105,163 research outputs found

    Analyticity of the Susceptibility Function for Unimodal Markovian Maps of the Interval

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    In a previous note [Ru] the susceptibility function was analyzed for some examples of maps of the interval. The purpose of the present note is to give a concise treatment of the general unimodal Markovian case (assuming ff real analytic). We hope that it will similarly be possible to analyze maps satisfying the Collet-Eckmann condition. Eventually, as explained in [Ru], application of a theorem of Whitney [Wh] should prove differentiability of the map fρff\mapsto\rho_f restricted to a suitable set.Comment: 8 page

    Bounded perturbation resilience of projected scaled gradient methods

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    We investigate projected scaled gradient (PSG) methods for convex minimization problems. These methods perform a descent step along a diagonally scaled gradient direction followed by a feasibility regaining step via orthogonal projection onto the constraint set. This constitutes a generalized algorithmic structure that encompasses as special cases the gradient projection method, the projected Newton method, the projected Landweber-type methods and the generalized Expectation-Maximization (EM)-type methods. We prove the convergence of the PSG methods in the presence of bounded perturbations. This resilience to bounded perturbations is relevant to the ability to apply the recently developed superiorization methodology to PSG methods, in particular to the EM algorithm.Comment: Computational Optimization and Applications, accepted for publicatio

    Critical behaviours of contact near phase transitions

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    A central quantity of importance for ultracold atoms is contact, which measures two-body correlations at short distances in dilute systems. It appears in universal relations among thermodynamic quantities, such as large momentum tails, energy, and dynamic structure factors, through the renowned Tan relations. However, a conceptual question remains open as to whether or not contact can signify phase transitions that are insensitive to short-range physics. Here we show that, near a continuous classical or quantum phase transition, contact exhibits a variety of critical behaviors, including scaling laws and critical exponents that are uniquely determined by the universality class of the phase transition and a constant contact per particle. We also use a prototypical exactly solvable model to demonstrate these critical behaviors in one-dimensional strongly interacting fermions. Our work establishes an intrinsic connection between the universality of dilute many-body systems and universal critical phenomena near a phase transition.Comment: Final version published in Nat. Commun. 5:5140 doi: 10.1038/ncomms6140 (2014

    Relation between directed polymers in random media and random bond dimer models

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    We reassess the relation between classical lattice dimer models and the continuum elastic description of a lattice of fluctuating polymers. In the absence of randomness we determine the density and line tension of the polymers in terms of the bond weights of hard-core dimers on the square and the hexagonal lattice. For the latter, we demonstrate the equivalence of the canonical ensemble for the dimer model and the grand-canonical description for polymers by performing explicitly the continuum limit. Using this equivalence for the random bond dimer model on a square lattice, we resolve a previously observed discrepancy between numerical results for the random dimer model and a replica approach for polymers in random media. Further potential applications of the equivalence are briefly discussed.Comment: 6 pages, 3 figure

    Relation of SiO maser emission to IR radiation in evolved stars based on the MSX observation

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    Based on the space MSX observation in bands A(8μ\mum), C(12μ\mum), D(15μ\mum) and E(21μ\mum), and the ground SiO maser observation of evolved stars by the Nobeyama 45-m telescope in the v=1 and v=2 J=1-0 transitions, the relation between SiO maser emission and mid-IR continuum radiation is analyzed. The relation between SiO maser emission and the IR radiation in the MSX bands A, C, D and E is all clearly correlated. The SiO maser emission can be explained by a radiative pumping mechanism according to its correlation with infrared radiation in the MSX band A.Comment: 11 pages, 4 figures, to appear in ApJ