7,397 research outputs found

    Error-correcting code on a cactus: a solvable model

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    An exact solution to a family of parity check error-correcting codes is provided by mapping the problem onto a Husimi cactus. The solution obtained in the thermodynamic limit recovers the replica symmetric theory results and provides a very good approximation to finite systems of moderate size. The probability propagation decoding algorithm emerges naturally from the analysis. A phase transition between decoding success and failure phases is found to coincide with an information-theoretic upper bound. The method is employed to compare Gallager and MN codes.Comment: 7 pages, 3 figures, with minor correction

    L∞ -estimates in optimal transport for non quadratic costs

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    For cost functions c(x, y) = h(x- y) , with h∈ C2(Rn\ { 0 }) ∩ C1(Rn) homogeneous of degree p> 1 , we show L∞-estimates of Tx- x on balls, where T is an h-monotone map. Estimates for the interpolating mappings Tt= t(T- I) + I are deduced from this

    A microscopic description of the aging dynamics: fluctuation-dissipation relations, effective temperature and heterogeneities

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    We consider the dynamics of a diluted mean-field spin glass model in the aging regime. The model presents a particularly rich heterogeneous behavior. In order to catch this behavior, we perform a **spin-by-spin analysis** for a **given disorder realization**. The results compare well with the outcome of a static calculation which uses the ``survey propagation'' algorithm of Mezard, Parisi, and Zecchina [Sciencexpress 10.1126/science.1073287 (2002)]. We thus confirm the connection between statics and dynamics at the level of single degrees of freedom. Moreover, working with single-site quantities, we can introduce a new response-vs-correlation plot, which clearly shows how heterogeneous degrees of freedom undergo coherent structural rearrangements. Finally we discuss the general scenario which emerges from our work and (possibly) applies to more realistic glassy models. Interestingly enough, some features of this scenario can be understood recurring to thermometric considerations.Comment: 4 pages, 5 figures (7 eps files

    The GRB Variability/Peak Luminosity Correlation: new results

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    We report test results of the correlation between time variability and peak luminosity of Gamma-Ray Bursts (GRBs), using a larger sample (32) of GRBs with known redshift than that available to Reichart et al. (2001), and using as variability measure that introduced by these authors. The results are puzzling. Assuming an isotropic-equivalent peak luminosity, as done by Reichart et al. (2001), a correlation is still found, but it is less relevant, and inconsistent with a power law as previously reported. Assuming as peak luminosity that corrected for GRB beaming for a subset of 16 GRBs with known beaming angle, the correlation becomes little less significant.Comment: 11 pages, 10 figures, MNRAS, accepte

    Probing the diffusive behaviour of beam-halo dynamics in circular accelerators

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    Circular particle accelerators at the energy frontier are based on superconducting magnets that are extremely sensitive to beam losses as these might induce quenches, i.e. transitions to the normal-conducting state. Furthermore, the energy stored in the circulating beam is so large that hardware integrity is put in serious danger, and machine protection becomes essential for reaching the nominal accelerator performance. In this challenging context, the beam halo becomes a potential source of performance limitations and its dynamics needs to be understood in detail to assess whether it could be an issue for the accelerator. In this paper, we discuss in detail a recent framework, based on a diffusive approach, to model beam-halo dynamics. The functional form of the optimal estimate of the perturbative series, as given by Nekhoroshev’s theorem, is used to provide the functional form of the action diffusion coefficient. The goal is to propose an effective model for the beam-halo dynamics and to devise an efficient experimental procedure to obtain an accurate measurement of the diffusion coefficient

    Cavity method for quantum spin glasses on the Bethe lattice

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    We propose a generalization of the cavity method to quantum spin glasses on fixed connectivity lattices. Our work is motivated by the recent refinements of the classical technique and its potential application to quantum computational problems. We numerically solve for the phase structure of a connectivity q=3q=3 transverse field Ising model on a Bethe lattice with ±J\pm J couplings, and investigate the distribution of various classical and quantum observables.Comment: 27 pages, 9 figure
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