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

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

The Gribov problem in Noncommutative QED

It is shown that in the noncommutative version of QED (NCQED) Gribov copies induced by the noncommutativity of space-time appear in the Landau gauge. This is a genuine effect of noncommutative geometry which disappears when the noncommutative parameter vanishes.Comment: 19 pages, 3 figures. Published. The paper has been shortened and many references have been judged unnecessary or not suitable during the reviewing proces

Comments on the Non-Commutative Description of Classical Gravity

We find a one-parameter family of Lagrangian descriptions for classical general relativity in terms of tetrads which are not c-numbers. Rather, they obey exotic commutation relations. These noncommutative properties drop out in the metric sector of the theory, where the Christoffel symbols and the Riemann tensor are ordinary commuting objects and they are given by the usual expression in terms of the metric tensor. Although the metric tensor is not a c-number, we argue that all measurements one can make in this theory are associated with c-numbers, and thus that the common invariant sector of our one--parameter family of deformed gauge theories (for the case of zero torsion) is physically equivalent to Einstein's general relativity.Comment: Latex file, 13 pages, no figure