Karlovich, Alexei Yu., and Ilya M. Spitkovsky. "
Pseudodifferential operators on variable Lebesgue spaces."
Operator Theory, Pseudo-Differential Equations, and Mathematical Physics. Operator Theory: Advances and Applications, 228. Eds. Yuri I. Karlovich, Luigi Rodino, Bernd Silbermann, and Ilya M. Spitkovsky. Basel: Birkhäuser, 2013. 173-183.
AbstractLet \(\mathcal{M}(\mathbb{R}^n)\) be the class of bounded away from one and infinity functions \(p:\mathbb{R}^n\to[1,\infty]\) such that the Hardy-Littlewood maximal operator is bounded on the variable Lebesgue space \(L^{p(\cdot)}(\mathbb{R}^n)\). We show that if \(a\) belongs to the Hörmander class \(S_{\rho,\delta}^{n(\rho-1)}\) with \(0<\rho\le 1\), \(0\le\delta<1\), then the pseudodifferential operator \(\operatorname{Op}(a)\) is bounded on the variable Lebesgue space \(L^{p(\cdot)}(\mathbb{R}^n)\) provided that \(p\in\mathcal{M}(\mathbb{R}^n)\). Let \(\mathcal{M}^*(\mathbb{R}^n)\) be the class of variable exponents \(p\in\mathcal{M}(\mathbb{R}^n)\) represented as \(1/p(x)=\theta/p_0+(1-\theta)/p_1(x)\) where \(p_0\in(1,\infty)\), \(\theta\in(0,1)\), and \(p_1\in\mathcal{M}(\mathbb{R}^n)\). We prove that if \(a\in S_{1,0}^0\) slowly oscillates at infinity in the first variable, then the condition \[ \lim_{R\to\infty}\inf_{|x|+|\xi|\ge R}|a(x,\xi)|>0 \] is sufficient for the Fredholmness of \(\operatorname{Op}(a)\) on \(L^{p(\cdot)}(\mathbb{R}^n)\) whenever \(p\in\mathcal{M}^*(\mathbb{R}^n)\). Both theorems generalize pioneering results by Rabinovich and Samko [RS08] obtained for globally log-Hölder continuous exponents \(p\), constituting a proper subset of \(\mathcal{M}^*(\mathbb{R}^n)\).
Cunha, Jácome, João Paulo Fernandes, Jorge Mendes, Rui Pereira, and João Saraiva. "
Querying Model-Driven Spreadsheets."
Proceedings of the 2013 IEEE Symposium on Visual Languages and Human-Centric Computing. VLHCC '13. Washington, DC, USA: IEEE Computer Society, 2013. 83-86.
AbstractSpreadsheets are being used with many different purposes that range from toy applications to complete information systems. In any of these cases, they are often used as data repositories that can grow significantly. As the amount of data grows, it also becomes more difficult to extract concrete information out of them. This paper focuses on the problem of spreadsheet querying. In particular, we propose an expressive and composable technique where intuitive queries can be defined. Our approach builds on a model-driven spreadsheet development environment, and queries are expressed referencing entities in the model of a spreadsheet instead of in its actual data. Finally, the system that we have implemented relies on Google's query function for spreadsheets.
Belo, Orlando, Jácome Cunha, João Paulo Fernandes, Jorge Mendes, Rui Pereira, and João Saraiva. "
QuerySheet: A Bidirectional Query Environment for Model-Driven Spreadsheets."
Proceedings of the 2013 IEEE Symposium on Visual Languages and Human-Centric Computing. VLHCC '13. Washington, DC, USA: IEEE Computer Society, 2013. 199-200.
AbstractThis paper presents a tool, named QUERYSHEET, to query spreadsheets. We defined a language to write the queries, which resembles SQL, the language to query databases. This allows to write queries which are more related to the spreadsheet content than with current approaches.
Liu, H., Â. Mestre, and Teresa Sousa. "
Rainbow vertex k-connection in graphs."
Discrete Applied Mathematics. 161.16-17 (2013): 2549-2555.
AbstractLet k be a positive integer and G be a k-connected graph. An edge-coloured path is rainbow if its edges have distinct colours. The rainbow k-connection number of G, denoted by rc_k(G), is the minimum number of colours required to colour the edges of G so that any two vertices of G are connected by k internally vertex-disjoint rainbow paths. The function rc_k(G) was first introduced by Chartrand, Johns, McKeon, and Zhang in 2009, and has since attracted considerable interest. In this paper, we consider a version of the function rc_k(G) which involves vertex-colourings. A vertex-coloured path is vertex-rainbow if its internal vertices have distinct colours. The rainbow vertex k-connection number of G, denoted by rvc_k(G), is the minimum number of colours required to colour the vertices of G so that any two vertices of G are connected by k internally vertex-disjoint vertex-rainbow paths. We shall study the function rvc_k(G) when G is a cycle, a wheel, and a complete multipartite graph. We also construct graphs G where rc_k(G) is much larger than rvc_k(G) and vice versa so that we cannot in general bound one of rc_k(G) and rvc_k(G) in terms of the other.
Silva, João A., Tiago M. Vale, João M. Lourenço, and Hervé Paulino. "
Replicação Parcial com Memória Transacional Distribuída."
Proceedings of INForum Simpósio de Informática. INForum 2013. Lisbon, Portugal: Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, 2013. 310-321.
AbstractOs sistemas de memória transacional distribuída atuais recorrem essencialmente à distribuição ou à replicação total para distribuir os seus dados pelos múltiplos nós do sistema. No entanto, estas estratégias de replicação de dados apresentam limitações. A distribuição não oferece tolerância a falhas e a replicação total limita a capacidade de armazenamento do sistema. Nesse contexto, a replicação parcial de dados surge como uma solução intermédia, que combina o melhor das duas anteriores com o intuito de mitigar as suas desvantagens. Esta estratégia tem sido explorada no contexto das bases de dados distribuídas, mas tem sido pouco abordada no contexto da memória transacional e, tanto quanto sabemos, nunca antes tinha sido incorporada num sistema de memória transacional distribuída para uma linguagem de propósito geral. Assim, neste artigo propomos e avaliamos uma infraestrutura para replicação parcial de dados para programas Java bytecode, que foi desenvolvida com base num sistema já existente de memória transacional distribuída. A modularidade da infraestrutura que apresentamos permite a implementação de múltiplos algoritmos e, por conseguinte, avaliar em que contextos de utilização (workloads, número de nós, etc.) a replicação parcial se apresenta como uma alternativa viável a outras estratégias de replicação de dados.