Maps have been extensively studied and are important in many research fields. A map is a 2-cell embedding of a graph on an orientable surface. Motivated by a new way to read the information provided by the skeleton of a map, we introduce new objects called plane permutations. Plane permutations not only provide new insight into enumeration of maps and related graph embedding problems, but they also provide a powerful framework to study less related genome rearrangement problems. As results, we refine and extend several existing results on enumeration of maps by counting plane permutations filtered by different criteria. In the spirit of the topological, graph theoretical study of graph embeddings, we study the behavior of graph embeddings under local changes. We obtain a local version of the interpolation theorem, local genus distribution as well as an easy-to-check necessary condition for a given embedding to be of minimum genus. Applying the plane permutation paradigm to genome rearrangement problems, we present a unified simple framework to study transposition distances and block-interchange distances of permutations as well as reversal distances of signed permutations. The essential idea is associating a plane permutation to a given permutation or signed permutation to sort, and then applying the developed plane permutation theory. / Ph. D.

Les TBH SiGe sont parmi les composants les plus rapides et sont utilisés pour les applications millimétriques. Des systèmes fonctionnent à 820GHz avec ces composants ont été déjà mis en œuvre. Afin de concevoir des circuits fonctionnant à ces fréquences très élevées, une analyse détaillée du comportement intrinsèque doit être effectuée. L’objectif principal de cette thèse est la caractérisation de la partie intrinsèque de ces composants. Une bonne précision de mesure dans la gamme de fréquences ondes millimétriques représente un vrai challenge, puisque les grandeurs intrinsèques du dispositifs ont beaucoup plus faibles que les données brutes de mesure auxquelles est associée la partie extrinsèque du composant. Afin de corriger la partie extrinsèque, des techniques de de-embedding spécifiques sont mises au point pour obtenir ces caractéristiques intrinsèques réelles. De plus, une technique de calibration directement sur la puce, sans utiliser de calkit, a été élaborée. Ceci permet de s’affranchir des effets de couplage entre la surface du standard de calibrage et les pointes de test hyperfréquences. L’ensemble a été validé par des simulations de type électromagnétique. / SiGe HBTs have proven their capability to support large bandwidth and high data ratesfor high-speed communication systems. Systems operating at 820GHz with these componentshave already been implemented. To design circuits operating at high frequencies, adetailed analysis of the intrinsic behavior should be performed. The main objective of thisthesis is the characterization of the intrinsic part of these components. Good accuracy inthe millimeter wave frequency range represents a real challenge, since the intrinsic deviceparameters are much lower than the raw data measurement that is associated with theextrinsic part of the component. However, existing on-wafer de-embedding techniquesare known to be inadequate to remove completely the parasitic effects and to get thereal intrinsic characteristics. In addition, an on-wafer calibration technique has beendeveloped. This overcomes the effects of coupling between the surface of the standard calibrationand RF probe tips. The set has been validated by an electromagnetic simulation.

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A strong risk culture is critical for any organisation to manage its risks. Recent reports from the Auditor-General about a South African government institution (Auditor General of South Africa, 2014) demonstrated that its risks were not being adequately mitigated. The purpose of the study reported on here has therefore been to put this judgement to the test and, because no recognised instrument could be found to evaluate the risk culture, an instrument was developed. Many of the risk culture assessment frameworks available have been developed by consulting companies which could be of value to organisations however this study chose to focus mainly on academic literature. In this descriptive study we used a focus group to identify the possible strengths and weaknesses of the prevailing risk culture, following which a questionnaire was designed and used to assess the current risk culture of the organisation. The results were used to evaluate the risk culture with the aim of proposing steps in which to embed a risk culture. We found that the existing risk culture does not contribute to this organisation’s capacity to manage its risks. We also found that managers in this organisation are not encouraged to take risks to achieve their objectives and employees are not held accountable for the management of risks. In agreement with previous studies which found that training in risk management is important, this study suggests that training should be compulsory for all senior management. This study also found that factors of tone at the top, accountability, communication, risk competence and risk capacity are critical to embed a risk culture in an organisation. This study contributes to the existing literature by suggesting ways in which a risk culture could be embedded in an organisation. The results of this research could be useful to organisations, boards, and risk committees.

A strong risk culture is critical for any organisation to manage its risks. Recent reports from the Auditor-General about a South African government institution (Auditor General of South Africa, 2014) demonstrated that its risks were not being adequately mitigated. The purpose of the study reported on here has therefore been to put this judgement to the test and, because no recognised instrument could be found to evaluate the risk culture, an instrument was developed. Many of the risk culture assessment frameworks available have been developed by consulting companies which could be of value to organisations however this study chose to focus mainly on academic literature. In this descriptive study we used a focus group to identify the possible strengths and weaknesses of the prevailing risk culture, following which a questionnaire was designed and used to assess the current risk culture of the organisation. The results were used to evaluate the risk culture with the aim of proposing steps in which to embed a risk culture. We found that the existing risk culture does not contribute to this organisation’s capacity to manage its risks. We also found that managers in this organisation are not encouraged to take risks to achieve their objectives and employees are not held accountable for the management of risks. In agreement with previous studies which found that training in risk management is important, this study suggests that training should be compulsory for all senior management. This study also found that factors of tone at the top, accountability, communication, risk competence and risk capacity are critical to embed a risk culture in an organisation. This study contributes to the existing literature by suggesting ways in which a risk culture could be embedded in an organisation. The results of this research could be useful to organisations, boards, and risk committees.

The objective of the proposed research is to design, fabricate, characterize and test silicon-embedded magnetic components for on-chip integrated power applications. Driven by the trend towards continued system multi-functionality and miniaturization, MEMS technology can be used to enable fabrication of three-dimensional (3-D) functional devices into the silicon bulk, taking advantage of the 'dead volume' in the substrate and achieving a greater level of miniaturization and integration. As an example, one of the challenges in realizing ultra-compact high-frequency power converters lies in the integration of magnetic components due to their relatively large volume. Embedding 3-D magnetic components within the wafer volume and implementing high-power, through-wafer interconnect for connection to circuitry on the wafer surface is a promising solution for achieving ultra-compact power converters, in which digital control circuitry and power switches are located on the wafer surface, and suitable magnetic components are embedded within the silicon substrate. In order to do this, key tasks in the following areas have been accomplished: development of new fabrication technologies for silicon embedding and 3-D structure realization; creation of high-current, through-wafer interconnects for connection of the device to circuitry; ability to incorporate a variety of magnetic materials when performance enhancement of the device is needed; exploration of a new design space for the devices due to ultra-compactness and silicon interaction; understanding of the complicated loss mechanisms in the embedded devices; and demonstration of device performance and in-circuit operation.

Dois problemas combinatórios são estudados: (i) determinar a quantidade de cópias de um hipergrafo fixo em um hipergrafo uniforme pseudoaleatório, e (ii) estimar números de Ramsey de ordem dois e três para grafos com largura de banda pequena e grau máximo limitado. Apresentamos um lema de contagem para estimar a quantidade de cópias de um hipergrafo k-uniforme linear livre de conectores (conector é uma generalização de triângulo, para hipergrafos) que estão presentes em um hipergrafo esparso pseudoaleatório G. Considere um hipergrafo k-uniforme linear H que é livre de conectores e um hipergrafo k-uniforme G com n vértices. Seja d_H=\\max\\{\\delta(J): J\\subset H\\} e D_H=\\min\\{k d_H,\\Delta(H)\\}. Estabelecemos que, se os vértices de G não possuem grau grande, famílias pequenas de conjuntos de k-1 elementos de V(G) não possuem vizinhança comum grande, e a maioria dos pares de conjuntos em {V(G)\\choose k-1} possuem a quantidade ``correta\'\' de vizinhos, então a quantidade de imersões de H em G é (1+o(1))n^{|V(H)|}p^{|E(H)|}, desde que p\\gg n^{1/D_H} e |E(G)|={n\\choose k}p. Isso generaliza um resultado de Kohayakawa, Rödl e Sissokho [Embedding graphs with bounded degree in sparse pseudo\\-random graphs, Israel J. Math. 139 (2004), 93--137], que provaram que, para p dado como acima, esse lema de imersão vale para grafos, onde H é um grafo livre de triângulos. Determinamos assintoticamente os números de Ramsey de ordem dois e três para grafos bipartidos com largura de banda pequena e grau máximo limitado. Mais especificamente, determinamos assintoticamente o número de Ramsey de ordem dois para grafos bipartidos com largura de banda pequena e grau máximo limitado, e o número de Ramsey de ordem três para tais grafos, com a suposição adicional de que ambas as classes do grafo bipartido têm aproximadamente o mesmo tamanho. / Two combinatorial problems are studied: (i) determining the number of copies of a fixed hipergraph in uniform pseudorandom hypergraphs, and (ii) estimating the two and three color Ramsey numbers for graphs with small bandwidth and bounded maximum degree. We give a counting lemma for the number of copies of linear k-uniform \\emph hypergraphs (connector is a generalization of triangle for hypergraphs) that are contained in some sparse hypergraphs G. Let H be a linear k-uniform connector-free hypergraph and let G be a k-uniform hypergraph with n vertices. Set d_H=\\max\\{\\delta(J)\\colon J\\subset H\\} and D_H=\\min\\{kd_H,\\Delta(H)\\}. We proved that if the vertices of G do not have large degree, small families of (k-1)-element sets of V(G) do not have large common neighbourhood and most of the pairs of sets in {V(G)\\choose k-1} have the `right\' number of common neighbours, then the number of embeddings of H in G is (1+o(1))n^p^, given that p\\gg n^ and |E(G)|=p. This generalizes a result by Kohayakawa, R\\\"odl and Sissokho [Embedding graphs with bounded degree in sparse pseudo\\-random graphs, Israel J. Math. 139 (2004), 93--137], who proved that, for p as above, this result holds for graphs, where H is a triangle-free graph. We determine asymptotically the two and three Ramsey numbers for bipartite graphs with small bandwidth and bounded maximum degree. More generally, we determine asymptotically the two color Ramsey number for bipartite graphs with small bandwidth and bounded maximum degree and the three color Ramsey number for such graphs with the additional assumption that both classes of the bipartite graph have almost the same size.

Ce document traite de la caractérisation et la modélisation des transistors multi-ports. Une caractérisation des transistors pHEMT à base de l'AsGa est réalisée. Une importance particulière est donné aux méthodes de caractérisation RF sous pointes. En effet, une étude sur les méthodes d’épluchage est réalisée. Ensuite, après avoir relevé un défaut dans la méthode choisie (à savoir la méthode Pad-Open-Short), une solution est proposée concernant les standards non idéaux. Finalement, des modèles non linéaires 3 et 4 ports sont développés, ils ont pour objectifs de réduire le temps, des phases de conception et de fiabiliser le prototypage des fonctions micro-ondes utilisant ces composants. Les travaux présentés ici sont dédiés à l’amélioration de la modélisation électrique des transistors axée, comme leur application, sur la bande Ku. / This paper presents an approach for the de-embedding and modeling of multi-port transistors. First, the proposed de-embedding method is an extension of a three step method (Pad-Open-Short) for accurate on wafer (MMIC) S-parameters measurements. The novelty of this approach lies in the fact that the proposed de-embedding method for multi-port devices takes into account the imperfections of the standards. Then, we present two approach for the modeling of 3 and 4 ports GaAs HEMT transistors. The non-linear model was developed from I-V and S-parameters measurements. The methodology for 3-port device modeling allows us to determine accurate non-linear model in high frequencies. The second approach is dedicated for the distributed modeling of a 4-port transistor. The original electrical models of multi-port transistors developed in this thesis aims to reduce the time and the design phases, and to make reliable the prototyping of microwave functions using these components. The work presented here is therefore dedicated to improving the electrical modeling of transistors focused as their application on the Ku band.

Dans quelles conditions une application entre variétés différentiables est-elle homotope à un plongement lisse ? L'objet de la thèse est de compléter les obstructions rationnelles déjà connues, de façon à réduire le problème initial de topologie différentiable à un problème de calcul algébrique. Le théorème principal de la thèse permet de construire un plongement entre variétés lisses dans une classe d'homotopie rationnelle d'une application donnée, lorsque le problème algébrique a une solution. Plusieurs cas génériques de réalisabilité sont présentés, ainsi que des exemples mettant en évidence les nouvelles obstructions au plongement. Enfin, l'utilisation des techniques de chirurgie plongée dans le rang métastable aboutit à de nouveaux théorèmes de réalisation de plongements à cohomologie rationnelle près dans une variété fixée. / When does there exist a smooth embedding in a homotopy class of map between differentiable manifolds ? Rational homotopy theory provides computation machinery to such questions in differential topology. The purpose of this thesis is the completion of rational obstructions which prevent a map from being an embedding. More precisely, we show that a solution to the underlying algebraic problem gives rise to a smooth embedding with the same rational invariants. Several generic cases of realizability are detailed, as well as some examples which illustrate our new obstructions. We also use techniques of embedded surgery in metastable range, in order to state a theorem about realizability of an embedding up to rational cohomolgy into a fixed manifold.

El reconeixement de patrons és la tasca que pretén distingir objectes entre diferents classes. Quan aquesta tasca es vol solucionar de forma automàtica un pas crucial és el com representar formalment els patrons a l'ordinador. En funció d'aquests formalismes, podem distingir entre el reconeixement estadístic i l'estructural. El primer descriu objectes com un conjunt de mesures col·locats en forma del que s'anomena un vector de característiques. El segon assumeix que hi ha relacions entre parts dels objectes que han de quedar explícitament representades i per tant fa servir estructures relacionals com els grafs per codificar la seva informació inherent. Els espais vectorials són una estructura matemàtica molt flexible que ha permès definir diverses maneres eficients d'analitzar patrons sota la forma de vectors de característiques. De totes maneres, la representació vectorial no és capaç d'expressar explícitament relacions binàries entre parts dels objectes i està restrigida a mesurar sempre, independentment de la complexitat dels patrons, el mateix nombre de característiques per cadascun d'ells. Les representacions en forma de graf presenten la situació contrària. Poden adaptar-se fàcilment a la complexitat inherent dels patrons però introdueixen un problema d'alta complexitat computational, dificultant el disseny d'eines eficients per al procés i l'anàlisis de patrons. Resoldre aquesta paradoxa és el principal objectiu d'aquesta tesi. La situació ideal per resoldre problemes de reconeixement de patrons seria el representar-los fent servir estructures relacionals com els grafs, i a l'hora, poder fer ús del ric repositori d'eines pel processament de dades del reconeixement estadístic. Una solució elegant a aquest problema és la de transformar el domini dels grafs en el domini dels vectors, on podem aplicar qualsevol algorisme de processament de dades. En altres paraules, assignant a cada graf un punt en un espai vectorial, automàticament tenim accés al conjunt d'algorismes del món estadístic per aplicar-los al domini dels grafs. Aquesta metodologia s'anomena graph embedding. En aquesta tesi proposem de fer una associació de grafs a vectors de característiques de forma simple i eficient fixant l'atenció en la informació d'etiquetatge dels grafs. En particular, comptem les freqüències de les etiquetes dels nodes així com de les aretes entre etiquetes determinades. Tot i la seva localitat, aquestes característiques donen una representació prou robusta de les propietats globals dels grafs. Primer tractem el cas de grafs amb etiquetes discretes, on les característiques són sencilles de calcular. El cas continu és abordat com una generalització del cas discret, on enlloc de comptar freqüències d'etiquetes, ho fem de representants d'aquestes. Ens trobem que les representacions vectorials que proposem pateixen d'alta dimensionalitat i correlació entre components, i tractem aquests problems mitjançant algorismes de selecció de característiques. També estudiem com la diversitat de diferents representacions pot ser explotada per tal de millorar el rendiment de classificadors base en el marc d'un sistema de múltiples classificadors. Finalment, amb una extensa evaluació experimental mostrem com la metodologia proposada pot ser calculada de forma eficient i com aquesta pot competir amb altres metodologies per a la comparació de grafs. / Pattern recognition is the task that aims at distinguishing objects among different classes. When such a task wants to be solved in an automatic way a crucial step is how to formally represent such patterns to the computer. Based on the different representational formalisms, we may distinguish between statistical and structural pattern recognition. The former describes objects as a set of measurements arranged in the form of what is called a feature vector. The latter assumes that relations between parts of the underlying objects need to be explicitly represented and thus it uses relational structures such as graphs for encoding their inherent information. Vector spaces are a very flexible mathematical structure that has allowed to come up with several efficient ways for the analysis of patterns under the form of feature vectors. Nevertheless, such a representation cannot explicitly cope with binary relations between parts of the objects and it is restricted to measure the exact same number of features for each pattern under study regardless of their complexity. Graph-based representations present the contrary situation. They can easily adapt to the inherent complexity of the patterns but introduce a problem of high computational complexity, hindering the design of efficient tools to process and analyze patterns. Solving this paradox is the main goal of this thesis. The ideal situation for solving pattern recognition problems would be to represent the patterns using relational structures such as graphs, and to be able to use the wealthy repository of data processing tools from the statistical pattern recognition domain. An elegant solution to this problem is to transform the graph domain into a vector domain where any processing algorithm can be applied. In other words, by mapping each graph to a point in a vector space we automatically get access to the rich set of algorithms from the statistical domain to be applied in the graph domain. Such methodology is called graph embedding. In this thesis we propose to associate feature vectors to graphs in a simple and very efficient way by just putting attention on the labelling information that graphs store. In particular, we count frequencies of node labels and of edges between labels. Although their locality, these features are able to robustly represent structurally global properties of graphs, when considered together in the form of a vector. We initially deal with the case of discrete attributed graphs, where features are easy to compute. The continuous case is tackled as a natural generalization of the discrete one, where rather than counting node and edge labelling instances, we count statistics of some representatives of them. We encounter how the proposed vectorial representations of graphs suffer from high dimensionality and correlation among components and we face these problems by feature selection algorithms. We also explore how the diversity of different embedding representations can be exploited in order to boost the performance of base classifiers in a multiple classifier systems framework. An extensive experimental evaluation finally shows how the methodology we propose can be efficiently computed and compete with other graph matching and embedding methodologies.