Random attractors for stochastic porous media equations perturbed by space-time linear multiplicative noise

Unique existence of solutions to porous media equations driven by continuous linear multiplicative space-time rough signals is proven for initial data in $L^1(\mathcal {O})$ on bounded domains $\mathcal {O}$. The generation of a continuous, order-preserving random dynamical system on $L^1(\mathcal {O})$ and the existence of a random attractor for stochastic porous media equations perturbed by linear multiplicative noise in space and time is obtained. The random attractor is shown to be compact and attracting in $L^{\infty}(\mathcal {O})$ norm. Uniform $L^{\infty}$ bounds and uniform space-time continuity of the solutions is shown. General noise including fractional Brownian motion for all Hurst parameters is treated and a pathwise Wong-Zakai result for driving noise given by a continuous semimartingale is obtained. For fast diffusion equations driven by continuous linear multiplicative space-time rough signals, existence of solutions is proven for initial data in $L^{m+1}(\mathcal {O})$.Comment: Published in at http://dx.doi.org/10.1214/13-AOP869 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The Brera Multi-scale Wavelet (BMW) ROSAT HRI source catalog. I: the algorithm

We present a new detection algorithm based on the wavelet transform for the analysis of high energy astronomical images. The wavelet transform, due to its multi-scale structure, is suited for the optimal detection of point-like as well as extended sources, regardless of any loss of resolution with the off-axis angle. Sources are detected as significant enhancements in the wavelet space, after the subtraction of the non-flat components of the background. Detection thresholds are computed through Monte Carlo simulations in order to establish the expected number of spurious sources per field. The source characterization is performed through a multi-source fitting in the wavelet space. The procedure is designed to correctly deal with very crowded fields, allowing for the simultaneous characterization of nearby sources. To obtain a fast and reliable estimate of the source parameters and related errors, we apply a novel decimation technique which, taking into account the correlation properties of the wavelet transform, extracts a subset of almost independent coefficients. We test the performance of this algorithm on synthetic fields, analyzing with particular care the characterization of sources in poor background situations, where the assumption of Gaussian statistics does not hold. For these cases, where standard wavelet algorithms generally provide underestimated errors, we infer errors through a procedure which relies on robust basic statistics. Our algorithm is well suited for the analysis of images taken with the new generation of X-ray instruments equipped with CCD technology which will produce images with very low background and/or high source density.Comment: 8 pages, 6 figures, ApJ in pres

Using the Zeldovich dynamics to test expansion schemes

We apply various expansion schemes that may be used to study gravitational clustering to the simple case of the Zeldovich dynamics. Using the well-known exact solution of the Zeldovich dynamics we can compare the predictions of these various perturbative methods with the exact nonlinear result and study their convergence properties. We find that most systematic expansions fail to recover the decay of the response function in the highly nonlinear regime. ``Linear methods'' lead to increasingly fast growth in the nonlinear regime for higher orders, except for Pade approximants that give a bounded response at any order. ``Nonlinear methods'' manage to obtain some damping at one-loop order but they fail at higher orders. Although it recovers the exact Gaussian damping, a resummation in the high-k limit is not justified very well as the generation of nonlinear power does not originate from a finite range of wavenumbers (hence there is no simple separation of scales). No method is able to recover the relaxation of the matter power spectrum on highly nonlinear scales. It is possible to impose a Gaussian cutoff in a somewhat ad-hoc fashion to reproduce the behavior of the exact two-point functions for two different times. However, this cutoff is not directly related to the clustering of matter and disappears in exact equal-time statistics such as the matter power spectrum. On a quantitative level, the usual perturbation theory, and the nonlinear scheme to which one adds an ansatz for the response function with such a Gaussian cutoff, are the two most efficient methods. These results should hold for the gravitational dynamics as well (this has been checked at one-loop order), since the structure of the equations of motion is identical for both dynamics.Comment: 29 pages, published in A&

Electrical Tuning of Integrated III-V Quantum Dots in Quantum Nano-Photonic Circuits

This thesis describes optical measurements on nanophotonic devices with integrated electrically tuneable quantum dots. The quantum dots enable a range of non-linear behaviour, including single photon generation and the generation of entangled photonic states on-chip. Device behaviour can be controlled by applying electric fields to the devices, enabling fast switching and tuning of device behaviour. A waveguide-coupled electrically-driven single-photon source is demonstrated. Electroluminescence from a single quantum dot is coupled to a single-mode suspended nanobeam waveguide. The number of quantum dots coupled to the waveguide is limited in order to isolate emission from a single source. The single-photon nature of the emission is confirmed using correlation measurements. The non-linear behaviour of a quantum dot in a single mode photonic crystal waveguide is investigated. In this work three charge states of the same quantum dot are investigated using resonance fluorescence and resonant waveguide transmission. A strong non-linear effect is generated by the single quantum dot, enabling interactions between pairs of photons and the generation of a two photon bound state. Fast switching of the device is demonstrated by the application of an electric field. A waveguide-coupled quantum optical filter is presented. This device utilises Fano interference in a QD-waveguide system to modulate a coherent photonic input, generating a bunched or antibunched output. The photon statistics of the output can be tuned by changing the bias applied to the device

Income and Wealth Status of Russian and Tomsk Region’s Pensioners

In the article the results of a study of income and material well-being of old generation of Russia and Tomsk Region are presented. Data of Russian federal and regional statistics shows that income of pensioners is growing fast and their wealth status in 2014 can be estimated as acceptable. Analysis of the data of an opinion survey of older people of the Tomsk region does not support this conclusion. According to the regression model in order to achieve a satisfactory standard of living pensioner's income should be at least 13-18 thousand rubles per month, while in 2014 the average pension was lower (about 11-12 thousand rubles). In our opinion state regulation requires further increase in the average pensions, as well as the revision of the minimum consumption basket and minimum needs of subsistence for this group

Multivariate soft rank via entropic optimal transport: sample efficiency and generative modeling

The framework of optimal transport has been leveraged to extend the notion of rank to the multivariate setting while preserving desirable properties of the resulting goodness of-fit (GoF) statistics. In particular, the rank energy (RE) and rank maximum mean discrepancy (RMMD) are distribution-free under the null, exhibit high power in statistical testing, and are robust to outliers. In this paper, we point to and alleviate some of the practical shortcomings of these proposed GoF statistics, namely their high computational cost, high statistical sample complexity, and lack of differentiability with respect to the data. We show that all these practically important issues are addressed by considering entropy-regularized optimal transport maps in place of the rank map, which we refer to as the soft rank. We consequently propose two new statistics, the soft rank energy (sRE) and soft rank maximum mean discrepancy (sRMMD), which exhibit several desirable properties. Given $n$ sample data points, we provide non-asymptotic convergence rates for the sample estimate of the entropic transport map to its population version that are essentially of the order $n^{-1/2}$. This compares favorably to non-regularized estimates, which typically suffer from the curse-of-dimensionality and converge at rate that is exponential in the data dimension. We leverage this fast convergence rate to demonstrate the sample estimate of the proposed statistics converge rapidly to their population versions, enabling efficient rank-based GoF statistical computation, even in high dimensions. Our statistics are differentiable and amenable to popular machine learning frameworks that rely on gradient methods. We leverage these properties towards showcasing the utility of the proposed statistics for generative modeling on two important problems: image generation and generating valid knockoffs for controlled feature selection.Comment: 43 pages, 10 figures. Replacement note: Title change, author changes, new theoretical results, revised and expanded experimental evaluation

ANGSD:analysis of next generation sequencing data

BACKGROUND: High-throughput DNA sequencing technologies are generating vast amounts of data. Fast, flexible and memory efficient implementations are needed in order to facilitate analyses of thousands of samples simultaneously. RESULTS: We present a multithreaded program suite called ANGSD. This program can calculate various summary statistics, and perform association mapping and population genetic analyses utilizing the full information in next generation sequencing data by working directly on the raw sequencing data or by using genotype likelihoods. CONCLUSIONS: The open source c/c++ program ANGSD is available at http://www.popgen.dk/angsd. The program is tested and validated on GNU/Linux systems. The program facilitates multiple input formats including BAM and imputed beagle genotype probability files. The program allow the user to choose between combinations of existing methods and can perform analysis that is not implemented elsewhere. ELECTRONIC SUPPLEMENTARY MATERIAL: The online version of this article (doi:10.1186/s12859-014-0356-4) contains supplementary material, which is available to authorized users