Abstract We study the structure of branch set solutions to Plateau’s problem in metric spaces satisfying a quadratic isoperimetric inequality. In our 1st result, we give examples with constant arbitrarily close Euclidean $(4\pi )^{-1}$ for which have large set. This complements recent results Lytchak–Wenger and Stadler stating, respectively, that any space is CAT($0$) only isolated points. also...

A partition is a subdivision of a set into disjoint subsets called parts. Partitions are instrumental in tasks such as classification, pattern recognition and network analysis. In the past, a wide spectrum of similarity measures for pairs of partitions P = {P1, . . . , P|P|} and P ′ = {P ′ 1, . . . , P ′ |P′|} of the same set V have been proposed. Such a measure for the overall similarity of P ...

In this PhD, we present some algorithms and complexity results for two general problems that arise in the analysis of a metabolic network: the search for elementary modes of a network and the search for minimal precursors sets. Elementary modes is a common tool in the study of the cellular characteristic of a metabolic network. An elementary mode can be seen as a minimal set of reactions that c...

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Let V be a finite set and M a collection of subsets of V . Then M is an alignment of V if and only if M is closed under taking intersections and contains both V and the empty set. If M is an alignment of V , then the elements of M are called convex sets and the pair (V,M) is called an alignment or a convexity. If S ⊆ V , then the convex hull of S is the smallest convex set that contains S. Supp...

A co-biclique of a simple undirected graph G = (V, E) is the edge-set of two disjoint complete subgraphs of G. (A co-biclique is the complement of a biclique.) A subset F ⊆ E is an independent of G if there is a co-biclique B such that F ⊆ B, otherwise F is a dependent of G. This paper describes the minimal dependents of G. (A minimal dependent is a dependent C such that any proper subset of C ...