Aubry sets vs Mather sets in two degrees of freedom

We study autonomous Tonelli Lagrangians on closed surfaces. We aim to clarify the relationship between the Aubry set and the Mather set, when the latter consists of periodic orbits which are not fixed points. Our main result says that in that case the Aubry set and the Mather set almost always coincide.Comment: Revised and expanded version. New proof of Lemma 2.3 (formerly Lemma 14

A linear CO chemistry parameterization in a chemistry-transport model: evaluation and application to data assimilation

This paper presents an evaluation of a new linear parameterization valid for the troposphere and the stratosphere, based on a first order approximation of the carbon monoxide (CO) continuity equation. This linear scheme (hereinafter noted LINCO) has been implemented in the 3-D Chemical Transport Model (CTM) MOCAGE (MOdèle de Chimie Atmospherique Grande Echelle). First, a one and a half years of LINCO simulation has been compared to output obtained from a detailed chemical scheme output. The mean differences between both schemes are about ±25 ppbv (part per billion by volume) or 15% in the troposphere and ±10 ppbv or 100% in the stratosphere. Second, LINCO has been compared to diverse observations from satellite instruments covering the troposphere (Measurements Of Pollution In The Troposphere: MOPITT) and the stratosphere (Microwave Limb Sounder: MLS) and also from aircraft (Measurements of ozone and water vapour by Airbus in-service aircraft: MOZAIC programme) mostly flying in the upper troposphere and lower stratosphere (UTLS). In the troposphere, the LINCO seasonal variations as well as the vertical and horizontal distributions are quite close to MOPITT CO observations. However, a bias of ~−40 ppbv is observed at 700 Pa between LINCO and MOPITT. In the stratosphere, MLS and LINCO present similar large-scale patterns, except over the poles where the CO concentration is underestimated by the model. In the UTLS, LINCO presents small biases less than 2% compared to independent MOZAIC profiles. Third, we assimilated MOPITT CO using a variational 3D-FGAT (First Guess at Appropriate Time) method in conjunction with MOCAGE for a long run of one and a half years. The data assimilation greatly improves the vertical CO distribution in the troposphere from 700 to 350 hPa compared to independent MOZAIC profiles. At 146 hPa, the assimilated CO distribution is also improved compared to MLS observations by reducing the bias up to a factor of 2 in the tropics. This study confirms that the linear scheme is able to simulate reasonably well the CO distribution in the troposphere and in the lower stratosphere. Therefore, the low computing cost of the linear scheme opens new perspectives to make free runs and CO data assimilation runs at high resolution and over periods of several years

Sparsity and Incoherence in Compressive Sampling

We consider the problem of reconstructing a sparse signal $x^0\in\R^n$ from a limited number of linear measurements. Given $m$ randomly selected samples of $U x^0$, where $U$ is an orthonormal matrix, we show that $\ell_1$ minimization recovers $x^0$ exactly when the number of measurements exceeds $$m\geq \mathrm{Const}\cdot\mu^2(U)\cdot S\cdot\log n,$$ where $S$ is the number of nonzero components in $x^0$, and $\mu$ is the largest entry in $U$ properly normalized: $\mu(U) = \sqrt{n} \cdot \max_{k,j} |U_{k,j}|$. The smaller $\mu$, the fewer samples needed. The result holds for ``most'' sparse signals $x^0$ supported on a fixed (but arbitrary) set $T$. Given $T$, if the sign of $x^0$ for each nonzero entry on $T$ and the observed values of $Ux^0$ are drawn at random, the signal is recovered with overwhelming probability. Moreover, there is a sense in which this is nearly optimal since any method succeeding with the same probability would require just about this many samples

First report of cucurbit aphid-borne yellows virus in cucurbita pepo and cucurbita maxima in Slovenia

peer reviewe

User-friendly tail bounds for sums of random matrices

This paper presents new probability inequalities for sums of independent, random, self-adjoint matrices. These results place simple and easily verifiable hypotheses on the summands, and they deliver strong conclusions about the large-deviation behavior of the maximum eigenvalue of the sum. Tail bounds for the norm of a sum of random rectangular matrices follow as an immediate corollary. The proof techniques also yield some information about matrix-valued martingales. In other words, this paper provides noncommutative generalizations of the classical bounds associated with the names Azuma, Bennett, Bernstein, Chernoff, Hoeffding, and McDiarmid. The matrix inequalities promise the same diversity of application, ease of use, and strength of conclusion that have made the scalar inequalities so valuable.Comment: Current paper is the version of record. The material on Freedman's inequality has been moved to a separate note; other martingale bounds are described in Caltech ACM Report 2011-0

Interactions between Magnetic Nanowires and Living Cells : Uptake, Toxicity and Degradation

We report on the uptake, toxicity and degradation of magnetic nanowires by NIH/3T3 mouse fibroblasts. Magnetic nanowires of diameters 200 nm and lengths comprised between 1 {\mu}m and 40 {\mu}m are fabricated by controlled assembly of iron oxide ({\gamma}-Fe2O3) nanoparticles. Using optical and electron microscopy, we show that after 24 h incubation the wires are internalized by the cells and located either in membrane-bound compartments or dispersed in the cytosol. Using fluorescence microscopy, the membrane-bound compartments were identified as late endosomal/lysosomal endosomes labeled with lysosomal associated membrane protein (Lamp1). Toxicity assays evaluating the mitochondrial activity, cell proliferation and production of reactive oxygen species show that the wires do not display acute short-term (< 100 h) toxicity towards the cells. Interestingly, the cells are able to degrade the wires and to transform them into smaller aggregates, even in short time periods (days). This degradation is likely to occur as a consequence of the internal structure of the wires, which is that of a non-covalently bound aggregate. We anticipate that this degradation should prevent long-term asbestos-like toxicity effects related to high aspect ratio morphologies and that these wires represent a promising class of nanomaterials for cell manipulation and microrheology.Comment: 21 pages 12 figure

Midlatitude stratosphere - troposphere exchange as diagnosed by MLS O3 and MOPITT CO assimilated fields

International audienceThis paper presents a comprehensive characterization of a very deep stratospheric intrusion which occurred over the British Isles on 15 August 2007. The signature of this event is diagnosed using ozonesonde measurements over Lerwick, UK (60.14 N, 1.19 W) and is also well characterized using meteorological analyses from the global operational weather prediction model of Météo-France, ARPEGE. Modelled as well as assimilated fields of both ozone (O3) and carbon monoxide (CO) have been used in order to better document this event. O3 and CO from Aura/MLS and Terra/MOPITT instruments, respectively, are assimilated into the three-dimensional chemical transport model MOCAGE of Météo-France using a variational 3-DFGAT (First Guess at Appropriate Time) method. The validation of O3 and CO assimilated fields is done using selfconsistency diagnostics and by comparison with independent observations such as MOZAIC (O3 and CO), AIRS (CO) and OMI (O3). It particularly shows in the upper troposphere and lower stratosphere region that the assimilated fields are closer to MOZAIC than the free model run. The O3 bias between MOZAIC and the analyses is −11.5 ppbv with a RMS of 22.4 ppbv and a correlation coefficient of 0.93, whereas between MOZAIC and the free model run, the corresponding values are 33 ppbv, 38.5 ppbv and 0.83, respectively. In the same way, for CO, the bias, RMS and correlation coefficient between MOZAIC and the analyses are −3.16 ppbv, 13 ppbv and 0.79, respectively, whereas between MOZAIC and the free model run, the corresponding values are 33 ppbv, 38.5 ppbv and 0.83, respectively. In the same way, for CO, the bias, RMS and correlation coefficient between MOZAIC and the analyses are −3.16 ppbv, 13 ppbv and 0.79, respectively, whereas between MOZAIC and the free model they are 6.3 ppbv, 16.6 ppbv and 0.71, respectively. The paper also presents a demonstration of the capability of O3 and CO assimilated fields to better describe a stratosphere-troposphere exchange (STE) event in comparison with the free run modelled O3 and CO fields. Although the assimilation of MLS data improves the distribution of O3 above the tropopause compared to the free model run, it is not sufficient to reproduce the STE event well. Assimilated MOPITT CO allows a better qualitative description of the stratospheric intrusion event. The MOPITT CO analyses appear more promising than the MLS O3 analyses in terms of their ability to capture a deep STE event. Therefore, the results of this study open the perspectives for using MOPITT CO in the STE studies

On the sequential massart algorithm for statistical model checking

Several schemes have been provided in Statistical Model Checking (SMC) for the estimation of property occurrence based on predefined confidence and absolute or relative error. Simulations might be however costly if many samples are required and the usual algorithms implemented in statistical model checkers tend to be conservative. Bayesian and rare event techniques can be used to reduce the sample size but they can not be applied without prerequisite or knowledge about the system under scrutiny. Recently, sequential algorithms based on Monte Carlo estimations and Massart bounds have been proposed to reduce the sample size while providing guarantees on error bounds which has been shown to outperform alternative frequentist approaches [15]. In this work, we discuss some features regarding the distribution and the optimisation of these algorithms.No Full Tex