Dependent coordinates in path integral measure factorization

The transformation of the path integral measure under the reduction procedure in the dynamical systems with a symmetry is considered. The investigation is carried out in the case of the Wiener--type path integrals that are used for description of the diffusion on a smooth compact Riemannian manifold with the given free isometric action of the compact semisimple unimodular Lie group. The transformation of the path integral, which factorizes the path integral measure, is based on the application of the optimal nonlinear filtering equation from the stochastic theory. The integral relation between the kernels of the original and reduced semigroup are obtained.Comment: LaTeX2e, 28 page

On "Dotsenko-Fateev" representation of the toric conformal blocks

We demonstrate that the recent ansatz of arXiv:1009.5553, inspired by the original remark due to R.Dijkgraaf and C.Vafa, reproduces the toric conformal blocks in the same sense that the spherical blocks are given by the integral representation of arXiv:1001.0563 with a peculiar choice of open integration contours for screening insertions. In other words, we provide some evidence that the toric conformal blocks are reproduced by appropriate beta-ensembles not only in the large-N limit, but also at finite N. The check is explicitly performed at the first two levels for the 1-point toric functions. Generalizations to higher genera are briefly discussed.Comment: 10 page

Challenges of beta-deformation

A brief review of problems, arising in the study of the beta-deformation, also known as "refinement", which appears as a central difficult element in a number of related modern subjects: beta \neq 1 is responsible for deviation from free fermions in 2d conformal theories, from symmetric omega-backgrounds with epsilon_2 = - epsilon_1 in instanton sums in 4d SYM theories, from eigenvalue matrix models to beta-ensembles, from HOMFLY to super-polynomials in Chern-Simons theory, from quantum groups to elliptic and hyperbolic algebras etc. The main attention is paid to the context of AGT relation and its possible generalizations.Comment: 20 page

The HIV-1 Integrase α4-Helix Involved in LTR-DNA Recognition Is also a Highly Antigenic Peptide Element

Monoclonal antibodies (MAbas) constitute remarkable tools to analyze the relationship between the structure and the function of a protein. By immunizing a mouse with a 29mer peptide (K159) formed by residues 147 to 175 of the HIV-1 integrase (IN), we obtained a monoclonal antibody (MAba4) recognizing an epitope lying in the N-terminal portion of K159 (residues 147–166 of IN). The boundaries of the epitope were determined in ELISA assays using peptide truncation and amino acid substitutions. The epitope in K159 or as a free peptide (pep-a4) was mostly a random coil in solution, while in the CCD (catalytic core domain) crystal, the homologous segment displayed an amphipathic helix structure (α4-helix) at the protein surface. Despite this conformational difference, a strong antigenic crossreactivity was observed between pep-a4 and the protein segment, as well as K156, a stabilized analogue of pep-a4 constrained into helix by seven helicogenic mutations, most of them involving hydrophobic residues. We concluded that the epitope is freely accessible to the antibody inside the protein and that its recognition by the antibody is not influenced by the conformation of its backbone and the chemistry of amino acids submitted to helicogenic mutations. In contrast, the AA →Glu mutations of the hydrophilic residues Gln148, Lys156 and Lys159, known for their interactions with LTRs (long terminal repeats) and inhibitors (

Structural Basis for Functional Tetramerization of Lentiviral Integrase

Experimental evidence suggests that a tetramer of integrase (IN) is the protagonist of the concerted strand transfer reaction, whereby both ends of retroviral DNA are inserted into a host cell chromosome. Herein we present two crystal structures containing the N-terminal and the catalytic core domains of maedi-visna virus IN in complex with the IN binding domain of the common lentiviral integration co-factor LEDGF. The structures reveal that the dimer-of-dimers architecture of the IN tetramer is stabilized by swapping N-terminal domains between the inner pair of monomers poised to execute catalytic function. Comparison of four independent IN tetramers in our crystal structures elucidate the basis for the closure of the highly flexible dimer-dimer interface, allowing us to model how a pair of active sites become situated for concerted integration. Using a range of complementary approaches, we demonstrate that the dimer-dimer interface is essential for HIV-1 IN tetramerization, concerted integration in vitro, and virus infectivity. Our structures moreover highlight adaptable changes at the interfaces of individual IN dimers that allow divergent lentiviruses to utilize a highly-conserved, common integration co-factor

Organic pollutants in sea-surface microlayer and aerosol in thecoastal environment of Leghorn—(Tyrrhenian Sea)

The levels of dissolved and particle-associated n-alkanes, alkylbenzenes, phthalates, PAHs, anionic surfactants and surfactant fluorescent organic matter ŽSFOM. were measured in sea-surface microlayer ŽSML. and sub-surface water ŽSSL. samples collected in the Leghorn marine environment in September and October 1999. Nine stations, located in the Leghorn harbour and at increasing distances from the Port, were sampled three times on the same day. At all the stations, SML concentrations of the selected organic compounds were significantly higher than SSL values and the enrichment factors ŽEFsSML concentrationrSSL concentration. were greater in the particulate phase than in the dissolved phase. SML concentrations varied greatly among the sampling sites, the highest levels Žn-alkanes 3674 mgrl, phthalates 177 mgrl, total PAHs 226 mgrl. being found in the particulate phase in the Leghorn harbour. To improve the knowledge on pollutant exchanges between sea-surface waters and atmosphere, the validity of spray drop adsorption model ŽSDAM. was verified for SFOM, surface-active agents, such as phthalates, and compounds which can interact with SFOM, such as n-alkanes and PAHs. q2001 Elsevier Science B.V. All rights reserved

Recurrence relations for toric N=1 superconformal blocks

General 1-point toric blocks in all sectors of N=1 superconformal field theories are analyzed. The recurrence relations for blocks coefficients are derived by calculating their residues and large $\Delta$ asymptotics