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Consider a time-dependent optimal control problem, where the state evolution is described by an initial value problem. There are a variety of numerical methods to solve these problems. The so-called indirect approach is considered detailed in this thesis. The indirect methods solve decoupled boundary value problems resulting from the necessary conditions for the optimal control problem. The so-called Pantoja method describes a computationally efficient stage-wise construction of the Newton direction for the discrete-time optimal control problem. There are many relationships between multiple shooting techniques and Pantoja method, which are investigated in this thesis. In this context, the equivalence of Pantoja method and multiple shooting method of Riccati type is shown. Moreover, Pantoja method is extended to the case where the state equations are discretised using one of implicit numerical methods. Furthermore, the concept of symplecticness and Hamiltonian systems is introduced. In this regard, a suitable numerical method is presented, which can be applied to unconstrained optimal control problems. It is proved that this method is a symplectic one. The iterative solution of optimal control problems in ordinary differential equations by Pantoja or Riccati equivalent methods leads to a succession of triple sweeps through the discretised time interval. The second (adjoint) sweep relies on information from the first (original) sweep, and the third (final) sweep depends on both of them. Typically, the steps on the adjoint sweep involve more operations and require more storage than the other two. The key difficulty is given by the enormous amount of memory required for the implementation of these methods if all states throughout forward and adjoint sweeps are stored. One of goals of this thesis is to present checkpointing techniques for memory reduced implementation of these methods. For this purpose, the well known aspect of checkpointing has to be extended to a `nested checkpointing` for multiple transversals. The proposed nested reversal schedules drastically reduce the required spatial complexity. The schedules are designed to minimise the overall execution time given a certain total amount of storage for the checkpoints. The proposed scheduling schemes are applied to the memory reduced implementation of the optimal control problem of laser surface hardening and other optimal control problems. / Es wird ein Problem der optimalen Steuerung betrachtet. Die dazugehoerigen Zustandsgleichungen sind mit einer Anfangswertaufgabe definiert. Es existieren zahlreiche numerische Methoden, um Probleme der optimalen Steuerung zu loesen. Der so genannte indirekte Ansatz wird in diesen Thesen detailliert betrachtet. Die indirekten Methoden loesen das aus den Notwendigkeitsbedingungen resultierende Randwertproblem. Das so genannte Pantoja Verfahren beschreibt eine zeiteffiziente schrittweise Berechnung der Newton Richtung fuer diskrete Probleme der optimalen Steuerung. Es gibt mehrere Beziehungen zwischen den unterschiedlichen Mehrzielmethoden und dem Pantoja Verfahren, die in diesen Thesen detailliert zu untersuchen sind. In diesem Zusammenhang wird die aequivalence zwischen dem Pantoja Verfahren und der Mehrzielmethode vom Riccati Typ gezeigt. Ausserdem wird das herkoemlige Pantoja Verfahren dahingehend erweitert, dass die Zustandsgleichungen mit Hilfe einer impliziten numerischen Methode diskretisiert sind. Weiterhin wird das Symplektische Konzept eingefuehrt. In diesem Zusammenhang wird eine geeignete numerische Methode praesentiert, die fuer ein unrestringiertes Problem der optimalen Steuerung angewendet werden kann. In diesen Thesen wird bewiesen, dass diese Methode symplectisch ist. Das iterative Loesen eines Problems der optimalen Steuerung in gewoenlichen Differentialgleichungen mit Hilfe von Pantoja oder Riccati aequivalenten Verfahren fuehrt auf eine Aufeinanderfolge der Durchlaeufetripeln in einem diskretisierten Zeitintervall. Der zweite (adjungierte) Lauf haengt von der Information des ersten (primalen) Laufes, und der dritte (finale) Lauf haeng von den beiden vorherigen ab. Ueblicherweise beinhalten Schritte und Zustaende des adjungierten Laufes wesentlich mehr Operationen und benoetigen auch wesentlich mehr Speicherplatzkapazitaet als Schritte und Zustaende der anderen zwei Durchlaeufe. Das Grundproblem besteht in einer enormen Speicherplatzkapazitaet, die fuer die Implementierung dieser Methoden benutzt wird, falls alle Zustaende des primalen und des adjungierten Durchlaufes zu speichern sind. Ein Ziel dieser Thesen besteht darin, Checkpointing Strategien zu praesentieren, um diese Methoden speichereffizient zu implementieren. Diese geschachtelten Umkehrschemata sind so konstruiert, dass fuer einen gegebenen Speicherplatz die gesamte Laufzeit zur Abarbeitung des Umkehrschemas minimiert wird. Die aufgestellten Umkehrschemata wurden fuer eine speichereffiziente Implementierung von Problemen der optimalen Steuerung angewendet. Insbesondere betrifft dies das Problem einer Oberflaechenabhaertung mit Laserbehandlung.

Cette thèse présente une étude des applications des groupes de réflexion finis aux problems liés aux réseaux bidimensionnels et aux polytopes tridimensionnels. Plusieurs familles de fonctions orbitales, appelées fonctions orbitales de Weyl, sont associées aux groupes de réflexion cristallographique. Les propriétés exceptionnelles de ces fonctions, telles que l’orthogonalité continue et discrète, permettent une analyse de type Fourier sur le domaine fondamental d’un groupe de Weyl affine correspondant. Dans cette considération, les fonctions d’orbite de Weyl constituent des outils efficaces pour les transformées discrètes de type Fourier correspondantes connues sous le nom de transformées de Fourier–Weyl. Cette recherche limite notre attention aux fonctions d’orbite de Weyl symétriques et antisymétriques à deux variables du groupe de réflexion cristallographique A2. L’objectif principal est de décomposer deux types de transformations de Fourier–Weyl du réseau de poids correspondant en transformées plus petites en utilisant la technique de division centrale. Pour les cas non cristallographiques, nous définissons les indices de degré pair et impair pour les orbites des groupes de réflexion non cristallographique avec une symétrie quintuple en utilisant un remplacement de représentation-orbite. De plus, nous formulons l’algorithme qui permet de déterminer les structures de polytopes imbriquées. Par ailleurs, compte tenu de la pertinence de la symétrie icosaédrique pour la description de diverses molécules sphériques et virus, nous étudions la brisure de symétrie des polytopes doubles de type non cristallographique et des structures tubulaires associées. De plus, nous appliquons une procédure de stellation à la famille des polytopes considérés. Puisque cette recherche se concentre en partie sur les fullerènes icosaédriques, nous présentons la construction des nanotubes de carbone correspondants. De plus, l’approche considérée pour les cas non cristallographiques est appliquée aux structures cristallographiques. Nous considérons un mécanisme de brisure de symétrie appliqué aux polytopes obtenus en utilisant les groupes Weyl tridimensionnels pour déterminer leurs extensions structurelles possibles en nanotubes. / This thesis presents a study of applications of finite reflection groups to the problems related to two-dimensional lattices and three-dimensional polytopes. Several families of orbit functions, known as Weyl orbit functions, are associated with the crystallographic reflection groups. The exceptional properties of these functions, such as continuous and discrete orthogonality, permit Fourier-like analysis on the fundamental domain of a corresponding affine Weyl group. In this consideration, Weyl orbit functions constitute efficient tools for corresponding Fourier-like discrete transforms known as Fourier–Weyl transforms. This research restricts our attention to the two-variable symmetric and antisymmetric Weyl orbit functions of the crystallographic reflection group A2. The main goal is to decompose two types of the corresponding weight lattice Fourier–Weyl transforms into smaller transforms using the central splitting technique. For the non-crystallographic cases, we define the even- and odd-degree indices for orbits of the non-crystallographic reflection groups with 5-fold symmetry by using a representation-orbit replacement. Besides, we formulate the algorithm that allows determining the structures of nested polytopes. Moreover, in light of the relevance of the icosahedral symmetry to the description of various spherical molecules and viruses, we study symmetry breaking of the dual polytopes of non-crystallographic type and related tube-like structures. As well, we apply a stellation procedure to the family of considered polytopes. Since this research partly focuses on the icosahedral fullerenes, we present the construction of the corresponding carbon nanotubes. Furthermore, the approach considered for the non-crystallographic cases is applied to crystallographic structures. We consider a symmetry-breaking mechanism applied to the polytopes obtained using the three-dimensional Weyl groups to determine their possible structural extensions into nanotubes.

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In this project, we address the task of nested noun phrase identification in English sentences, where a phrase is defined as a group of words functioning as one unit in a sentence. Prior research has extensively explored the identification of various phrases for language understanding and text generation tasks. Our aim is to tackle the novel challenge of identifying nested noun phrases within sentences. To accomplish this, we first review existing work on related topics such as partial parsing and noun phrase identification. Subsequently, we propose a novel approach based on transformer models to recursively identify nested noun phrases in sentences. We fine-tune a pre-trained uncased BERT model to detect phrase structures in a sentence and determine whether they represent noun phrases. Our recursive approach involves merging relevant segments of a sentence and assigning labels to the noun phrases at each step, facilitating the identification of nested structures. The evaluation of our model demonstrates promising results, achieving a high accuracy of up to 93.6% when considering all noun phrases in isolation and 90.9% when accounting for the predicted phrase structure of the sentence. Additionally, our model exhibits a recall rate of 83.5% and 81.2% at both levels, respectively. Overall, our model proves to be effective in identifying nested noun phrases, showcasing the potential of transformer-based models in phrase structure identification. Future research should explore further applications and enhancements of such models in this domain. / I detta projekt tar vi upp uppgiften att identifiera nästlade substantivfraser i engelska meningar, där en fras definieras som en grupp ord som fungerar som en enhet i en mening. Tidigare forskning har utförligt utforskat identifieringen av olika fraser för språkförståelse och textgenereringsuppgifter. Vårt mål är att ta itu med den nya utmaningen att identifiera nästlade substantivfraser i meningar. För att åstadkomma detta granskar vi först befintligt arbete med relaterade ämnen som partiell analys och identifiering av substantivfraser. Därefter föreslår vi en ny metod baserad på transformers-modeller för att rekursivt identifiera nästlade substantivfraser i meningar. Vi finjusterar en förtränad BERT-modell utan kapsling för att upptäcka frasstrukturer i en mening och avgöra om de representerar substantivfraser. Vårt rekursiva tillvägagångssätt innebär att sammanfoga relevanta segment av en mening och att tilldela etiketter till substantivfraserna vid varje steg, vilket underlättar identifieringen av nästlade strukturer. Utvärderingen av vår modell visar lovande resultat och uppnår en hög precision på upp till 93,6% när man tar hänsyn till alla substantivfraser isolerat och 90,9% när man tar hänsyn till meningens förutsagda frasstruktur. Dessutom uppvisar vår modell en täckning (recall) på 83,5% respektive 81,2% på båda nivåerna. Sammantaget visar vår modell sig vara effektiv för att identifiera nästlade substantivfraser, vilket visar potentialen hos transformers-modeller för identifiering av frasstruktur. Framtida forskning bör utforska ytterligare tillämpningar och förbättringar av sådana modeller på detta område.

[pt] Transmission switching já foi apresentado anteriormente como uma ferramenta capaz de prover benefícios significativos na operação de sistemas de potência, como redução de custos e aumento de confiabilidade. Dentro do contexto de mercados co-otimizados para energia e reservas, este trabalho endereça a co-otimização de transmission switching pós-contingência no planejamento da operação de sistemas elétricos. Os modelos propostos para programação diária e despacho econômico diferem de formulações existentes devido à consideração conjunta de três fatores complicadores. Primeiro, ações de transmission switching são consideradas nos estados pré e pós-contingência, portanto requerendo variáveis binárias pós-contingência. Adicionalmente, a programação de geradores e as ações de transmission switching são co-otimizadas. Além disso, a operação de geradores é caracterizada temporalmente em um contexto multi-período. Os modelos propostos são formulados como programas inteiros-mistos desafiadores para os quais os softwares comerciais comumente utilizados para modelos mais simples podem levar à intratabilidade até para instâncias de tamanho moderado. Como metodologia de solução, nós apresentamos uma versão aperfeiçoada de um algoritmo de geração de colunas e restrições aninhado, com a adição de restrições válidas para melhorar o desempenho computacional. Simulações numéricas demonstram o desempenho efetivo da abordagem proposta, assim como suas vantagens econômicas e operacionais sobre modelos existentes que desconsideram o transmission switching pós-contingência. / [en] Transmission switching has been previously shown to offer significant benefits to power system operation, such as cost savings and reliability enhancements. Within the context of co-optimized electricity markets for energy and reserves, this work addresses the co-optimization of post contingency transmission switching in power system operation planning. The proposed models for unit commitment and economic dispatch differ from existing formulations due to the joint consideration of three major complicating factors. First, transmission switching actions are considered both in the preand post-contingency states, thereby requiring binary post-contingency variables. Secondly, generation scheduling and transmission switching actions are co-optimized. In addition, the time coupled operation of generating units is precisely characterized. The proposed models are formulated as challenging mixed-integer programs for which the off-the-shelf software customarily used for simpler models may lead to intractability even for moderatelysized instances. As a solution methodology, we present enhanced versions of an exact nested column-and-constraint generation algorithm featuring the inclusion of valid constraints to improve the overall computational performance. Numerical simulations demonstrate the effective performance of the proposed approach as well as its economic and operational advantages over existing models disregarding post-contingency transmission switching.

The quest towards resolving concerns about transportation energy consumption and emissions across nations has created more interests to investigate factors responsible for households’ car ownership. While literature holds an extensive body of investigation usually compartmentalised in individual different disciplines, limited efforts have been made to promote inter-linkages of this strand of research across different disciplines. To fill this gap, this study developed an integrating Multinomial logit (MNL) model to examine the impact of some rarely-investigated and conventional explanatory variables, including: ethnicity, accommodation tenure, settlement nature, mental belief, environmental concern, geographical regions, household structure, driving licence, number of household income earners and household income, on car ownership. Analysis based on rich data sets of British Household Survey and US Consumer Expenditure Survey found not only the conventional explanatory variables to be significantly linked to the number of cars in the US and UK households, but also the rarely-investigated psychological variables were found to be significantly linked as well. As Socio-demography, Geography and Psychology impact on how people and households process information and assess market offers (e.g., products and services), this study presents findings which have beneficial implications for policymakers and transportations planners, including those who would like to alter people’s behaviour from private car ownership to public transportation use, car sellers in terms of how to identify and reach potential customers, provision of alternative forecasting approaches to car ownership scholars as well as possible consideration for general car ownership decision making. Caution should be taken when interpreting the relationship between psychological factors and car ownership since the psychological factors adopted are measure representatives from databases used with limitations in the factor structure for a representative sample of the countries’ population.

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The notion of a fuzzy metric space due to George and Veeramani has many advantages in analysis since many notions and results from classical metric space theory can be extended and generalized to the setting of fuzzy metric spaces, for instance: the notion of completeness, completion of spaces as well as extension of maps. The layout of the dissertation is as follows: Chapter 1 provide the necessary background in the context of metric spaces, while chapter 2 presents some concepts and results from classical metric spaces in the setting of fuzzy metric spaces. In chapter 3 we continue with the study of fuzzy metric spaces, among others we show that: the product of two complete fuzzy metric spaces is also a complete fuzzy metric space. Our main contribution is in chapter 4. We introduce the concept of a standard fuzzy pseudo metric space and present some results on fuzzy metric identification. Furthermore, we discuss some properties of t-nonexpansive maps. / Mathematical Sciences / M. Sc. (Mathematics)

The purpose of this project is to argue that we possess a minimal self. It will demonstrate that minimal selfhood arrives early in our development and continues to remain and influence us throughout our entire life. There are two areas of research which shape my understanding of the minimal self: phenomenology and enactivism. Phenomenology emphasizes the sense of givenness, ownership, or mineness that accompanies all of our experiences. Enactivism says there is a sensorimotor coupling that occurs between us and the environment in a way which modulates the dynamic patterns of our self development; the laying down of these basic patterns helps make us who we are and gives rise to the phenomenological, experiential mineness. Drawing on these two core ideas, I will be arguing for a Phenomenological-Enactive Minimal Self (abbreviated PEMS). I will be emphasizing the role of the body and the role of affects (moods, feelings, and emotions) as the most important components relevant to understanding minimal selfhood. Put more concretely, the set of conditions which constitute the PEMS view are: (i) The minimal self is the experiential subject; the minimal sense of self is present whenever there is awareness. It is the subjectivity of experience, the sense of mineness, or givenness which our experiences contain. (ii) The phenomenological part of the PEMS view turns on the idea of a bodily and dynamic integration of sensorimotor coupling and affective experience. It is, ontologically speaking, the lived body in enactive engagement with the environment. It is this embodied subject which anchors and forms the foundation for the later ‘narrative' self, which emerges from it and which is continually influenced by it. It is the subject enactively engaged with others, dependent on sensorimotor processes and affects. We have an identity, but it emerges from relational and dynamic processes.