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This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

Based on the superposition principle, any two states of a quantum system may be coherently superposed to yield a novel state. Such a simple construction is at the heart of genuinely quantum phenomena such as interference of massive particles or quantum entanglement. Yet, these superpositions are susceptible to environmental influences, eventually leading to a complete disappearance of the system's quantum character. In principle, two distinct mechanisms responsible for this process of decoherence may be identified. In a classical decoherence setting, on the one hand, stochastic fluctuations of classical, ambient fields are the relevant source. This approach leads to a formulation in terms of stochastic Hamiltonians; the dynamics is unitary, yet stochastic. In a quantum decoherence scenario, on the other hand, the system is described in the language of open quantum systems. Here, the environmental degrees of freedom are to be treated quantum mechanically, too. The loss of coherence is then a direct consequence of growing correlations between system and environment. The purpose of the present thesis is to clarify the distinction between classical and quantum decoherence. It is known that there exist decoherence processes that are not reconcilable with the classical approach. We deem it desirable to have a simple, feasible model at hand of which it is known that it cannot be understood in terms of fluctuating fields. Indeed, we find such an example of true quantum decoherence. The calculation of the norm distance to the convex set of classical dynamics allows for a quantitative assessment of the results. In order to incorporate genuine irreversibility, we extend the original toy model by an additional bath. Here, the fragility of the true quantum nature of the dynamics under increasing coupling strength is evident. The geometric character of our findings offers remarkable insights into the geometry of the set of non-classical decoherence maps. We give a very intuitive geometrical measure---a volume---for the quantumness of dynamics. This enables us to identify the decoherence process of maximum quantumness, that is, having maximal distance to the convex set of dynamics consistent with the stochastic, classical approach. In addition, we observe a distinct correlation between the decoherence potential of a given dynamics and its achievable quantumness. In a last step, we study the notion of quantum decoherence in the context of a bipartite system which couples locally to the subsystems' respective environments. A simple argument shows that in the case of a separable environment the resulting dynamics is of classical nature. Based on a realistic experiment, we analyze the impact of entanglement between the local environments on the nature of the dynamics. Interestingly, despite the variety of entangled environmental states scrutinized, no single instance of true quantum decoherence is encountered. In part, the identification of the classical nature relies on numerical schemes. However, for a large class of dynamics, we are able to exclude analytically the true quantum nature.

We characterize various types of σ-porosity via an infinite game in terms of winning strategies. We use a modification of the game to prove and reprove some new and older in- scribing theorems for σ-ideals of σ-porous type in locally compact metric spaces. We show that there exists a closed set which is σ-(1 − ε)-symmetrically porous for every 0 < ε < 1 but which is not σ-1-symmetrically porous. Next, we prove that the realizable by an action unitary representations of a finite abelian group Γ on an infinite-dimensional complex Hilbert space H form a comeager set in Rep(Γ, H). 1

Esta tese investiga proximidades entre as proposições de Hélio Oiticica e conceitos como \'construção de situação\', \'deriva\' e \'urbanismo unitário\' desenvolvidos pela Internacional Situacionista - IS (1957-1972). Além da literatura da área, foram explorados dois corpus documental, os Boletins da Internacional Situacionista e o Catalogue Raisonné de Hélio Oiticica. A partir dos Boletins foi possível compreender a formulação dos principais conceitos situacionistas, enquanto o Catalogue Raisonné de Hélio Oiticica possibilitou reconstituir suas deambulações urbanas. Suas caminhadas pela cidade refletem sua crítica à cidade e aos modos de vida urbano. Este caráter crítico está presente no desenvolvimento de seu Programa Ambiental, onde suas proposições estéticas buscam reestabelecer, justamente, as relações entre o indivíduo e a cidade. Os arquivos consultados, manuscritos, cartas, entrevistas, e um grande número de documentos inéditos foram fundamentais para a reconstrução de seus \'passos\' e o entendimento, a partir de seu próprio discurso, de suas relações com a crítica social e urbana desenvolvida pelos situacionistas. / This thesis investigates proximities between propositions of Hélio Oiticica and concepts such as \'situation\', \'dérive\' and \'unitary urbanism\' developed by the Situationist International - IS (1957-1972). Besides the literature of the field, two documentary corpus were explored, the Bulletins of the Situationist International and Catalogue Raisonné of Hélio Oiticica. From the Bulletins it was possible to understand fundamental Situationist concepts, while the Catalogue Raisonné of Hélio Oiticica allowed to reconstitute its urban wanderings. His strolls reflect his criticism to the city and urban lifestyles. This criticality is present in the developing of his Environmental Program, where his aesthetic propositions seek to reestablish precisely the relationship between the individual and the city. The archives consulted, manuscripts, letters, interviews, and a large number of unpublished documents were key elements to rebuilding his \'steps\' and the understanding, based on his own speech, of the relationship between Oiticica and social and urban critics developed by the Situationists.

La consommation énergétique en France a pour origine principale le secteur résidentiel et tertiaire. En environnement urbain, l’habitat est encore principalement ancien, avec des déperditions importantes. L’amélioration des performances énergétiques passe par la quantification des pertes, basée sur une méthode globale de mesure par caméra infrarouge à haute résolution spatiale.L’interprétation des images obtenues nécessite une description des termes radiatifs composant le signal, pour cela un simulateur original est mis au point. A partir d’une scène tridimensionnelle maillée, le champ de température est calculé pour les parois 1D et pour les ponts thermiques 2D, par le programme thermique développé à cet effet, SUSHI qui s’appuie sur un pré-calcul d’éclairement solaire et un pré-calcul de réponse indicielle 2D. Le signal du capteur infrarouge est alors modélisé en adaptant le code radiatif MOHICANS.Cette chaîne logicielle a l’originalité de proposer une fusion efficace des simulations de la réponse dynamique en température et en luminance de zones présentant un transfert 1Dà travers la paroi et de zones présentant un transfert 2D.La mise en œuvre de la campagne expérimentale BATIR a permis de mesurer le comportement thermique d’une façade de bâtiment et de son environnement radiato-convectif. Une validation ponctuelle des températures calculées par SUSHI a été réalisée par confrontation à une mesure par thermocouple. Des caméras infrarouges ont été mises en œuvre afin de collecter la luminance issue de la façade étudiée en bande II et III. Les luminances calculées par MOHICANS sont comparées à ces acquisitions, et valident la chaîne logicielle à ce niveau. / The main origin of the energy consumption in France is the residential and commercial sector. In urban environment, housing is mostly old, which means high heat losses. The improvement of energy performances requires the quantification of heat losses. This quantification may be based on a global measurement by an infrared camera with high spatial resolution.The infrared image interpretation requires a description of the radiative terms that make up the signal. For that purpose, a novel simulator is developed. The temperature field is calculated from a meshed three-dimensional scene composed of 1D walls and 2D thermal bridges. This operation is realized by the developed thermal software SUSHI, which is based on solar irradiance pre-computation and on 2D unitary response pre-computation. The software uses as input environmental data measured in the field. The infrared sensor signal is then modelled by adapting the radiative program MOHICANS. This software chain has the distinct advantage of an efficient fusion of dynamic response simulations of temperature and radiance, for areas with unidirectional and 2D heat transfer.The experimental campaign BATIR was set-up for measuring the thermal behavior of a building façade and its convective and radiative environment. A local validation of temperature calculation by SUSHI was realized through a comparison with thermocouple measurement results. Infrared cameras were operated in order to collect the radiance coming from the analyzed façade in band II and III. The radiances calculated by MOHICANS were compared with these acquisitions in order to validate the software chain at this level.

This thesis investigates a technique to estimate the risk of the mean-variance (MV) portfolio optimization problem. We call this technique the Scaling technique. It provides a better estimator of the risk of the MV optimal portfolio. We obtain this result for a general estimator of the covariance matrix of the returns which includes the correlated sampling case as well as the independent sampling case and the exponentially weighted moving average case. This gave rise to the paper, [CMcS]. Our result concerning the Scaling technique relies on the moments of the inverse of compound Wishart matrices. This is an open problem in the theory of random matrices. We actually tackle a much more general setup, where we consider any random matrix provided that its distribution has an appropriate invariance property (orthogonal or unitary) under an appropriate action (by conjugation, or by a left-right action). Our approach is based on Weingarten calculus. As an interesting byproduct of our study - and as a preliminary to the solution of our problem of computing the moments of the inverse of a compound Wishart random matrix, we obtain explicit moment formulas for the pseudo-inverse of Ginibre random matrices. These results are also given in the paper, [CMS]. Using the moments of the inverse of compound Wishart matrices, we obtain asymptotically unbiased estimators of the risk and the weights of the MV portfolio. Finally, we have some numerical results which are part of our future work.

This master thesis deals with cost management. Master thesis is firstly focused on definition of terminology in costing area. On example of Synthos Kralupy, company that passed deep change of information system, I try to demonstrate strength and weaknesses of tools and instruments which enable cost control. However the information system provides required information, it is necessary to define it and specify it. Even information system has to be developed and updated according to the management requirement and the latest trends. Each of information systems bring both, advantages and disadvantages described in this master thesis. Despite the high quality information base, the company faces difficulties with accuracy and accessibility of data. The main problem is methodology of stock evaluation of semi-finished and finished products. Due to change of IS, there was changed principle of evaluation from standard price to weight average with monthly period. Description of new calculation is described below. Based on processes applied in the company, I proposed new changes and I evaluated improvements done.

Cette thèse est consacrée à l'étude asymptotique d'objets liés au mouvement brownien sur le groupe unitaire en grande dimension, ainsi qu'à l'étude, dans le cadre des probabilités libres, des versions non-commutatives de ces objets. Elle se subdivise essentiellement en trois parties.Dans le chapitre 2, nous résolvons le problème initial de cette thèse, à savoir la convergence de la transformation de Hall sur le groupe unitaire vers la transformation de Hall libre, lorsque la dimension tend vers l'infini. Pour résoudre ce problème, nous établissons des théorèmes d'existence de noyaux de transition pour la convolution libre. Enfin, nous utilisons ces résultats pour prouver que, pareillement au mouvement brownien sur le groupe unitaire, le mouvement brownien sur le groupe linéaire converge en distribution non-commutative vers sa version libre. Nous étudions les fluctuations autour de cette convergence dans le chapitre 3. Le chapitre 4 présente un morphisme entre les mesures infiniment divisibles pour la convolution libre additive d'une part et multiplicative de l'autre. Nous montrons que ce morphisme possède une version matricielle qui s'appuie sur un nouveau modèle de matrices aléatoires pour les processus de Lévy libres multiplicatifs. / This thesis focuses on the asymptotic of objects related to the Brownian motion on the unitary group in large dimension, and on the study, in free probability, of the non-commutative versions of those objects. It subdivides into essentially three parts.In Chapter 2, we solve the original problem of this thesis: the convergence of the Hall transform on the unitary group to the free Hall transform, as the dimension tends to infinity. To solve this problem, we establish theorems of existence of transition kernel for the free convolution. Finally, we use these results to prove that, exactly as the Brownian motion on the unitary group, the Brownian motion on the linear group converges in noncommutative distribution to its free version. Then we study the fluctuations around this convergence in Chapter 3. Chapter 4 presents a homomorphism between infinitely divisible measures for the free convolution, in respectively the additive case and the multiplicative case. We show that this homomorphism has a matricialversion which is based on a new model of random matrices for the free multiplicative Lévy processes.