3,305 research outputs found
Matching with shift for one-dimensional Gibbs measures
We consider matching with shifts for Gibbsian sequences. We prove that the
maximal overlap behaves as , where is explicitly identified in
terms of the thermodynamic quantities (pressure) of the underlying potential.
Our approach is based on the analysis of the first and second moment of the
number of overlaps of a given size. We treat both the case of equal sequences
(and nonzero shifts) and independent sequences.Comment: Published in at http://dx.doi.org/10.1214/08-AAP588 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A numerical study of infinitely renormalizable area-preserving maps
It has been shown in (Gaidashev et al, 2010) and (Gaidashev et al, 2011) that
infinitely renormalizable area-preserving maps admit invariant Cantor sets with
a maximal Lyapunov exponent equal to zero. Furthermore, the dynamics on these
Cantor sets for any two infinitely renormalizable maps is conjugated by a
transformation that extends to a differentiable function whose derivative is
Holder continuous of exponent alpha>0.
In this paper we investigate numerically the specific value of alpha. We also
present numerical evidence that the normalized derivative cocycle with the base
dynamics in the Cantor set is ergodic. Finally, we compute renormalization
eigenvalues to a high accuracy to support a conjecture that the renormalization
spectrum is real
The Hierarchical Random Energy Model
We introduce a Random Energy Model on a hierarchical lattice where the
interaction strength between variables is a decreasing function of their mutual
hierarchical distance, making it a non-mean field model. Through small coupling
series expansion and a direct numerical solution of the model, we provide
evidence for a spin glass condensation transition similar to the one occuring
in the usual mean field Random Energy Model. At variance with mean field, the
high temperature branch of the free-energy is non-analytic at the transition
point
Spectral degeneracy and escape dynamics for intermittent maps with a hole
We study intermittent maps from the point of view of metastability. Small
neighbourhoods of an intermittent fixed point and their complements form pairs
of almost-invariant sets. Treating the small neighbourhood as a hole, we first
show that the absolutely continuous conditional invariant measures (ACCIMs)
converge to the ACIM as the length of the small neighbourhood shrinks to zero.
We then quantify how the escape dynamics from these almost-invariant sets are
connected with the second eigenfunctions of Perron-Frobenius (transfer)
operators when a small perturbation is applied near the intermittent fixed
point. In particular, we describe precisely the scaling of the second
eigenvalue with the perturbation size, provide upper and lower bounds, and
demonstrate convergence of the positive part of the second eigenfunction
to the ACIM as the perturbation goes to zero. This perturbation and associated
eigenvalue scalings and convergence results are all compatible with Ulam's
method and provide a formal explanation for the numerical behaviour of Ulam's
method in this nonuniformly hyperbolic setting. The main results of the paper
are illustrated with numerical computations.Comment: 34 page
Brain MRI segmentation and lesion detection using generalized Gaussian and Rician modeling
In this paper we propose a mixed noise modeling so as to segment the brain and to detect lesion. Indeed, accurate segmentation of multimodal (T1, T2 and Flair) brain MR images is of great interest for many brain disorders but requires to efficiently manage multivariate correlated noise between available modalities. We addressed this problem in1 by proposing an entirely unsupervised segmentation scheme, taking into account multivariate Gaussian noise, imaging artifacts,intrinsic tissue variation and partial volume effects in a Bayesian framework. Nevertheless, tissue classification remains a challenging task especially when one addresses the lesion detection during segmentation process2 as we did. In order to improve brain segmentation into White and Gray Matter (resp. WM and GM) and cerebro-spinal fluid (CSF), we propose to fit a Rician (RC) density distribution for CSF whereas Generalized Gaussian (GG) models are used to fit the likelihood between model and data corresponding to WM and GM. In this way, we present in this paper promising results showing that in a multimodal segmentation-detection scheme, this model fits better with the data and increases lesion detection rate. One of the main challenges consists in being able to take into account various pdf (Gaussian and non- Gaussian) for correlated noise between modalities and to show that lesion-detection is then clearly improved, probably because non-Gaussian noise better fits to the physic of MRI image acquisition
A Numerical Study of the Hierarchical Ising Model: High Temperature Versus Epsilon Expansion
We study numerically the magnetic susceptibility of the hierarchical model
with Ising spins () above the critical temperature and for two
values of the epsilon parameter. The integrations are performed exactly, using
recursive methods which exploit the symmetries of the model. Lattices with up
to sites have been used. Surprisingly, the numerical data can be fitted
very well with a simple power law of the form for the {\it whole} temperature range. The numerical values for
agree within a few percent with the values calculated with a high-temperature
expansion but show significant discrepancies with the epsilon-expansion. We
would appreciate comments about these results.Comment: 15 Pages, 12 Figures not included (hard copies available on request),
uses phyzzx.te
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