Clustering at High Redshift

Together with the CMB, the three sources of information that astronomers have at high redshift as probes of the formation and evolution of the LSS are QSOs, galaxies and absorbers observed in the spectrum of distant background objects. In this contribution I try to give a hint of historical perspective, following how the technological advances have driven the emphasis from one class to another, in order to show what are the likely forthcoming milestones.Comment: 8 pages Latex, with 3 PostScript figures. To appear in the Proceedings of the VLT Opening Symposium, Antofagasta, Chile 1-4 March 199

Blending Brownian motion and heat equation

In this short communication we present an original way to couple the Brownian motion and the heat equation. More in general, we suggest a way for coupling the Langevin equation for a particle, which describes a single realization of its trajectory, with the associated Fokker-Planck equation, which instead describes the evolution of the particle's probability density function. Numerical results show that it is indeed possible to obtain a regularized Brownian motion and a Brownianized heat equation still preserving the global statistical properties of the solutions. The results also suggest that the more macroscale leads the dynamics the more one can reduce the microscopic degrees of freedom

Reducing complexity of multiagent systems with symmetry breaking: an application to opinion dynamics with polls

In this paper we investigate the possibility of reducing the complexity of a system composed of a large number of interacting agents, whose dynamics feature a symmetry breaking. We consider first order stochastic differential equations describing the behavior of the system at the particle (i.e., Lagrangian) level and we get its continuous (i.e., Eulerian) counterpart via a kinetic description. However, the resulting continuous model alone fails to describe adequately the evolution of the system, due to the loss of granularity which prevents it from reproducing the symmetry breaking of the particle system. By suitably coupling the two models we are able to reduce considerably the necessary number of particles while still keeping the symmetry breaking and some of its large-scale statistical properties. We describe such a multiscale technique in the context of opinion dynamics, where the symmetry breaking is induced by the results of some opinion polls reported by the media

A destination-preserving model for simulating Wardrop equilibria in traffic flow on networks

In this paper we propose a LWR-like model for traffic flow on networks which allows one to track several groups of drivers, each of them being characterized only by their destination in the network. The path actually followed to reach the destination is not assigned a priori, and can be chosen by the drivers during the journey, taking decisions at junctions. The model is then used to describe three possible behaviors of drivers, associated to three different ways to solve the route choice problem: 1. Drivers ignore the presence of the other vehicles; 2. Drivers react to the current distribution of traffic, but they do not forecast what will happen at later times; 3. Drivers take into account the current and future distribution of vehicles. Notice that, in the latter case, we enter the field of differential games, and, if a solution exists, it likely represents a global equilibrium among drivers. Numerical simulations highlight the differences between the three behaviors and suggest the existence of multiple Wardrop equilibria

The Asiago-ESO/RASS QSO Survey II. The Southern Sample

This is the second paper of a series describing the Asiago-ESO/RASS QSO survey, a project aimed at the construction of an all-sky statistically well-defined sample of very bright QSOs (B_J < 15). Such a survey is required to remove the present uncertainties about the properties of the local QSO population and constitutes an homogeneous database for detailed evolutionary studies of AGN. We present here the complete Southern Sample, which comprises 243 bright (12.60 < B_J < 15.13) QSO candidates at high galactic latitudes (|b_{gal}| > 30^{\circ}). The area covered by the survey is 5660 sq. deg. Spectroscopy for the 137 still unidentified objects has been obtained. The total number of AGN turns out to be 111, 63 of which are new identifications. The properties of the selection are discussed. The completeness and the success rate for this survey at the final stage are 63% and 46%, respectively.Comment: 36 pages Latex, with 15 PostScript figures. Accepted for publication in Astronomical Journa

A level set based method for fixing overhangs in 3D printing

3D printers based on the Fused Decomposition Modeling create objects layer-by-layer dropping fused material. As a consequence, strong overhangs cannot be printed because the new-come material does not find a suitable support over the last deposed layer. In these cases, one can add some support structures (scaffolds) which make the object printable, to be removed at the end. In this paper we propose a level set method to create object-dependent support structures, specifically conceived to reduce both the amount of additional material and the printing time. We also review some open problems about 3D printing which can be of interests for the mathematical community