Inverse hyperbolic problems and optical black holes

In this paper we give a more geometrical formulation of the main theorem in [E1] on the inverse problem for the second order hyperbolic equation of general form with coefficients independent of the time variable. We apply this theorem to the inverse problem for the equation of the propagation of light in a moving medium (the Gordon equation). Then we study the existence of black and white holes for the general hyperbolic and for the Gordon equation and we discuss the impact of this phenomenon on the inverse problems

Optical Aharonov-Bohm effect: an inverse hyperbolic problems approach

We describe the general setting for the optical Aharonov-Bohm effect based on the inverse problem of the identification of the coefficients of the governing hyperbolic equation by the boundary measurements. We interpret the inverse problem result as a possibility in principle to detect the optical Aharonov-Bohm effect by the boundary measurements.Comment: 34 pages. Minor changes, references adde

Inverse Scattering for Gratings and Wave Guides

We consider the problem of unique identification of dielectric coefficients for gratings and sound speeds for wave guides from scattering data. We prove that the "propagating modes" given for all frequencies uniquely determine these coefficients. The gratings may contain conductors as well as dielectrics and the boundaries of the conductors are also determined by the propagating modes.Comment: 12 page

Calpain 3 and CaMKIIβ signaling are required to induce HSP70 necessary for adaptive muscle growth after atrophy.

Mutations in CAPN3 cause autosomal recessive limb girdle muscular dystrophy 2A. Calpain 3 (CAPN3) is a calcium dependent protease residing in the myofibrillar, cytosolic and triad fractions of skeletal muscle. At the triad, it colocalizes with calcium calmodulin kinase IIβ (CaMKIIβ). CAPN3 knock out mice (C3KO) show reduced triad integrity and blunted CaMKIIβ signaling, which correlates with impaired transcriptional activation of myofibrillar and oxidative metabolism genes in response to running exercise. These data suggest a role for CAPN3 and CaMKIIβ in gene regulation that takes place during adaptation to endurance exercise. To assess whether CAPN3- CaMKIIβ signaling influences skeletal muscle remodeling in other contexts, we subjected C3KO and wild type mice to hindlimb unloading and reloading and assessed CaMKIIβ signaling and gene expression by RNA-sequencing. After induced atrophy followed by 4 days of reloading, both CaMKIIβ activation and expression of inflammatory and cellular stress genes were increased. C3KO muscles failed to activate CaMKIIβ signaling, did not activate the same pattern of gene expression and demonstrated impaired growth at 4 days of reloading. Moreover, C3KO muscles failed to activate inducible HSP70, which was previously shown to be indispensible for the inflammatory response needed to promote muscle recovery. Likewise, C3KO showed diminished immune cell infiltration and decreased expression of pro-myogenic genes. These data support a role for CaMKIIβ signaling in induction of HSP70 and promotion of the inflammatory response during muscle growth and remodeling that occurs after atrophy, suggesting that CaMKIIβ regulates remodeling in multiple contexts: endurance exercise and growth after atrophy

Spherical averages in the space of marked lattices

A marked lattice is a $d$-dimensional Euclidean lattice, where each lattice point is assigned a mark via a given random field on ${\mathbb Z}^d$. We prove that, if the field is strongly mixing with a faster-than-logarithmic rate, then for every given lattice and almost every marking, large spheres become equidistributed in the space of marked lattices. A key aspect of our study is that the space of marked lattices is not a homogeneous space, but rather a non-trivial fiber bundle over such a space. As an application, we prove that the free path length in a crystal with random defects has a limiting distribution in the Boltzmann-Grad limit

A new Al-Zr-Ti master alloy for ultrasonic grain refinement of wrought and foundry aluminum alloys

A new grain refiner master alloy based on the Al-Zr-Ti system was prepared by salt assisted synthesis. 90% of Al3Zr particles in the master alloy were ranged between 1 and 13 μm. 80% reduction of grain size was observed with the addition of 0.2wt% Zr equivalent master alloy combined with ultrasonic treatment in an Al alloy. The new master alloy demonstrated 30% improvement in grain refinement efficiency compared to the one prepared by a conventional alloy route.The authors wish to acknowledge financial support from the ExoMet Project, which is co-funded by the European Commission in the 7th Framework Programme (contract FP7-NMP3-LA-2012-280421), by the European Space Agency and by the individual partner organisations

Cell-type-specific resolution epigenetics without the need for cell sorting or single-cell biology.

High costs and technical limitations of cell sorting and single-cell techniques currently restrict the collection of large-scale, cell-type-specific DNA methylation data. This, in turn, impedes our ability to tackle key biological questions that pertain to variation within a population, such as identification of disease-associated genes at a cell-type-specific resolution. Here, we show mathematically and empirically that cell-type-specific methylation levels of an individual can be learned from its tissue-level bulk data, conceptually emulating the case where the individual has been profiled with a single-cell resolution and then signals were aggregated in each cell population separately. Provided with this unprecedented way to perform powerful large-scale epigenetic studies with cell-type-specific resolution, we revisit previous studies with tissue-level bulk methylation and reveal novel associations with leukocyte composition in blood and with rheumatoid arthritis. For the latter, we further show consistency with validation data collected from sorted leukocyte sub-types

A grain refinement mechanism of cast commercial purity aluminium by vanadium

Grain refinement of cast commercial purity aluminium by vanadium and the underlying mechanism have been investigated. Addition of 0.3 wt% and 0.4 wt% vanadium leads to columnar to equiaxed transition and the average grain sizes are refined to around 196 μm and 154 μm, respectively. Pro-peritectic equilibrium Al_{10}V particles are identified near the grain centres. These Al_{10}V particles have either octahedron or plate morphology with the bound planes belonging to {111} crystallographic planes. Three orientation relationships are also determined between the Al_{10}V particles and aluminium grains. Crystallographic analysis based on the experimental orientation relationships indicates that the Al_{10}V particles have relatively high nucleation potency for solid aluminium. Calculation of free growth undercooling based on the size distribution of the Al_{10}V particles reveals that the relatively large size of Al_{10}V particles facilitates the grain initiation of aluminium grains on these particles. Moreover, it is found that the level of vanadium added provides sufficient growth restriction effect in the aluminium melt as quantified by its growth restriction factor. All the three factors, i.e., sufficient potency of Al_{10}V particles, relatively large size of the Al_{10}V particles and adequate growth restriction effect by solute vanadium work in concert to achieve the grain refinement observed in Al-V alloys