Rate of lineage origin explains the diversity anomaly in the World’s mangrove vegetation

The contribution of nonecological factors to global patterns in diversity is evident when species richness differs between regions with similar habitats and geographic area. Mangrove environments in the Eastern Hemisphere harbor six times as many species of trees and shrubs as similar environments in the New World. Genetic divergence of mangrove lineages from terrestrial relatives, in combination with fossil evidence, suggests that mangrove diversity is limited by evolutionary transition into the stressful marine environment, the number of mangrove lineages has increased steadily over the Tertiary with little global extinction, and the diversity anomaly in mangrove vegetation reflects regional differences in the rate of origin of new mangrove lineages

Classification of real three-dimensional Lie bialgebras and their Poisson-Lie groups

Classical r-matrices of the three-dimensional real Lie bialgebras are obtained. In this way all three-dimensional real coboundary Lie bialgebras and their types (triangular, quasitriangular or factorizable) are classified. Then, by using the Sklyanin bracket, the Poisson structures on the related Poisson-Lie groups are obtained.Comment: 17 page

The graded Jacobi algebras and (co)homology

Jacobi algebroids (i.e. `Jacobi versions' of Lie algebroids) are studied in the context of graded Jacobi brackets on graded commutative algebras. This unifies varios concepts of graded Lie structures in geometry and physics. A method of describing such structures by classical Lie algebroids via certain gauging (in the spirit of E.Witten's gauging of exterior derivative) is developed. One constructs a corresponding Cartan differential calculus (graded commutative one) in a natural manner. This, in turn, gives canonical generating operators for triangular Jacobi algebroids. One gets, in particular, the Lichnerowicz-Jacobi homology operators associated with classical Jacobi structures. Courant-Jacobi brackets are obtained in a similar way and use to define an abstract notion of a Courant-Jacobi algebroid and Dirac-Jacobi structure. All this offers a new flavour in understanding the Batalin-Vilkovisky formalism.Comment: 20 pages, a few typos corrected; final version to be published in J. Phys. A: Math. Ge

Jacobi structures revisited

Jacobi algebroids, that is graded Lie brackets on the Grassmann algebra associated with a vector bundle which satisfy a property similar to that of the Jacobi brackets, are introduced. They turn out to be equivalent to generalized Lie algebroids in the sense of Iglesias and Marrero and can be viewed also as odd Jacobi brackets on the supermanifolds associated with the vector bundles. Jacobi bialgebroids are defined in the same manner. A lifting procedure of elements of this Grassmann algebra to multivector fields on the total space of the vector bundle which preserves the corresponding brackets is developed. This gives the possibility of associating canonically a Lie algebroid with any local Lie algebra in the sense of Kirillov.Comment: 20 page

Poisson sigma model on the sphere

We evaluate the path integral of the Poisson sigma model on sphere and study the correlators of quantum observables. We argue that for the path integral to be well-defined the corresponding Poisson structure should be unimodular. The construction of the finite dimensional BV theory is presented and we argue that it is responsible for the leading semiclassical contribution. For a (twisted) generalized Kahler manifold we discuss the gauge fixed action for the Poisson sigma model. Using the localization we prove that for the holomorphic Poisson structure the semiclassical result for the correlators is indeed the full quantum result.Comment: 38 page

Apo B100 similarities to viral proteins suggest basis for LDL-DNA binding and transfection capacity

LDL mediates transfection with plasmid DNA in a variety of cell types in vitro and in several tissues in vivo in the rat. The transfection capacity of LDL is based on apo B100, as arginine/lysine clusters, suggestive of nucleic acid-binding domains and nuclear localization signal sequences, are present throughout the molecule. Apo E may also contribute to this capacity because of its similarity to the Dengue virus capsid proteins and its ability to bind DNA. Synthetic peptides representing two apo B100 regions with prominent Arg/Lys clusters were shown to bind DNA. Region 1 (0014Lys-Ser 0160) shares sequence motifs present in DNA binding domains of Interferon Regulatory Factors and Flaviviridae capsid/core proteins. It also contains a close analog of the B/E receptor ligand of apo E. Region 1 peptides, B1-1 (0014Lys-Glu0054) and B1-2 (0055Leu- Ala0096), mediate transfection of HeLa cells but are cytotoxic. Region 2 (3313Asp-Thr3431), containing the known B/E receptor ligand, shares analog motifs with the human herpesvirus 5 immediate-early transcriptional regulator ( UL122) and Flaviviridae NS3 helicases. Region 2 peptides, B2-1 (3313Asp-Glu3355), and B2-2 (3356Gly-Thr3431) are ineffective in cell transfection and are noncytotoxic.jlr These results confirm the role of LDL as a natural transfection vector in vivo, a capacity imparted by the apo B100, and suggest a basis for Flaviviridae cell entry. Copyright © 2010 by the American Society for Biochemistry and Molecular Biology, Inc

Extension of Hereditary Symmetry Operators

Two models of candidates for hereditary symmetry operators are proposed and thus many nonlinear systems of evolution equations possessing infinitely many commutative symmetries may be generated. Some concrete structures of hereditary symmetry operators are carefully analyzed on the base of the resulting general conditions and several corresponding nonlinear systems are explicitly given out as illustrative examples.Comment: 13 pages, LaTe