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Continuous reinforcement operator applied to resilience in disaster rescue networks
Publication . Jassbi, Javad J.; Ribeiro, Rita A.; Camarinha-Matos, Luis M.; Barata, José; Gomes, Maria Isabel; CTS - Centro de Tecnologia e Sistemas; UNINOVA-Instituto de Desenvolvimento de Novas Tecnologias; CMA - Centro de Matemática e Aplicações
Resilience measurement can be viewed as a multicriteria hierarchical decision making problem since calculating the final level of resilience involves measuring different criteria, at several hierarchical levels, and then merging the information together. In this paper, a resilience model for disaster rescue networks is discussed with a full-reinforcement operator, denoted continuous reinforcement operator. This approach is tested with different levels of reinforcement and the results are compared with those from a Fuzzy Inference System. The proposed approach offers interesting features to support balanced development of disaster rescue networks and facilitates managerial decisions by imposing standards for criteria to penalize or reward the information fusion process.
Μηδεὶς ἀγεωμέτρητοϛ εἰσίτω
Publication . Kahle, Reinhard; DM - Departamento de Matemática; CMA - Centro de Matemática e Aplicações
This paper provides a discussion to which extent the Mathematician David Hilbert could or should be considered as a Philosopher, too. In the first part, we discuss some aspects of the relation of Mathematicians and Philosophers. In the second part we give an analysis of David Hilbert as Philosopher.
The number of P-vertices in a matrix with maximum nullity
Publication . Fernandes, Maria do Rosário Silva Franco; da Cruz, Henrique F.; DM - Departamento de Matemática
Let T be a tree with n >= 2 vertices. Set 8(T) for the set of all real symmetric matrices whose graph is T. Let A is an element of S(T) and i is an element of {1, . . . , n}. We denote by A(i) the principal submatrix of A obtained after deleting the row and column i. We set m(A) (0) for the multiplicity of the eigenvalue zero in A (the nullity of A). When m(A(i)) (0) = m(A) (0) + 1, we say that i is a P-vertex of A. As usual, M(T) denotes the maximum nullity occurring of B is an element of S(T). In this paper we determine an upper bound and a lower bound for the number of P-vertices in a matrix A is an element of S(T) with nullity M(T). We also prove that if the integer b is between these two bounds, then there is a matrix E is an element of S(T) with b P-vertices and maximum nullity. (C) 2018 Elsevier Inc. All rights reserved.
Model validation and vec operators
Publication . Dias, Cristina; Santos, Carla; Varadinov, Maria; Mexia, João Tiago; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática
We use the vec and other relater operators to carry out inference for structured families of symmetric stochastic matrices M. These are obtained through the sum of the respective mean matrix and a symmetric stochastic matrix with null mean. We consider that the vec operator of the matrix E is normal homoscedastic. The matrices on these families correspond to the treatments of a base design, and the inference is centered on model validation and the action of the factors in the base model on mean matrices.
On the Bruhat order of labeled graphs
Publication . Brualdi, Richard A.; Fernandes, Rosário; Furtado, Susana; CMA - Centro de Matemática e Aplicações; DM - Departamento de Matemática; Elsevier Science B.V., Inc
We investigate two Bruhat (partial) orders on graphs with vertices labeled 1,2,…,n and with a specified degree sequence R, equivalently, symmetric (0,1)-matrices with zero trace and a specified row sum vector R (adjacency matrices of such graphs). One is motivated by the classical Bruhat order on permutations while the other one, more restrictive, is defined by a switch of a pair of disjoint edges. In the Bruhat order, one seeks to concentrate the edges of a graph with a given degree sequence among the vertices with smallest labels, thereby producing a minimal graph in this order. We begin with a discussion of graphs whose isomorphism class does not change under a switch. Then we are interested in when the two Bruhat orders are identical. For labeled graphs of regular degree k, we show that the two orders are identical for k≤2 but not for k=3.
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Fundação para a Ciência e a Tecnologia
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5876
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147204