Dans cette thèse nous étudions l'estimation de modèles probabilistes discriminants, surtout des aspects d'apprentissage semi-supervisé et de sélection de caractéristiques. Le but de l'apprentissage semi-supervisé est d'améliorer l'efficacité de l'apprentissage supervisé en utilisant des données non-étiquetées. Cet objectif est difficile à atteindre dans les cas des modèles discriminants. Les modèles probabilistes discriminants permettent de manipuler des représentations linguistiques riches, sous la forme de vecteurs de caractéristiques de très grande taille. Travailler en grande dimension pose des problèmes, en particulier computationnels, qui sont exacerbés dans le cadre de modèles de séquences tels que les champs aléatoires conditionnels (CRF). Notre contribution est double. Nous introduisons une méthode originale et simple pour intégrer des données non étiquetées dans une fonction objectif semi-supervisée. Nous démontrons alors que l'estimateur semi-supervisé correspondant est asymptotiquement optimal. Le cas de la régression logistique est illustré par des résultats d'expèriences. Dans cette étude, nous proposons un algorithme d'estimation pour les CRF qui réalise une sélection de modèle, par le truchement d'une pénalisation $L_1$. Nous présentons également les résultats d'expériences menées sur des tâches de traitement des langues (le chunking et la détection des entités nommées), en analysant les performances en généralisation et les caractéristiques sélectionnées. Nous proposons finalement diverses pistes pour améliorer l'efficacité computationelle de cette technique.

This paper examines the probability that a random polynomial of specific degree over a field has a specific number of distinct roots in that field. Probabilities are found for random quadratic polynomials with respect to various probability measures on the real numbers and p-adic numbers. In the process, some properties of the p-adic integer uniform random variable are explored. The measure Witt ring, a generalization of the canonical Witt ring, is introduced as a way to link quadratic forms and measures, and examples are found for various fields and measures. Special properties of the Haar measure in connection with the measure Witt ring are explored. Higher-degree polynomials are explored with the aid of numerical methods, and some conjectures are made regarding higher-degree p-adic polynomials. Other open questions about measure Witt rings are stated. / Graduation date: 1999

Consider a multi-priority, nonpreemptive, N-server Poisson arrival queueing system. The number of servers requested by an arrival has a known probability distribution. Service times are negative exponential. In order to save available servers for higher priority customers, arriving customers of each lower priority are deliberately queued whenever the number of servers busy equals or exceeds a given priority-dependent cutoff number. A queued priority i customer enters service the instant the number of servers busy is at most the respective cutoff number of servers minus the number of servers requested (by the customer) and all higher priority queues are empty. In other words the queueing discipline is in a sense HOL by priorities, FCFS within a priority. All servers requested by a customer start service simultaneously; service completion instants are independent. We derive the priority i waiting time distribution (in transform domain) and other system statistics.

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This thesis consists of two parts, Papers A and B, in which some stochastic processes, originating from random matrix theory (RMT), are studied. In the first paper we study the fluctuations of the kth largest eigenvalue, xk, of the Gaussian unitary ensemble (GUE). That is, let N be the dimension of the matrix and k depend on N in such a way that k and N-k both tend to infinity as N - ∞. The main result is that xk, when appropriately rescaled, converges in distribution to a Gaussian random variable as N → ∞. Furthermore, if k1 < ...< km are such that k1, ki+1 - ki and N - km, i =1, ... ,m - 1, tend to infinity as N → ∞ it is shown that (xk1 , ... , xkm) is multivariate Gaussian in the rescaled N → ∞ limit. In the second paper we study the Airy process, A(t), and prove that it fluctuates like a Brownian motion on a local scale. We also prove that the Discrete polynuclear growth process (PNG) fluctuates like a Brownian motion in a scaling limit smaller than the one where one gets the Airy process. / QC 20100716

Quantum key distribution (QKD) can provide unconditional security based on the fundamental laws of quantum physics. Unfortunately, real-life implementations of a QKD system may contain overlooked imperfections and thus violate the practical security of QKD. It is vital to explore these imperfections. In this thesis, I study two practical imperfections in QKD: i) Discovering security loophole in a commercial QKD system: I perform a proof-of-principle experiment to demonstrate a technically feasible quantum attack on top of a commercial QKD system. The attack I utilize is called phase-remapping attack. ii) Generating high-speed truly random numbers: I propose and experimentally demonstrate an ultrafast QRNG at a rate over 6 Gb/s, which is based on the quantum phase fluctuations of a laser. Moreover, I consider a potential adversary who has partial knowledge of the raw data and discuss how one can rigorously remove such partial knowledge with post-processing.

Quantum key distribution (QKD) can provide unconditional security based on the fundamental laws of quantum physics. Unfortunately, real-life implementations of a QKD system may contain overlooked imperfections and thus violate the practical security of QKD. It is vital to explore these imperfections. In this thesis, I study two practical imperfections in QKD: i) Discovering security loophole in a commercial QKD system: I perform a proof-of-principle experiment to demonstrate a technically feasible quantum attack on top of a commercial QKD system. The attack I utilize is called phase-remapping attack. ii) Generating high-speed truly random numbers: I propose and experimentally demonstrate an ultrafast QRNG at a rate over 6 Gb/s, which is based on the quantum phase fluctuations of a laser. Moreover, I consider a potential adversary who has partial knowledge of the raw data and discuss how one can rigorously remove such partial knowledge with post-processing.