Damage as Gamma-limit of microfractures in anti-plane linearized elasticity

A homogenization result is given for a material having brittle inclusions arranged in a periodic structure. <br/> According to the relation between the softness parameter and the size of the microstructure, three different limit models are deduced via Gamma-convergence. <br/> In particular, damage is obtained as limit of periodically distributed microfractures

Perimeter of sublevel sets in infinite dimensional spaces

We compare the perimeter measure with the Airault-Malliavin surface measure and we prove that all open convex subsets of abstract Wiener spaces have finite perimeter. By an explicit counter-example, we show that in general this is not true for compact convex domains

Search for a Lorentz invariance violation contribution in atmospheric neutrino oscillations using MACRO data

Neutrino-induced upward-going muons in MACRO have been analysed in terms of relativity principles violating effects, keeping standard mass-induced atmospheric neutrino oscillations as the dominant source of nu_mu -> nu_tau transitions. The data disfavor these exotic possibilities even at a sub-dominant level, and stringent 90% C.L. limits are placed on the Lorentz invariance violation parameter |Delta v| < 6 * 10^(-24) at sin2theta_v = 0 and |Delta v| < 2.5--5 * 10^(-26) at sin2theta_v = +/-1. These limits can also be re-interpreted as upper bounds on the parameters describing violation of the Equivalence Principle.Comment: 8 pages, 2 figures, submitted to Physics Letters

Distortions of Experimental Muon Arrival Time Distributions of Extensive Air Showers by the Observation Conditions

Event-by-event measured arrival time distributions of Extensive Air Shower (EAS) muons are affected and distorted by various interrelated effects which originate from the time resolution of the timing detectors, from fluctuations of the reference time and the number (multiplicity) of detected muons spanning the arrival time distribution of the individual EAS events. The origin of these effects is discussed, and different correction procedures, which involve detailed simulations, are proposed and illustrated. The discussed distortions are relevant for relatively small observation distances (R < 200 m) from the EAS core. Their significance decreases with increasing observation distance and increasing primary energies. Local arrival time distributions which refer to the observed arrival time of the first local muon prove to be less sensitive to the mass of the primary. This feature points to the necessity of arrival time measurements with additional information on the curvature of the EAS disk.Comment: 10 pages, 6 figures, accepted for publication in Astroparticle Physic

Signal transducer and activator of transcription-1 localizes to the mitochondria and modulates mitophagy

The signal transducer and activator of transcription (STAT) proteins are latent transcription factors that have been shown to be involved in cell proliferation, development, apoptosis, and autophagy. STAT proteins undergo activation by phosphorylation at tyrosine 701 and serine 727 where they translocate to the nucleus to regulate gene expression. STAT1 has been shown to be involved in promoting apoptotic cell death in response to cardiac ischemia/reperfusion and has recently been shown by our laboratory to be involved in negatively regulating autophagy. These processes are thought to promote cell death and restrict cell survival leading to the generation of an infarct. Here we present data that shows STAT1 localizes to the mitochondria and co-immunoprecipitates with LC3. Furthermore, electron microscopy studies also reveal mitochondria from ex vivo I/R treated hearts of STAT1KO mice contained within a double membrane autophagosome indicating that STAT1 may be involved in negatively regulating mitophagy. This is the first description of STAT1 being localized to the mitochondria and also having a role in mitophagy

Analysis of an Inverse Problem Arising in Photolithography

We consider the inverse problem of determining an optical mask that produces a desired circuit pattern in photolithography. We set the problem as a shape design problem in which the unknown is a two-dimensional domain. The relationship between the target shape and the unknown is modeled through diffractive optics. We develop a variational formulation that is well-posed and propose an approximation that can be shown to have convergence properties. The approximate problem can serve as a foundation to numerical methods.Comment: 28 pages, 1 figur

Energy solutions to one-dimensional singular parabolic problems with BVBV data are viscosity solutions

We study one-dimensional very singular parabolic equations with periodic boundary conditions and initial data in $BV$, which is the energy space. We show existence of solutions in this energy space and then we prove that they are viscosity solutions in the sense of Giga-Giga.Comment: 15 page

Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below

This paper is devoted to a deeper understanding of the heat flow and to the refinement of calculus tools on metric measure spaces (X,d,m). Our main results are: - A general study of the relations between the Hopf-Lax semigroup and Hamilton-Jacobi equation in metric spaces (X,d). - The equivalence of the heat flow in L^2(X,m) generated by a suitable Dirichlet energy and the Wasserstein gradient flow of the relative entropy functional in the space of probability measures P(X). - The proof of density in energy of Lipschitz functions in the Sobolev space W^{1,2}(X,d,m). - A fine and very general analysis of the differentiability properties of a large class of Kantorovich potentials, in connection with the optimal transport problem. Our results apply in particular to spaces satisfying Ricci curvature bounds in the sense of Lott & Villani [30] and Sturm [39,40], and require neither the doubling property nor the validity of the local Poincar\'e inequality.Comment: Minor typos corrected and many small improvements added. Lemma 2.4, Lemma 2.10, Prop. 5.7, Rem. 5.8, Thm. 6.3 added. Rem. 4.7, Prop. 4.8, Prop. 4.15 and Thm 4.16 augmented/reenforced. Proof of Thm. 4.16 and Lemma 9.6 simplified. Thm. 8.6 corrected. A simpler axiomatization of weak gradients, still equivalent to all other ones, has been propose

Dynamic sampling schemes for optimal noise learning under multiple nonsmooth constraints

We consider the bilevel optimisation approach proposed by De Los Reyes, Sch\"onlieb (2013) for learning the optimal parameters in a Total Variation (TV) denoising model featuring for multiple noise distributions. In applications, the use of databases (dictionaries) allows an accurate estimation of the parameters, but reflects in high computational costs due to the size of the databases and to the nonsmooth nature of the PDE constraints. To overcome this computational barrier we propose an optimisation algorithm that by sampling dynamically from the set of constraints and using a quasi-Newton method, solves the problem accurately and in an efficient way