Generalizing Minimal Dark Matter: Millicharge or Decay

The Minimal Dark Matter framework classifies viable Dark Matter (DM) candidates that are obtained by simply augmenting the Standard Model of particle interactions with a new multiplet, without adding new ad hoc symmetries to make the DM stable. The model has no free parameters and is therefore extremely predictive; moreover, recent studies singled out a Majorana $SU(2)_\text{L}$ quintuplet as the only viable candidate. The model can be constrained by both direct and indirect DM searches, with present time gamma-ray line searches in the Galactic Center being particularly sensitive. It is therefore timely to critically review this paradigm and point out possible generalizations. We propose and explore two distinct directions. One is to lower the cutoff of the model, which was originally fixed at the Planck scale, to allow for decays of the DM quintuplet. We analyze the decay spectrum of this candidate in detail and show that gamma-ray data constrain the cutoff to lie above the GUT scale. Another possibility is to abandon the assumption of DM electric neutrality in favor of absolutely stable, millicharged DM candidates. We explicitly study a few examples, and find that a Dirac $SU(2)_\text{L}$ triplet is the candidate least constrained by indirect searches.Comment: 5+1 pages. Contribution to the EPS conference on High Energy Physics, Venice, Italy, 5-12 July 201

Solving the Dirac equation on QPACE

We discuss the implementation and optimization challenges for a Wilson-Dirac solver with Clover term on QPACE, a parallel machine based on Cell processors and a torus network. We choose the mixed-precision Schwarz preconditioned FGCR algorithm in order to circumvent network bandwidth and latency constraints, to make efficient use of the multicore parallelism and on-chip memory, and to achieve flexibility in the choice of lattice sizes. We present benchmarks on up to 256 QPACE nodes showing an aggregate sustained performance of about 10 TFlops for the complete solver and very good scaling.Comment: 7 pages, Lattice 2010 Proceeding

On the posterior distribution of the number of components in a finite mixture

The posterior distribution of the number of components k in a finite mixture satisfies a set of inequality constraints. The result holds irrespective of the parametric form of the mixture components and under assumptions on the prior distribution weaker than those routinely made in the literature on Bayesian analysis of finite mixtures. The inequality constraints can be used to perform an ``internal'' consistency check of MCMC estimates of the posterior distribution of k and to provide improved estimates which are required to satisfy the constraints. Bounds on the posterior probability of k components are derived using the constraints. Implications on prior distribution specification and on the adequacy of the posterior distribution of k as a tool for selecting an adequate number of components in the mixture are also explored.Comment: Published at http://dx.doi.org/10.1214/009053604000000788 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org

Sparse approximation of multilinear problems with applications to kernel-based methods in UQ

We provide a framework for the sparse approximation of multilinear problems and show that several problems in uncertainty quantification fit within this framework. In these problems, the value of a multilinear map has to be approximated using approximations of different accuracy and computational work of the arguments of this map. We propose and analyze a generalized version of Smolyak's algorithm, which provides sparse approximation formulas with convergence rates that mitigate the curse of dimension that appears in multilinear approximation problems with a large number of arguments. We apply the general framework to response surface approximation and optimization under uncertainty for parametric partial differential equations using kernel-based approximation. The theoretical results are supplemented by numerical experiments

The Employment of Airships for the Transport of Passengers

It was a conclusion of this detailed study of the practicality of using airships for carrying passengers that, although slow, airships are capable of carrying useful loads over long distances. However, it is noted that there is a certain limit to the advantages of large cubature. Beyond a certain point, the maximum altitude of the airship goes on decreasing, in spite of the fact that the range of action in the horizontal plane and the useful load go on increasing. The possibility of rapid climb is an essential factor of security in aerial navigation in the case of storms, as is velocity. To rise above and run ahead of storms are ways of avoiding them. However, high altitude and high speed are antithetical. This investigation concluded that a maximum velocity of 120 km/h is as far as we ought to go. This figure can only be exceeded by excessive reduction of the altitude of ceiling, range of flight, and useful load. The essential requisites of a public transport service are discussed, as are flight security, regularity of service, competition with other forms of passenger transportation, and the choice between rigid and semi-rigid airships

Wavelet-Fourier CORSING techniques for multi-dimensional advection-diffusion-reaction equations

We present and analyze a novel wavelet-Fourier technique for the numerical treatment of multidimensional advection-diffusion-reaction equations based on the CORSING (COmpRessed SolvING) paradigm. Combining the Petrov-Galerkin technique with the compressed sensing approach, the proposed method is able to approximate the largest coefficients of the solution with respect to a biorthogonal wavelet basis. Namely, we assemble a compressed discretization based on randomized subsampling of the Fourier test space and we employ sparse recovery techniques to approximate the solution to the PDE. In this paper, we provide the first rigorous recovery error bounds and effective recipes for the implementation of the CORSING technique in the multi-dimensional setting. Our theoretical analysis relies on new estimates for the local a-coherence, which measures interferences between wavelet and Fourier basis functions with respect to the metric induced by the PDE operator. The stability and robustness of the proposed scheme is shown by numerical illustrations in the one-, two-, and three-dimensional case