In this talk we analyze the evolution of the relative error in the state of linear systems subject to perturbations. For this purpose we introduce the property of relative stability. The relevance of this property is illustrated by means of a case study, namely the computation of the Erlang-B function, which is well-known in the context of Queueing Theory and Teletraffic Engineering.

The talk consists of two parts. The first part is devoted to the abstract minimization problem with constraints, which is called the mathematical programming problem. In the second part we discuss local properties of smooth nonlinear mappings in a neighborhood of an abnormal point. The problems that are studied in this talk (of course, in addition to their extremal nature) are united by the fact that we are mainly interested in studying the so-called abnormal or nonlinearized problems.

Dados n discos de raio r no plano, que representam antenas, radares, sensores ou outros equipamentos de vigilância com alcance limitado. Um ponto no plano está 2-coberto se estiver coberto por pelo menos dois destes discos. Na sequência da importância prática desta classe de problemas e dos resultados obtidos para minimizar o alcance dos equipamentos de vigilância para 2-cobrir um ponto, apresentaremos alguns resultados relacionados com o cálculo do alcance mínimo para a 2-cobertura de um segmento de recta,uma linha poligonal, um polígono arbitrário e um conjunto de pontos no plano. Como último caso, analisaremos como encontrar a melhor rota segura (2-coberta) entre duas localizações (vértices) num grafo não dirigido, grafo esse que representa um mapeamento de estradas.

A partir da subdivisão Gv de um grafo arbitrário G, verifica-se a existência de um 2-factor e introduz-se um algoritmo para o reconhecimento de ciclos de Hamilton. Estende-se a análise de grafos com dois valores próprios principais a famílias de grafos com no máximo k valores próprios principais, com 2 <= k <= n, e apresentam-se alguns problemas em aberto.

A partir dos conceitos de valor próprio principal e polinómio característico principal de um grafo G, deduzem-se várias propriedades e algumas relações com a designada Walking Matrix de G. Determinam-se famílias de grafos não regulares de ordem arbitrária com maior valor próprio constante e, como aplicação de alguns dos resultados introduzidos, apresenta-se um algoritmo para o reconhecimento de grafos de Hamilton.

Faz-se uma interpretação, segundo a teoria dos grafos, dos vértices e arestas do politopo de Birkhoff acíclico, Omega_n(T) = Tau_n, onde T é uma árvore com n vértices, e generaliza-se um resultado relativo ao diâmetro do politopo de Birkhoff tridiagonal.

Variational principles of elasticity theory consisting in minimization of the stored energy functional under some constraints give rise to the finite element formulation of the deformation model. In this way the elasticity theory problem is reduced to numerical solution of a large system of nonlinear equations. The dimension of the system, N, is so high that the Newton method cannot be applied in its classical form. The inverse matrix has to be calculated approximately, for example using a Krylov subspace method. If the Petrov-Galerkin method is used, the matrix is not necessarily symmetric. How many iterations of the Krylov subspace method we need in order to guarantee a linear convergence of a corresponding Newton-Krylov method?(...)

A body in a parallel flow of non-interacting particles is considered. We introduce the notions of a body of zero resistance, a body that leaves no trace, and a transparent body, and prove that all such kinds of bodies do exist.

Nowadays huge amounts of data have been collected. However comprehension of these data remains a topic problem so far. It is very difficult for a human being to make use of such an amount of information and to be able to find basic patterns, relations, or trends in the data. In such a manner data become ever less and less valuable. Data mining could be useful for comprehension of data and help to make decisions. The combination and integrated use of data mining methods (classification, clustering, visualisation, etc.) of a different nature are under a rapid development. The combination of different methods can be applied to make a data analysis, while minimizing the shortcomings of individual methods. There are investigated following data mining methods (...)

Apresentação do Instituto de Matemática e Informática de Vilnus. Integration of Data Mining Methods for Various Applications Abstract: Nowadays huge amounts of data have been collected. However comprehension of these data remains a topic problem so far. It is very difficult for a human being to make use of such an amount of information and to be able to find basic patterns, relations, or trends in the data. Short information about the lecturer: Olga Kurasova is a senior researcher at Institute of Mathematics and Informatics (IMI), Vilnius, Lithuania. She also is a senior lecturer of Information Technologies Department at Vilnius Pedagogical University.

The main reason for the interest in and importance of fractional programming stems from the fact that various problems, ranging from engineering to economics, consider the optimization of a ratio between physical and/or economic linear functions.(...)

How can we play "Minesweeper" without a computer? It is shown that certain configurations of open cells guarantee the existence and the uniqueness of the solution. Moreover, we propose an algorithm for automatic generation of the initial table.

A graph G is singular of nullity n(G)>=1, if the dimension of the nullspace ker(A) of its adjacency matrix A is n(G) . Singular graphs model various scientic situations, molecular structures and networks, in particular. We look at the substructures that make a graph singular and present characterizing criteria, both algebraic and geometric.

Irene Sciriha, Department of Mathematics, Faculty of Science, University of Malta. (Details)

Nesta apresentação discute-se a utilização do método de partição e geração de colunas (branch-and-price) na resolução de problemas de Programação Inteira. Primeiramente, introduz-se o método de geração de colunas no contexto da decomposição de Dantzig-Wolf, bem como, as principais questões levantadas. Posteriormente, abordam-se duas aplicações do método de partição e geração de colunas.

Filipe Pereira e Alvelos, Universidade do Minho (Details in Portuguese)

The historical background to modern optimal control theory will be outlined, starting from Newton’s Problem, the brachystochrone problem (Johann Bernoulli 1697) and the Calculus of Variations. Further developments led after a few centuries to Pontryagin’s Maximum Principle in 1961 and important further results in differential geometry techniques after 1980.

Alan Zinober, University of Sheffield (Details)

Dados n discos de raio r no plano, que representam luzes, guardas, radares, sensores ou outros equipamentos de vigilância com alcance limitado, um ponto no plano está k-iluminado se estiver coberto por pelo menos k discos. Um caminho que une dois pontos está k-iluminado se todos os seus pontos estiverem k-iluminados.

Inês Matos, Universidade de Aveiro (Details in Portuguese)

The talk is devoted to some aspects of theory of integer minima of linear forms. Recent results together with classical ones concerning Lagrange spectrum will be described. Particularly, some achievements in constructing linear forms of a given Diophantine will be presented.

Oleg German, Moscow University (Details)

The representation of combinatorial objects is decisive for the feasibility of several enumerative tasks. In this work, we present a unique string representation for complete initially-connected deterministic automata (ICDFAs) with n states over an alphabet of k symbols. For these strings we give a regular expression and show how they are adequate for exact and random generation, allow an alternative way for enumeration and lead to an upper bound for the number of ICDFAs in order to parallelize the counting of minimal automata, and thus of regular languages. A uniform random generator for ICDFAs is presented that uses a table of pre-calculated values. Based on same table, an optimal coding for ICDFAs is obtained.

Rogério Reis, Faculdade de Ciências da Universidade do Porto (Details)

Leonhard Euler, who would be 300 years old if he had not unfortunately died, was the preeminent mathematician of 18th century. His many fundamental contributions range from number theory to geometry, differential equations to infinite series, optimization to probability, and optics to mechanics. Euler may not have been the most colourful scientist. He was not persecuted by the Church, no apple fell on is head. He did not die in a duel. (…)

Francis Clarke, Institute Universitaire de France and Universtité de Lyon (Details)

Nesta comunicação serão apresentadas abordagens evolucionarias (algoritmos genéticos e estratégias evolutivas) para a resolução de problemas multiobjectivo. Alguns problemas da area da engenharia química e mecânica onde estas abordagens tiverem sucesso serão discutidos. Serão também apresentadas algumas perspectivas de trabalho,nomeadamente ao nível da resolução de problemas com objectivos que podem ser considerados redundantes.

Pedro Nuno Oliveira, Universidade do Minho (Details in Portuguese)

In this talk, we survey available results on graph transformations preserving the stability number and propose a unified approach for the description and development of such transformations. This approach leads to a generalization of several previously known transformations. We illustrate it by a number of new examples.

Vadim Lozin, University of Warwick (Details) )

Alargamentos de grafos infinitos. Complementos descritivos sobre conexão. Métricas ordinais.

Vítor Neves, Universidade de Aveiro (Abstract in Portuguese)

The Maximum Hidden Vertex Set problem asks for a set of maximum cardinality of vertices of a given simple polygon, such that no two vertices in see each other. It is known that this problem is NP-Hard, therefore in this talk we are going to present four strategies to tackle it, the first two are based on greedy constructive search and are designed specifically to solve it, and the other two are based on the general metaheuristics Simulated Annealing and Genetic Algorithms. We are going, also, to present a comparative study of the solutions obtained by the different algorithms and introduce a method that allow determining the approximation ratio of our best algorithm.

Ana Mafalda Martins, Universidade de Aveiro (Details)

In this talk, we consider blood in small vessels modeled as an incompressible shear-thinning fluid in a straight rigid and impermeable tube with circular cross-section. The full 3D unsteady model is simplified using a one-dimensional hierarchical approach based on the Cosserat theory related to fluid dynamics. From this approach, we obtain the unsteady relationship between mean pressure gradient (wall shear stress, respectively) and volume flow rate over a finite section of the tubewith constant radius for the specific case of power law viscosity function.Attention is focused on some numerical simulation of steady/unsteady flows and on the analysis of perturbed flows.

Fernando Carapau, Universidade de Évora (Details)

Edouard Oudet, University of Savoie

O dimensionamento de uma rede de telecomunicações envolve a determinação da configuração física de menor custo capaz de suportar o tráfego esperado e obedecendo a requisitos que podem ser impostos: (i) pelas tecnologias da rede a implementar e/ou (ii) pela qualidade de serviço que o operador pretende fornecer. A gestão de recursos de uma rede de telecomunicações envolve a determinação do encaminhamento óptimo do tráfego a suportar numa rede existente com uma configuração física conhecida. A optimalidade do encaminhamento depende da qualidade de serviço que o operador pretende fornecer.

Amaro F. de Sousa, Universidade de Aveiro (Details in Portuguese)