector fields which is close to the original family of discontinuous vector fields. In the literature there is a list of codimension one bifurcation, in the Filippov sense, presented more completely, in the article of Yu. A. Kuznetsov, A. Gragnani e S. Rinaldi, One-Parameter Bifurcations in Planar Filippov Systems, Int. Journal of Bifurcation and Chaos, vol. 13, No. 8: 2157--2188, (2003). Some of those cases was already known by Kozlova, Filippov and Machado. In this work we propose to study the bifurcations of some of those cases, presented in the article of Kuznetsov et. al, by the method of regularization of those families. In this thesis we justify mathematically the following conclusion: The bifurcations of the analysed discontinuous families are completelly known by the bifurcations contained in the respective regularized families, using the methods of the classical theory of regular vector fields.

Este trabalho consiste em um estudo sobre a propriedade de hipoeliticidade global para campos vetoriais complexos não singulares no plano. As órbitas de Sussmann de um tal campo desempenham um papel fundamental nesta análise. Mostramos que se todas as órbitas são unidimensionais o campo não é globalmente hipoelítico. Quando o campo apresenta uma órbita bidimensional e ao menos uma órbita unidimensional mergulhada também foi demonstrado que este campo não é globalmente hipoelítico. No caso em que o plano é a única órbita, define-se, como em Hounie (1982), uma determinada relação de equivalência entre pontos em que o campo deixa de ser elítico. As classes de equivalência desta relação são homeomorfas a um ponto, a um intervalo compacto ou a uma semirreta. Se todas as classes de equivalência são compactas, o campo é globalmente hipoelítico. Caso haja uma classe de equivalência fechada e homeomorfa a uma semirreta, o campo não é globalmente hipoelítico. / This work is a study about global hypoellipticity for nonsingular complex vector fields in the plane. Sussmanns orbits play a fundamental role in this analysis. We show that if all the orbits are one-dimensional then the vector field is not globally hypoelliptic. When there exist a two-dimensional orbit and an embedded one-dimensional one then the vector field is not globally hypoelliptic. In the case when the plane is the only orbit, one defines, as in Hounie (1982), a certain equivalence relation between points where the vector field is not elliptic. The equivalence classes are homeomorphic to a single point, a compact interval or a ray. If all the equivalence classes are compact then the vector field is globally hypoelliptic. If there exists an equivalence class that is closed and homeomorphic to a ray then the vector field is not globally hypoelliptic.

A study is presented on the production of vector boson (W and Z0) events in association with recoiling hadronic activity in the form of hadronic jets, using proton-proton collisions at the LHC. The dataset was taken by the ATLAS detector during the 2011 data-taking run, at a centre of mass energy p s = 7 TeV, and corresponds to an integrated luminosity of 4.6 fb 1. A measurement of the cross-section ratio of W+jets Z+jets events is de ned, reducing the large systematic uncertainties inherent in the experimental measurement of such events. Inclusive and di erential cross-sections are presented for W+jets Z+jets , as a function of a range of kinematic variables, and are compared to state-of- the-art theoretical predictions.

As technology scaling slows down in the nanometer CMOS regime and mobile computing becomes more ubiquitous, designing energy-efficient hardware for mobile systems is becoming increasingly critical and challenging. Although various approaches like near-threshold computing (NTC), aggressive voltage scaling with shadow latches, etc. have been proposed to get the most out of limited battery life, there is still no “silver bullet” to increasing power-performance demands of the mobile systems. Moreover, given that a mobile system could operate in a variety of environmental conditions, like different temperatures, have varying performance requirements, etc., there is a growing need for designing tunable/reconfigurable systems in order to achieve energy-efficient operation. In this work we propose to address the energy- efficiency problem of mobile systems using two different approaches: circuit tunability and distributed adaptive algorithms. Inspired by the communication systems, we developed feedback equalization based digital logic that changes the threshold of its gates based on the input pattern. We showed that feedback equalization in static complementary CMOS logic enabled up to 20% reduction in energy dissipation while maintaining the performance metrics. We also achieved 30% reduction in energy dissipation for pass-transistor digital logic (PTL) with equalization while maintaining performance. In addition, we proposed a mechanism that leverages feedback equalization techniques to achieve near optimal operation of static complementary CMOS logic blocks over the entire voltage range from near threshold supply voltage to nominal supply voltage. Using energy-delay product (EDP) as a metric we analyzed the use of the feedback equalizer as part of various sequential computational blocks. Our analysis shows that for near-threshold voltage operation, when equalization was used, we can improve the operating frequency by up to 30%, while the energy increase was less than 15%, with an overall EDP reduction of ≈10%. We also observe an EDP reduction of close to 5% across entire above-threshold voltage range. On the distributed adaptive algorithm front, we explored energy-efficient hardware implementation of machine learning algorithms. We proposed an adaptive classifier that leverages the wide variability in data complexity to enable energy-efficient data classification operations for mobile systems. Our approach takes advantage of varying classification hardness across data to dynamically allocate resources and improve energy efficiency. On average, our adaptive classifier is ≈100× more energy efficient but has ≈1% higher error rate than a complex radial basis function classifier and is ≈10× less energy efficient but has ≈40% lower error rate than a simple linear classifier across a wide range of classification data sets. We also developed a field of groves (FoG) implementation of random forests (RF) that achieves an accuracy comparable to Convolutional Neural Networks (CNN) and Support Vector Machines (SVM) under tight energy budgets. The FoG architecture takes advantage of the fact that in random forests a small portion of the weak classifiers (decision trees) might be sufficient to achieve high statistical performance. By dividing the random forest into smaller forests (Groves), and conditionally executing the rest of the forest, FoG is able to achieve much higher energy efficiency levels for comparable error rates. We also take advantage of the distributed nature of the FoG to achieve high level of parallelism. Our evaluation shows that at maximum achievable accuracies FoG consumes ≈1.48×, ≈24×, ≈2.5×, and ≈34.7× lower energy per classification compared to conventional RF, SVM-RBF , Multi-Layer Perceptron Network (MLP), and CNN, respectively. FoG is 6.5× less energy efficient than SVM-LR, but achieves 18% higher accuracy on average across all considered datasets.

Les vecteurs lentiviraux (LV) sont des outils efficaces de transfert de gène, largement utilisés en thérapie génique, en particulier pour la transduction ex vivo de cellules souches et progénitrices hématopoïétiques (CSPH). Afin d’étudier simultanément la fusion et la transduction dans les CSPH avec les LV, nous avons adapté une méthode basée sur latechnologie du transfert d’énergie entre deux molécules fluorescentes (FRET). Pour mettre en place cette technique, des LV capables d’incorporer spécifiquement une enzyme, la bétalactamase (BLAM-LV) et de coder une forme tronquée du récepteur au facteur de croissance nerveuse (DELTA-NGFR), sont produits. Nos résultats montrent que les LV sont soumis à une restriction post-entrée forte dans les cellules hématopoïétiques, que ce soit dans des lymphocytes T immortalisés ou bien des CSH CD34+. Nous montrons également que cette inhibition post-entrée peut être partiellement saturée après une forte augmentation de la multiplicité d’infection ou en présence d’additifs de culture, comme la Vectofusin-1® ou laRetronectin®. De plus, nous avons montré lors de la transduction de CSPH avec des vecteurs BLAM-LV que la Vectofusin-1® agit sur l’étape d’entrée en augmentant l’adhésion et la fusion entre les membranes virale et cellulaire. Cette technique représente donc un nouvel outil sensible et efficace pour étudier de façon concomitante l’étape de fusion et le niveau de transduction dans les cellules cibles. A terme, ce travail permettra une meilleure compréhension de la biologie des LV mais pourra également conduire à l’élaboration de protocoles de transduction lentivirale plus efficaces. / Lentiviral vectors (LV) are used for various gene transfer applications, notably for hematopoietic gene therapy, but methods are lacking to precisely evaluate parameters that control the efficiency of transduction in relation with the entry of vectors into target cells. We adapted a fluorescence resonance energy transfer (FRET)-based HIV-1 fusion assay to measure the entry of non-replicative recombinant LV in various cell types, including primary human hematopoietic stem and progenitor cells, and to quantify the level of transduction of he same initially-infected cells. The assay utilizes recombinant LV containing betalactamase (BLAM)-Vpr chimeric proteins (BLAM-LV) and encoding a truncated form of thelow affinity nerve growth factor receptor (DELTA-NGFR). This LV-based fusion/transduction assay is a dynamic and versatile tool, revealing for instance the extent of lentiviral post-entry restrictions occuring in cells of hematopoietic origin. The assay also shows that transduction enhancers like Vectofusin®-1 or Retronectin® can partially relieve this post-entry block but their effects differ in the way to promote LV entry. Furthermore, our results show that Vectofusin®-1 acts at the entry step by promoting the adhesion and the fusion between lentiviral and cellular membranes. In conclusion, one such assay should be useful to study hematopoietic post-entry restrictions directed against LV and should allow improvements in various LV-based gene therapy protocols.

Made available in DSpace on 2014-06-12T17:39:31Z (GMT). No. of bitstreams: 2 arquivo519_1.pdf: 8081494 bytes, checksum: ba2427869f3a7c683fd296629937e553 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2010 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Um projeto de inovação tecnológica consiste em uma série de análises e procedimentos que tem como fim estimar o valor de uma tecnologia, ou seja, gerar uma estimativa dos rendimentos futuros que tal empreendimento/tecnologia possa proporcionar. A abordagem tradicional da análise de investimentos para esta categoria de projetos possui uma limitação no que tange a: 1 estimação do valor da tecnologia que exige a incorporação de variáveis qualitativas que não são consideradas por essa modelagem; e 2 a elevada variabilidade das estimativas do fluxo de caixa projetado, em virtude das diferentes categorias de risco inerentes a esse tipo de projeto. A partir desta limitação apresentada no estado da arte da avaliação deste tipo de projeto, esta pesquisa de cunho exploratório pretende utilizar a metodologia de rating como uma alternativa a avaliação de projetos de inovação. Pois um sistema de classificação através de rating possui a flexibilidade necessária para a incorporação de variáveis qualitativas que podem auxiliar na mensuração do valor da tecnologia, bem como fornece uma série de procedimentos que permitem a estimação do risco de tais projetos. Tal aplicação da metodologia de rating gera o Sistema de Classificação de Risco de Projetos de Inovação (SCRP), que a partir de uma amostra de 40 projetos de investimento industrial fornecidos pelo Banco do Nordeste do Brasil, indicadores setoriais, macroeconômicos e tecnológicos, provê uma classificação de viabilidade e risco para tais projetos. As Support Vector Machines, técnica de inteligência artificial com resultados exitosos em várias áreas das finanças, inclusive com ratings é introduzida nesta pesquisa para testar a classificação gerada pelo SCRP. A aplicação do SVM fez uso do código LIBSVM e do Software Matlab. A classificação obtida pelo SCRP apresentou um ajuste médio de 83,6% quando comparado aos 10 melhores projetos classificados pelo critério da TIR e de 87,6% de ajuste médio para com os 8 piores projetos classificados pelo critério do VPL, a classificação obtida através do SVM, apresentou uma acuracia de 37,5% frente aos dados de teste