Logic-based formalizations of dynamical systems are central to the field of knowledge representation and reasoning. These formalizations can be used to model agents that act, reason,and perceive in a changing and incompletely known environment. A key aspect of reasoning about agents and their behaviors is the notion of joint ability. A team of agents is jointly able to achieve a goal if despite any incomplete knowledge or even false beliefs about the world or each other, they still know enough to be able to get to a goal state, should they choose to do so. A particularly challenging issue associated with joint ability is how team members can coordinate their actions. Existing approaches often require the agents to communicate to agree on a joint plan. In this thesis, we propose an account of joint ability that supports coordination among agents without requiring communication, and that allows for agents to have incomplete (or even false) beliefs about the world or the beliefs of other agents. We use ideas from game theory to address coordination among agents. We introduce the notion of a strategy for each agent which is basically a plan that the agent knows how to follow. Each agent compares her strategies and iteratively discards those that she believes are not good considering the strategies that the other agents have kept. Our account is developed in the situation calculus, a logical language suitable for representing and reasoning about action and change that is extended to support reasoning about multiple agents. Through several examples involving public, private, and sensing actions, we demonstrate how symbolic proof techniques allow us to reason about team ability despite incomplete specifications about the beliefs of agents.

Hoare and He's Unifying Theories of Programming (UTP) provides a rich model of programs as relational predicates. This theory is intended to provide a single framework in which any programming paradigms, languages, and features, can be modelled, compared and contrasted. The UTP already has models for several programming formalisms, such as imperative programming, higher-order programming (e.g. programing with procedures), several styles of concurrent programming (or reactive systems), class-based object-orientation, and transaction processing. We believe that the UTP ought to be able to represent all significant computer programming language formalisms, in order for it to be considered a unifying theory. One gap in the UTP work is that of object-based object-orientation, such as that presented in Abadi and Cardelli's untyped object calculi (sigma-calculi). These sigma-calculi provide a prominent formalism of object-based object-oriented (OO) programs, which models programs as objects. We address this gap within this dissertation by presenting an embedding of an Abadi--Cardelli-style object calculus in the UTP. More formally, the thesis that his dissertation argues is that it is possible to provide an object-based object rientation to the UTP, with value- and reference-based objects, and a fully abstract model of references. We have made three contributions to our area of study: first, to extend the UTP with a notion of object-based object orientation, in contrast with the existing class-based models; second, to provide an alternative model of pointers (references) for the UTP that supports both value-based compound values (e.g. objects) and references (pointers), in contrast to existing UTP models with pointers that have reference-based compound values; and third, to model an Abadi-Cardelli notion of an object in the UTP, and thus demonstrate that it can unify this style of object formalism.

This thesis discusses linguistic constraints on scrambling and flexibility in word order in spoken Persian (Farsi) and presents a computational model for efficient implementation of these constraints for a subset of Persian. Linguistic phenomena which we have studies include local scrambling, long distance scrambling, extrapolation of clauses, topicalisation, case tendancy and the discourse marker ra. The work extends previous work on Persian based on Government and Binding (GB) theory by considering the pragmatic aspects of Persian Grammar and long distance scrambling.

Les réseaux ad hoc dynamiques qui évoluent de manière non planifiée et imprévisible sont souvent étudiés en faisant l’hypothèse d’une composition et d’une topologie qui évoluent peu et relativement lentement. Il est alors possible de proposer dans ce contexte faiblement mobile des mécanismes (comme par exemple du routage, des infrastructures PKI, etc.) qui permettent aux applications conçues pour les réseaux statiques de continuer à fonctionner. Les travaux présentés dans cette thèse sont au contraire centrés sur lesréseaux ad hoc fortement dynamiques (iMANets). Les nœuds qui les constituent sont extrêmement mobiles et volatils, ce qui engendre des modifications incessantes et rapides de topologie. Les contributions principales de cette thèse sont (i) la définition d’une algèbre nommée CiMAN (Calculus for highly Mobile Ad hoc Networks) qui permet de modéliser les processus communicants dans ces réseaux ad hoc fortement mobiles, (ii) l’utilisation de cette algèbre pour prouver la correction d’algorithmes dédiés à ces réseaux, et (iii) unmiddleware et des applications de référence adaptés à ce contexte. / Mobile ad hoc networks that evolve in an unplanned and unpredictable mannerare often studied assuming that their composition and their topology evolve relatively slowly. In this context of weak mobility, it is then possible to propose mechanisms (such asrouting, Public Key Infrastructure, etc.) which make the application designed for a static context still operational. At the opposite, the work presented in this thesis focuses on highlymobile ad hoc networks (iMANets). The nodes of these networks are extremely mobile,bringing ceaseless and fast changes in the network topology. The main contributions of this thesis are (i) the definition of an algebra called CiMAN (Calculus for highly Mobile Adhoc Networks) which makes it possible to model communicating processes in these highly mobile ad hoc networks, (ii) the use of this algebra to prove the correctness of algorithms dedicated to these networks, and (iii) a middleware and reference applications specifically designed for this context.

Des travaux récents dans le domaine des mathématiques financières ont fait émerger l'importance de l'étude de la régularité et du comportement fin des queues de distribution pour certaines classes de diffusions à coefficients non globalement réguliers. Dans cette thèse, nous traitons des problèmes issus de ce contexte. Nous étudions d'abord l'existence, la régularité et l'asymptotique en espace de densités pour les solutions d'équations différentielles stochastiques en n'imposant que des conditions locales sur les coefficients de l'équation. Notre analyse se base sur les outils du calcul de Malliavin et sur des estimations pour les processus d'Ito confinés dans un tube autour d'une courbe déterministe. Nous obtenons des estimations significatives de la fonction de répartition et de la densité dans des classes de modèles comprenant des généralisations du CIR et du CEV et des modèles à volatilité locale-stochastique : dans ce deuxième cas, les estimations entraînent l'explosion des moments du sous-jacent et ont ainsi un impact sur le comportement asymptotique en strike de la volatilité implicite. La modélisation paramétrique de la surface de volatilité, à son tour, fait l'objet de la deuxième partie. Nous considérons le modèle SVI de J. Gatheral, en proposant une nouvelle stratégie de calibration quasi-explicite, dont nous illustrons les performances sur des données de marché. Ensuite, nous analysons la capacité du SVI à générer des approximations pour les smiles symétriques, en le généralisant à un modèle dépendant du temps. Nous en testons l'application à un modèle de Heston (sans et avec déplacement), en générant des approximations semi-fermées pour le smile de volatilité / Some recent works in the field of mathematical finance have brought new light on the importance of studying the regularity and the tail asymptotics of distributions for certain classes of diffusions with non-globally smooth coefficients. In this Ph.D. dissertation we deal with some issues in this framework. In a first part, we study the existence, smoothness and space asymptotics of densities for the solutions of stochastic differential equations assuming only local conditions on the coefficients of the equation. Our analysis is based on Malliavin calculus tools and on « tube estimates » for Ito processes, namely estimates for the probability that the trajectory of an Ito process remains close to a deterministic curve. We obtain significant estimates of densities and distribution functions in general classes of option pricing models, including generalisations of CIR and CEV processes and Local-Stochastic Volatility models. In the latter case, the estimates we derive have an impact on the moment explosion of the underlying price and, consequently, on the large-strike behaviour of the implied volatility. Parametric implied volatility modeling, in its turn, makes the object of the second part. In particular, we focus on J. Gatheral's SVI model, first proposing an effective quasi-explicit calibration procedure and displaying its performances on market data. Then, we analyse the capability of SVI to generate efficient approximations of symmetric smiles, building an explicit time-dependent parameterization. We provide and test the numerical application to the Heston model (without and with displacement), for which we generate semi-closed expressions of the smile

The main object of this thesis is to obtain numerous applications of fractional derivative operator concerning analytic and ρ-valent (or multivalent) functions in the open unit disk by introducing new classes and deriving new properties. Our finding will provide interesting new results and indicate extensions of a number of known results. In this thesis we investigate a wide class of problems. First, by making use of certain fractional derivative operator, we define various new classes of ρ-valent functions with negative coefficients in the open unit disk such as classes of ρ-valent starlike functions involving results of (Owa, 1985a), classes of ρ-valent starlike and convex functions involving the Hadamard product (or convolution) and classes of κ-uniformly ρ-valent starlike and convex functions, in obtaining, coefficient estimates, distortion properties, extreme points, closure theorems, modified Hadmard products and inclusion properties. Also, we obtain radii of convexity, starlikeness and close-to-convexity for functions belonging to those classes. Moreover, we derive several new sufficient conditions for starlikeness and convexity of the fractional derivative operator by using certain results of (Owa, 1985a), convolution, Jack's lemma and Nunokakawa' Lemma. In addition, we obtain coefficient bounds for the functional |α_ρ+2-θα²_ρ+1| of functions belonging to certain classes of p-valent functions of complex order which generalized the concepts of starlike, Bazilevič and non-Bazilevič functions. We use the method of differential subordination and superordination for analytic functions in the open unit disk in order to derive various new subordination, superordination and sandwich results involving the fractional derivative operator. Finally, we obtain some new strong differential subordination, superordination, sandwich results for ρ-valent functions associated with the fractional derivative operator by investigating appropriate classes of admissible functions. First order linear strong differential subordination properties are studied. Further results including strong differential subordination and superordination based on the fact that the coefficients of the functions associated with the fractional derivative operator are not constants but complex-valued functions are also studied.

<p>Doktorska disertacija prezentuje nov i opštiji način analiziranja&nbsp;semantike strukturiranih i objektno orijentisanih programa i to&nbsp;isključivo u okvirima predikatske logike prvog reda. Doktorska&nbsp;disertacija razmatra sledeće teme:<br />1.) S-programski račun,<br />2.) Definicija i osobine dinamičkih postuslova u S-računu,<br />3.) Konceptualne definicije objekta, klase i invarijante,<br />4.) Analiza invarijanata u klasi (SP-analiza i DP-analiza).</p> / <p>Doctoral thesis presents a new and more general method for analizing of&nbsp;structured and object-oriented program semantics, based on the first-order&nbsp;predicate logic. Doctoral thesis consideres next topics:<br />1.) S-program calculus,<br />2.) Definition and characteristics of dynamic postconditions in S-calculus,<br />3.) Conceptual definitions of object, class and invariant,<br />4.) Analyses of invariants in class (SP-analyses and DP-analyses).</p>

This thesis studies the categorical formalisation of quantum computing, through the prism of type theory, in a three-tier process. The first stage of our investigation involves the creation of the dagger lambda calculus, a lambda calculus for dagger compact categories. Our second contribution lifts the expressive power of the dagger lambda calculus, to that of a quantum programming language, by adding classical control in the form of complementary classical structures and dualisers. Finally, our third contribution demonstrates how our lambda calculus can be applied to various well known problems in quantum computation: Quantum Key Distribution, the quantum Fourier transform, and the teleportation protocol.

L'approximation adiabatique en mécanique quantique stipule que si un système quantique évolue assez lentement, alors il demeurera dans le même état propre. Récemment, une faille dans l'application de l'approximation adiabatique a été découverte. Les limites du théorème seront expliquées lors de sa dérivation. Ce mémoire à pour but d'optimiser la probabilité de se maintenir dans le même état propre connaissant le système initial, final et le temps d'évolution total. Cette contrainte sur le temps empêche le système d'être assez lent pour être adiabatique. Pour solutionner ce problème, une méthode variationnelle est utilisée. Cette méthode suppose connaître l'évolution optimale et y ajoute une petite variation. Par après, nous insérons cette variation dans l'équation de la probabilité d'être adiabatique et développons en série. Puisque la série est développée autour d'un optimum, le terme d'ordre un doit nécessairement être nul. Ceci devrait nous donner un critère sur l'évolution la plus adiabatique possible et permettre de la déterminer. Les systèmes quantiques dépendants du temps sont très complexes. Ainsi, nous commencerons par les systèmes ayant des énergies propres indépendantes du temps. Puis, les systèmes sans contrainte et avec des fonctions d'onde initiale et finale libres seront étudiés. / The adiabatic approximation in quantum mechanics states that if the Hamiltonian of a physical system evolves slowly enough, then it will remain in the instantaneous eigenstate related to the initial eigenstate. Recently, two researchers found an inconsistency in the application of the approximation. A discussion about the limit of this idea will be presented. Our goal is to optimize the probability to be in the instantaneous eigenstate related to the initial eigenstate knowing the initial and final system, with the total time of the experiment fixed to $T$. This last condition prevents us from being slow enough to use the adiabatic approximation. To solve this problem, we turn to the calculus of variation. We suppose the ideal evolution is known and we add a small variation to it. We take the result, put it in the probability to be adiabatic and expand in powers of the variation. The first order term must be zero. This enables us to derive a criterion which will give us conditions on the ideal Hamiltonian. Those conditions should define the ideal Hamiltonian. Time dependent quantum systems are very complicated. To simplify the problem, we will start by considering systems with time independent energies. Afterward, the general case will be treated.

Dans la première partie de cette thèse, on présente des inégalités de concentration convexe pour des intégrales stochastiques. Ces résultats sont obtenus par calcul stochastique e tpar calcul de Malliavin forward/backward. On présente également des inégalités de déviation pour les exponentielles martingales à saut.Dans une deuxième partie on présente des théorèmes limites pour le conditionnement du mouvement brownien. / In the first part of this thesis, we present some convex concentration inequalities for stochastic integrals. These results are obtained by forward/backward stochastic calculus combined with Malliavin calculus. We also present deviation inequalities for exponentialjump-diffusion.In the second part, we present some limit theorems for the conditionning of Brownian motion.