Wide Area Measurements (WAMs) have been widely used in the energy management system (EMS) of power system for monitoring, operation and control. In recent years, the advent of synchronized Phasor Measurements Unit (PMU) has added another dimension to the field of wide-area measurement. However, the high cost of the PMU, which includes the manufacture and deployment fee, is a hurdle to the wide use of the PMU in power systems. Unlike traditional PMUs, the frequency monitoring network (FNET) developed by the Virginia Tech Power IT lab is an Internet—based, GPS—synchronized, wide-area frequency monitoring network deployed at the distribution level, providing a low-cost and easily deployable WAMs solution. In this dissertation, the research work can be categorized into two parts: FNET Design and Situation Awareness Algorithm Development. / Ph. D.

Der Vortrag beschreibt die zugrunde liegende Theorie und die Softwarefunktionalität des in PTC Creo Simulate 3.0 eingeführten Kontaktmodells mit endlicher Reibung und vergleicht dieses mit den bis Creo Simulate 2.0 exklusiv verwendeten Kontaktmodellen (ideal reibungsfrei und unendlich reibungsbehaftet). An zwei Modellbeispielen (ein von zwei Bremsbacken geklemmtes Bremsschwert und ein verschraubtes Schwungrad) wird versucht, die Funktionsweise des neuen Modells zu demonstrieren. Wegen aktueller Qualitätsprobleme der Software wird die Brauchbarkeit der Kontaktmodelle für den Anwender bewertet (Stand Creo 3.0 M080 / Creo 2.0 M200) und umfangreiches Feedback an den Softwarehersteller PTC gegeben. / The presentation describes the underlying theory and software functionality of the finite friction contact model introduced with PTC Creo Simulate 3.0. It is being compared with the friction-free and infinite friction contact model used exclusively until Creo Simulate 2.0. It is being tried to demonstrate the mode of operation of the new model with help of two examples: A brake sword clamped by two brake pads and a bolted flywheel. Because of actual software quality problems, the usability of the contact model for the user is being rated (status Creo 3.0 M080 / Creo 2.0 M200). Furthermore, comprehensive feedback is given to the software developer PTC.

Inspired by Happel's question, whether the exchange graph and the simplicial complex of tilting modules over a quiver algebra are independent from the multiplicities of multiple arrows in the quiver, we study quantitative aspects of Fomin and Zelevinsky's quiver mutation rule. Our results turn out to be very useful in the mutation-infinite case for understanding combinatorial structures as the cluster exchange graph or the simplicial complex of tilting modules, which are governed by quiver mutation. Using a class of quivers we call forks we can show that any such quiver yields a tree in the exchange graph. This allows us to provide a good global description of the exchange graphs of arbitrary mutation-infinite quivers. In particular we show that the exchange graph of an acyclic quiver is a tree if (and in fact only if) any two vertices are connected by at least two arrows. Furthermore we give classification results for the simplicial complexes and thereby obtain a partial positive answer to Happel's question. Another consequence of our findings is a confirmation of Unger's conjecture about the infinite number of components of the tilting exchange graph in all but finitely many cases. Finally we generalise and conceptualise our results by introducing what we call "polynomial quivers", stating several conjectures about "polynomial quiver mutation", and giving proofs in special cases.

Today’s communication systems are in need of spectrally efficient and high throughput techniques more than ever because of high data rate applications and the scarcity and expense of bandwidth. To cope with increased data rate demands, more base stations are needed which is not cost and energy efficient in cellular networks. It has been shown that wireless relay networks can provide higher network throughput and increase power efficiency with low complexity and cost. Furthermore, network resources can be utilized more efficiently by using network coding in relay networks. A wireless relay network in which multiple nodes exchange information with the help of relay node(s) is called a multi-way relay channel (MWRC). MWRCs are expected to be an integral part of next generation wireless standards. The main focus of this dissertation is the investigation of transmission schemes in an MWRC to improve the throughput and error performance. An MWRC with full data exchange is assumed in which a half-duplex relay station (RS) is the enabler of communication. One of the challenges with signal demodulation in MWRCs is the existence of ambiguous points in the received constellation. The first part of this dissertation investigates a transmission scheme for full data exchange in MWRC that benefits from these points and improves its throughput by 33% compared to traditional relaying. Then an MWRC is considered where a RS assists multiple nodes to exchange messages. A different approach is taken to avoid ambiguous points in the superposition of user symbols at the relay. This can be achieved by employing complex field network coding (CFNC) which results in full data exchange in two communication phases. CFNC may lead to small Euclidean distances between constellation points, resulting in poor error performance. To improve this performance, the optimal user precoding values are derived such that the power efficiency of the relay constellation is highest when channel state information is available at the users. The error performance of each user is then analyzed and compared with other relaying schemes. Finally, focusing on the uplink of multi-way relay systems, the performance of an MWRC is studied in which users can employ arbitrary modulation schemes and the links between the users and the relay have different gains, e.g. Rayleigh fading. Analytical expressions for the exact average pairwise error probability of these MWRCs are derived. The probability density function (PDF) and the mean of the minimum Euclidean distance of the relay constellation are closely approximated, and a tight upper bound on the symbol error probability is developed. / Graduate

Réalisé en cotutelle avec l'École normale supérieure de Cachan – Université Paris-Saclay / L'un des aspects fondamentaux des systèmes informatiques modernes, et en particulier des systèmes critiques, est la possibilité d'exécuter plusieurs processus, partageant des ressources communes, de façon simultanée. De par leur nature concurrentielle, le bon fonctionnement de ces systèmes n'est assuré que lorsque leurs comportements ne dépendent pas d'un ordre d'exécution prédéterminé. En raison de cette caractéristique, il est particulièrement difficile de s'assurer qu'un système concurrent ne possède pas de faille. Dans cette thèse, nous étudions la vérification formelle, une approche algorithmique qui vise à automatiser la vérification du bon fonctionnement de systèmes concurrents en procédant par une abstraction vers des modèles mathématiques. Nous considérons deux de ces modèles, les réseaux de Petri et les systèmes d'addition de vecteurs, et les problèmes de vérification qui leur sont associés. Nous montrons que le problème d'accessibilité pour les systèmes d'addition de vecteurs (avec états) à deux compteurs est PSPACE-complet, c'est-à-dire complet pour la classe des problèmes solubles à l'aide d'une quantité polynomiale de mémoire. Nous établissons ainsi la complexité calculatoire précise de ce problème, répondant à une question demeurée ouverte depuis plus de trente ans. Nous proposons une nouvelle approche au problème de couverture pour les réseaux de Petri, basée sur un algorithme arrière guidé par une caractérisation logique de l'accessibilité dans les réseaux de Petri continus. Cette approche nous a permis de mettre au point un nouvel algorithme qui s'avère particulièrement efficace en pratique, tel que démontré par notre implémentation logicielle nommée QCover. Nous complétons ces résultats par une étude des systèmes de transitions bien structurés qui constituent une abstraction générale des systèmes d'addition de vecteurs et des réseaux de Petri. Nous considérons le cas des systèmes de transitions bien structurés à branchement infini, une classe qui inclut les réseaux de Petri possédant des arcs pouvant consommer ou produire un nombre arbitraire de jetons. Nous développons des outils mathématiques facilitant l'étude de ces systèmes et nous délimitons les frontières au-delà desquelles la décidabilité des problèmes de terminaison, de finitude, de maintenabilité et de couverture est perdue. / One fundamental aspect of computer systems, and in particular of critical systems, is the ability to run simultaneously many processes sharing resources. Such concurrent systems only work correctly when their behaviours are independent of any execution ordering. For this reason, it is particularly difficult to ensure the correctness of concurrent systems. In this thesis, we study formal verification, an algorithmic approach to the verification of concurrent systems based on mathematical modeling. We consider two of the most prominent models, Petri nets and vector addition systems, and their usual verification problems considered in the literature. We show that the reachability problem for vector addition systems (with states) restricted to two counters is PSPACE-complete, that is, it is complete for the class of problems solvable with a polynomial amount of memory. Hence, we establish the precise computational complexity of this problem, left open for more than thirty years. We develop a new approach to the coverability problem for Petri nets which is primarily based on applying forward coverability in continuous Petri nets as a pruning criterion inside a backward coverability framework. We demonstrate the effectiveness of our approach by implementing it in a tool named QCover. We complement these results with a study of well-structured transition systems which form a general abstraction of vector addition systems and Petri nets. We consider infinitely branching well-structured transition systems, a class that includes Petri nets with special transitions that may consume or produce arbitrarily many tokens. We develop mathematical tools in order to study these systems and we delineate the decidability frontier for the termination, boundedness, maintainability and coverability problems.

Ce travail a comme objectif d‘analyser la voix et le silence dans l‘œuvre fragmentaire de deux écrivains, Fernando Pessoa (1888-1935) et Maurice Maeterlinck (1862-1949), héritiers de plusieurs cultures, auteurs dont l‘écriture gagne un surplus de sens grâce aux voix qu‘elle crée et qui font entendre leurs mots ou bien le silence de leur absence.A travers l‘analyse de quelques-unes de leurs oeuvres, nous essayons de comprendre jusqu‘à quel point ces deux poètes, rattachés aux mouvements moderniste et symboliste, vécurent l‘inquiétude propre à leur siècle, réfléchissant sur les raisons qui les menèrent à transformer la vie en un éternel mouvement vers l‘absolu, une quête d‘un état d‘âme impossible en dehors de leur création poétique ou théâtrale. Nous tenterons ainsi de justifier, dans la mesure du possible, la forme inachevée d‘une grande partie de leurs écrits, marqués par la dépersonnalisation et le questionnement concernant l‘énigme de l‘existence.Fernando Pessoa et ses hétéronymes seront les voix (im)possibles dans le silence de Maeterlinck, deux formes d‘une même polyphonie, placée en rapport avec la fragmentation formelle des personnages des oeuvres de chacun des auteurs. / This work pretends to analyse voice and silence having in mind the fragmentation of Fernando Pessoa (1888-1935) and Maurice Maeterlinck‘s (1862-1949) work, heirs to several cultures and owners of a writing where the meaning of words depend on the voices or on the silence of their absence.Through some of their works, we try to understand how these poets of symbolism and modernism lived the disquietude of a century, to analyse the causes that made them change life into an eternal movement in direction of the absolute, looking for a state of soul, only possible in their poetry and theatre, and justify, whenever possible, the infinite form that determined the unaccomplishement of most of their writings, which they developped together with the depersonalization and the irreducibility that caracterizes the enigma of life.Fernando Pessoa and his heteronymous are the (im)possible voices in Maeterlinck‘s silence, two forms of the same polyphony, in relation with the formal fragmentation of the characters of their works. / Este trabalho tem como objectivo analisar a voz e o silêncio na fragmentação da obra de dois autores, Fernando Pessoa (1888-1935) e Maurice Maeterlinck (1862- 1949), herdeiros de várias culturas e donos de uma escrita em que as palavras ganham sentido pelas vozes a que dão corpo ou pelo silêncio da sua ausência.Através da apreciação de algumas das suas obras, tentamos compreender até que ponto estes dois poetas do modernismo e do simbolismo viveram a inquietude de um século, reflectir sobre os motivos que os levaram a transformar a vida num eterno movimento em direcção ao absoluto, na busca de um estado de alma só possível no acontecer da sua poesia ou teatro e justificar, sempre que possível, a forma infinita que definiu o inacabamento de grande parte dos seus escritos, desenvolvidos a par com uma despersonalização e a irredutibilidade que caracteriza o enigma da existência.Fernando Pessoa e os seus heterónimos são as vozes (im)possíveis no silêncio de Maeterlinck, duas formas de uma mesma polifonia, colocada em relação com a fragmentação formal das personagens nas obras de cada um dos autores.

Avec l'augmentation considérable d'acquisitions de données temporelles dans les dernières décennies comme les systèmes GPS, les séquences vidéo ou les suivis médicaux de pathologies ; le besoin en algorithmes de traitement et d'analyse efficaces d'acquisition longitudinales n'a fait qu'augmenter. Dans cette thèse, nous proposons une extension du formalisme mean-shift, classiquement utilisé en traitement d'images, pour le groupement de séries temporelles multidimensionnelles. Nous proposons aussi un algorithme de groupement hiérarchique des séries temporelles basé sur la mesure de dynamic time warping afin de prendre en compte les déphasages temporels. Ces choix ont été motivés par la nécessité d'analyser des images acquises en imagerie par résonance magnétique sur des patients atteints de sclérose en plaques. Cette maladie est encore très méconnue tant dans sa genèse que sur les causes des handicaps qu'elle peut induire. De plus aucun traitement efficace n'est connu à l'heure actuelle. Le besoin de valider des hypothèses sur les lésions de sclérose en plaque nous a conduit à proposer des méthodes de groupement de séries temporelles ne nécessitant pas d'a priori sur le résultat final, méthodes encore peu développées en traitement d'images. / Due to the dramatic increase of longitudinal acquisitions in the past decades such as video sequences, global positioning system (GPS) tracking or medical follow-up, many applications for time-series data mining have been developed. Thus, unsupervised time-series data mining has become highly relevant with the aim to automatically detect and identify similar temporal patterns between time-series. In this work, we propose a new spatio-temporal filtering scheme based on the mean-shift procedure, a state of the art approach in the field of image processing, which clusters multivariate spatio-temporal data. We also propose a hierarchical time-series clustering algorithm based on the dynamic time warping measure that identifies similar but asynchronous temporal patterns. Our choices have been motivated by the need to analyse magnetic resonance images acquired on people affected by multiple sclerosis. The genetics and environmental factors triggering and governing the disease evolution, as well as the occurrence and evolution of individual lesions, are still mostly unknown and under intense investigation. Therefore, there is a strong need to develop new methods allowing automatic extraction and quantification of lesion characteristics. This has motivated our work on time-series clustering methods, which are not widely used in image processing yet and allow to process image sequences without prior knowledge on the final results.

This paper deals with the consensus problem under communication network inducing delays. It is well-known that introducing a delay leads in general to a reduction of the performance or to instability due to the fact that timedelay systems are infinite dimensional. For instance, the set of initial conditions of a time-delay system is not a vector but a function taken in an interval. Therefore, investigating the effect of time-delays in the consensus problem is an important issue. In the present paper, we assume that each agent receives instantaneously its own state information but receives the state information from its neighbors after a constant delay. Two stability criteria are provided based on the frequency approach and on Lyapunov-Krasovskii techniques given in terms of LMI. An analytic expression of the consensus equilibrium which depends on the delay and on the initial conditions taken in an interval is derived. The efficiency of the method is tested for different network communication schemes. / <p>QC 20110120</p>

In Chapter 2, we propose several two-timescale simulation-based actor-critic algorithms for solution of infinite horizon Markov Decision Processes (MDPs) with finite state-space under the average cost criterion. On the slower timescale, all the algorithms perform a gradient search over corresponding policy spaces using two different Simultaneous Perturbation Stochastic Approximation (SPSA) gradient estimates. On the faster timescale, the differential cost function corresponding to a given stationary policy is updated and averaged for enhanced performance. A proof of convergence to a locally optimal policy is presented. Next, a memory efficient implementation using a feature-vector representation of the state-space and TD (0) learning along the faster timescale is discussed. A three-timescale simulation based algorithm for solution of infinite horizon discounted-cost MDPs via the Value Iteration approach is also proposed. An approximation of the Dynamic Programming operator T is applied to the value function iterates. A sketch of convergence explaining the dynamics of the algorithm using associated ODEs is presented. Numerical experiments on rate based flow control on a bottleneck node using a continuous-time queueing model are presented using the proposed algorithms. Next, in Chapter 3, we develop three simulation-based algorithms for finite-horizon MDPs (FHMDPs). The first algorithm is developed for finite state and compact action spaces while the other two are for finite state and finite action spaces. Convergence analysis is briefly sketched. We then concentrate on methods to mitigate the curse of dimensionality that affects FH-MDPs severely, as there is one probability transition matrix per stage. Two parametrized actor-critic algorithms for FHMDPs with compact action sets are proposed, the ‘critic’ in both algorithms learning the policy gradient. We show w.p1convergence to a set with the necessary condition for constrained optima. Further, a third algorithm for stochastic control of stopping time processes is presented. Numerical experiments with the proposed finite-horizon algorithms are shown for a problem of flow control in communication networks. Towards stochastic optimization, in Chapter 4, we propose five algorithms which are variants of SPSA. The original one measurement SPSA uses an estimate of the gradient of objective function L containing an additional bias term not seen in two-measurement SPSA. We propose a one-measurement algorithm that eliminates this bias, and has asymptotic convergence properties making for easier comparison with the two-measurement SPSA. The algorithm, under certain conditions, outperforms both forms of SPSA with the only overhead being the storage of a single measurement. We also propose a similar algorithm that uses perturbations obtained from normalized Hadamard matrices. The convergence w.p.1 of both algorithms is established. We extend measurement reuse to design three second-order SPSA algorithms, sketch the convergence analysis and present simulation results on an illustrative minimization problem. We then propose several stochastic approximation implementations for related algorithms in flow-control of communication networks, beginning with a discrete-time implementation of Kelly’s primal flow-control algorithm. Convergence with probability1 is shown, even in the presence of communication delays and stochastic effects seen in link congestion indications. Two relevant enhancements are then pursued :a) an implementation of the primal algorithm using second-order information, and b) an implementation where edge-routers rectify misbehaving flows. Also, discrete-time implementations of Kelly’s dual algorithm and primal-dual algorithm are proposed. Simulation results a) verifying the proposed algorithms and, b) comparing stability properties with an algorithm in the literature are presented.

Cette dissertation se divise en deux parties, distinctes mais connexes, qui sont le reflet de la cotutelle. Nous étudions et résolvons des problèmes concernant d'une part la combinatoire des mots dans un contexte abélien et d'autre part des problèmes de couverture dans des graphes. Chaque question fait l'objet d'un chapitre. En combinatoire des mots, le premier problème considéré s'intéresse à la régularité des suites au sens défini par Allouche et Shallit. Nous montrons qu'une suite qui satisfait une certaine propriété de symétrie est 2-régulière. Ensuite, nous appliquons ce théorème pour montrer que les fonctions de complexité 2-abélienne du mot de Thue--Morse ainsi que du mot appelé ''period-doubling'' sont 2-régulières. Les calculs et arguments développés dans ces démonstrations s'inscrivent dans un schéma plus général que nous espérons pouvoir utiliser à nouveau pour prouver d'autres résultats de régularité. Le deuxième problème poursuit le développement de la notion de mot de retour abélien introduite par Puzynina et Zamboni. Nous obtenons une caractérisation des mots sturmiens avec un intercepte non nul en termes du cardinal (fini ou non) de l'ensemble des mots de retour abélien par rapport à tous les préfixes. Nous décrivons cet ensemble pour Fibonacci ainsi que pour Thue--Morse (bien que cela ne soit pas un mot sturmien). Nous étudions la relation existante entre la complexité abélienne et le cardinal de cet ensemble. En théorie des graphes, le premier problème considéré traite des codes identifiants dans les graphes. Ces codes ont été introduits par Karpovsky, Chakrabarty et Levitin pour modéliser un problème de détection de défaillance dans des réseaux multiprocesseurs. Le rapport entre la taille optimale d'un code identifiant et la taille optimale du relâchement fractionnaire d'un code identifiant est comprise entre 1 et 2 ln(|V|)+1 où V est l'ensemble des sommets du graphe. Nous nous concentrons sur les graphes sommet-transitifs, car nous pouvons y calculer précisément la solution fractionnaire. Nous exhibons des familles infinies, appelées quadrangles généralisés, de graphes sommet-transitifs pour lesquelles les solutions entière et fractionnaire sont de l'ordre |V|^k avec k dans {1/4, 1/3, 2/5}. Le second problème concerne les (r,a,b)-codes couvrants de la grille infinie déjà étudiés par Axenovich et Puzynina. Nous introduisons la notion de 2-coloriages constants de graphes pondérés et nous les étudions dans le cas de quatre cycles pondérés particuliers. Nous présentons une méthode permettant de lier ces 2-coloriages aux codes couvrants. Enfin, nous déterminons les valeurs exactes des constantes a et b de tout (r,a,b)-code couvrant de la grille infinie avec |a-b|>4. Il s'agit d'une extension d'un théorème d'Axenovich. / This dissertation is divided into two (distinct but connected) parts that reflect the joint PhD. We study and we solve several questions regarding on the one hand combinatorics on words in an abelian context and on the other hand covering problems in graphs. Each particular problem is the topic of a chapter. In combinatorics on words, the first problem considered focuses on the 2-regularity of sequences in the sense of Allouche and Shallit. We prove that a sequence satisfying a certain symmetry property is 2-regular. Then we apply this theorem to show that the 2-abelian complexity functions of the Thue--Morse word and the period-doubling word are 2-regular. The computation and arguments leading to these results fit into a quite general scheme that we hope can be used again to prove additional regularity results. The second question concerns the notion of return words up to abelian equivalence, introduced by Puzynina and Zamboni. We obtain a characterization of Sturmian words with non-zero intercept in terms of the finiteness of the set of abelian return words to all prefixes. We describe this set of abelian returns for the Fibonacci word but also for the Thue-Morse word (which is not Sturmian). We investigate the relationship existing between the abelian complexity and the finiteness of this set. In graph theory, the first problem considered deals with identifying codes in graphs. These codes were introduced by Karpovsky, Chakrabarty and Levitin to model fault-diagnosis in multiprocessor systems. The ratio between the optimal size of an identifying code and the optimal size of a fractional relaxation of an identifying code is between 1 and 2 ln(|V|)+1 where V is the vertex set of the graph. We focus on vertex-transitive graphs, since we can compute the exact fractional solution for them. We exhibit infinite families, called generalized quadrangles, of vertex-transitive graphs with integer and fractional identifying codes of order |V|^k with k in {1/4,1/3,2/5}. The second problem concerns (r,a,b)-covering codes of the infinite grid already studied by Axenovich and Puzynina. We introduce the notion of constant 2-labellings of weighted graphs and study them in four particular weighted cycles. We present a method to link these labellings with covering codes. Finally, we determine the precise values of the constants a and b of any (r,a,b)-covering code of the infinite grid with |a-b|>4. This is an extension of a theorem of Axenovich.