490 research outputs found

    Discovery and Assessment of New Target Sites for Anti-HIV Therapies

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    Human immunodeficiency virus (HIV) infects cells by endocytosis and takes over parts of the cell’s reaction pathways in order to reproduce itself and spread the infection. One such pathway taken over by HIV becomes the inflammatory pathway which uses Nuclear Factor κB (NF-κB) as the principal transcription factor. Therefore, knocking out the NF-κB pathway would prevent HIV from reproducing itself. In this report, our goal is to produce a simple model for this pathway with which we can identify potential targets for anti-HIV therapies and test out various hypotheses. We present a very simple model with four coupled first-order ODEs and see what happens if we treat IκK concentration as a parameter that can be controlled (by some unspecified means). In Section 3, we augment this model to account for activation and deactivation of IκK, which is controlled (again, by some unspecified means) by TNF

    Self-avoiding walks crossing a square

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    We study a restricted class of self-avoiding walks (SAW) which start at the origin (0, 0), end at (L,L)(L, L), and are entirely contained in the square [0,L]×[0,L][0, L] \times [0, L] on the square lattice Z2{\mathbb Z}^2. The number of distinct walks is known to grow as λL2+o(L2)\lambda^{L^2+o(L^2)}. We estimate λ=1.744550±0.000005\lambda = 1.744550 \pm 0.000005 as well as obtaining strict upper and lower bounds, 1.628<λ<1.782.1.628 < \lambda < 1.782. We give exact results for the number of SAW of length 2L+2K2L + 2K for K=0,1,2K = 0, 1, 2 and asymptotic results for K=o(L1/3)K = o(L^{1/3}). We also consider the model in which a weight or {\em fugacity} xx is associated with each step of the walk. This gives rise to a canonical model of a phase transition. For x<1/μx < 1/\mu the average length of a SAW grows as LL, while for x>1/μx > 1/\mu it grows as L2L^2. Here μ\mu is the growth constant of unconstrained SAW in Z2{\mathbb Z}^2. For x=1/μx = 1/\mu we provide numerical evidence, but no proof, that the average walk length grows as L4/3L^{4/3}. We also consider Hamiltonian walks under the same restriction. They are known to grow as τL2+o(L2)\tau^{L^2+o(L^2)} on the same L×LL \times L lattice. We give precise estimates for τ\tau as well as upper and lower bounds, and prove that τ<λ.\tau < \lambda.Comment: 27 pages, 9 figures. Paper updated and reorganised following refereein

    Equilibrium size of large ring molecules

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    The equilibrium properties of isolated ring molecules were investigated using an off-lattice model with no excluded volume but with dynamics that preserve the topological class. Using an efficient set of long range moves, chains of more than 2000 monomers were studied. Despite the lack of any excluded volume interaction, the radius of gyration scaled like that of a self avoiding walk, as had been previously conjectured. However this scaling was only seen for chains greater than 500 monomers.Comment: 11 pages, 3 eps figures, latex, psfi

    A new transfer-matrix algorithm for exact enumerations: Self-avoiding polygons on the square lattice

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    We present a new and more efficient implementation of transfer-matrix methods for exact enumerations of lattice objects. The new method is illustrated by an application to the enumeration of self-avoiding polygons on the square lattice. A detailed comparison with the previous best algorithm shows significant improvement in the running time of the algorithm. The new algorithm is used to extend the enumeration of polygons to length 130 from the previous record of 110.Comment: 17 pages, 8 figures, IoP style file

    Determination of the exponent gamma for SAWs on the two-dimensional Manhattan lattice

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    We present a high-statistics Monte Carlo determination of the exponent gamma for self-avoiding walks on a Manhattan lattice in two dimensions. A conservative estimate is \gamma \gtapprox 1.3425(3), in agreement with the universal value 43/32 on regular lattices, but in conflict with predictions from conformal field theory and with a recent estimate from exact enumerations. We find strong corrections to scaling that seem to indicate the presence of a non-analytic exponent Delta < 1. If we assume Delta = 11/16 we find gamma = 1.3436(3), where the error is purely statistical.Comment: 24 pages, LaTeX2e, 4 figure

    A Swendsen-Wang update algorithm for the Symanzik improved sigma model

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    We study a generalization of Swendsen-Wang algorithm suited for Potts models with next-next-neighborhood interactions. Using the embedding technique proposed by Wolff we test it on the Symanzik improved bidimensional non-linear σ\sigma model. For some long range observables we find a little slowing down exponent (z0.3z \simeq 0.3) that we interpret as an effect of the partial frustration of the induced spin model.Comment: Self extracting archive fil

    On the Dominance of Trivial Knots among SAPs on a Cubic Lattice

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    The knotting probability is defined by the probability with which an NN-step self-avoiding polygon (SAP) with a fixed type of knot appears in the configuration space. We evaluate these probabilities for some knot types on a simple cubic lattice. For the trivial knot, we find that the knotting probability decays much slower for the SAP on the cubic lattice than for continuum models of the SAP as a function of NN. In particular the characteristic length of the trivial knot that corresponds to a `half-life' of the knotting probability is estimated to be 2.5×1052.5 \times 10^5 on the cubic lattice.Comment: LaTeX2e, 21 pages, 8 figur

    Persistence length of a polyelectrolyte in salty water: a Monte-Carlo study

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    We address the long standing problem of the dependence of the electrostatic persistence length lel_e of a flexible polyelectrolyte (PE) on the screening length rsr_s of the solution within the linear Debye-Huckel theory. The standard Odijk, Skolnick and Fixman (OSF) theory suggests lers2l_e \propto r_s^2, while some variational theories and computer simulations suggest lersl_e \propto r_s. In this paper, we use Monte-Carlo simulations to study the conformation of a simple polyelectrolyte. Using four times longer PEs than in previous simulations and refined methods for the treatment of the simulation data, we show that the results are consistent with the OSF dependence lers2l_e \propto r_s^2. The linear charge density of the PE which enters in the coefficient of this dependence is properly renormalized to take into account local fluctuations.Comment: 7 pages, 6 figures. Various corrections in text and reference

    Staircase polygons: moments of diagonal lengths and column heights

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    We consider staircase polygons, counted by perimeter and sums of k-th powers of their diagonal lengths, k being a positive integer. We derive limit distributions for these parameters in the limit of large perimeter and compare the results to Monte-Carlo simulations of self-avoiding polygons. We also analyse staircase polygons, counted by width and sums of powers of their column heights, and we apply our methods to related models of directed walks.Comment: 24 pages, 7 figures; to appear in proceedings of Counting Complexity: An International Workshop On Statistical Mechanics And Combinatorics, 10-15 July 2005, Queensland, Australi

    Asymptotic Behavior of Inflated Lattice Polygons

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    We study the inflated phase of two dimensional lattice polygons with fixed perimeter NN and variable area, associating a weight exp[pAJb]\exp[pA - Jb ] to a polygon with area AA and bb bends. For convex and column-convex polygons, we show that /Amax=1K(J)/p~2+O(ρp~)/A_{max} = 1 - K(J)/\tilde{p}^2 + \mathcal{O}(\rho^{-\tilde{p}}), where p~=pN1\tilde{p}=pN \gg 1, and ρ<1\rho<1. The constant K(J)K(J) is found to be the same for both types of polygons. We argue that self-avoiding polygons should exhibit the same asymptotic behavior. For self-avoiding polygons, our predictions are in good agreement with exact enumeration data for J=0 and Monte Carlo simulations for J0J \neq 0. We also study polygons where self-intersections are allowed, verifying numerically that the asymptotic behavior described above continues to hold.Comment: 7 page
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