Sparse Distributed Learning Based on Diffusion Adaptation

This article proposes diffusion LMS strategies for distributed estimation over adaptive networks that are able to exploit sparsity in the underlying system model. The approach relies on convex regularization, common in compressive sensing, to enhance the detection of sparsity via a diffusive process over the network. The resulting algorithms endow networks with learning abilities and allow them to learn the sparse structure from the incoming data in real-time, and also to track variations in the sparsity of the model. We provide convergence and mean-square performance analysis of the proposed method and show under what conditions it outperforms the unregularized diffusion version. We also show how to adaptively select the regularization parameter. Simulation results illustrate the advantage of the proposed filters for sparse data recovery.Comment: to appear in IEEE Trans. on Signal Processing, 201

qq-independent slow-dynamics in atomic and molecular systems

Investigating million-atom systems for very long simulation times, we demonstrate that the collective density-density correlation time ($\tau_{\alpha}$) in simulated supercooled water and silica becomes wavevector independent ($q^0$) when the probing wavelength is several times larger than the interparticle distance. The $q$-independence of the collective density-density correlation functions, a feature clearly observed in light-scattering studies of some soft-matter systems, is thus a genuine feature of many (but not all) slow-dynamics systems, either atomic, molecular or colloidal. Indeed, we show that when the dynamics of the density fluctuations is due to particle-type diffusion, as in the case of the Lennard Jones binary mixture model, the $q^0$ regime does not set in and the relaxation time continues to scale as $\tau_{\alpha} \sim q^{-2}$ even at small $q$.Comment: Includes the supplementary materia

Full counting statistics of weak measurement

A weak measurement consists in coupling a system to a probe in such a way that constructive interference generates a large output. So far, only the average output of the probe and its variance were studied. Here, the characteristic function for the moments of the output is provided. The outputs considered are not limited to the eigenstates of the pointer or of its conjugate variable, so that the results apply to any observable \Hat{o} of the probe. Furthermore, a family of well behaved complex quantities, the normal weak values, is introduced, in terms of which the statistics of the weak measurement can be described. It is shown that, within a good approximation, the whole statistics of weak measurement is described by a complex parameter, the weak value, and a real one.Comment: Expanded version: 9 pages, 3 Figs. Now the validity of the expansion for the moments is analysed. Introduced a one-parameter family of weak values, useful to express the correct characteristic function. More figures added. Thanks to Referee C of PRL for asking stimulating question

RR Lyrae in XSTPS: The halo density profile in the North Galactic Cap

We present a catalog of RR Lyrae stars (RRLs) observed by the Xuyi Schmidt Telescope Photometric Survey (XDSS). The area we consider is located in the North Galactic Cap, covering 376.75 sq deg at RA $\approx$ 150 deg and Dec $\approx$ 27 deg down to a magnitude limit of i $\approx$ 19. Using the variability information afforded by the multi-epoch nature of our XDSS data, combined with colors from the Sloan Digital Sky Survey, we are able to identify candidate RRLs. We find 318 candidates, derive distances to them and estimate the detection efficiency. The majority of our candidates have more than 12 observations and for these we are able to calculate periods. These also allows us to estimate our contamination level, which we predict is between 30% to 40%. Finally we use the sample to probe the halo density profile in the 9-49 kpc range and find that it can be well fitted by a double power law. We find good agreement between this model and the models derived for the South Galactic Cap using the Watkins et al. (2009) and Sesar et al. (2010) RRL data-sets, after accounting for possible contamination in our data-set from Sagittarius stream members. We consider non-spherical double power law models of the halo density profile and again find agreement with literature data-sets, although we have limited power to constrain the flattening due to our small survey area. Much tighter constraints will be placed by current and future wide-area surveys, most notably ESA's astrometric Gaia mission. Our analysis demonstrates that surveys with a limited number of epochs can effectively be mined for RRLs. Our complete sample is provided as accompanying online material.Comment: 14 pages, ApJ (in press

Tuning non-Markovianity by spin-dynamics control

We study the interplay between forgetful and memory-keeping evolution enforced on a two-level system by a multi-spin environment whose elements are coupled to local bosonic baths. Contrarily to the expectation that any non-Markovian effect would be buried by the forgetful mechanism induced by the spin-bath coupling, one can actually induce a full Markovian-to-non-Markovian transition of the two-level system's dynamics, controllable by parameters such as the mismatch between the energy of the two-level system and of the spin environment. For a symmetric coupling, the amount of non-Markovianity surprisingly grows with the number of decoherence channels.Comment: 7 pages, 6 figures, PRA versio

Constraining galaxy cluster temperatures and redshifts with eROSITA survey data

The nature of dark energy is imprinted in the large-scale structure of the Universe and thus in the mass and redshift distribution of galaxy clusters. The upcoming eROSITA mission will exploit this method of probing dark energy by detecting roughly 100,000 clusters of galaxies in X-rays. For a precise cosmological analysis the various galaxy cluster properties need to be measured with high precision and accuracy. To predict these characteristics of eROSITA galaxy clusters and to optimise optical follow-up observations, we estimate the precision and the accuracy with which eROSITA will be able to determine galaxy cluster temperatures and redshifts from X-ray spectra. Additionally, we present the total number of clusters for which these two properties will be available from the eROSITA survey directly. During its four years of all-sky surveys, eROSITA will determine cluster temperatures with relative uncertainties of Delta(T)/T<10% at the 68%-confidence level for clusters up to redshifts of z~0.16 which corresponds to ~1,670 new clusters with precise properties. Redshift information itself will become available with a precision of Delta(z)/(1+z)<10% for clusters up to z~0.45. Additionally, we estimate how the number of clusters with precise properties increases with a deepening of the exposure. Furthermore, the biases in the best-fit temperatures as well as in the estimated uncertainties are quantified and shown to be negligible in the relevant parameter range in general. For the remaining parameter sets, we provide correction functions and factors. The eROSITA survey will increase the number of galaxy clusters with precise temperature measurements by a factor of 5-10. Thus the instrument presents itself as a powerful tool for the determination of tight constraints on the cosmological parameters.Comment: accepted for publication in A&A; 17 pages, 20 figure

Drops on soft solids: Free energy and double transition of contact angles

The equilibrium shape of liquid drops on elastic substrates is determined by minimising elastic and capillary free energies, focusing on thick incompressible substrates. The problem is governed by three length scales: the size of the drop $R$, the molecular size $a$, and the ratio of surface tension to elastic modulus $\gamma/E$. We show that the contact angles undergo two transitions upon changing the substrates from rigid to soft. The microscopic wetting angles deviate from Young's law when $\gamma/Ea \gg 1$, while the apparent macroscopic angle only changes in the very soft limit $\gamma/ER \gg 1$. The elastic deformations are worked out in the simplifying case where the solid surface energy is assumed constant. The total free energy turns out lower on softer substrates, consistent with recent experiments