Combinatorial Scoring of Phylogenetic Networks

Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for tree/network construction, it becomes important to measure how well the constructed networks capture the given character relationship across the species. In the current study, we propose a novel method for measuring the specificity of a given phylogenetic network in terms of the total number of distributions of character states at the leaves that the network may impose. While for binary phylogenetic trees, this number has an exact formula and depends only on the number of leaves and character states but not on the tree topology, the situation is much more complicated for non-binary trees or networks. Nevertheless, we develop an algorithm for combinatorial enumeration of such distributions, which is applicable for arbitrary trees and networks under some reasonable assumptions.Comment: 12 pages; 3 figure

A generating functional approach to the Hubbard model

The method of generating functional is generalized to the case of strongly correlated systems, and applied to the Hubbard model. For the electronic Green's function constructed for Hubbard operators, an equation using variational derivatives with respect to the fluctuating fields has been derived and its multiplicative form has been determined. Corrections for the electronic self-energy are calculated up to the second order with respect to the parameter W/U (W width of the band), and a mean field type approximation was formulated, including both charge and spin static fluctuations. The equations for the Bose-like Green's functions have been derived, describing the collective modes: the magnons and doublons. The properties of the poles of the doublon Green's functions depend on electronic filling. The investigation of the special case n=1 demonstrates that the doublon Green's function has a soft mode at the wave vector Q=(pi,pi,...), indicating possible instability of the uniform paramagnetic phase relatively to the two sublattices charge ordering. However this instability should compete with an instability to antiferromagnetic ordering.Comment: 31 pages, 7 figures, to be published in Eur. Phys. J.

Cosmogenic Mn-53 in meteorites

The distributions of the Mn-53 contents in 106 nonantarctic and 112 antarctic chondrites were analyzed. A correlation analysis of these distributions showed that the correlation coefficient is a maximum r sub max = 0.75 plus or minus 0.03) when the histogram for antarctic chondrites is displaced by 40 plus or minus 8 dpm kg-1Fe towards lower Mn-53 contents. The distribution of Mn-53 saturated contents in nonantarctic ordinary chondrites was investigated as a function of their radiation age (T). It is found that the Mn-53 average content is higher by (21 plus or minus 9)% in H-chondrites with radiation age T approximately 12 Myr than in thse with T 12 Myr. This effect can be attributed to the fact that a considerable proportion of H-chondrites with T 12 Myr originates from a comet or from the objects of Chiron like, with the orbits more inclined to the ecliptic plane and/or more extended, which caused their irradiation by cosmic rays of higher intensity

Measurement of the neutron electric dipole moment by crystal diffraction

An experiment using a prototype setup to search for the neutron electric dipole moment by measuring spin-rotation in a non-centrosymmetric crystal (quartz) was carried out to investigate statistical sensitivity and systematic effects of the method. It has been demonstrated that the concept of the method works. The preliminary result of the experiment is $d_{\rm n}=(2.5\pm 6.5)\cdot 10^{-24}$ e$\cdot$cm. The experiment showed that an accuracy of $\sim 2.5\cdot 10^{-26}$ e$\cdot$cm can be obtained in 100 days data taking, using available quartz crystals and neutron beams.Comment: 13 pages, 4 figure