Model reduction by separation of variables: A comparison between hierarchical model reduction and proper generalized decomposition

Hierarchical Model reduction and Proper Generalized Decomposition both exploit separation of variables to perform a model reduction. After setting the basics, we exemplify these techniques on some standard elliptic problems to highlight pros and cons of the two procedures, both from a methodological and a numerical viewpoint

Reconstruction of the cosmic microwave background lensing for Planck

Aims. We prepare real-life cosmic microwave background (CMB) lensing extraction with the forthcoming Planck satellite data by studying two systematic effects related to the foreground contamination: the impact of foreground residuals after a component separation on the lensed CMB map, and the impact of removing a large contaminated region of the sky. Methods. We first use the generalized morphological component analysis (GMCA) method to perform a component separation within a simplified framework, which allows a high statistics Monte-Carlo study. For the second systematic, we apply a realistic mask on the temperature maps and then restore them with a recently developed inpainting technique on the sphere. We investigate the reconstruction of the CMB lensing from the resultant maps using a quadratic estimator in the flat sky limit and on the full sphere. Results. We find that the foreground residuals from the GMCA method does not significantly alter the lensed signal, which is also true for the mask corrected with the inpainting method, even in the presence of point source residuals

A new fluid-based strategy for the connection of non-matching lattice materials

We present a new algorithm for the design of the connection region between di erent lattice materials. We solve a Stokes- type topology optimization problem on a narrow morphing region to smoothly connect two di erent unit cells. The proposed procedure turns out to be e ective and provides a local re-design of the materials, leading to a very mild modi cation of the mechanical behavior characterizing the original lattices. The robustness of the algorithm is assessed in terms of sensitivity of the nal layout to di erent parameters. Both the cases of Cartesian and non-Cartesian morphing regions are successfully investigated

Free Differential Algebras: Their Use in Field Theory and Dual Formulation

The gauging of free differential algebras (FDA's) produces gauge field theories containing antisymmetric tensors. The FDA's extend the Cartan-Maurer equations of ordinary Lie algebras by incorporating p-form potentials ($p > 1$). We study here the algebra of FDA transformations. To every p-form in the FDA we associate an extended Lie derivative $\ell$ generating a corresponding ``gauge" transformation. The field theory based on the FDA is invariant under these new transformations. This gives geometrical meaning to the antisymmetric tensors. The algebra of Lie derivatives is shown to close and provides the dual formulation of FDA's.Comment: 10 pages, latex, no figures. Talk presented at the 4-th Colloquium on "Quantum Groups and Integrable Sysytems", Prague, June 199

A PDE-regularized smoothing method for space-time data over manifolds with application to medical data

We propose an innovative statistical-numerical method to model spatio- temporal data, observed over a generic two-dimensional Riemanian manifold. The proposed approach consists of a regression model completed with a regu- larizing term based on the heat equation. The model is discretized through a finite element scheme set on the manifold, and solved by resorting to a fixed point-based iterative algorithm. This choice leads to a procedure which is highly efficient when compared with a monolithic approach, and which allows us to deal with massive datasets. After a preliminary assessment on simulation study cases, we investigate the performance of the new estimation tool in prac- tical contexts, by dealing with neuroimaging and hemodynamic data

Evidence of cross-correlation between the CMB lensing and the gamma-ray sky

We report the measurement of the angular power spectrum of cross-correlation between the unresolved component of the Fermi-LAT gamma-ray sky-maps and the CMB lensing potential map reconstructed by the Planck satellite. The matter distribution in the Universe determines the bending of light coming from the last scattering surface. At the same time, the matter density drives the growth history of astrophysical objects, including their capability at generating non-thermal phenomena, which in turn give rise to gamma-ray emissions. The Planck lensing map provides information on the integrated distribution of matter, while the integrated history of gamma-ray emitters is imprinted in the Fermi-LAT sky maps. We report here the first evidence of their correlation. We find that the multipole dependence of the cross-correlation measurement is in agreement with current models of the gamma-ray luminosity function for AGN and star forming galaxies, with a statistical evidence of 3.0$\sigma$. Moreover, its amplitude can in general be matched only assuming that these extra-galactic emitters are also the bulk contribution of the measured isotopic gamma-ray background (IGRB) intensity. This leaves little room for a big contribution from galactic sources to the IGRB measured by Fermi-LAT, pointing toward a direct evidence of the extragalactic origin of the IGRB.Comment: 6 pages, 2 figures. v2: analysis updated with Planck 2015 lensing map and 3FGL catalogue, conclusions strengthened; to appear in ApJ Letter

New Challenges in Grid Generation and Adaptivity for Scientific Computing

This volume collects selected contributions from the “Fourth Tetrahedron Workshop on Grid Generation for Numerical Computations”, which was held in Verbania, Italy in July 2013. The previous editions of this Workshop were hosted by the Weierstrass Institute in Berlin (2005), by INRIA Rocquencourt in Paris (2007), and by Swansea University (2010). This book covers different, though related, aspects of the field: the generation of quality grids for complex three-dimensional geometries; parallel mesh generation algorithms; mesh adaptation, including both theoretical and implementation aspects; grid generation and adaptation on surfaces – all with an interesting mix of numerical analysis, computer science and strongly application-oriented problems

Reconstruction of the CMB lensing for Planck

We prepare real-life Cosmic Microwave Background (CMB) lensing extraction with the forthcoming Planck satellite data, by studying two systematic effects related to the foregrounds contamination: the impact of foreground residuals after a component separation on the lensed CMB map, and of removing a large contaminated region of the sky. We first use the Generalized Morphological Component Analysis (GMCA) method to perform a component separation within a simplified framework which allows a high statistics Monte-Carlo study. For the second systematic, we apply a realistic mask on the temperature maps and then, restore them using a recent inpainting technique on the sphere. We investigate the reconstruction of the CMB lensing from the resultant maps using a quadratic estimator in the flat sky limit and on the full sphere. We find that the foreground residuals from the GMCA method does not alter significantly the lensed signal, nor does the mask corrected with the inpainting method, even in the presence of point sources residuals.Comment: 14 pages, 7 figures, major update to account for the impact of the point sources emissio