Comment on "Regge Trajectories for All Flavors"

We show that Regge trajectories for all flavors suggested recently by Filipponi et al. cannot combine both meson spectroscopy and additivity of intercepts. Other defects of these trajectories are also discussed.Comment: 2 pages, LaTe

An asymptotic form of the reciprocity theorem with applications in x-ray scattering

The emission of electromagnetic waves from a source within or near a non-trivial medium (with or without boundaries, crystalline or amorphous, with inhomogeneities, absorption and so on) is sometimes studied using the reciprocity principle. This is a variation of the method of Green's functions. If one is only interested in the asymptotic radiation fields the generality of these methods may actually be a shortcoming: obtaining expressions valid for the uninteresting near fields is not just a wasted effort but may be prohibitively difficult. In this work we obtain a modified form the reciprocity principle which gives the asymptotic radiation field directly. The method may be used to obtain the radiation from a prescribed source, and also to study scattering problems. To illustrate the power of the method we study a few pedagogical examples and then, as a more challenging application we tackle two related problems. We calculate the specular reflection of x rays by a rough surface and by a smoothly graded surface taking polarization effects into account. In conventional treatments of reflection x rays are treated as scalar waves, polarization effects are neglected. This is a good approximation at grazing incidence but becomes increasingly questionable for soft x rays and UV at higher incidence angles. PACs: 61.10.Dp, 61.10.Kw, 03.50.DeComment: 19 pages, 4 figure

Nambu-Poisson manifolds and associated n-ary Lie algebroids

We introduce an n-ary Lie algebroid canonically associated with a Nambu-Poisson manifold. We also prove that every Nambu-Poisson bracket defined on functions is induced by some differential operator on the exterior algebra, and characterize such operators. Some physical examples are presented

Characteristic cohomology of pp-form gauge theories

The characteristic cohomology $H^k_{char}(d)$ for an arbitrary set of free $p$-form gauge fields is explicitly worked out in all form degrees $k<n-1$, where $n$ is the spacetime dimension. It is shown that this cohomology is finite-dimensional and completely generated by the forms dual to the field strengths. The gauge invariant characteristic cohomology is also computed. The results are extended to interacting $p$-form gauge theories with gauge invariant interactions. Implications for the BRST cohomology are mentioned.Comment: Latex file, no figures, 44 page

Results on the Wess-Zumino consistency condition for arbitrary Lie algebras

The so-called covariant Poincare lemma on the induced cohomology of the spacetime exterior derivative in the cohomology of the gauge part of the BRST differential is extended to cover the case of arbitrary, non reductive Lie algebras. As a consequence, the general solution of the Wess-Zumino consistency condition with a non trivial descent can, for arbitrary (super) Lie algebras, be computed in the small algebra of the 1 form potentials, the ghosts and their exterior derivatives. For particular Lie algebras that are the semidirect sum of a semisimple Lie subalgebra with an ideal, a theorem by Hochschild and Serre is used to characterize more precisely the cohomology of the gauge part of the BRST differential in the small algebra. In the case of an abelian ideal, this leads to a complete solution of the Wess-Zumino consistency condition in this space. As an application, the consistent deformations of 2+1 dimensional Chern-Simons theory based on iso(2,1) are rediscussed.Comment: 39 pages Latex file, 1 eps figure, typos and proof of lemma 5 correcte

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

Gauge transformations and symmetries of integrable systems

We analyze several integrable systems in zero-curvature form within the framework of $SL(2,\R)$ invariant gauge theory. In the Drienfeld-Sokolov gauge we derive a two-parameter family of nonlinear evolution equations which as special cases include the Kortweg-de Vries (KdV) and Harry Dym equations. We find residual gauge transformations which lead to infinintesimal symmetries of this family of equations. For KdV and Harry Dym equations we find an infinite hierarchy of such symmetry transformations, and we investigate their relation with local conservation laws, constants of the motion and the bi-Hamiltonian structure of the equations. Applying successive gauge transformatinos of Miura type we obtain a sequence of gauge equivalent integrable systems, among them the modified KdV and Calogero KdV equations.Comment: 18pages, no figure Journal versio

Chromosomes. CENP-C reshapes and stabilizes CENP-A nucleosomes at the centromere

Inheritance of each chromosome depends upon its centromere. A histone H3 variant, centromere protein A (CENP-A), is essential for epigenetically marking centromere location. We find that CENP-A is quantitatively retained at the centromere upon which it is initially assembled. CENP-C binds to CENP-A nucleosomes and is a prime candidate to stabilize centromeric chromatin. Using purified components, we find that CENP-C reshapes the octameric histone core of CENP-A nucleosomes, rigidifies both surface and internal nucleosome structure, and modulates terminal DNA to match the loose wrap that is found on native CENP-A nucleosomes at functional human centromeres. Thus, CENP-C affects nucleosome shape and dynamics in a manner analogous to allosteric regulation of enzymes. CENP-C depletion leads to rapid removal of CENP-A from centromeres, indicating their collaboration in maintaining centromere identity.NIH grants: (GM082989, CA186430, GM008275, GM008216, GM007229); American Heart Association predoctoral fellowship; American Cancer Society postdoctoral fellowship; NSF grant: (agreement DMR-0944772)

The Random Nature of Genome Architecture: Predicting Open Reading Frame Distributions

Background: A better understanding of the size and abundance of open reading frames (ORFS) in whole genomes may shed light on the factors that control genome complexity. Here we examine the statistical distributions of open reading frames (i.e. distribution of start and stop codons) in the fully sequenced genomes of 297 prokaryotes, and 14 eukaryotes. Methodology/Principal Findings: By fitting mixture models to data from whole genome sequences we show that the size-frequency distributions for ORFS are strikingly similar across prokaryotic and eukaryotic genomes. Moreover, we show that i) a large fraction (60–80%) of ORF size-frequency distributions can be predicted a priori with a stochastic assembly model based on GC content, and that (ii) size-frequency distributions of the remaining “non-random” ORFs are well-fitted by log-normal or gamma distributions, and similar to the size distributions of annotated proteins. Conclusions/Significance: Our findings suggest stochastic processes have played a primary role in the evolution of genome complexity, and that common processes govern the conservation and loss of functional genomics units in both prokaryotes and eukaryotes.8 page(s