544 research outputs found
Merging partially labelled trees: hardness and a declarative programming solution
International audienceIntraspecific studies often make use of haplotype networks instead of gene genealogies to represent the evolution of a set of genes. Cassens et al. proposed one such network reconstruction method, based on the global maximum parsimony principle, which was later recast by the first author of the present work as the problem of finding a minimum common supergraph of a set of t partially labelled trees. Although algorithms were proposed for solving the problem on two graphs, the complexity of the general problem remains unknown. In this paper, we show that the corresponding decision problem is NP-complete for t = 3. We then propose a declarative programming approach to solving the problem to optimality in practice, as well as a heuristic approach, both based on the IDP system, and assess the performance of both methods on randomly generated data
Energy landscapes, supergraphs, and "folding funnels" in spin systems
Dynamical connectivity graphs, which describe dynamical transition rates
between local energy minima of a system, can be displayed against the
background of a disconnectivity graph which represents the energy landscape of
the system. The resulting supergraph describes both dynamics and statics of the
system in a unified coarse-grained sense. We give examples of the supergraphs
for several two dimensional spin and protein-related systems. We demonstrate
that disordered ferromagnets have supergraphs akin to those of model proteins
whereas spin glasses behave like random sequences of aminoacids which fold
badly.Comment: REVTeX, 9 pages, two-column, 13 EPS figures include
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