51 research outputs found
Computing the Determinant of the Distance Matrix of a Bicyclic Graph
Let G be a connected graph with vertex set V = {v1, ..., vn}. The distance d(vi, vj) between two vertices vi and vj is the number of edges of a shortest path linking them. The distance matrix of G is the n Ă— n matrix such that its (i, j)-entry is equal to d(vi, vj). A formula to compute the determinant of this matrix in terms of the number of vertices was found when the graph either is a tree or is a unicyclic graph. For a byciclic graph, the determinant is known in the case where the cycles have no common edges. In this paper, we present some advances for the remaining cases; i.e., when the cycles share at least one edge. We also present a conjecture for the unsolved cases.Fil: Dratman, Ezequiel. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Grippo, Luciano Norberto. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; Argentina. Universidad Nacional de General Sarmiento. Instituto de Ciencias; ArgentinaFil: Safe, Martin Dario. Universidad Nacional del Sur. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas; ArgentinaFil: da Silva Jr., Celso M. Centro Federal de Educação TecnolĂłgica; BrasilFil: Del Vecchio, Renata R.. Universidade Federal Fluminense; BrasilLAGOS 2019: X Latin and American Algorithms, Graphs and Optimization SymposiumBelo HorizonteBrasilUniversidad Federal de Minas Gerai
Isomeric discrimination and quantification of thyroid hormones, T3 and rT3, by the single ratio kinetic method using electrospray ionization mass spectrometry
Numeric vs. symbolic homotopy algorithms in polynomial system solving: A case study
We consider a family of polynomial systems which arises in the analysis of the stationary solutions of a standard discretization of certain semi-linear second-order parabolic partial differential equations. We prove that this family is well-conditioned from the numeric point of view, and ill-conditioned from the symbolic point of view. We exhibit a polynomial-time numeric algorithm solving any member of this family, which significantly contrasts the exponential behavior of all known symbolic algorithms solving a generic instance of this family of systems. © 2005 Elsevier Inc. All rights reserved.Fil:De Leo, M. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Dratman, E. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.Fil:Matera, G. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina
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