Investigating the high-frequency spectral features of SNRs Tycho, W44 and IC443 with the Sardinia Radio Telescope

The main characteristics in the radio continuum spectra of Supernova Remnants (SNRs) result from simple synchrotron emission. In addition, electron acceleration mechanisms can shape the spectra in specific ways, especially at high radio frequencies. These features are connected to the age and the peculiar conditions of the local interstellar medium interacting with the SNR. Whereas the bulk radio emission is expected at up to $20-50$ GHz, sensitive high-resolution images of SNRs above 10 GHz are lacking and are not easily achievable, especially in the confused regions of the Galactic Plane. In the framework of the early science observations with the Sardinia Radio Telescope in February-March 2016, we obtained high-resolution images of SNRs Tycho, W44 and IC443 that provided accurate integrated flux density measurements at 21.4 GHz: 8.8 $\pm$ 0.9 Jy for Tycho, 25 $\pm$ 3 Jy for W44 and 66 $\pm$ 7 Jy for IC443. We coupled the SRT measurements with radio data available in the literature in order to characterise the integrated and spatially-resolved spectra of these SNRs, and to find significant frequency- and region-dependent spectral slope variations. For the first time, we provide direct evidence of a spectral break in the radio spectral energy distribution of W44 at an exponential cutoff frequency of 15 $\pm$ 2 GHz. This result constrains the maximum energy of the accelerated electrons in the range $6-13$ GeV, in agreement with predictions indirectly derived from AGILE and \textit{Fermi}-LAT gamma-ray observations. With regard to IC443, our results confirm the noticeable presence of a bump in the integrated spectrum around $20-70$ GHz that could result from a spinning dust emission mechanism.Comment: 12 pages, 9 figure

On stability of discretizations of the Helmholtz equation (extended version)

We review the stability properties of several discretizations of the Helmholtz equation at large wavenumbers. For a model problem in a polygon, a complete $k$-explicit stability (including $k$-explicit stability of the continuous problem) and convergence theory for high order finite element methods is developed. In particular, quasi-optimality is shown for a fixed number of degrees of freedom per wavelength if the mesh size $h$ and the approximation order $p$ are selected such that $kh/p$ is sufficiently small and $p = O(\log k)$, and, additionally, appropriate mesh refinement is used near the vertices. We also review the stability properties of two classes of numerical schemes that use piecewise solutions of the homogeneous Helmholtz equation, namely, Least Squares methods and Discontinuous Galerkin (DG) methods. The latter includes the Ultra Weak Variational Formulation

Imaging of SNR IC443 and W44 with the Sardinia Radio Telescope at 1.5 GHz and 7 GHz

Observations of supernova remnants (SNRs) are a powerful tool for investigating the later stages of stellar evolution, the properties of the ambient interstellar medium, and the physics of particle acceleration and shocks. For a fraction of SNRs, multi-wavelength coverage from radio to ultra high-energies has been provided, constraining their contributions to the production of Galactic cosmic rays. Although radio emission is the most common identifier of SNRs and a prime probe for refining models, high-resolution images at frequencies above 5 GHz are surprisingly lacking, even for bright and well-known SNRs such as IC443 and W44. In the frameworks of the Astronomical Validation and Early Science Program with the 64-m single-dish Sardinia Radio Telescope, we provided, for the first time, single-dish deep imaging at 7 GHz of the IC443 and W44 complexes coupled with spatially-resolved spectra in the 1.5-7 GHz frequency range. Our images were obtained through on-the-fly mapping techniques, providing antenna beam oversampling and resulting in accurate continuum flux density measurements. The integrated flux densities associated with IC443 are S_1.5GHz = 134 +/- 4 Jy and S_7GHz = 67 +/- 3 Jy. For W44, we measured total flux densities of S_1.5GHz = 214 +/- 6 Jy and S_7GHz = 94 +/- 4 Jy. Spectral index maps provide evidence of a wide physical parameter scatter among different SNR regions: a flat spectrum is observed from the brightest SNR regions at the shock, while steeper spectral indices (up to 0.7) are observed in fainter cooling regions, disentangling in this way different populations and spectra of radio/gamma-ray-emitting electrons in these SNRs.Comment: 13 pages, 9 figures, accepted for publication to MNRAS on 18 May 201

Comparison of some Reduced Representation Approximations

In the field of numerical approximation, specialists considering highly complex problems have recently proposed various ways to simplify their underlying problems. In this field, depending on the problem they were tackling and the community that are at work, different approaches have been developed with some success and have even gained some maturity, the applications can now be applied to information analysis or for numerical simulation of PDE's. At this point, a crossed analysis and effort for understanding the similarities and the differences between these approaches that found their starting points in different backgrounds is of interest. It is the purpose of this paper to contribute to this effort by comparing some constructive reduced representations of complex functions. We present here in full details the Adaptive Cross Approximation (ACA) and the Empirical Interpolation Method (EIM) together with other approaches that enter in the same category

Molecular excitation in the Interstellar Medium: recent advances in collisional, radiative and chemical processes

We review the different excitation processes in the interstellar mediumComment: Accepted in Chem. Re

Translational study identifies XPF and MUS81 as predictive biomarkers for oxaliplatin-based peri-operative chemotherapy in patients with esophageal adenocarcinoma

Oxaliplatin-based chemotherapy is used to treat patients with esophageal adenocarcinoma (EAC), but no biomarkers are currently available for patient selection. We performed a prospective, clinical trial to identify potential biomarkers associated with clinical outcomes. Tumor tissue was obtained from 38 patients with resectable EAC before and after 2 cycles of oxaliplatin-fluorouracil chemotherapy. Pre-treatment mRNA expression of 280 DNA repair (DNAR) genes was tested for association with histopathological regression at surgery, disease-free survival (DFS) and overall survival (OS). High expression of 13 DNA damage repair genes was associated with DFS less than one year (P < 0.05); expression of 11 DNAR genes were associated with worse OS (P < 0.05). From clinical associations with outcomes, two genes, ERCC1 and EME1, were identified as candidate biomarkers. In cell lines in vitro, we showed the mechanism of action related to repair of oxaliplatin-induced DNA damage by depletion and knockout of protein binding partners of the candidate biomarkers, XPF and MUS81 respectively. In clinical samples from the clinical trial, pre-treatment XPF protein levels were associated with pathological response, and MUS81 protein was associated with 1-year DFS. XPF and MUS81 merit further validation in prospective clinical trials as biomarkers that may predict clinical response of EAC to oxaliplatin-based chemotherapy

Efficient Resolution of Anisotropic Structures

We highlight some recent new delevelopments concerning the sparse representation of possibly high-dimensional functions exhibiting strong anisotropic features and low regularity in isotropic Sobolev or Besov scales. Specifically, we focus on the solution of transport equations which exhibit propagation of singularities where, additionally, high-dimensionality enters when the convection field, and hence the solutions, depend on parameters varying over some compact set. Important constituents of our approach are directionally adaptive discretization concepts motivated by compactly supported shearlet systems, and well-conditioned stable variational formulations that support trial spaces with anisotropic refinements with arbitrary directionalities. We prove that they provide tight error-residual relations which are used to contrive rigorously founded adaptive refinement schemes which converge in $L_2$. Moreover, in the context of parameter dependent problems we discuss two approaches serving different purposes and working under different regularity assumptions. For frequent query problems, making essential use of the novel well-conditioned variational formulations, a new Reduced Basis Method is outlined which exhibits a certain rate-optimal performance for indefinite, unsymmetric or singularly perturbed problems. For the radiative transfer problem with scattering a sparse tensor method is presented which mitigates or even overcomes the curse of dimensionality under suitable (so far still isotropic) regularity assumptions. Numerical examples for both methods illustrate the theoretical findings