Dans cette thèse, on s'intéresse à des algorithmes d'analyse de données utilisant des marches aléatoires sur des graphes de voisinage, ou graphes géométriques aléatoires, construits à partir des données. On sait que les marches aléatoires sur ces graphes sont des approximations d'objets continus appelés processus de diffusion. Dans un premier temps, nous utilisons ce résultat pour proposer un nouvel algorithme de partitionnement de données flou de type recherche de modes. Dans cet algorithme, on définit les paquets en utilisant les propriétés d'un certain processus de diffusion que l'on approche par une marche aléatoire sur un graphe de voisinage. Après avoir prouvé la convergence de notre algorithme, nous étudions ses performances empiriques sur plusieurs jeux de données. Nous nous intéressons ensuite à la convergence des mesures stationnaires des marches aléatoires sur des graphes géométriques aléatoires vers la mesure stationnaire du processus de diffusion limite. En utilisant une approche basée sur la méthode de Stein, nous arrivons à quantifier cette convergence. Notre résultat s'applique en fait dans un cadre plus général que les marches aléatoires sur les graphes de voisinage et nous l'utilisons pour prouver d'autres résultats : par exemple, nous arrivons à obtenir des vitesses de convergence pour le théorème central limite. Dans la dernière partie de cette thèse, nous utilisons un concept de topologie algébrique appelé homologie persistante afin d'améliorer l'étape de "pooling" dans l'approche "sac-de-mots" pour la reconnaissance de formes 3D. / In this thesis, we study data analysis algorithms using random walks on neighborhood graphs, or random geometric graphs. It is known random walks on such graphs approximate continuous objects called diffusion processes. In the first part of this thesis, we use this approximation result to propose a new soft clustering algorithm based on the mode seeking framework. For our algorithm, we want to define clusters using the properties of a diffusion process. Since we do not have access to this continuous process, our algorithm uses a random walk on a random geometric graph instead. After proving the consistency of our algorithm, we evaluate its efficiency on both real and synthetic data. We then deal tackle the issue of the convergence of invariant measures of random walks on random geometric graphs. As these random walks converge to a diffusion process, we can expect their invariant measures to converge to the invariant measure of this diffusion process. Using an approach based on Stein's method, we manage to obtain quantitfy this convergence. Moreover, the method we use is more general and can be used to obtain other results such as convergence rates for the Central Limit Theorem. In the last part of this thesis, we use the concept of persistent homology, a concept of algebraic topology, to improve the pooling step of the bag-of-words approach for 3D shapes.

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Two efficient methods for solving generalized Lyapunov equations and their implementations in FORTRAN 77 are presented. The first one is a generalization of the Bartels--Stewart method and the second is an extension of Hammarling's method to generalized Lyapunov equations. Our LAPACK based subroutines are implemented in a quite flexible way. They can handle the transposed equations and provide scaling to avoid overflow in the solution. Moreover, the Bartels--Stewart subroutine offers the optional estimation of the separation and the reciprocal condition number. A brief description of both algorithms is given. The performance of the software is demonstrated by numerical experiments.

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Arnold Schoenberg's teaching career spanned over fifty years and included experiences in Austria, Germany, and the United States. Schoenberg's teaching assistant, Leonard Stein, transcribed Schoenberg's class lectures at UCLA from 1936 to 1944. Most of these notes resulted in publications that provide pedagogical examples of combined elements from Schoenberg's European years of teaching with his years of teaching in America. There are also class notes from Schoenberg's later lectures that have gone unexamined. These notes contain substantial examples of Schoenberg's later theories with analyses of masterworks that have never been published. Both the class notes and the subsequent publications reveal Schoenberg's comprehensive approach to understanding the presentation of the Gedanke or musical idea. In his later classes especially, Schoenberg demonstrated a method of analyzing musical compositions using illustrations of elements of the Grundgestalt or "basic shape," which contains the technical aspects of the musical parts. Through an examination of his published and unpublished manuscripts, this study will demonstrate Schoenberg's commitment to a comprehensive approach to teaching. Schoenberg's heritage of eighteenth- and nineteenth-century music theory is evident in his Harmonielehre and in his other European writings. The latter include Zusammenhang, Kontrapunkt, Instrumentation, Formenlehre (ZKIF), and Der musikalische Gedanke und die Logik, Technik, und Kunst seiner Darstellung (the Gedanke manuscripts), written over the course of several years from the 1920s to the early 1930s. After emigrating to the United States in 1933, Schoenberg immediately began teaching and writing in an attempt to arrive at a comprehensive approach to his pedagogy. The remainder of Schoenberg's textbook publications, with the exception of Models for Beginners in Composition, were left unfinished, were edited primarily by Leonard Stein and published after Schoenberg's death in 1951. Preliminary Exercises in Counterpoint, Fundamentals of Musical Composition, and Structural Functions of Harmony complete his ouevre of theory publications. An examination of the Stein notes offers contributing evidence to Schoenberg's lifelong pursuit to find a comprehensive approach for teaching an understanding of the musikalische Gedanke. With the addition of an analysis of the first movement of Mozart's G minor Symphony, K. 550, which Schoenberg used often to illustrate examples of basic concepts as liquidation, transition, neutralization in the minor key, the role of the subordinate theme, retransitions, codettas, melodic and harmonic overlapping, and motivic analysis, this study focuses on Schoenberg's comprehensive approach to both analyzing the musical work and teaching methods of composing.

We construct and investigate random geometric structures that are based on a homogeneous Poisson point process. We investigate the random Vietoris-Rips complex constructed as the clique complex of the well known gilbert graph as an infinite random simplicial complex and prove that every realizable finite sub-complex will occur infinitely many times almost sure as isolated complex and also in the case of percolations connected to the unique giant component. Similar results are derived for the Cech complex. We derive limit theorems for the f-vector of the Vietoris-Rips complex on the unit cube centered at the origin and provide a central limit theorem and a Poisson limit theorem based on the model parameters. Finally we investigate random polytopes that are given as convex hulls of a Poisson point process in a smooth convex body. We establish a central limit theorem for certain linear combinations of intrinsic volumes. A multivariate limit theorem involving the sequence of intrinsic volumes and the number of i-dimensional faces is derived. We derive the asymptotic normality of the oracle estimator of minimal variance for estimation of the volume of a convex body.

Cryptography is the study of encryptying and decrypting messages and deciphering encrypted messages when the code is unknown. We consider Λπ(Δx, Δy) which is a count of how many ways a permutation satisfies a certain property. According to Hawkes and O'Connor, the distribution of Λπ(Δx, Δy) tends to a Poisson distribution with parameter ½ as m → ∞ for all Δx,Δy ∈ (Z/qZ)m - 0. We give a proof of this theorem using the Stein-Chen method: As qm approaches infinity, the distribution of Λπ(Δx, Δy) is approximately Poisson with parameter ½. Error bounds for this approximation are provided.

La presente investigación tiene como objetivo el estudio de la relevancia de la memoria cultural en la puesta en escena de La Orestiada, dirigida por Peter Stein. En ella se evoca, a través de diversos signos teatrales, una memoria perteneciente a la cultura griega, pero que permite ver las grandes similitudes que esta aún guarda con el mundo contemporáneo. A partir de una negociación entre los signos referentes a dos épocas y culturas distintas, la memoria cultural presente en la puesta en escena permite que Stein realice sutiles, pero profundos paralelos entre la tragedia griega y la Alemania de los ochenta. Percepciones respecto al color, ciertos rituales y la vigencia del sistema democrático, acreditan este paralelo que permite identificar modelos culturales en la obra de Stein.

Comedy has typically been derided as second-tier to drama in all aspects of narrative. Throughout history, comedy has seen short shrift in both critical reception and academic investigation. Merit is simply placed on drama far before that of comedy. This is not for comedy’s own lack of skill or craft, but simply for comedy’s misappropriation as a narrative form. Throughout the years, by way of either competition or economic superiority, comedy has been pigeonholed into the typified dramatic structure that drama so thoroughly encapsulates. Being forced into a form that exemplifies complex, climactic structure and explicit character development, comedy in its purest form has suffered through the ages. Gertrude Stein’s theory of Landscape Drama, and, more specifically, immediacy, is best attuned to comedy in its truest form. Comedy does not require sweeping character development, obtuse narrative design, or fantastic spectacle to produce superior works of art. Comedy, when compared to drama, exists best in a much more punctuated format. Stein’s theories, while never intended for comedy, align absolutely perfectly with the comedic genre’s design. And epitomized through long form improv on the stage, and the newly-fashioned digital short made profitable by the proliferation of the internet and digital culture, comedy’s purest form has become more readily available as narrative has progressed throughout history. With this thesis, I intend to display the disparity between comedy and drama due to comedy’s misallotment into a format that does not properly encapsulate it to its most fulfilling embodiment. Through this display, I seek to uncover the debt done to the comedic form from centuries of neglect in academic query and merit in order to best prove comedy’s need for ii critical scrutiny. Further, in doing so I hope to better construe a community of comedic research and criticism in order to create better art and more diverse comedic offerings.