The study of geometric group theory has suggested several theorems related to subdivision tilings that have a natural hyperbolic structure. However, few examples exist. We construct subdivision tilings for the complement of every nonsingular, prime alternating link and all torus links, and explore some of their properties and applications. Several examples are exhibited with color coding of tiles.

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The research in this dissertation is focused on the synthesis and characterization of sterically crowded, precisely charged polyelectrolytes based on substituted stilbene comonomers. New sterically crowded polyelectrolytes based on functionalized stilbenes with maleic anhydride or functionalized N-phenylmaleimides were prepared via a "protected" precursor polymer strategy. The polyelectrolyte precursors readily dissolved in organic solvents and were characterized by 1H NMR, SEC, TGA, and DSC. The polyelectrolytes were obtained via simple deprotection chemistries. The use of different combinations of the donor-acceptor comonomer pairs and the alternating copolymerization of these comonomers lead to precise control over charge density and placement of charged groups along the polymer backbone. Analogous styrenic copolymers, for direct comparison to the stilbene structures, were also prepared. Broad peaks in 1H NMR spectra were observed. There were no thermal transitions measured by DSC below the degradation temperature. A strong polyelectrolyte effect, for both stilbene and styrene copolymers, occurred in deionized water and was suppressed by adding NaCl to the polymer solution. These results are not consistent with "rigid" rod polyelectrolytes in which chain collapse in the presence of added salt and chain expansion on dilution should not be observed. In response to these observations persistence length measurements were conducted on the stilbene and styrene copolymers to assess directly the steric crowding effect of added phenyl groups in stilbene copolymers. Both SEC and SAXS measurements were used to obtain persistence lengths. The results from three different approaches, Bohdanecký, graphical and Sharp and Bloomfield Global, were in good agreement. The persistence lengths of stilbene containing copolymers range from 3 to 6 nm and the added phenyl groups increase the rigidity of the polymer chain by about 30-50%. This puts these polymers into a broadly defined "semi-rigid" category of polymers and is consistent with the solution polyelectrolyte effect observed. In dilute solution characterization of stilbene containing polyanions, a 2-step dissociation behavior was observed for the two adjacent carboxylic acids in maleic acid containing polyanions. Stilbene polyanion solutions showed high Rh values in deionized water as shown by DLS measurements and a decrease of Rh values followed by aggregation upon gradual addition of salt. Bimodal peaks were observed in SEC measurements with the copolymer of 4-methylstilbene and maleic anhydride. DLS measurements indicated interchain aggregation as the origin of the apparent high molecular weight fraction. The antiviral activity of the polyanion based on sodium 4-styrenesulfonate and N-(4-sodium sulfophenyl)maleimide was found to be ~50 times higher than the microbicide, sodium poly(styrene sulfonate). The early study of antiviral activities of carboxylated stilbene and styrene polyanions also showed promising results. The synthesis of methyl sulfonate ester-functionalized polyanion precursors was attempted because they can be characterized without the complications caused by directly using charged sulfonate groups. / Ph. D.

The primary purpose of this thesis is to present, in clear and logical form, an analysis of high-frequency modulation. This will be done in order to explain each of the various methods of obtaining modulation, and the characteristics of the resultant waves. The question of side bands will be considered in detail. The subject of circuits and associated apparatus is of secondary importance, emphasis being placed on the fundamental electric theory. From this point of view, possibilities for improvement and new developments will be investigated. / Master of Science

Stilbene containing polymers are a group of interesting and versatile polymers. The pendent phenyl ring along the polymer backbone can impart unusual rigidity to the polymer backbone due to steric repulsion. By functionalizing stilbene, a variety of functional groups and ionic groups can be precisely placed along the polymer chain with tunable charge density. Therefore, stilbene containing polymers are potentially rod-like polyelectrolytes with controllable charges and charge density. They are the basis of a novel group of rigid synthetic polyelectrolytes and can be used for furthering our knowledge of rigid polyelectrolytes. A novel series of methyl substituted stilbenes were synthesized and copolymerized with maleic anhydride. A conversion-time study was undertaken to understand the methyl substituent effect on copolymerization rates. Methyl substituted stilbene-maleic anhydride copolymer compositions were determined by quantitative ¹³C 1D NMR. SEC measurements showed the weight average molecular weights of these copolymers vary from 3 000 to over 1 000 000 g/mol. No glass transition temperature or crystalline melting temperature was observed between 0 °C and 250 °C by DSC. TGA showed that these polymers have 5% weight loss around 290 °C. Precursors to a polycation and a polyanion based on functionalized stilbenes and maleimides have been prepared: poly(di-t-butyl-(E)-4,4′-stilbenedicarboxylate-co- N-(4-(t-butoxycarbonyl)phenyl)maleimide) and poly(N,N,Nâ ,Nâ -tetraalkyl-4,4′-di- aminostilbenes-co-N-4-(N′,N′-dimethylaminophenyl)-maleimide). These copolymer precursors were characterized by ¹H NMR, SEC, TGA, and DSC. The ¹H NMR spectrum indicated the rigidity of copolymer backbones. SEC measurements showed the weight average molecular weights of these copolymers vary from 5 000 to 11 700 g/mol. No glass transition temperature or crystalline melting temperature was observed between 0 °C and 175 °C by DSC for poly(di-t-butyl-(E)-4,4′-stilbenedicarboxylate-co-N-(4-(t-butoxy- carbonyl)phenyl)maleimide). TGA showed that this polymer has 5% weight loss around 210 °C and 26% weight loss on the first stage of decomposition which corresponds to elimination of t-butyl functional group in the copolymer. The homopolymerization of EMS-III via free radical polymerization, anionic polymerization and cationic polymerization was attempted. However, no polymer was obtained from any of these polymerization methods. In anionic polymerization, the solution changed to red upon the addition of the initiator sec-bu-Li, indicating the successful addition of the sec-bu-Li to EMS-III. However, the initiated monomer did not propagate to form homopolymer. / Master of Science

The dissertation presents a new control strategy for two terminal HVDC systems embedded in an AC network. The control is based upon real-time measurements performed on the AC/DC system. Use is made of a technique for high speed accurate measurement of positive sequence voltages and currents, first developed in the field of computer relaying. The real-time measurements provides a term in the control law to compensate for inaccuracies following departure from the operating point. The control criterion is to damp out the electromechanical oscillations following a disturbance. The main contribution of the dissertation is to describe a new optimal controller formulation which contains a measurement based component. Optimal controllers are commonly constructed using linearized equations of the system around the operating point. In DC systems this approach is of a very limited value because of a highly nonlinear nature of the system. With the controller developed in this dissertation, it becomes possible to describe the system as a nonlinear dynamic system. The approximation resulting from the usual linearization of the system equations is thus avoided, and leads to a better controller design. The control technique is illustrated with a small AC/DC system. However, the equations formulated are sufficiently general, so that the technique can be applied to a larger system. Simulation results are included to represent the effectiveness of the developed controller. / Ph. D.

Beethoven's early sonatas have already revealed a complex and varied technique that can present significant difficulties for intermediate piano students. In particular, the absence of systematic methodological guidance, as well as the lack of suitable and high-quality repertoire, can result in students struggling to learn Beethoven's piano technique and not being satisfied with the results. By examining and analyzing the theories of great educators, pedagogues, and performers, some of the standard technical patterns are identified and methods of mastering them are summarized. A sampling of related late-elementary level and intermediate level repertoire is identified, providing study material for students starting to learn the Beethoven sonatas, and serving as a guide for their teachers.

Alternating minimization (AltMin) is a generic term for a widely popular approach in non-convex learning: often, it is possible to partition the variables into two (or more) sets, so that the problem is convex/tractable in one set if the other is held fixed (and vice versa). This allows for alternating between optimally updating one set of variables, and then the other. AltMin methods typically do not have associated global consistency guarantees; even though they are empirically observed to perform better than methods (e.g. based on convex optimization) that do have guarantees. In this thesis, we obtain rigorous performance guarantees for AltMin in three statistical learning settings: low rank matrix completion, phase retrieval and learning sparsely-used dictionaries. The overarching theme behind our results consists of two parts: (i) devising new initialization procedures (as opposed to doing so randomly, as is typical), and (ii) establishing exponential local convergence from this initialization. Our work shows that the pursuit of statistical guarantees can yield algorithmic improvements (initialization in our case) that perform better in practice. / text

Notre société étant plus dépendante que jamais au vecteur électrique, la moindre perturbation du transport ou de l’acheminement de l’électricité a un impact social et économique important. La fiabilité et la sécurité des réseaux électriques sont donc cruciales pour les gestionnaires de réseaux, en plus des aspects économiques. De plus, les réseaux de transport sont interconnectés pour réduire les coûts des opérations et pour améliorer la sécurité. Un des plus grand défis des gestionnaires des réseaux de transport est ainsi de se coordonner avec les réseaux voisins, ce qui soulève des problèmes liés à la taille du problème, à l’interopérabilité et à la confidentialité des données.Cette thèse se focalise principalement sur la sécurité des opérations sur les réseaux électriques, c’est pourquoi l’évolution des principales caractéristiques des blackouts, qui sont des échecs de la sécurité des réseaux, sont étudiés sur la période 2005-2016. L’approche de cette étude consiste à déterminer quelles sont les principales caractéristiques des incidents de ces 10 dernières années, afin d’identifier ce qui devrait être intégré pour réduire le risque que ces incidents se reproduisent. L’évolution a été étudiée et comparé avec les caractéristiques des blackouts qui se sont produit avant 2005. L’étude se focalise sur les préconditions qui ont mené à ces blackouts et sur les cascades, et particulièrement sur le rôle de la vitesse des cascades. Les caractéristiques importante sont extraites et intégrées dans la suite de notre travail.Un algorithme résolvant un problème préventif d’Optimal Power Flow avec contraintes de sécurité (SCOPF) de manière distribuée est ainsi développé. Ce problème consiste en l’ajout de contraintes qui assure qu’après la perte de n’importe quel appareil d’importance, le nouveau point d’équilibre, atteint suite au réglage primaire en fréquence, respecte les contraintes du système. L’algorithme développé utilise une décomposition fine du problème et est implémenté sous le paradigme multi-agent, basé sur deux catégories d’agents : les appareils et les bus. Les agents sont coordonnés grâce à l’ « Alternating Direction Method of Multipliers (ADMM)» et grâce à un problème de consensus. Cette décomposition procure l’autonomie et la confidentialité nécessaire aux différents acteurs du système, mais aussi, un bon passage à l’échelle par rapport à la taille du problème. Cet algorithme a aussi pour avantage d’être robuste à n’importe quelle perturbation, incluant la séparation du système en plusieurs régions.Puis, pour prendre en compte l’incertitude sur la production créée par les erreurs de prédiction des fermes éoliennes, une approche distribuée à deux étapes est développée pour résoudre un problème d’Optimal Power Flow avec contraintes probabilistes (CCOPF), d’une manière complétement distribuée. Les erreurs de prédiction des fermes éoliennes sont modélisées par des lois normales indépendantes et les écarts par rapport aux plannings de production sont considérés compensés par le réglage primaire en fréquence. La première étape de l’algorithme a pour but de déterminer des paramètres de sensibilités nécessaires pour formuler le problème. Les résultats de cette étape sont ensuite des paramètres d’entrée de la seconde étape qui, elle, résout le problème de CCOPF. Une extension de cette formulation permet d’ajouter de la flexibilité au problème en permettant la réduction de la production éolienne. Cet algorithme est basé sur la même décomposition fine que précédemment où les agents sont également coordonnés par l’ADMM et grâce à un problème de consensus. En conclusion, cet algorithme en deux étapes garantit la confidentialité et l’autonomie des différents acteurs, et est parallèle et adaptée aux plateformes hautes performances. / Our societies are more dependent on electricity than ever, thus any disturbance in the power transmission and delivery has major economic and social impact. The reliability and security of power systems are then crucial to keep, for power system operators, in addition to minimizing the system operating cost. Moreover, transmission systems are interconnected to decrease the cost of operation and improve the system security. One of the main challenges for transmission system operators is therefore to coordinate with interconnected power systems, which raises scalability, interoperability and privacy issues. Hence, this thesis is concerned with how TSOs can operate their networks in a decentralized way but coordinating their operation with other neighboring TSOs to find a cost-effective scheduling that is globally secure.The main focus of this thesis is the security of power systems, this is why the evolution of the main characteristics of the blackouts that are failures in power system security, of the period 2005-2016 is studied. The approach consists in determining what the major characteristics of the incidents of the past 10 years are, to identify what should be taken into account to mitigate the risk of incidents. The evolution have been studied and compared with the characteristics of the blackouts before 2005. The study focuses on the pre-conditions that led to those blackouts and on the cascades, and especially the role of the cascade speed. Some important features are extracted and later integrated in our work.An algorithm that solve the preventive Security Constrained Optimal Power Flow (SCOPF) problem in a fully distributed manner, is thus developed. The preventive SCOPF problem consists in adding constraints that ensure that, after the loss of any major device of the system, the new steady-state reached, as a result of the primary frequency control, does not violate any constraint. The developed algorithm uses a fine-grained decomposition and is implemented under the multi-agent system paradigm based on two categories of agents: devices and buses. The agents are coordinated with the Alternating Direction method of multipliers in conjunction with a consensus problem. This decomposition provides the autonomy and privacy to the different actors of the system and the fine-grained decomposition allows to take the most of the decomposition and provides a good scalability regarding the size of the problem. This algorithm also have the advantage of being robust to any disturbance of the system, including the separation of the system into regions.Then, to account for the uncertainty of production brought by wind farms forecast error, a two-step distributed approach is developed to solve the Chance-Constrained Optimal Power Flow problem, in a fully distributed manner. The wind farms forecast errors are modeled by independent Gaussian distributions and the mismatches with the initials are assumed to be compensated by the primary frequency response of generators. The first step of this algorithm aims at determining the sensitivity factors of the system, needed to formulate the problem. The results of this first step are inputs of the second step that is the CCOPF. An extension of this formulation provides more flexibility to the problem and consists in including the possibility to curtail the wind farms. This algorithm relies on the same fine-grained decomposition where the agents are again coordinated by the ADMM and a consensus problem. In conclusion, this two-step algorithm ensures the privacy and autonomy of the different system actors and it is de facto parallel and adapted to high performance platforms.