Independent large scale duplications in multiple M. tuberculosis lineages overlapping the same genomic region

Mycobacterium tuberculosis, the causative agent of most human tuberculosis, infects one third of the world's population and kills an estimated 1.7 million people a year. With the world-wide emergence of drug resistance, and the finding of more functional genetic diversity than previously expected, there is a renewed interest in understanding the forces driving genome evolution of this important pathogen. Genetic diversity in M. tuberculosis is dominated by single nucleotide polymorphisms and small scale gene deletion, with little or no evidence for large scale genome rearrangements seen in other bacteria. Recently, a single report described a large scale genome duplication that was suggested to be specific to the Beijing lineage. We report here multiple independent large-scale duplications of the same genomic region of M. tuberculosis detected through whole-genome sequencing. The duplications occur in strains belonging to both M. tuberculosis lineage 2 and 4, and are thus not limited to Beijing strains. The duplications occur in both drug-resistant and drug susceptible strains. The duplicated regions also have substantially different boundaries in different strains, indicating different originating duplication events. We further identify a smaller segmental duplication of a different genomic region of a lab strain of H37Rv. The presence of multiple independent duplications of the same genomic region suggests either instability in this region, a selective advantage conferred by the duplication, or both. The identified duplications suggest that large-scale gene duplication may be more common in M. tuberculosis than previously considere

Prepotentials of N=2 SU(2) Yang-Mills theories coupled with massive matter multiplets

We discuss N=2 SU(2) Yang-Mills gauge theories coupled with N_f (=2,3) massive hypermultiplets in the weak coupling limit. We determine the exact massive prepotentials and the monodromy matrices around the weak coupling limit. We also study that the double scaling limit of these massive theories and find that the massive N_f -1 theory can be obtained from the massive N_f theory. New formulae for the massive prepotentials and the monodromy matrices are proposed. In these formulae, N_f dependences are clarified.Comment: A version is published in J. Math. Phys. 38 (1997) 68

Two-particle decays of B_c meson into charmonium states

The factorization of hard and soft contributions into the hadronic decays of B_c meson at large recoils is explored in order to evaluate the decay rates into the S, P and D-wave charmonia associated with rho and pi. The constraints of approach applicability and uncertainties of numerical estimates are discussed. The mode with the J/psi in the final state is evaluated taking into account the cascade radiative electromagnetic decays of excited P-wave states, that enlarges the branching ratio by 20-25%.Comment: 13 pages, LaTeX axodraw-style, 1 figure, 2 table

Enumeration of graphs with a heavy-tailed degree sequence

In this paper, we asymptotically enumerate graphs with a given degree sequence d=(d_1,...,d_n) satisfying restrictions designed to permit heavy-tailed sequences in the sparse case (i.e. where the average degree is rather small). Our general result requires upper bounds on functions of M_k= \sum_{i=1}^n [d_i]_k for a few small integers k\ge 1. Note that M_1 is simply the total degree of the graphs. As special cases, we asymptotically enumerate graphs with (i) degree sequences satisfying M_2=o(M_1^{ 9/8}); (ii) degree sequences following a power law with parameter gamma>5/2; (iii) power-law degree sequences that mimic independent power-law "degrees" with parameter gamma>1+\sqrt{3}\approx 2.732; (iv) degree sequences following a certain "long-tailed" power law; (v) certain bi-valued sequences. A previous result on sparse graphs by McKay and the second author applies to a wide range of degree sequences but requires Delta =o(M_1^{1/3}), where Delta is the maximum degree. Our new result applies in some cases when Delta is only barely o(M_1^ {3/5}). Case (i) above generalises a result of Janson which requires M_2=O(M_1) (and hence M_1=O(n) and Delta=O(n^{1/2})). Cases (ii) and (iii) provide the first asymptotic enumeration results applicable to degree sequences of real-world networks following a power law, for which it has been empirically observed that 2<gamma<3.Comment: 34 page

Dark energy, cosmological constant and neutrino mixing

The today estimated value of dark energy can be achieved by the vacuum condensate induced by neutrino mixing phenomenon. Such a tiny value is recovered for a cut-off of the order of Planck scale and it is linked to the sub eV neutrino mass scale. Contributions to dark energy from auxiliary fields or mechanisms are not necessary in this approach.Comment: 10 pages, 2 figure

New Examples of Marginally Trapped Surfaces and Tubes in Warped Spacetimes

In the present paper we provide new examples of marginally trapped surfaces and tubes in FLRW spacetimes by using a basic relation between these objects and CMC surfaces in 3-manifolds. We also provide a new method to construct marginally trapped surfaces in closed FLRW spacetimes, which is based on the classical Hopf map. The utility of this method is illustrated by providing marginally trapped surfaces crossing expanding and collapsing regions of a closed FLRW spacetime. The approach introduced in this paper is also extended to twisted spaces.Comment: 20 page