Evolutionary trees: an integer multicommodity max-flow-min-cut theorem

In biomathematics, the extensions of a leaf-colouration of a binary tree to the whole vertex set with minimum number of colour-changing edges are extensively studied. Our paper generalizes the problem for trees; algorithms and a Menger-type theorem are presented. The LP dual of the problem is a multicommodity flow problem, for which a max-flow-min-cut theorem holds. The problem that we solve is an instance of the NP-hard multiway cut problem

Radiofrequency ablation of focal atrial tachycardia: Benefit of electroanatomical mapping over conventional mapping

Background Catheter ablation is a proven therapy of focal atrial tachycardia. However limited information is available about the additional value of electroanatomical over conventional mapping methods for this specific arrhythmia. Methods Consecutive catheter ablation procedures of FAT were analyzed in two cardiology centres. Only conventional mapping was used in 30 of the 60 procedures whereas additionally CARTO mapping was performed in another 30 procedures. Acute, six-month success rate, and procedural data were analyzed. Results Localization of ectopic foci is congruent with previously published data. There was no statistically significant difference between procedure time and fluoroscopy time using additionally CARTO mapping, compared to conventional mapping only. Acute success rate was higher in procedures guided by CARTO mapping than in procedures based on conventional mapping (27/30 vs. 18/30, p = 0.0081). During the 6-month follow-up period there was a better outcome (p = 0.045) in case of CARTO guided procedures (success: 11 cases, partial success: 12 cases, failure: 4 cases) compared to conventional mapping (success: 4 cases, partial success: 18 cases, failure: 7 cases). Conclusions Catheter ablation of focal atrial tachycardias using the CARTO electroanatomical mapping system seems to provide higher acute and 6-month success rate compared to ablation using conventional mapping methods only

Annals of Combinatorics

Abstract. In this paper we study how to invert random functions under different criteria. The motivation for this study is phylogeny reconstruction, since the evolution of biomolecular se-quences may be considered as a random function from the set of possible phylogenetic trees to the set of collections of biomolecular sequences of observed species. Our results may affect how we think about maximum likelihood estimation (MLE) in phylogeny. For inverting random func-tions, MLE is optimal under a first criterion, although it is not optimal under a second criterion which is at least equally natural but more conservative. Furthermore, MLE has to be used dif-ferently from the way it has been used in the phylogeny literature, if we have a prior distribution on trees and mutation mechanisms and want to keep MLE optimal under the same first criterion. Some of the results of this paper have been known in the setting of statistical decision theory, but have never been discussed in the context of phylogeny