Propagation of exponential phase space singularities for Schr\"odinger equations with quadratic Hamiltonians

We study propagation of phase space singularities for the initial value Cauchy problem for a class of Schr\"odinger equations. The Hamiltonian is the Weyl quantization of a quadratic form whose real part is non-negative. The equations are studied in the framework of projective Gelfand--Shilov spaces and their distribution duals. The corresponding notion of singularities is called the Gelfand--Shilov wave front set and means the lack of exponential decay in open cones in phase space. Our main result shows that the propagation is determined by the singular space of the quadratic form, just as in the framework of the Schwartz space, where the notion of singularity is the Gabor wave front set.Comment: 39 pages. To appear in J. Fourier Anal. App

Radially resolved simulations of collapsing pebble clouds in protoplanetary discs

We study the collapse of pebble clouds with a statistical model to find the internal structure of comet-sized planetesimals. Pebble-pebble collisions occur during the collapse and the outcome of these collisions affect the resulting structure of the planetesimal. We expand our previous models by allowing the individual pebble sub-clouds to contract at different rates and by including the effect of gas drag on the contraction speed and in energy dissipation. Our results yield comets that are porous pebble-piles with particle sizes varying with depth. In the surface layers there is a mixture of primordial pebbles and pebble fragments. The interior, on the other hand, consists only of primordial pebbles with a narrower size distribution, yielding higher porosity there. Our results imply that the gas in the protoplanetary disc plays an important role in determining the radial distribution of pebble sizes and porosity inside planetesimals.Comment: 10 pages, 6 figures, accepted for publication in MNRAS special issue 'Comets: A new vision after Rosetta and Philae

Minority Challenge of Majority Actions in a Close Corporation in Italy and the United States

This paper addresses the problem of segmenting a time-series with respect to changes in the mean value or in the variance. The first case is when the time data is modeled as a sequence of independent and normal distributed random variables with unknown, possibly changing, mean value but fixed variance. The main assumption is that the mean value is piecewise constant in time, and the task is to estimate the change times and the mean values within the segments. The second case is when the mean value is constant, but the variance can change. The assumption is that the variance is piecewise constant in time, and we want to estimate change times and the variance values within the segments. To find solutions to these problems, we will study an l_1 regularized maximum likelihood method, related to the fused lasso method and l_1 trend filtering, where the parameters to be estimated are free to vary at each sample. To penalize variations in the estimated parameters, the $l_1$-norm of the time difference of the parameters is used as a regularization term. This idea is closely related to total variation denoising. The main contribution is that a convex formulation of this variance estimation problem, where the parametrization is based on the inverse of the variance, can be formulated as a certain $l_1$ mean estimation problem. This implies that results and methods for mean estimation can be applied to the challenging problem of variance segmentation/estimationQC 20140908</p