Distributed Learning from Interactions in Social Networks

We consider a network scenario in which agents can evaluate each other according to a score graph that models some interactions. The goal is to design a distributed protocol, run by the agents, that allows them to learn their unknown state among a finite set of possible values. We propose a Bayesian framework in which scores and states are associated to probabilistic events with unknown parameters and hyperparameters, respectively. We show that each agent can learn its state by means of a local Bayesian classifier and a (centralized) Maximum-Likelihood (ML) estimator of parameter-hyperparameter that combines plain ML and Empirical Bayes approaches. By using tools from graphical models, which allow us to gain insight on conditional dependencies of scores and states, we provide a relaxed probabilistic model that ultimately leads to a parameter-hyperparameter estimator amenable to distributed computation. To highlight the appropriateness of the proposed relaxation, we demonstrate the distributed estimators on a social interaction set-up for user profiling.Comment: This submission is a shorter work (for conference publication) of a more comprehensive paper, already submitted as arXiv:1706.04081 (under review for journal publication). In this short submission only one social set-up is considered and only one of the relaxed estimators is proposed. Moreover, the exhaustive analysis, carried out in the longer manuscript, is completely missing in this versio

Modelling solar low-lying cool loops with optically thick radiative losses

We investigate the increase of the DEM (differential emission measure) towards the chromosphere due to small and cool magnetic loops (height $\lesssim8$~Mm, $T\lesssim10^5$~K). In a previous paper we analysed the conditions of existence and stability of these loops through hydrodynamic simulations, focusing on their dependence on the details of the optically thin radiative loss function used. In this paper, we extend those hydrodynamic simulations to verify if this class of loops exists and it is stable when using an optically thick radiative loss function. We study two cases: constant background heating and a heating depending on the density. The contribution to the transition region EUV output of these loops is also calculated and presented. We find that stable, quasi-static cool loops can be obtained by using an optically thick radiative loss function and a background heating depending on the density. The DEMs of these loops, however, fail to reproduce the observed DEM for temperatures between $4.6<\log T<4.8$. We also show the transient phase of a dynamic loop obtained by considering constant heating rate and find that its average DEM, interpreted as a set of evolving dynamic loops, reproduces quite well the observed DEM.Comment: Accepted for publication in A&A on Aug 21st 2015. arXiv admin note: text overlap with arXiv:1112.030

Diffraction effects in length measurements by laser interferometry

High-accuracy dimensional measurements by laser interferometers require corrections because of diffraction, which makes the effective fringe-period different from the wavelength of a plane (or spherical) wave $\lambda_0$. By using a combined X-ray and optical interferometer as a tool to investigate diffraction across a laser beam, we observed wavelength variations as large as $10^{-8}\lambda_0$. We show that they originate from the wavefront evolution under paraxial propagation in the presence of wavefront- and intensity-profile perturbations.Comment: preprint, 10 pages, 6 figures, submitted to Optics Expres

Longterm Influence of Inertia on the Diffusion of a Brownian Particle

We demonstrate experimentally that a Brownian particle is subject to inertial effects at long time scales. By using a blinking optical tweezers, we extend the range of previous experiments by several orders of magnitude up to a few seconds. The measured mean square displacement of a freely diffusing Brownian particle in a liquid shows a deviation from the Einstein-Smoluchowsky theory that diverges with time. These results are consistent with a generalized theory that takes into account not only the particle inertia but also the inertia of the fluid surrounding the particle. This can lead to a bias in the estimation of the diffusion coefficient from finite-time measurements. We show that the decay of the relative error is polynomial and not exponential and, therefore, can have significant effects at time scales relevant for experiments.Comment: 5 pages, 4 figure