Multivariate medians and measure-symmetrization

We discuss two research areas dealing respectively with (1) a class of multivariate medians and (2) a symmetrization algorithm for probability measures.Comment: Published at http://dx.doi.org/10.1214/074921707000000201 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

The Indirect Search for Dark Matter from the centre of the Galaxy with the Fermi LAT

Dark matter (DM) constitutes around a 25% of the Universe, while baryons only a 4%. DM can be reasonably assumed to be made of particles, and many theories (Super-symmetry, Universal Extra Dimensions, etc.) predict Weakly Interacting Massive Particles (WIMPs) as natural DM candidates at the weak scale. Self-annihilation (or decay) of WIMPs might produce secondary gamma-rays, via hadronization or as final state radiation. Since its launch in the 2008, the Large Area Telescope on-board of the Fermi gamma-ray Space Telescope has detected the largest amount of gamma-rays to date, in the 20MeV 300GeV energy range, allowing to perform a very sensitive indirect experimental search for DM (by means of high-energy gamma-rays). DM forms large gravitationally bounded structures, the halos, which can host entire galaxies, such as the Milky Way. The DM distribution in the central part of the halos is not experimentally know, despite a very large density enhancement might be present. As secondary gamma rays production is very sensitive to WIMP density, a very effective search can be performed from the regions where the largest density is expected. Therefore the information provided by the DM halo N-body simulations are crucial. The largest gamma-ray signal from DM annihilation is expected from the centre of the Galaxy. In the same region a large gamma-ray background is produced by bright discrete sources and the cosmic-rays interacting with the interstellar gas and the photons fields. Here we report an update of the indirect search for DM from the Galactic Center (GC).Comment: 6 pages, 2 figures. Invited talk presented at the Workshop "SciNeGHE 2010", September 8-10, 2010, Trieste, Italy. To appear in Il Nuovo Cimento C - Colloquia on physic

Role of heat generation and thermal diffusion during frontal photopolymerization

Frontal photopolymerization (FPP) is a rapid and versatile solidification process that can be used to fabricate complex three-dimensional structures by selectively exposing a photosensitive monomer-rich bath to light. A characteristic feature of FPP is the appearance of a sharp polymerization front that propagates into the bath as a planar traveling wave. In this paper, we introduce a theoretical model to determine how heat generation during photopolymerization influences the kinetics of wave propagation as well as the monomer-to-polymer conversion profile, both of which are relevant for FPP applications and experimentally measurable. When thermal diffusion is sufficiently fast relative to the rate of polymerization, the system evolves as if it were isothermal. However, when thermal diffusion is slow, a thermal wavefront develops and propagates at the same rate as the polymerization front. This leads to an accumulation of heat behind the polymerization front which can result in a significant sharpening of the conversion profile and acceleration of the growth of the solid. Our results also suggest that a novel way to tailor the dynamics of FPP is by imposing a temperature gradient along the growth directio

Conformal Truncation of Chern-Simons Theory at Large NfN_f

We set up and analyze the lightcone Hamiltonian for an abelian Chern-Simons field coupled to $N_f$ fermions in the limit of large $N_f$ using conformal truncation, i.e. with a truncated space of states corresponding to primary operators with dimension below a maximum cutoff $\Delta_{\rm max}$. In both the Chern-Simons theory, and in the $O(N)$ model at infinite $N$, we compute the current spectral functions analytically as a function of $\Delta_{\rm max}$ and reproduce previous results in the limit that the truncation $\Delta_{\rm max}$ is taken to $\infty$. Along the way, we determine how to preserve gauge invariance and how to choose an optimal discrete basis for the momenta of states in the truncation space.Comment: 32+25 pages, 8 figures. v2: updated ref

On Reduced Time Evolution for Initially Correlated Pure States

A new method to deal with reduced dynamics of open systems by means of the Schr\"odinger equation is presented. It allows one to consider the reduced time evolution for correlated and uncorrelated initial conditions.Comment: accepted in Open Sys. Information Dy