Local regularity for parabolic nonlocal operators

Weak solutions to parabolic integro-differential operators of order $\alpha \in (\alpha_0, 2)$ are studied. Local a priori estimates of H\"older norms and a weak Harnack inequality are proved. These results are robust with respect to $\alpha \nearrow 2$. In this sense, the presentation is an extension of Moser's result in 1971.Comment: 31 pages, 3 figure

Heat Kernel Bounds for the Laplacian on Metric Graphs of Polygonal Tilings

We obtain an upper heat kernel bound for the Laplacian on metric graphs arising as one skeletons of certain polygonal tilings of the plane, which reflects the one dimensional as well as the two dimensional nature of these graphs.Comment: 8 page

An analysis of the production-regeneration system in the coastal upwelling area off N.W. Africa based on oxygen, nitrate and ammonium distributions

Using the hydrographic and nutrient data from the R/V Jean Charcot CINECA-V cruise and Broenkow\u27s (1965) mixing model, we have calculated the biologically induced changes in the oxygen, nitrate and ammonium distribution patterns of the upwelling system off Cape Blanc, N .W. Africa...

Single Strand Annealing Plays a Major Role in RecA-Independent Recombination between Repeated Sequences in the Radioresistant Deinococcus radiodurans Bacterium

© 2015 Ithurbide et al. The bacterium Deinococcus radiodurans is one of the most radioresistant organisms known. It is able to reconstruct a functional genome from hundreds of radiation-induced chromosomal fragments. Our work aims to highlight the genes involved in recombination between 438 bp direct repeats separated by intervening sequences of various lengths ranging from 1,479 bp to 10,500 bp to restore a functional tetA gene in the presence or absence of radiation-induced DNA double strand breaks. The frequency of spontaneous deletion events between the chromosomal direct repeats were the same in recA+ and in ΔrecA, ΔrecF, and ΔrecO bacteria, whereas recombination between chromosomal and plasmid DNA was shown to be strictly dependent on the RecA and RecF proteins. The presence of mutations in one of the repeated sequence reduced, in a MutS-dependent manner, the frequency of the deletion events. The distance between the repeats did not influence the frequencies of deletion events in recA+as well in ΔrecA bacteria. The absence of the UvrD protein stimulated the recombination between the direct repeats whereas the absence of the DdrB protein, previously shown to be involved in DNA double strand break repair through a single strand annealing (SSA) pathway, strongly reduces the frequency of RecA- (and RecO-) independent deletions events. The absence of the DdrB protein also increased the lethal sectoring of cells devoid of RecA or RecO protein. γ-irradiation of recA+cells increased about 10-fold the frequencies of the deletion events, but at a lesser extend in cells devoid of the DdrB protein. Altogether, our results suggest a major role of single strand annealing in DNA repeat deletion events in bacteria devoid of the RecA protein, and also in recA+bacteria exposed to ionizing radiation

Cutoff for the Ising model on the lattice

Introduced in 1963, Glauber dynamics is one of the most practiced and extensively studied methods for sampling the Ising model on lattices. It is well known that at high temperatures, the time it takes this chain to mix in $L^1$ on a system of size $n$ is $O(\log n)$. Whether in this regime there is cutoff, i.e. a sharp transition in the $L^1$-convergence to equilibrium, is a fundamental open problem: If so, as conjectured by Peres, it would imply that mixing occurs abruptly at $(c+o(1))\log n$ for some fixed $c>0$, thus providing a rigorous stopping rule for this MCMC sampler. However, obtaining the precise asymptotics of the mixing and proving cutoff can be extremely challenging even for fairly simple Markov chains. Already for the one-dimensional Ising model, showing cutoff is a longstanding open problem. We settle the above by establishing cutoff and its location at the high temperature regime of the Ising model on the lattice with periodic boundary conditions. Our results hold for any dimension and at any temperature where there is strong spatial mixing: For $\Z^2$ this carries all the way to the critical temperature. Specifically, for fixed $d\geq 1$, the continuous-time Glauber dynamics for the Ising model on $(\Z/n\Z)^d$ with periodic boundary conditions has cutoff at $(d/2\lambda_\infty)\log n$, where $\lambda_\infty$ is the spectral gap of the dynamics on the infinite-volume lattice. To our knowledge, this is the first time where cutoff is shown for a Markov chain where even understanding its stationary distribution is limited. The proof hinges on a new technique for translating $L^1$ to $L^2$ mixing which enables the application of log-Sobolev inequalities. The technique is general and carries to other monotone and anti-monotone spin-systems.Comment: 34 pages, 3 figure

On the regularization scheme and gauge choice ambiguities in topologically massive gauge theories

It is demonstrated that in the (2+1)-dimensional topologically massive gauge theories an agreement of the Pauli-Villars regularization scheme with the other schemes can be achieved by employing pairs of auxiliary fermions with the opposite sign masses. This approach does not introduce additional violation of discrete (P and T) symmetries. Although it breaks the local gauge symmetry only in the regulator fields' sector, its trace disappears completely after removing the regularization as a result of superrenormalizability of the model. It is shown also that analogous extension of the Pauli-Villars regularization in the vector particle sector can be used to agree the arbitrary covariant gauge results with the Landau ones. The source of ambiguities in the covariant gauges is studied in detail. It is demonstrated that in gauges that are softer in the infrared region (e.g. Coulomb or axial) nonphysical ambiguities inherent to the covariant gauges do not arise.Comment: Latex, 13 pages. Replaced mainly to change preprint references to journal one

Automating the measurement of physiological parameters: a case study in the image analysis of cilia motion

International audienceAs image processing and analysis techniques improve, an increasing number of procedures in bio-medical analyses can be automated. This brings many benefits, e.g improved speed and accuracy, leading to more reliable diagnoses and follow-up, ultimately improving patients outcome. Many automated procedures in bio-medical imaging are well established and typically consist of detecting and counting various types of cells (e.g. blood cells, abnormal cells in Pap smears, and so on). In this article we propose to automate a different and difficult set of measurements, which is conducted on the cilia of people suffering from a variety of respiratory tract diseases. Cilia are slender, microscopic, hair-like structures or organelles that extend from the surface of nearly all mammalian cells. Motile cilia, such as those found in the lungs and respiratory tract, present a periodic beating motion that keep the airways clear of mucus and dirt. In this paper, we propose a fully automated method that computes various measurements regarding the motion of cilia, taken with high-speed video-microscopy. The advantage of our approach is its capacity to automatically compute robust, adaptive and regionalized measurements, i.e. associated with different regions in the image. We validate the robustness of our approach, and illustrate its performance in comparison to the state-of-the-art