184 research outputs found

    Constructing and exploring wells of energy landscapes

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    Landscape paradigm is ubiquitous in physics and other natural sciences, but it has to be supplemented with both quantitative and qualitatively meaningful tools for analyzing the topography of a given landscape. We here consider dynamic explorations of the relief and introduce as basic topographic features ``wells of duration TT and altitude yy''. We determine an intrinsic exploration mechanism governing the evolutions from an initial state in the well up to its rim in a prescribed time, whose finite-difference approximations on finite grids yield a constructive algorithm for determining the wells. Our main results are thus (i) a quantitative characterization of landscape topography rooted in a dynamic exploration of the landscape, (ii) an alternative to stochastic gradient dynamics for performing such an exploration, (iii) a constructive access to the wells and (iv) the determination of some bare dynamic features inherent to the landscape. The mathematical tools used here are not familiar in physics: They come from set-valued analysis (differential calculus of set-valued maps and differential inclusions) and viability theory (capture basins of targets under evolutionary systems) which have been developed during the last two decades; we therefore propose a minimal appendix exposing them at the end of this paper to bridge the possible gap.Comment: 28 pages, submitted to J. Math. Phys -

    A homomorphism between link and XXZ modules over the periodic Temperley-Lieb algebra

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    We study finite loop models on a lattice wrapped around a cylinder. A section of the cylinder has N sites. We use a family of link modules over the periodic Temperley-Lieb algebra EPTL_N(\beta, \alpha) introduced by Martin and Saleur, and Graham and Lehrer. These are labeled by the numbers of sites N and of defects d, and extend the standard modules of the original Temperley-Lieb algebra. Beside the defining parameters \beta=u^2+u^{-2} with u=e^{i\lambda/2} (weight of contractible loops) and \alpha (weight of non-contractible loops), this family also depends on a twist parameter v that keeps track of how the defects wind around the cylinder. The transfer matrix T_N(\lambda, \nu) depends on the anisotropy \nu and the spectral parameter \lambda that fixes the model. (The thermodynamic limit of T_N is believed to describe a conformal field theory of central charge c=1-6\lambda^2/(\pi(\lambda-\pi)).) The family of periodic XXZ Hamiltonians is extended to depend on this new parameter v and the relationship between this family and the loop models is established. The Gram determinant for the natural bilinear form on these link modules is shown to factorize in terms of an intertwiner i_N^d between these link representations and the eigenspaces of S^z of the XXZ models. This map is shown to be an isomorphism for generic values of u and v and the critical curves in the plane of these parameters for which i_N^d fails to be an isomorphism are given.Comment: Replacement of "The Gram matrix as a connection between periodic loop models and XXZ Hamiltonians", 31 page

    Rapid determination of HLA B*07 ligands from the West Nile virus NY99 genome.

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    Defined T cell epitopes for West Nile (WN) virus may be useful for developing subunit vaccines against WN virus infection and diagnostic reagents to detect WN virus-specific immune response. We applied a bioinformatics (EpiMatrix) approach to search the WN virus NY99 genome for HLA B*07 restricted cytotoxic T cell (CTL) epitopes. Ninety-five of 3,433 WN virus peptides scored above a predetermined cutoff, suggesting that these would be likely to bind to HLA B*07 and would also be likely candidate CTL epitopes. Compared with other methods for genome mapping, derivation of these ligands was rapid and inexpensive. Major histocompatibility complex ligands identified by this method may be used to screen T cells from WN virus-exposed persons for cell-mediated response to WN virus or to develop diagnostic reagents for immunopathogenesis studies and epidemiologic surveillance
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