1,584 research outputs found
LIPIcs, Volume 251, ITCS 2023, Complete Volume
LIPIcs, Volume 251, ITCS 2023, Complete Volum
Integrated Tip-Tilt Sensing for Single-Mode Fiber Coupling
This thesis presents the development and on-sky tests of the novel Microlens-Ring Tip-Tilt (MLR-TT) sensor. The sensor consists of a micro-lens ring (MLR) that is printed directly on the face of a fiber bundle with a central single-mode fiber (SMF) accepting the light almost unclipped if the beam is aligned. The edge of the beam, however, is refracted by the MLR to couple into six surrounding multi-mode fibers (MMFs). Detecting the flux in these sensor fibers allows reconstruction of the beam position, i.e. the tip and tilt aberrations of the wavefront.
The lenses are manufactured in collaboration with Karlsruhe Institute for Technology (KIT) with state-of-the-art two-proton polymerization, a novel technology that allows the fabrication of very precise and freeform lenses. The sensor is integrated with the instrument’s fiber link and features a small physical size of 380 µm. This novel integration of a sensor into existing components reduced opto-mechanical footprint and complexity, as well as reducing non-common path aberrations (NCPAs) to a bare minimum.
This thesis describes the various steps that were part of this development, starting with designing, optimizing, and characterizing the sensor itself, setting up a corresponding laboratory environment, and developing a control system for on-sky testing. The system is tested on-sky with iLocater fiber coupling front-end (acquisition camera) at the Large Binocular Telescope (LBT). It was found that principle reconstruction is possible but the observed accuracy is ∼0.19 λ/D both for tip and for tilt. With this accuracy, it was not possible to improve the resulting SMF coupling efficiency. A strong correlation between sensor accuracy and the instantaneous Strehl ratio (SR), i.e. residual adaptive optics (AO) aberrations, is found. Additionally, the corresponding power spectral density (PSD) reveals that most of the reconstruction inaccuracy occurs in low temporal frequencies. This suggests that the dominating limitations of the accuracy of the MLR-TT sensor arise from residual AO aberrations and the false signal they introduce in the sensor.
These findings are discussed in detail and the future prospects of further analysis and development are outlined in the context of the most beneficial application environment
The Potts model and the independence polynomial:Uniqueness of the Gibbs measure and distributions of complex zeros
Part 1 of this dissertation studies the antiferromagnetic Potts model, which originates in statistical physics. In particular the transition from multiple Gibbs measures to a unique Gibbs measure for the antiferromagnetic Potts model on the infinite regular tree is studied. This is called a uniqueness phase transition. A folklore conjecture about the parameter at which the uniqueness phase transition occurs is partly confirmed. The proof uses a geometric condition, which comes from analysing an associated dynamical system.Part 2 of this dissertation concerns zeros of the independence polynomial. The independence polynomial originates in statistical physics as the partition function of the hard-core model. The location of the complex zeros of the independence polynomial is related to phase transitions in terms of the analycity of the free energy and plays an important role in the design of efficient algorithms to approximately compute evaluations of the independence polynomial. Chapter 5 directly relates the location of the complex zeros of the independence polynomial to computational hardness of approximating evaluations of the independence polynomial. This is done by moreover relating the set of zeros of the independence polynomial to chaotic behaviour of a naturally associated family of rational functions; the occupation ratios. Chapter 6 studies boundedness of zeros of the independence polynomial of tori for sequences of tori converging to the integer lattice. It is shown that zeros are bounded for sequences of balanced tori, but unbounded for sequences of highly unbalanced tori
LIPIcs, Volume 261, ICALP 2023, Complete Volume
LIPIcs, Volume 261, ICALP 2023, Complete Volum
From images to signs: Cretan Hieroglyphic and Linear A in context
This dissertation adopts a multidisciplinary approach to investigate graphical and formal features of Cretan Hieroglyphic and Linear A. Drawing on theories which understand inscribed artefacts as an interplay of materials, iconography, and texts, I combine archaeological and philological considerations with statistical and experimental observations. The work is formulated on three key-questions.
The first deals with the origins of Cretan Hieroglyphic. After providing a fresh view on Prepalatial seals chronology, I identify a number of forerunners of Hieroglyphic signs in iconographic motifs attested among the Prepalatial glyptic and material culture. I further identified a specific style-group, i.e., the ‘Border and Leaf Complex’, as the decisive step towards the emergence of the Hieroglyphic graphic repertoire.
The second deals with the interweaving of formal, iconographical, and epigraphic features of Hieroglyphic seals with the sequences they bear and the contexts of their usage. By means of two Correspondence Analyses, I showed that the iconography on seals in some materials and shapes is closer to Cretan Hieroglyphics, than that on the other ones. Through two Social Network Analyses, I showed that Hieroglyphic impressions, especially at Knossos, follow a precise sealing pattern due to their shapes and sequences. Furthermore, prisms with a high number of inscribed faces adhere to formal features of jasper ones. Finally, through experimental engravings, I showed differences in cutting rates among materials, as well as the efficiency of abrasives and tools unearthed within the Quartier Mu.
The third question concerns overlaps in chronology, findspots and signaries between Cretan Hieroglyphic and Linear A. I discussed all possible earliest instances of both scripts and argued for some items datable to the MM I-IIA period. I further provide an insight into the Hieroglyphic-Linear A dubitanda and criteria for their interpretation. Finally, I suggest four different patterns in the creation and diversification of the two signaries
Enhancing Mesh Deformation Realism: Dynamic Mesostructure Detailing and Procedural Microstructure Synthesis
Propomos uma solução para gerar dados de mapas de relevo dinâmicos para simular deformações em superfícies macias, com foco na pele humana. A solução incorpora a simulação de rugas ao nível mesoestrutural e utiliza texturas procedurais para adicionar detalhes de microestrutura estáticos. Oferece flexibilidade além da pele humana, permitindo a geração de padrões que imitam deformações em outros materiais macios, como couro, durante a animação.
As soluções existentes para simular rugas e pistas de deformação frequentemente dependem de hardware especializado, que é dispendioso e de difícil acesso. Além disso, depender exclusivamente de dados capturados limita a direção artística e dificulta a adaptação a mudanças. Em contraste, a solução proposta permite a síntese dinâmica de texturas que se adaptam às deformações subjacentes da malha de forma fisicamente plausível.
Vários métodos foram explorados para sintetizar rugas diretamente na geometria, mas sofrem de limitações como auto-interseções e maiores requisitos de armazenamento. A intervenção manual de artistas na criação de mapas de rugas e mapas de tensão permite controle, mas pode ser limitada em deformações complexas ou onde maior realismo seja necessário.
O nosso trabalho destaca o potencial dos métodos procedimentais para aprimorar a geração de padrões de deformação dinâmica, incluindo rugas, com maior controle criativo e sem depender de dados capturados. A incorporação de padrões procedimentais estáticos melhora o realismo, e a abordagem pode ser estendida além da pele para outros materiais macios.We propose a solution for generating dynamic heightmap data to simulate deformations for soft surfaces, with a focus on human skin. The solution incorporates mesostructure-level wrinkles and utilizes procedural textures to add static microstructure details. It offers flexibility beyond human skin, enabling the generation of patterns mimicking deformations in other soft materials, such as leater, during animation.
Existing solutions for simulating wrinkles and deformation cues often rely on specialized hardware, which is costly and not easily accessible. Moreover, relying solely on captured data limits artistic direction and hinders adaptability to changes. In contrast, our proposed solution provides dynamic texture synthesis that adapts to underlying mesh deformations.
Various methods have been explored to synthesize wrinkles directly to the geometry, but they suffer from limitations such as self-intersections and increased storage requirements. Manual intervention by artists using wrinkle maps and tension maps provides control but may be limited to the physics-based simulations.
Our research presents the potential of procedural methods to enhance the generation of dynamic deformation patterns, including wrinkles, with greater creative control and without reliance on captured data. Incorporating static procedural patterns improves realism, and the approach can be extended to other soft-materials beyond skin
On the structure of graphs with forbidden induced substructures
One of the central goals in extremal combinatorics is to understand how the global structure of a combinatorial object, e.g. a graph, hypergraph or set system, is affected by local constraints.
In this thesis we are concerned with structural properties of graphs and hypergraphs which locally do not look like some type of forbidden induced pattern. Patterns can be single subgraphs, families of subgraphs, or in the multicolour version colourings or families of colourings of subgraphs.
Erdős and Szekeres\u27s quantitative version of Ramsey\u27s theorem asserts that in every -edge-colouring of the complete graph on vertices there is a monochromatic clique on at least vertices. The famous Erdős-Hajnal conjecture asserts that forbidding fixed colourings on subgraphs ensures much larger monochromatic cliques. The conjecture is open in general, though a few partial results are known. The first part of this thesis will be concerned with different variants of this conjecture: A bipartite variant, a multicolour variant, and an order-size variant for hypergraphs.
In the second part of this thesis we focus more on order-size pairs; an order-size pair is the family consisting of all graphs of order and size , i.e. on vertices with edges. We consider order-size pairs in different settings: The graph setting, the bipartite setting and the hypergraph setting. In all these settings we investigate the existence of absolutely avoidable pairs, i.e. fixed pairs that are avoided by all order-size pairs with sufficiently large order, and also forcing densities of order-size pairs , i.e. for approaching infinity, the limit superior of the fraction of all possible sizes , such that the order-size pair does not avoid the pair
Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization
Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes
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