Spatial Mixing and Non-local Markov chains

We consider spin systems with nearest-neighbor interactions on an $n$-vertex $d$-dimensional cube of the integer lattice graph $\mathbb{Z}^d$. We study the effects that exponential decay with distance of spin correlations, specifically the strong spatial mixing condition (SSM), has on the rate of convergence to equilibrium distribution of non-local Markov chains. We prove that SSM implies $O(\log n)$ mixing of a block dynamics whose steps can be implemented efficiently. We then develop a methodology, consisting of several new comparison inequalities concerning various block dynamics, that allow us to extend this result to other non-local dynamics. As a first application of our method we prove that, if SSM holds, then the relaxation time (i.e., the inverse spectral gap) of general block dynamics is $O(r)$, where $r$ is the number of blocks. A second application of our technology concerns the Swendsen-Wang dynamics for the ferromagnetic Ising and Potts models. We show that SSM implies an $O(1)$ bound for the relaxation time. As a by-product of this implication we observe that the relaxation time of the Swendsen-Wang dynamics in square boxes of $\mathbb{Z}^2$ is $O(1)$ throughout the subcritical regime of the $q$-state Potts model, for all $q \ge 2$. We also prove that for monotone spin systems SSM implies that the mixing time of systematic scan dynamics is $O(\log n (\log \log n)^2)$. Systematic scan dynamics are widely employed in practice but have proved hard to analyze. Our proofs use a variety of techniques for the analysis of Markov chains including coupling, functional analysis and linear algebra

Synthesis by the polyol process and ionic conductivity of nanostructured La2Mo2O9 powders

International audienceLa2Mo2O9 nanostructured powders were synthesized by the polyol process. The effects of the nature of the polyol, the refluxing time, the hydrolysis ratio, the metal concentration and the addition of hydroxide ions, on the purity and morphology of the powders are determined. Two main morphologies are observed, the particles being in the shape of platelets or spheres, with respectively diethylene glycol or ethylene glycol as solvent. A specific surface area of 24 m2/g was reached by varying the metal concentration. The conductivity measurements were recorded on pellets that present in some cases a closed porosity, the relative density reaching 95% without any milling step. According to the synthesis parameters, the grain conductivity can be slightly increased, the total conductivity remaining only slightly lower than that of pellets made of powders synthesized by solid state reaction

Uncertainty inequalities on groups and homogeneous spaces via isoperimetric inequalities

We prove a family of $L^p$ uncertainty inequalities on fairly general groups and homogeneous spaces, both in the smooth and in the discrete setting. The crucial point is the proof of the $L^1$ endpoint, which is derived from a general weak isoperimetric inequality.Comment: 17 page

Architecture for Integrated Mems Resonators Quality Factor Measurement

In this paper, an architecture designed for electrical measurement of the quality factor of MEMS resonators is proposed. An estimation of the measurement performance is made using PSPICE simulations taking into account the component's non-idealities. An error on the measured Q value of only several percent is achievable, at a small integration cost, for sufficiently high quality factor values (Q > 100).Comment: Submitted on behalf of EDA Publishing Association (http://irevues.inist.fr/EDA-Publishing

The running coupling of 8 flavors and 3 colors

We compute the renormalized running coupling of SU(3) gauge theory coupled to N_f = 8 flavors of massless fundamental Dirac fermions. The recently proposed finite volume gradient flow scheme is used. The calculations are performed at several lattice spacings allowing for a controlled continuum extrapolation. The results for the discrete beta-function show that it is monotonic without any sign of a fixed point in the range of couplings we cover. As a cross check the continuum results are compared with the well-known perturbative continuum beta-function for small values of the renormalized coupling and perfect agreement is found.Comment: 15 pages, 17 figures, published versio

Properties making a chaotic system a good Pseudo Random Number Generator

We discuss two properties making a deterministic algorithm suitable to generate a pseudo random sequence of numbers: high value of Kolmogorov-Sinai entropy and high-dimensionality. We propose the multi dimensional Anosov symplectic (cat) map as a Pseudo Random Number Generator. We show what chaotic features of this map are useful for generating Pseudo Random Numbers and investigate numerically which of them survive in the discrete version of the map. Testing and comparisons with other generators are performed.Comment: 10 pages, 3 figures, new version, title changed and minor correction

Effect of a 6-month brisk walking program on walking endurance in sedentary and physically deconditioned women aged 60 or older: A randomized trial

International audienceBACKGROUND:Walking endurance is a predictor of healthy ageing.OBJECTIVE:To examine if a 6-month brisk walking program can increase walking endurance in sedentary and physically deconditioned older women.TRIAL DESIGN:Randomized controlled trial.SETTING:Women recruited from public meetings aimed at promoting physical activity in women aged 60 or older.SUBJECTS:121 women aged 65.7 ± 4.3 years, with sedentary lifestyle (Physical Activity Questionnaire for the Elderly score 46%) were those with baseline lowest values of 6MWD (p=0.001) and highest values of body mass index (BMI) (p<0.01).CONCLUSION:Present results support recommendation that brisk walking programs should be encouraged to improve walking endurance in physically deconditioned women aged 60 or older, especially in those with high BMI

The evaluation of liver fibrosis regression in chronic hepatitis C patients after the treatment with direct-acting antiviral agents – A review of the literature

The second-generation of direct-acting antiviral agents are the current treatment for chronic viral hepatitis C infection. To evaluate the regression of liver fibrosis in patients receiving this therapy, liver biopsy remains the most accurate method, but the invasiveness of this procedure is its major drawback. Different non-invasive tests have been used to study changes in the stage of liver fibrosis in patients with chronic viral hepatitis treated with the second-generation of direct-acting antiviral agents: liver stiffness measurements (with transient elastography or acoustic radiation force impulse elastography) or different scores that use serum markers to calculate a fibrosis score. We prepared a literature review of the available data regarding the long-term evolution of liver fibrosis after the treatment with direct-acting antiviral agents for chronic viral hepatitis C

Power-Laws in Nonlinear Granular Chain under Gravity

The signal generated by a weak impulse propagates in an oscillatory way and dispersively in a gravitationally compacted granular chain. For the power-law type contact force, we show analytically that the type of dispersion follows power-laws in depth. The power-law for grain displacement signal is given by $h^{-1/4(1-1/p)}$ where $h$ and $p$ denote depth and the exponent of contact force, and the power-law for the grain velocity is $h^{-1/4({1/3}+1/p)}$. Other depth-dependent power-laws for oscillation frequency, wavelength, and period are given by combining above two and the phase velocity power-law $h^{1/2(1-1/p)}$. We verify above power-laws by comparing with the data obtained by numerical simulations.Comment: 12 pages, 3 figures; Changed conten

Phase spaces related to standard classical rr-matrices

Fundamental representations of real simple Poisson Lie groups are Poisson actions with a suitable choice of the Poisson structure on the underlying (real) vector space. We study these (mostly quadratic) Poisson structures and corresponding phase spaces (symplectic groupoids).Comment: 20 pages, LaTeX, no figure