Carlos E. Valencia

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We study irreducible representations of Rees cones and characterize the maxflow min-cut property of clutters in terms of the normality of Rees algebras and the integrality of certain polyhedra. Then we present some applications to combinatorial optimization and commutative algebra. As a byproduct we obtain an effective method, based on the program Normaliz(More)
BACKGROUND Vitamin D is a secosteroid hormone with important roles in the control of bone and mineral metabolism of vertebrates and in the maintenance of systemic homeostasis. This study aimed (i) to evaluate the serum concentrations of 25-hydroxy-vitamin D levels [25(OH)D], parathyroid hormone (PTH) and ionized calcium (iCa) of wild Callithrix penicillata(More)
The statistical analysis of tree structured data is a new topic in statistics with wide application areas. Some Principal Component Analysis (PCA) ideas were previously developed for binary tree spaces. In this study, we extend these ideas to the more general space of rooted and labeled trees. We re-define concepts such as tree-line and forward principal(More)
For a bipartite graph G we are able to characterize the complete intersection property of the edge subring in terms of the multiplicity and we give optimal bounds for this number. We give a method to obtain a regular sequence for the atomic ideal of G, when G is embedded on an orientable surface. We also give a graph theoretical condition for the edge(More)
Let G be a graph without isolated vertices and let α(G) be its stability number and τ(G) its covering number. The σv-cover number of a graph, denoted by σv(G), is the maximum natural number m such that every vertex of G belongs to a maximal independent set with at least m vertices. In the first part of this paper we prove that α(G) ≤ τ(G)[1 + α(G)− σv(G)].(More)
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