Global ETD Search

131	Stark-Heegner points and p-adic L-functions / Points de Stark-Heegner et fonctions L p-adiques Casazza, Daniele 28 October 2016 (has links) Soit K\|Q un corps de nombres et soit ζK(s) sa fonction L complexe associée. La formule analytique du nombre de classes fournit un lien entre les valeurs spéciales de ζK(s) et les invariants du corps K. Elle admet une version Galois-équivariante. On a un schema similaire pour les courbes elliptiques. Soit E/Q une courbe elliptique et soit L(E/Q, s) sa fonction L complexe associée. La conjecture de Birch et Swinnerton-Dyer prédit un lien entre le comportement de L(E/Q, s) au point s = 1 et la structure des solutions rationnelles de l’équation definie par E. Comme la formule analytique du nombre de classes, la conjecture de Birch et Swinnerton-Dyer admet une version équivariante. La conjecture de Stark elliptique formulée par H. Darmon, A. Lauder et V. Rotger propose un analogue p-adique de la conjecture de Birch et Swinnerton-Dyer équivariante, qui nécessite certaines hypothèses. Dans leur article, les auteurs formulent la conjecture et donnent une démonstration dans certains cas où E a bonne réduction en p. Pour cela, ils utilisent la méthode de Garrett-Hida qui conduit à une factorisation de fonctions L p-adiques. Dans cette thèse on se concentre sur la conjecture de Stark elliptique et l’on montre comme il est possible d’étendre le résultat de Darmon, Lauder et Rotger. Dans le cas où E a bonne réduction en p on peut étendre le résultat en utilisant la méthode de Hida- Rankin. Cette méthode nous donne un contrôle meilleur sur les constantes apparaissant dans les formules et nous amène à une formule explicite contenant les invariants de la courbe elliptique. Pour obtenir le résultat on adapte la preuve du théorème principal de Darmon, Lauder et Rotger à notre cas et on utilise une formule p-adique de Gross et Zagier qui relie les valeurs spéciales de la fonction L padique de Bertolini-Darmon-Prasanna et les points de Heegner. Ensuite on voit comment étendre notre résultat et celui de Darmon-Lauder-Rotger au cas où E a réduction multiplicative en p. Dans ce cadre, on ne peut pas utiliser la fonction L p-adique de Bertolini-Darmon-Prasanna en raison de problèmes techniques. Pour éliminer cette difficulté on consid`ere la fonction L p-adique de Castellà. On utilise aussi la méthode de Garrett-Hida ainsi que la méthode d’Hida-Rankin et l’on obtient des résultats similaires aux cas de bonne réduction. / Let K\|Q be a number field and let ζK(s) be its associated complex L-function. The analytic class number formula relates special values of ζK(s) with algebraic invariants of the field K itself. It admits a Galois equivariant refinement known as Stark conjectures. We have a very similar picture in the case of elliptic curves. Let E/Q be an elliptic curve and let L(E/Q, s) be its associated complex L-function. The conjecture of Birch and Swinnerton-Dyer relates the behaviour of L(E/Q, s) at s = 1 to the structure of rational solutions of the equation defined by E. The equivariant Birch and Swinnerton- Dyer conjecture is obtained including in the picture the action of Galois groups. The elliptic Stark conjecture formulated by H. Darmon, A. Lauder and V. Rotger purposes a p-adic analogue of the equivariant Birch and Swinnerton-Dyer conjecture, under several assumption. In their paper, the authors formulate the conjecture and prove it in some cases of good reduction of E at p using Garrett-Hida method and performing a factorization of p-adic L-functions. In this dissertation we focus on the elliptic Stark conjecture and we show how it is possible to extend the result of Darmon, Lauder and Rotger. In the case of good reduction of E at p we can slightly extend the result using Hida- Rankin method. This method also gives us a better control of the constants appearing in the result, thus yielding an explicit formula which contains invariants associated with the elliptic curve. To achieve the proof we mimic the main result of Darmon, Lauder and Rotger in our setting and we make use of a p-adic Gross-Zagier formula which relates special values of the Bertolini-Darmon-Prasanna p-adic L-function to Heegner points. In a second moment we extend both our result and Darmon-Lauder-Rotger result to the case of multi- plicative reduction of E at p. In this setting we cannot use Bertolini- Darmon Prasanna p-adic L-function due to some technical reasons. In order to avoid the problem we consider Castellà’s two variables p-adic L-function. We use both Garrett-Hida method and Hida-Rankin method. In the two cases we obtain formulae which are similar to those of the good reduction setting. Courbes elliptiques Familles d’Hida Intégrales p-adiques iterées Unités elliptiques Unités de Stark Points de Heegner Valeurs spéciales Interpolation p-adique Fonctions L p-adiques Elliptic curves Hida families P-adic iterated integrals Elliptic units Stark units Heegner points Special values P-adic interpolation P-adic L-functions
132	Electric Vehicle Routing Problems : models and solution approaches / Problèmes de tournées de véhicules électriques : modèles et méthodes de résolution Montoya, Jose-Alejandro 09 December 2016 (has links) Étant donné leur faible impact environnemental, l’utilisation des véhicules électriques dans les activités de service a beaucoup augmenté depuis quelques années. Cependant, leur déploiement est freiné par des contraintes techniques telles qu’une autonomie limitée et de longs temps de charge des batteries. La prise en compte de ces contraintes a mené à l’apparition de nouveaux problèmes de tournées de véhicules pour lesquels, en plus d’organiser les tournées,il faut décider où et de combien charger les batteries. Dans cette thèse nous nous intéressons à ces problèmes au travers de quatre études. La première concerne le développement d’une métaheuristique en deux phases simple mais performante pour résoudre un problème particulier appelé "Green VRP”. Dans la seconde, nous nous concentrons sur la modélisation d’un aspect essentiel dans ces problèmes : le processus de chargement des batteries. Nous étudions différentes stratégies pour modéliser ce processus et montrons l’importance de considérer la nature non linéaire des fonctions de chargement. Dans la troisième étude nous proposons une recherche locale itérative pour résoudre des problèmes avec des fonctions de chargement non linéaires. Nous introduisons un voisinage dédié aux décisions de chargement basé sur un nouveau problème de chargement sur une tournée fixée. Dans la dernière étude, nous traitons un problème réel de tournées de techniciens avec des véhicules classiques et électriques. Ce problème est résolu par une métaheuristique qui décompose le problème en plusieurs sous-problèmes plus simples résolus en parallèle, puis qui assemble des parties des solutions trouvées pour construire la solution finale. / Electric vehicles (evs) are one of the most promising technologies to reduce the greenhouse gas emissions. For this reason, the use of evs in service operations has dramatically increased in recent years. Despite their environmental benefits, evs still face technical constraints such as short autonomy and long charging times. Taking into account these constraints when planning ev operations leads to a new breed of vehicle routing problems (vrps), known as electricVrps (evrps). In addition, to the standard routing decisions, evrps are concerned with charging decisions: where and how much to charge. In this ph. D thesis, we address evrps through 4 different studies. In the first study, we tackle the green vehicle routing problem. To solve the problem, we propose a simple, yet effective, two-phase matheuristic. In the second study, we focus a key modelling aspects in evrps: the battery charging process. We study different strategies to model this process and show the importance of considering the nonlinear nature of the battery charging functions. InThe third study, we propose an iterated local search to tackle evrp with non-linear charging functions. We introduce a particular local search operator for the charging decisions based on a new fixedroute charging problem. The fourth and last study considers a real technician routing problem with conventional and electric vehicles (trp-cev). To tackle this problem, we propose a parallel matheuristic that decomposes the problem into a set of easier-to-solve subproblemsThat are solved in parallel processors. Then the approach uses parts of the solutions found to the subproblems to assemble final solution to the trp-cev. Problèmes de tournées de techniciens Fonctions de chargement non linéaires Matheuristique Recherche locale itérative Electric vehicle routing problems Technician routing problems Green vehicle routing problems Fixed-Route vehicle charging problems Non linear charging functions Metaheuristic Matheuristic Iterated local search 004
133	On iterated learning for task-oriented dialogue Singhal, Soumye 01 1900 (has links) Dans le traitement de langue et des système de dialogue, il est courant de pré-entraîner des modèles de langue sur corpus humain avant de les affiner par le biais d'un simulateur et de résolution de tâches. Malheuresement, ce type d'entrainement tend aussi à induire un phénomène connu sous le nom de dérive du langage. Concrétement, les propriétés syntaxiques et sémantiques de la langue intiallement apprise se détériorent: les agents se concentrent uniquement sur la résolution de la tâche, et non plus sur la préservation de la langue. En s'inspirant des travaux en sciences cognitives, et notamment l'apprentigssage itératif Kirby and Griffiths (2014), nous proposons ici une approche générique pour contrer cette dérive du langage. Nous avons appelé cette méthode Seeded iterated learning (SIL), ou apprentissage itératif capitalisé. Ce travail a été publié sous le titre (Lu et al., 2020b) et est présenté au chapitre 2. Afin d'émuler la transmission de la langue entre chaque génération d'agents, un agent étudiant est d'abord pré-entrainé avant d'être affiné de manière itérative, et ceci, en imitant des données échantillonnées à partir d'un agent enseignant nouvellement formé. À chaque génération, l'enseignant est créé en copiant l'agent étudiant, avant d'être de nouveau affiné en maximisant le taux de réussite de la tâche sous-jacente. Dans un second temps, nous présentons Supervised Seeded iterated learning (SSIL) dans le chapitre 3, où apprentissage itératif capitalisé avec supervision, qui a été publié sous le titre (Lu et al., 2020b). SSIL s'appuie sur SIL en le combinant avec une autre méthode populaire appelée Supervised SelfPlay (S2P) (Gupta et al., 2019), où apprentissage supervisé par auto-jeu. SSIL est capable d'atténuer les problèmes de S2P et de SIL, i.e. la dérive du langage dans les dernier stades de l'entrainement tout en préservant une plus grande diversité linguistique. Tout d'abord, nous évaluons nos méthodes dans sous la forme d'une preuve de concept à traver le Jeu de Lewis avec du langage synthetique. Dans un second temps, nous l'étendons à un jeu de traduction se utilisant du langage naturel. Dans les deux cas, nous soulignons l'efficacité de nos méthodes par rapport aux autres méthodes de la litterature. Dans le chapitre 1, nous discutons des concepts de base nécessaires à la compréhension des articles présentés dans les chapitres 2 et 3. Nous décrivons le problème spécifique du dialogue orienté tâche, y compris les approches actuelles et les défis auxquels ils sont confrontés : en particulier, la dérive linguistique. Nous donnons également un aperçu du cadre d'apprentissage itéré. Certaines sections du chapitre 1 sont empruntées aux articles pour des raisons de cohérence et de facilité de compréhension. Le chapitre 2 comprend les travaux publiés sous le nom de (Lu et al., 2020b) et le chapitre 3 comprend les travaux publiés sous le nom de (Lu et al., 2020a), avant de conclure au chapitre 4. / In task-oriented dialogue, pretraining on human corpus followed by finetuning in a simulator using selfplay suffers from a phenomenon called language drift. The syntactic and semantic properties of the learned language deteriorates as the agents only focuses on solving the task. Inspired by the iterative learning framework in cognitive science Kirby and Griffiths (2014), we propose a generic approach to counter language drift called Seeded iterated learning (SIL). This work was published as (Lu et al., 2020b) and is presented in Chapter 2. In an attempt to emulate transmission of language between generations, a pretrained student agent is iteratively refined by imitating data sampled from a newly trained teacher agent. At each generation, the teacher is created by copying the student agent, before being finetuned to maximize task completion.We further introduce Supervised Seeded iterated learning (SSIL) in Chapter 3, work which was published as (Lu et al., 2020a). SSIL builds upon SIL by combining it with the other popular method called Supervised SelfPlay (S2P) (Gupta et al., 2019). SSIL is able to mitigate the problems of both S2P and SIL namely late-stage training collapse and low language diversity. We evaluate our methods in a toy setting of Lewis Game, and then scale it up to the translation game with natural language. In both settings, we highlight the efficacy of our methods compared to the baselines. In Chapter 1, we talk about the core concepts required for understanding the papers presented in Chapters 2 and 3. We describe the specific problem of task-oriented dialogue including current approaches and the challenges they face: particularly, the challenge of language drift. We also give an overview of the iterated learning framework. Some sections in Chapter 1 are borrowed from the papers for coherence and ease of understanding. Chapter 2 comprises of the work published as (Lu et al., 2020b) and Chapter 3 comprises of the work published as (Lu et al., 2020a). Chapter 4 gives a conclusion on the work. deep-learning multi-agent learning task-oriented dialogue iterated learning multi-task learning language drift apprentissage en profondeur apprentissage multi-agents dialogue orienté tâche apprentissage itératif apprentissage multi-tâches dérive du langage natural language processing traitement du langage naturel
134	Fraktály v počítačové grafice / Fractals in Computer Graphics Heiník, Jan Unknown Date (has links) This Master's thesis deals with history of Fractal geometry and describes the fractal science development. In the begining there are essential Fractal science terms explained. Then description of fractal types and typical or most known examples of them are mentioned. Fractal knowledge application besides computer graphics area is discussed. Thesis informs about fractal geometry practical usage. Few present software packages or more programs which can be used for making fractal pictures are described in this work. Some of theirs capabilities are described. Thesis' practical part consists of slides, demonstrational program and poster. Electronical slides represents brief scheme usable for fractal geometry realm lectures. Program generates selected fractal types. Thesis results are projected on poster.
135	[pt] CICLOS HETERODIMENSIONAIS DE CO- ÍNDICE DOIS E BLENDERS SIMBÓLICOS / [en] HETERODIMENSIONAL CYCLES OF CO-INDEX TWO AND SYMBOLIC BLENDERS 23 December 2021 (has links) [pt] Na primeira parte da tese, consideramos difeomorfismos com ciclos heterodimensionais associados a um par de selas P e Q de co-índice dois. Provamos que difeomorfismos com ciclos que possuem no mínimo um par de autovalores centrais do ciclo não real geram ciclos heterodimensionais robustos. Além disso, quando os autovalores centrais são não-reais, os ciclos robustos estão associados as continuações das selas iniciais (ou seja, os ciclos podem ser estabilizados). Na segunda parte deste trabalho estudamos mapas produto cruzado sobre aplicações deslocamento (do tipo Bernoulli) com fibras contrativas e dependência Holder nos pontos da base. Provamos que sistemas que satisfazem a propriedade de cobertura exibem blender simbólicos. Estes blenders são generalizações do blender usual cuja principal característica é que suas direções centrais podem ter qualquer dimensão d maior ou igual que 1. / [en] In the first part of the thesis, we consider diffeomorphisms having heterodimensional cycles associated with a pair of saddles P and Q of co-index two. We prove that diffeomorphisms with cycles, which have at least one pair of non-real central eigenvalues, generate robust heterodimensional cycles. Moreover, when both central eigenvalues are non-real, the robust cycles are associated with the continuation of the initial saddles (i.e. the cycle can be stabilized). In the second part of this work we study skew product maps over Bernoulli shifts with contracting fibers and Holder dependence on the base points. We prove that systems satisfying the covering property exhibit symbolic blenders. These blenders are generalizations of the usual blenders whose main property is that their central direction may have any dimension d greater than or equal to 1. [pt] APLICACAO PRODUTO CRUZADO [pt] SISTEMAS DE FUNCOES ITERADAS [pt] HIPERBOLICIDADE PARCIAL [pt] INTERSECCAO HOMOCLINICA FORTE [pt] CICLO ROBUSTO [pt] CICLO HETERODIMENSIONAL [pt] BLENDER SIMBOLICO [pt] BLENDER [pt] ATRATOR DE HUTCHINSON [en] SKEW PRODUCT MAPS [en] ITERATED FUNCTION SYSTEM [en] PARTIAL HYPERBOLICITY [en] STRONG HOMOCLINIC INTERSECTION [en] ROBUST CYCLE [en] HETERODIMENSIONAL CYCLE [en] SYMBOLIC BLENDER [en] BLENDER [en] HUTCHINSON ATTRACTOR
136	Nonlinear Dynamics and Chaos in Systems with Time-Varying Delay Müller-Bender, David 30 October 2020 (has links) Systeme mit Zeitverzögerung sind dadurch charakterisiert, dass deren zukünftige Entwicklung durch den Zustand zum aktuellen Zeitpunkt nicht eindeutig festgelegt ist. Die Historie des Zustands muss in einem Zeitraum bekannt sein, dessen Länge Totzeit genannt wird und die Gedächtnislänge festlegt. In dieser Arbeit werden fundamentale Effekte untersucht, die sich ergeben, wenn die Totzeit zeitlich variiert wird. Im ersten Teil werden zwei Klassen periodischer Totzeitvariationen eingeführt. Da diese von den dynamischen Eigenschaften einer eindimensionalen iterierten Abbildung abgeleitet werden, die über die Totzeit definiert wird, werden die Klassen entsprechend der zugehörigen Dynamik konservativ oder dissipativ genannt. Systeme mit konservativer Totzeit können in Systeme mit konstanter Totzeit transformiert werden und besitzen gleiche charakteristische Eigenschaften. Dagegen weisen Systeme mit dissipativer Totzeit fundamentale Unterschiede z.B. in der Tangentialraumdynamik auf. Im zweiten Teil werden diese Ergebnisse auf Systeme angewendet, deren Totzeit im Vergleich zur internen Relaxationszeit des Systems groß ist. Es zeigt sich, dass ein durch dissipative Totzeitvariationen induzierter Mechanismus, genannt resonanter Dopplereffekt, unter anderem zu neuen Arten chaotischer Dynamik führt. Diese sind im Vergleich zur bekannten chaotischen Dynamik in Systemen mit konstanter Totzeit sehr niedrig-dimensional. Als Spezialfall wird das so genannte laminare Chaos betrachtet, dessen Zeitreihen durch nahezu konstante Phasen periodischer Dauer gekennzeichnet sind, deren Amplitude chaotisch variiert. Im dritten Teil dieser Arbeit wird auf der Basis experimenteller Daten und durch die Analyse einer nichtlinearen retardierten Langevin-Gleichung gezeigt, dass laminares Chaos robust gegenüber Störungen wie zum Beispiel Rauschen ist und experimentell realisiert werden kann. Es werden Methoden zur Zeitreihenanalyse entwickelt, um laminares Chaos in experimentellen Daten ohne Kenntnis des erzeugenden Systems zu detektieren. Mit diesen Methoden ist selbst dann eine Detektion möglich, wenn das Rauschen so stark ist, dass laminares Chaos mit bloßem Auge nur schwer erkennbar ist.:1. Introduction 2. Dissipative and conservative delays in systems with time-varying delay 3. Laminar Chaos and the resonant Doppler effect 4. Laminar Chaos: a robust phenomenon 5. Summary and concluding remarks A. Appendix / In systems with time-delay, the evolution of a system is not uniquely determined by the state at the current time. The history of the state must be known for a time period of finite duration, where the duration is called delay and determines the memory length of the system. In this work, fundamental effects arising from a temporal variation of the time-delay are investigated. In the first part, two classes of periodically time-varying delays are introduced. They are related to a specific dynamics of a one-dimensional iterated map that is defined by the time-varying delay. Referring to the related map dynamics the classes are called conservative or dissipative. Systems with conservative delay can be transformed into systems with constant delay, and thus have the same characteristic properties as constant delay systems. In contrast, there are fundamental differences, for instance, in the tangent space dynamics, between systems with dissipative delay and systems with constant delay. In the second part, these results are applied to systems with a delay that is considered large compared to the internal relaxation time of the system. It is shown that a mechanism induced by dissipative delays leads to new kinds of regular and chaotic dynamics. The dynamics caused by the so-called resonant Doppler effect is fundamentally different from the behavior known from systems with constant delay. For instance, the chaotic attractors in systems with dissipative delay are very low-dimensional compared to typical ones arising in systems with constant delay. An example of this new kind of low-dimensional dynamics is given by the so-called Laminar Chaos. It is characterized by nearly constant laminar phases of periodic duration, where the amplitude varies chaotically. In the third part of this work, it is shown that Laminar Chaos is a robust phenomenon, which survives perturbations such as noise and can be observed experimentally. Therefore experimental data is provided and a nonlinear delayed Langevin equation is analyzed. Using the robust features that characterize Laminar Chaos, methods for time series analysis are developed, which enable us to detect Laminar Chaos without the knowledge of the specific system that has generated the time series. By these methods Laminar Chaos can be detected even for comparably large noise strengths, where the characteristic properties are nearly invisible to the eye.:1. Introduction 2. Dissipative and conservative delays in systems with time-varying delay 3. Laminar Chaos and the resonant Doppler effect 4. Laminar Chaos: a robust phenomenon 5. Summary and concluding remarks A. Appendix info:eu-repo/classification/ddc/530 ddc:530 info:eu-repo/classification/ddc/510 ddc:510
137	Evaluation of Target Tracking Using Multiple Sensors and Non-Causal Algorithms Vestin, Albin, Strandberg, Gustav January 2019 (has links) Today, the main research field for the automotive industry is to find solutions for active safety. In order to perceive the surrounding environment, tracking nearby traffic objects plays an important role. Validation of the tracking performance is often done in staged traffic scenarios, where additional sensors, mounted on the vehicles, are used to obtain their true positions and velocities. The difficulty of evaluating the tracking performance complicates its development. An alternative approach studied in this thesis, is to record sequences and use non-causal algorithms, such as smoothing, instead of filtering to estimate the true target states. With this method, validation data for online, causal, target tracking algorithms can be obtained for all traffic scenarios without the need of extra sensors. We investigate how non-causal algorithms affects the target tracking performance using multiple sensors and dynamic models of different complexity. This is done to evaluate real-time methods against estimates obtained from non-causal filtering. Two different measurement units, a monocular camera and a LIDAR sensor, and two dynamic models are evaluated and compared using both causal and non-causal methods. The system is tested in two single object scenarios where ground truth is available and in three multi object scenarios without ground truth. Results from the two single object scenarios shows that tracking using only a monocular camera performs poorly since it is unable to measure the distance to objects. Here, a complementary LIDAR sensor improves the tracking performance significantly. The dynamic models are shown to have a small impact on the tracking performance, while the non-causal application gives a distinct improvement when tracking objects at large distances. Since the sequence can be reversed, the non-causal estimates are propagated from more certain states when the target is closer to the ego vehicle. For multiple object tracking, we find that correct associations between measurements and tracks are crucial for improving the tracking performance with non-causal algorithms. evaluation target tracking multiple sensors non-causal smoother smoothing tracking vehicle tracking camera lidar estimate estimation prediction vehicle dynamics sensor fusion real-time tracking extended kalman filter filter validation validation position estimation velocity estimation dynamic model model complexity multi object tracking multiple object tracking single object tracking data association tracking fundamentals iterated kalman filter track management gnn global nearest neighbour mahalanobis mahalanobis distance performance evaluation differential gps dgps roi ego several sensors sensors rmse root mean square error invertible motion anti-causal motion anti-causal tracking constant velocity gnn imu tfs two filter smoother ekf rts radar inertial measurement unit nonlinear nonlinear systems mono camera monocular camera noise model tracking performance fixed interval smoothing m/n logic centralized fusion non-causal object tracker car tracking car dynamics automotive active safety object tracking automotive industry thesis master reverse dynamics reverse tracking reverse sequence sequence tracking data propagation ground truth estimating ground truth additional sensors mounted sensors true estimates environment comparison algorithm independent targets overlapping measurements occluded track switch improve lower uncertainty more certain state process noise covariance sampling image sprt adas cnn cv pdf track target ego tracker tentative track observatiom online tracking offline tracking online offline recorded sequences robust self driving self-driving car traffic trajectory true state scenario scenarios future accurate output advanced driver assistance systems non-linear complex noise pedestrian truck bus maneuvering vehicles processed measurement frame state correction probability density function tuning likelihood transition measurement motion model recursion gaussian approximation distribution linear jacobian multiplicative noise ratio ad hoc ad hoc state space approach backward auction euclidean distance statistical threshold gating association margin normalize covariance matrix fusion confirmed rejected tentative history absolute error modular ego motion parameters variables logg hardware specification fused causal factorization independent uncorrelated transform moving rotation translation oncoming overtaking Control Engineering Reglerteknik

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