Factorization by invariant embedding of elliptic problems: circular and star-shaped domains

Dissertação apresentada para obtenção do grau de Doutor em Matemática na especialidade de Equações Diferenciais, pela Universidade Nova de Lisboa,Faculdade de Ciências e Tecnologia

Factorization of elliptic boundary value problems by invariant embedding and application to overdetermined problems

Dissertação para obtenção do Grau de Doutor em Matemática

Riesz potential operators and inverses via fractional centred derivatives

International Journal of Mathematics and Mathematical Sciences, Vol.2006

Probabilistic constraint reasoning

Dissertação apresentada para obtenção do Grau de Doutor em Engenharia Informática, pela Universidade Nova de Lisboa, Faculdade de Ciências e Tecnologia

Credit cycle identification: A Markov-switching application

A Work Project, presented as part of the requirements for the Award of a Masters Degree in Finance from the NOVA – School of Business and Economics

The brushstroke and materials of Amadeo de Souza-Cardoso combined in an authentication tool

Nowadays, authentication studies for paintings require a multidisciplinary approach, based on the contribution of visual features analysis but also on characterizations of materials and techniques. Moreover, it is important that the assessment of the authorship of a painting is supported by technical studies of a selected number of original artworks that cover the entire career of an artist. This dissertation is concerned about the work of modernist painter Amadeo de Souza-Cardoso. It is divided in three parts. In the first part, we propose a tool based on image processing that combines information obtained by brushstroke and materials analysis. The resulting tool provides qualitative and quantitative evaluation of the authorship of the paintings; the quantitative element is particularly relevant, as it could be crucial in solving authorship controversies, such as judicial disputes. The brushstroke analysis was performed by combining two algorithms for feature detection, namely Gabor filter and Scale Invariant Feature Transform. Thanks to this combination (and to the use of the Bag-of-Features model), the proposed method shows an accuracy higher than 90% in distinguishing between images of Amadeo’s paintings and images of artworks by other contemporary artists. For the molecular analysis, we implemented a semi-automatic system that uses hyperspectral imaging and elemental analysis. The system provides as output an image that depicts the mapping of the pigments present, together with the areas made using materials not coherent with Amadeo’s palette, if any. This visual output is a simple and effective way of assessing the results of the system. The tool proposed based on the combination of brushstroke and molecular information was tested in twelve paintings obtaining promising results. The second part of the thesis presents a systematic study of four selected paintings made by Amadeo in 1917. Although untitled, three of these paintings are commonly known as BRUT, Entrada and Coty; they are considered as his most successful and genuine works. The materials and techniques of these artworks have never been studied before. The paintings were studied with a multi-analytical approach using micro-Energy Dispersive X-ray Fluorescence spectroscopy, micro-Infrared and Raman Spectroscopy, micro-Spectrofluorimetry and Scanning Electron Microscopy. The characterization of Amadeo’s materials and techniques used on his last paintings, as well as the investigation of some of the conservation problems that affect these paintings, is essential to enrich the knowledge on this artist. Moreover, the study of the materials in the four paintings reveals commonalities between the paintings BRUT and Entrada. This observation is supported also by the analysis of the elements present in a photograph of a collage (conserved at the Art Library of the Calouste Gulbenkian Foundation), the only remaining evidence of a supposed maquete of these paintings. The final part of the thesis describes the application of the image processing tools developed in the first part of the thesis on a set of case studies; this experience demonstrates the potential of the tool to support painting analysis and authentication studies. The brushstroke analysis was used as additional analysis on the evaluation process of four paintings attributed to Amadeo, and the system based on hyperspectral analysis was applied on the painting dated 1917. The case studies therefore serve as a bridge between the first two parts of the dissertation.

Rely-guarantee protocols for safe interference over shared memory

Mutable state can be useful in certain algorithms, to structure programs, or for efficiency purposes. However, when shared mutable state is used in non-local or nonobvious ways, the interactions that can occur via aliases to that shared memory can be a source of program errors. Undisciplined uses of shared state may unsafely interfere with local reasoning as other aliases may interleave their changes to the shared state in unexpected ways. We propose a novel technique, rely-guarantee protocols, that structures the interactions between aliases and ensures that only safe interference is possible. We present a linear type system outfitted with our novel sharing mechanism that enables controlled interference over shared mutable resources. Each alias is assigned separate, local roles encoded in a protocol abstraction that constrains how an alias can legally use that shared state. By following the spirit of rely-guarantee reasoning, our rely-guarantee protocols ensure that only safe interference can occur but still allow many interesting uses of shared state, such as going beyond invariant and monotonic usages. This thesis describes the three core mechanisms that enable our type-based technique to work: 1) we show how a protocol models an alias’s perspective on how the shared state evolves and constrains that alias’s interactions with the shared state; 2) we show how protocols can be used while enforcing the agreed interference contract; and finally, 3) we show how to check that all local protocols to some shared state can be safely composed to ensure globally safe interference over that shared memory. The interference caused by shared state is rooted at how the uses of di↵erent aliases to that state may be interleaved (perhaps even in non-deterministic ways) at run-time. Therefore, our technique is mostly agnostic as to whether this interference was the result of alias interleaving caused by sequential or concurrent semantics. We show implementations of our technique in both settings, and highlight their di↵erences. Because sharing is “first-class” (and not tied to a module), we show a polymorphic procedure that enables abstract compositions of protocols. Thus, protocols can be specialized or extended without requiring specific knowledge of the interference produce by other protocols to that state. We show that protocol composition can ensure safety even when considering abstracted protocols. We show that this core composition mechanism is sound, decidable (without the need for manual intervention), and provide an algorithm implementation.