"Weakly" Elliptic Gorenstein Singularities of Surfaces

The main message of the paper is that for Gorenstein singularities, whose (real) link is rational homology sphere, the Artin--Laufer program can be continued. Here we give the complete answer in the case of elliptic singularities. The main result of the paper says that in the case of an elliptic Gorenstein singularity whose link is rational homology sphere, the geometric genus is a topological invariant. Actually, it is exactly the length of the elliptic sequence in the minimal resolution (or, equivalently, in S. S.-T. Yau's terminology: these singularities are maximally elliptic). In the paper we characterize the singularities with this property, and we compute their Hilbert-Samuel function from their resolution graph (generalizing some results of Laufer and Yau). The obstruction for a normal surface singularity to be maximally elliptic can be connected with the torsion part of some Picard groups, this is the new idea of the paper.Comment: 21 pages, latex. To appear in Inventiones mat

Unification mechanism for gauge and spacetime symmetries

A group theoretical mechanism for unification of local gauge and spacetime symmetries is introduced. No-go theorems prohibiting such unification are circumvented by slightly relaxing the usual requirement on the gauge group: only the so called Levi factor of the gauge group needs to be compact semisimple, not the entire gauge group. This allows a non-conventional supersymmetry-like extension of the gauge group, glueing together the gauge and spacetime symmetries, but not needing any new exotic gauge particles. It is shown that this new relaxed requirement on the gauge group is nothing but the minimal condition for energy positivity. The mechanism is demonstrated to be mathematically possible and physically plausible on a U(1) based gauge theory setting. The unified group, being an extension of the group of spacetime symmetries, is shown to be different than that of the conventional supersymmetry group, thus overcoming the McGlinn and Coleman-Mandula no-go theorems in a non-supersymmetric way.Comment: 20 pages, 4 figure

Random walk on graphs with regular resistance and volume growth

In this paper characterizations of graphs satisfying heat kernel estimates for a wide class of space-time scaling functions are given. The equivalence of the two-sided heat kernel estimate and the parabolic Harnack inequality is also shown via the equivalence of the upper (lower) heat kernel estimate to the parabolic mean value (and super mean value) inequality

The NA61/SHINE Experiment at the CERN SPS

The physics goals, the detector and its performance as well as status and plans of the NA61/SHINE experiment at the CERN SPS accelerator are presented.Comment: 4 pages, 2 figures, 1 table - To appear in the conference proceedings for Quark Matter 2009, March 30 - April 4, Knoxville, Tennesse

Intelligent encoding and economical communication in the visual stream.

The theory of computational complexity is used to underpin a recent model of neocortical sensory processing. We argue that encoding into reconstruction networks is appealing for communicating agents using Hebbian learning and working on hard combinatorial problems, which are easy to verify. Computational definition of the concept of intelligence is provided. Simulations illustrate the idea

Propagation of singularities for the wave equation on manifolds with corners

In this paper we describe the propagation of smooth (C^\infty) and Sobolev singularities for the wave equation on smooth manifolds with corners M equipped with a Riemannian metric g. That is, for X=MxR, P=D_t^2-\Delta_M, and u locally in H^1 solving Pu=0 with homogeneous Dirichlet or Neumann boundary conditions, we show that the wave front set of u is a union of maximally extended generalized broken bicharacteristics. This result is a smooth counterpart of Lebeau's results for the propagation of analytic singularities on real analytic manifolds with appropriately stratified boundary. Our methods rely on b-microlocal positive commutator estimates, thus providing a new proof for the propagation of singularities at hyperbolic points even if M has a smooth boundary (and no corners)

The Visual Art Critic: A Survey of Art Critics at General Interest News Publications in America

Examines whether art critics provide sufficient exposure for artists and art institutions, given the recent dynamic growth in the visual arts over the past two decades

Numerical Awareness in Control

Algorithm development, sensitivity and accuracy issues, large-scale computations, and high-performance numerical softwar