Este trabalho tem dois objetivos principais. Primeiramente, analisamos a preservação de conexidade na extensão de espaços compactos por funções contínuas, técnica utilizada por Koszmider para obter $C(K)$ indecomponível com poucos operadores. Mostramos que para todo compacto metrizável $K$ existe um desconexo $L$ que é obtido a partir de $K$ por uma quantidade finita de extensões por funções contínuas. Em seguida, enfatizamos a construção de espaços de Banach da forma $C(K)$ com poucos operadores, com a propriedade de que $C(L)$ tem poucos operadores, para todo fechado $L \\subseteq K$. Assumindo o princípio diamante construímos uma família $(K_\\xi)_{\\xi < 2^{(2^\\omega)}}$ de espaços conexos e hereditariamente Koszmider tais que todo operador de $C(K_\\xi)$ em $C(K_\\eta)$ é fracamente compacto, para $\\xi$ diferente de $\\eta$. Em particular, $(C(K_\\xi))_{\\xi < 2^{(2^\\omega)}}$ é uma família de espaços de Banach indecomponíveis e dois a dois essencialmente incomparáveis, e cada espaço $K_\\xi$ responde positivamente ao problema de Efimov. Apresentamos também um método de construção via forcing de um espaço compacto e conexo $K$ hereditariamente fracamente Koszmider. / This work has two main objectives. First, we analyze the preservation of connectedness in the extension of compact spaces by continuous functions, a technique used by Koszmider to obtain an indecomposable Banach space $C(K)$ with few operators. We show that for any metrizable compactum $K$ there exists a disconnected $L$ which is obtained from $K$ by finitely many extensions by continuous functions. Next, we emphasize the construction of Banach spaces of the form $C(K)$ with the property that $C(L)$ has few operators, for every closed $L \\subseteq K$. Assuming the diamond principle we construct a family $(K_\\xi)_{\\xi < 2^{(2^\\omega)}}$ of connected and hereditarily Koszmider spaces such that every operator from $C(K_\\xi)$ into $C(K_\\eta)$ is weakly compact, for $\\xi$ different from $\\eta$. In particular, $(C(K_\\xi))_{\\xi < 2^{(2^\\omega)}}$ is a family of indecomposable and pairwise essentially incomparable Banach spaces, and each space $K_\\xi$ responds positively to the Efimov\'s problem. We also present a method of construction using forcing of a compact and connected hereditarily weakly Koszmider space $K$.

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This thesis concerns two topics. The first topic, that is related to the Dedekind-Mertens Lemma, the notion of the so-called content algebra, is discussed in chapter 2. Let $R$ be a commutative ring with identity and $M$ be a unitary $R$-module and $c$ the function from $M$ to the ideals of $R$ defined by $c(x) = \cap \lbrace I \colon I \text{~is an ideal of~} R \text{~and~} x \in IM \rbrace $. $M$ is said to be a \textit{content} $R$-module if $x \in c(x)M $, for all $x \in M$. The $R$-algebra $B$ is called a \textit{content} $R$-algebra, if it is a faithfully flat and content $R$-module and it satisfies the Dedekind-Mertens content formula. In chapter 2, it is proved that in content extensions, minimal primes extend to minimal primes, and zero-divisors of a content algebra over a ring which has Property (A) or whose set of zero-divisors is a finite union of prime ideals are discussed. The preservation of diameter of zero-divisor graph under content extensions is also examined. Gaussian and Armendariz algebras and localization of content algebras at the multiplicatively closed set $S^ \prime = \lbrace f \in B \colon c(f) = R \rbrace$ are considered as well. In chapter 3, the second topic of the thesis, that is about the grade of the zero-divisor modules, is discussed. Let $R$ be a commutative ring, $I$ a finitely generated ideal of $R$, and $M$ a zero-divisor $R$-module. It is shown that the $M$-grade of $I$ defined by the Koszul complex is consistent with the definition of $M$-grade of $I$ defined by the length of maximal $M$-sequences in I$. Chapter 1 is a preliminarily chapter and dedicated to the introduction of content modules and also locally Nakayama modules.

With the growing need for secure and high-capacity communications, innovative solutions are needed to meet the demands of tomorrow. One such innovation is to make use of the still unutilized spatial dimension of light in communications, which has promising applications in both enabling higher data traffic as well as the security protocols of the future in quantum communications. The perhaps most promising way of realizing this technology is through spatial division multiplexing (SDM) in optical fibers. There are many challenges and open questions in implementing this, such as how perturbations to the signal should be kept under control and which type of optical fiber to use. Consequently, this thesis focuses on the implementation of SDM in few-mode fibers where the perturbation effects on the spatial distribution have been investigated. Following this investigation, an implementation of adaptive spatial mode control using a motorized polarization controller has been implemented. The mode control has been done with the focus on having relevance for quantum technology applications such as Quantum Key Distribution (QKD) and quantum random number generation (QRNG) but also for spatial division multiplexing (SDM) for general communications. For this reason, two evaluation metrics have been optimized for: extinction ratio and equal amplitude. The control algorithm used is an adaptation of the optimization algorithm Stochastic Parallel Gradient Descent (SPGD). Control has been achieved in stabilizing the extinction ratio of LP11a and LP11b over 12 hours with an average extinction ratio of 98 %. Additionally, equal amplitude between LP11a and LP11b has been achieved over 1 hour with an average relative difference of 0.42 % and 0.45 %. Out of the perturbation effects investigated; temperature caused large disturbances to the signal which later is corrected for with the implemented algorithm.

This master’s thesis explores a space-division-multiplexing (SDM) platform fora delayed-choice experiment. SDM is a multiplexing technique for optical datatransmission that employs spatial modes in a multi- or few-mode fiber to increasethe transmission capacity. The spatial modes can thus be used as separate channels. SDM have shown great potential for quantum information systems, making it intriguing to investigate its broad applications by examining its use in adelayed-choice experiment. The delayed-choice experiment was proposed by J.A.Wheeler in 1978 explored the particle- and wave-like behavior of quantum particles and observe if the particle knows in advance if it should propagate as a waveor a particle through the experimental platform. Hence, it was suggested thatthe experiment should be changed after the particle entered the experimentalplatform. The experiment has afterward been realized in many different constellations but previous wave-particle delayed-choice experiments have not beendemonstrated with SDM nor with an all in fiber platform. The research involved modeling and constructing a SDM fiber-optic platform,only utilizing commercially available fiber optical telecommunication components. The platform was constructed with photonic lanterns, used as spatial division multiplexer and demultiplexer, and a two-input fiber Sagnac Interferometer,as a removable beam splitter. The system was tested with classical light but without difficulties, the platform could move to the quantum domain for performingthe delayed-choice experiment with single photons on the platform. The thesis resulted in a SDM platform with good performance for future measurement of bothparticle- and wave-like behavior of photons in a delayed-choice experiment.

<p>Nuclear engineering hosts diverse domains including, but not limited to, power plant automation, human-machine interfacing, detection and identification of special nuclear materials, modeling of reactor kinetics and dynamics that most frequently are described by systems of differential equations (DEs), either ordinary (ODEs) or partial ones (PDEs). In this work we study multiple problems related to safety and Special Nuclear Material detection, and numerical solutions for partial differential equations using neural networks. More specifically, this work is divided in six chapters. Chapter 1 is the introduction, in Chapter</p> <p>2 we discuss the development of a gamma-ray radionuclide library for the characterization</p> <p>of gamma-spectra. In Chapter 3, we present a new approach, the ”Variance Counterbalancing”, for stochastic</p> <p>large-scale learning. In Chapter 4, we introduce a systematic approach for constructing proper trial solutions to partial differential equations (PDEs) of up to second order, using neural forms that satisfy prescribed initial, boundary and interface conditions. Chapter 5 is about an alternative, less imposing development of neural-form trial solutions for PDEs, inside rectangular and non-rectangular convex boundaries. Chapter 6 presents an ensemble method that avoids the multicollinearity issue and provides</p> <p>enhanced generalization performance that could be suitable for handling ”few-shots”- problems frequently appearing in nuclear engineering.</p>

Les modélisateurs rencontrent souvent des défis ou des difficultés lorsqu’il s’agit de concevoir un modèle logiciel particulier. Dans cette thèse, nous avons exploré différentes voies et examiné différentes approches pour résoudre cette problématique. Nous proposons enfin une approche simple mais novatrice qui améliore la complétion des activités de modélisation de domaines. Cette approche exploite la puissance des modèles de langage de grande taille en utilisant l’apprentissage par seulement quelques exemples, éliminant ainsi la nécessité d’un apprentissage profond ou d’un ajustement fin (fine tuning) sur des ensembles de données rares dans ce domaine. L’un des points forts de notre approche est sa polyvalence, car elle peut s’intégrer fa cilement à de nombreuses activités de modélisation, fournissant un aide précieux et des recommendations aux modélisateurs. De plus, nous avons mené une étude utilisateur pour évaluer l’utilité de cette méthode et la valeur de l’assistance en modélisation; nous avons cherché à savoir si l’effort investi dans l’assistance en modélisation vaut la peine en recueillant les commentaires des concepteurs de modèles logiciels. / Modelers often encounter challenges or difficulties when it comes to designing a particular software model. Throughout this thesis, we have explored various paths and examined different approaches to address this issue. We finally propose a simple yet novel approach enhancing completion in domain modeling activities. This approach leverages the power of large language models by utilizing few-shot prompt learning, eliminating the need for extensive training or fine-tuning on scarce datasets in this field. One of the notable strengths of our approach lies in its versatility, as it can be seamlessly integrated into various modeling activities, providing valuable support and recommendations to software modelers. Additionally, we conducted a user study to evaluate the usefulness of this approach and determine the value of providing assistance in modeling; we aimed to determine if the effort invested in modeling assistance is worthwhile by gathering feedback from software modelers.

L'intelligence artificielle est un domaine en pleine évolution. Au premier plan des percées récentes se retrouve des approches connues sous le nom d'apprentissage automatique. Cependant, bien que l'apprentissage automatique ait montré des performances remarquables dans des tâches telles que la reconnaissance et la génération d'images, la génération et la traduction de textes et le traitement de la parole, il est connu pour échouer silencieusement dans des conditions courantes. Cela est dû au fait que les algorithmes modernes héritent des biais des données utilisées pour les créer, ce qui conduit à des prédictions incorrectes lorsqu'ils rencontrent de nouvelles données différentes des données d'entraînement. Ce problème est connu sous le nom de défaillance hors-distribution. Cela rend l'intelligence artificielle moderne peu fiable et constitue un obstacle important à son déploiement sécuritaire et généralisé. Ignorer l'échec de généralisation hors-distribution de l'apprentissage automatique pourrait entraîner des situations mettant des vies en danger. Cette thèse vise à aborder cette question et propose des solutions pour assurer le déploiement sûr et fiable de modèles d'intelligence artificielle modernes. Nous présentons trois articles qui couvrent différentes directions pour résoudre l'échec de généralisation hors-distribution de l'apprentissage automatique. Le premier article propose une approche directe qui démontre une performance améliorée par rapport à l'état de l'art. Le deuxième article établie les bases de recherches futures en généralisation hors distribution dans les séries temporelles, tandis que le troisième article fournit une solution simple pour corriger les échecs de généralisation des grands modèles pré-entraînés lorsqu'entraîné sur tes tâches en aval. Ces articles apportent des contributions précieuses au domaine et fournissent des pistes prometteuses pour la recherche future en généralisation hors distribution. / Artificial Intelligence (AI) is a rapidly advancing field, with data-driven approaches known as machine learning, at the forefront of many recent breakthroughs. However, while machine learning have shown remarkable performance in tasks such as image recognition and generation, text generation and translation, and speech processing, they are known to silently fail under common conditions. This is because modern AI algorithms inherit biases from the data used to train them, leading to incorrect predictions when encountering new data that is different from the training data. This problem is known as distribution shift or out-of-distribution (OOD) failure. This causes modern AI to be untrustworthy and is a significant barrier to the safe widespread deployment of AI. Failing to address the OOD generalization failure of machine learning could result in situations that put lives in danger or make it impossible to deploy AI in any significant manner. This thesis aims to tackle this issue and proposes solutions to ensure the safe and reliable deployment of modern deep learning models. We present three papers that cover different directions in solving the OOD generalization failure of machine learning. The first paper proposes a direct approach that demonstrates improved performance over the state-of-the-art. The second paper lays the groundwork for future research in OOD generalization in time series, while the third paper provides a straightforward solution for fixing generalization failures of large pretrained models when finetuned on downstream tasks. These papers make valuable contributions to the field and provide promising avenues for future research in OOD generalization.

Graph databases provide schema-flexible storage and support complex, expressive queries. However, the flexibility and expressiveness in these queries come at additional costs: queries can result in unexpected empty answers or too many answers, which are difficult to resolve manually. To address this, we introduce subgraph-based solutions for graph queries “Why Empty?” and “Why So Many?” that give an answer about which part of a graph query is responsible for an unexpected result. We also extend our solutions to consider the specifics of the used graph model and to increase efficiency and experimentally evaluate them in an in-memory column database.