Bayesian non-linear large scale structure inference of the Sloan Digital Sky Survey data release 7

In this work we present the first non-linear, non-Gaussian full Bayesian large scale structure analysis of the cosmic density field conducted so far. The density inference is based on the Sloan Digital Sky Survey data release 7, which covers the northern galactic cap. We employ a novel Bayesian sampling algorithm, which enables us to explore the extremely high dimensional non-Gaussian, non-linear log-normal Poissonian posterior of the three dimensional density field conditional on the data. These techniques are efficiently implemented in the HADES computer algorithm and permit the precise recovery of poorly sampled objects and non-linear density fields. The non-linear density inference is performed on a 750 Mpc cube with roughly 3 Mpc grid-resolution, while accounting for systematic effects, introduced by survey geometry and selection function of the SDSS, and the correct treatment of a Poissonian shot noise contribution. Our high resolution results represent remarkably well the cosmic web structure of the cosmic density field. Filaments, voids and clusters are clearly visible. Further, we also conduct a dynamical web classification, and estimated the web type posterior distribution conditional on the SDSS data.Comment: 18 pages, 11 figure

Clustering Properties of restframe UV selected galaxies II: Migration of Star Formation sites with cosmic time from GALEX and CFHTLS

We analyze the clustering properties of ultraviolet selected galaxies by using GALEX-SDSS data at z<0.6 and CFHTLS deep u' imaging at z=1. These datasets provide a unique basis at z< 1 which can be directly compared with high redshift samples built with similar selection criteria. We discuss the dependence of the correlation function parameters (r0, delta) on the ultraviolet luminosity as well as the linear bias evolution. We find that the bias parameter shows a gradual decline from high (b > 2) to low redshift (b ~ 0.79^{+0.1}_{-0.08}). When accounting for the fraction of the star formation activity enclosed in the different samples, our results suggest that the bulk of star formation migrated from high mass dark matter halos at z>2 (10^12 < M_min < 10^13 M_sun, located in high density regions), to less massive halos at low redshift (M_min < 10^12 M_sun, located in low density regions). This result extends the ``downsizing'' picture (shift of the star formation activity from high stellar mass systems at high z to low stellar mass at low z) to the dark matter distribution.Comment: Accepted for Publication in the Special GALEX Ap. J. Supplement, December 2007 Version with full resolution fig1 available at http://taltos.pha.jhu.edu/~sebastien/papers/Galex_p2.ps.g

Group Iterative Spectrum Thresholding for Super-Resolution Sparse Spectral Selection

Recently, sparsity-based algorithms are proposed for super-resolution spectrum estimation. However, to achieve adequately high resolution in real-world signal analysis, the dictionary atoms have to be close to each other in frequency, thereby resulting in a coherent design. The popular convex compressed sensing methods break down in presence of high coherence and large noise. We propose a new regularization approach to handle model collinearity and obtain parsimonious frequency selection simultaneously. It takes advantage of the pairing structure of sine and cosine atoms in the frequency dictionary. A probabilistic spectrum screening is also developed for fast computation in high dimensions. A data-resampling version of high-dimensional Bayesian Information Criterion is used to determine the regularization parameters. Experiments show the efficacy and efficiency of the proposed algorithms in challenging situations with small sample size, high frequency resolution, and low signal-to-noise ratio

A unified wavelet-based modelling framework for non-linear system identification: the WANARX model structure

A new unified modelling framework based on the superposition of additive submodels, functional components, and wavelet decompositions is proposed for non-linear system identification. A non-linear model, which is often represented using a multivariate non-linear function, is initially decomposed into a number of functional components via the wellknown analysis of variance (ANOVA) expression, which can be viewed as a special form of the NARX (non-linear autoregressive with exogenous inputs) model for representing dynamic input–output systems. By expanding each functional component using wavelet decompositions including the regular lattice frame decomposition, wavelet series and multiresolution wavelet decompositions, the multivariate non-linear model can then be converted into a linear-in-theparameters problem, which can be solved using least-squares type methods. An efficient model structure determination approach based upon a forward orthogonal least squares (OLS) algorithm, which involves a stepwise orthogonalization of the regressors and a forward selection of the relevant model terms based on the error reduction ratio (ERR), is employed to solve the linear-in-the-parameters problem in the present study. The new modelling structure is referred to as a wavelet-based ANOVA decomposition of the NARX model or simply WANARX model, and can be applied to represent high-order and high dimensional non-linear systems

Shower development of particles with momenta from 15 GeV to 150 GeV in the CALICE scintillator-tungsten hadronic calorimeter

We present a study of showers initiated by electrons, pions, kaons, and protons with momenta from 15 GeV to 150 GeV in the highly granular CALICE scintillator-tungsten analogue hadronic calorimeter. The data were recorded at the CERN Super Proton Synchrotron in 2011. The analysis includes measurements of the calorimeter response to each particle type as well as measurements of the energy resolution and studies of the longitudinal and radial shower development for selected particles. The results are compared to Geant4 simulations (version 9.6.p02). In the study of the energy resolution we include previously published data with beam momenta from 1 GeV to 10 GeV recorded at the CERN Proton Synchrotron in 2010.Comment: 35 pages, 21 figures, 8 table

Multi-Resolution Functional ANOVA for Large-Scale, Many-Input Computer Experiments

The Gaussian process is a standard tool for building emulators for both deterministic and stochastic computer experiments. However, application of Gaussian process models is greatly limited in practice, particularly for large-scale and many-input computer experiments that have become typical. We propose a multi-resolution functional ANOVA model as a computationally feasible emulation alternative. More generally, this model can be used for large-scale and many-input non-linear regression problems. An overlapping group lasso approach is used for estimation, ensuring computational feasibility in a large-scale and many-input setting. New results on consistency and inference for the (potentially overlapping) group lasso in a high-dimensional setting are developed and applied to the proposed multi-resolution functional ANOVA model. Importantly, these results allow us to quantify the uncertainty in our predictions. Numerical examples demonstrate that the proposed model enjoys marked computational advantages. Data capabilities, both in terms of sample size and dimension, meet or exceed best available emulation tools while meeting or exceeding emulation accuracy