The Bourque Distances for Mutation Trees of Cancers

Mutation trees are rooted trees of arbitrary node degree in which each node is labeled with a mutation set. These trees, also referred to as clonal trees, are used in computational oncology to represent the mutational history of tumours. Classical tree metrics such as the popular Robinson - Foulds distance are of limited use for the comparison of mutation trees. One reason is that mutation trees inferred with different methods or for different patients often contain different sets of mutation labels. Here, we generalize the Robinson - Foulds distance into a set of distance metrics called Bourque distances for comparing mutation trees. A connection between the Robinson - Foulds distance and the nearest neighbor interchange distance is also presented

Pressure dependence of the Curie temperature in Ni2MnSn Heusler alloy: A first-principles study

The pressure dependence of electronic structure, exchange interactions and Curie temperature in ferromagnetic Heusler alloy Ni2MnSn has been studied theoretically within the framework of the density-functional theory. The calculation of the exchange parameters is based on the frozen--magnon approach. The Curie temperature, Tc, is calculated within the mean-field approximation by solving the matrix equation for a multi-sublattice system. In agrement with experiment the Curie temperature increased from 362K at ambient pressure to 396 at 12 GPa. Extending the variation of the lattice parameter beyond the range studied experimentally we obtained non-monotonous pressure dependence of the Curie temperature and metamagnetic transition. We relate the theoretical dependence of Tc on the lattice constant to the corresponding dependence predicted by the empirical interaction curve. The Mn-Ni atomic interchange observed experimentally is simulated to study its influence on the Curie temperature.Comment: 8 pages, 8 figure

Consistency of Topological Moves Based on the Balanced Minimum Evolution Principle of Phylogenetic Inference

Many phylogenetic algorithms search the space of possible trees using topological rearrangements and some optimality criterion. FastME is such an approach that uses the balanced minimum evolution (BME) principle, which computer studies have demonstrated to have high accuracy. FastME includes two variants: balanced subtree prune and regraft (BSPR) and balanced nearest neighbor interchange (BNNI). These algorithms take as input a distance matrix and a putative phylogenetic tree. The tree is modified using SPR or NNI operations, respectively, to reduce the BME length relative to the distance matrix, until a tree with (locally) shortest BME length is found. Following computer simulations, it has been conjectured that BSPR and BNNI are consistent, i.e. for an input distance that is a tree-metric, they converge to the corresponding tree. We prove that the BSPR algorithm is consistent. Moreover, even if the input contains small errors relative to a tree-metric, we show that the BSPR algorithm still returns the corresponding tree. Whether BNNI is consistent remains open

On the Complexity of Parameterized Local Search for the Maximum Parsimony Problem

Maximum Parsimony is the problem of computing a most parsimonious phylogenetic tree for a taxa set X from character data for X. A common strategy to attack this notoriously hard problem is to perform a local search over the phylogenetic tree space. Here, one is given a phylogenetic tree T and wants to find a more parsimonious tree in the neighborhood of T. We study the complexity of this problem when the neighborhood contains all trees within distance k for several classic distance functions. For the nearest neighbor interchange (NNI), subtree prune and regraft (SPR), tree bisection and reconnection (TBR), and edge contraction and refinement (ECR) distances, we show that, under the exponential time hypothesis, there are no algorithms with running time |I|^o(k) where |I| is the total input size. Hence, brute-force algorithms with running time |X|^?(k) ? |I| are essentially optimal. In contrast to the above distances, we observe that for the sECR-distance, where the contracted edges are constrained to form a subtree, a better solution within distance k can be found in k^?(k) ? |I|^?(1) time