Prediction with Expert Advice under Discounted Loss

We study prediction with expert advice in the setting where the losses are accumulated with some discounting---the impact of old losses may gradually vanish. We generalize the Aggregating Algorithm and the Aggregating Algorithm for Regression to this case, propose a suitable new variant of exponential weights algorithm, and prove respective loss bounds.Comment: 26 pages; expanded (2 remarks -> theorems), some misprints correcte

Multifractal Analysis of the Coupling Space of Feed-Forward Neural Networks

Random input patterns induce a partition of the coupling space of feed-forward neural networks into different cells according to the generated output sequence. For the perceptron this partition forms a random multifractal for which the spectrum $f(\alpha)$ can be calculated analytically using the replica trick. Phase transition in the multifractal spectrum correspond to the crossover from percolating to non-percolating cell sizes. Instabilities of negative moments are related to the VC-dimension.Comment: 10 pages, Latex, submitted to PR

Cosmological weak lensing with the HST GEMS survey

We present our cosmic shear analysis of GEMS, one of the largest wide-field surveys ever undertaken by the Hubble Space Telescope. Imaged with the Advanced Camera for Surveys (ACS), GEMS spans 795 square arcmin in the Chandra Deep Field South. We detect weak lensing by large-scale structure in high resolution F606W GEMS data from ~60 resolved galaxies per square arcminute. We measure the two-point shear correlation function, the top-hat shear variance and the shear power spectrum, performing an E/B mode decomposition for each statistic. We show that we are not limited by systematic errors and use our results to place joint constraints on the matter density parameter Omega_m and the amplitude of the matter power spectrum sigma_8. We find sigma_8(Omega_m/0.3)^{0.65}=0.68 +/- 0.13 where the 1sigma error includes both our uncertainty on the median redshift of the survey and sampling variance. Removing image and point spread function (PSF) distortions are crucial to all weak lensing analyses. We therefore include a thorough discussion on the degree of ACS PSF distortion and anisotropy which we characterise directly from GEMS data. Consecutively imaged over 20 days, GEMS data also allows us to investigate PSF instability over time. We find that, even in the relatively short GEMS observing period, the ACS PSF ellipticity varies at the level of a few percent which we account for with a semi-time dependent PSF model. Our correction for the temporal and spatial variability of the PSF is shown to be successful through a series of diagnostic tests.Comment: 17 pages, 16 figures. Version accepted by MNRA

The size evolution of galaxies since z~3: combining SDSS, GEMS and FIRES

We present the evolution of the luminosity-size and stellar mass-size relations of luminous (L_V>3.4x10^10h_70^-2L_sun) and of massive (M_*>3x10^10h_70^-2M_sun) galaxies in the last ~11 Gyr. We use very deep near-infrared images of the Hubble Deep Field-South and the MS1054-03 field in the J_s, H and K_s bands from FIRES to retrieve the sizes in the optical rest-frame for galaxies with z>1. We combine our results with those from GEMS at 0.2<z<1 and SDSS at z~0.1 to achieve a comprehensive picture of the optical rest-frame size evolution from z=0 to z=3. Galaxies are differentiated according to their light concentration using the Sersic index n. For less concentrated objects, the galaxies at a given luminosity were typically ~3+-0.5 (+-2 sigma) times smaller at z~2.5 than those we see today. The stellar mass-size relation has evolved less: the mean size at a given stellar mass was \~2+-0.5 times smaller at z~2.5, evolving proportional to (1+z)^{-0.40+-0.06}. Simple scaling relations between dark matter halos and baryons in a hierarchical cosmogony predict a stronger (although consistent within the error bars) than observed evolution of the stellar mass-size relation. The observed luminosity-size evolution out to z~2.5 matches well recent infall model predictions for Milky-Way type objects. For low-n galaxies, the evolution of the stellar mass-size relation would follow naturally if the individual galaxies grow inside-out. For highly concentrated objects, the situation is as follows: at a given luminosity, these galaxies were ~2.7+-1.1 times smaller at z~2.5 (or put differently, were typically ~2.2+-0.7 mag brighter at a given size than they are today), and at a given stellar mass the size has evolved proportional to (1+z)^{-0.45+-0.10}.Comment: Accepted for publication in ApJ. The new version includes several improvements: much accurate size estimations and a better completeness and robustness analysis. Tables of data are included. 29 pages and 14 figures (one low resolution

Statistical hadronization phenomenology in K/πK/\pi fluctuations at ultra-relativistic energies

We discuss the information that can be obtained from an analysis of fluctuations in heavy ion collisions within the context of the statistical model of particle production. We then examine the recently published experimental data on ratio fluctuations, and use it to obtain constraints on the statistical properties (physically relevant ensemble, degree of chemical equilibration, scaling across energies and system sizes) and freeze-out dynamics (amount of reinteraction between chemical and thermal freeze-out) of the system.Comment: Proceedings, SQM2009. Fig. 4, the main results figure, was wrong due to editing mistake, now correcte

GEMS: Galaxy Evolution from Morphologies and SEDs

GEMS, Galaxy Evolution from Morphologies and SEDs, is a large-area (800 arcmin2) two-color (F606W and F850LP) imaging survey with the Advanced Camera for Surveys on HST. Centered on the Chandra Deep Field South, it covers an area of ~28'x28', or about 120 Hubble Deep Field areas, to a depth of m_AB(F606W)=28.3 (5sigma and m_AB(F850LP)=27.1 (5sigma) for compact sources. In its central ~1/4, GEMS incorporates ACS imaging from the GOODS project. Focusing on the redshift range 0.2<=z<=1.1, GEMS provides morphologies and structural parameters for nearly 10,000 galaxies where redshift estimates, luminosities and SEDs exist from COMBO-17. At the same time, GEMS contains detectable host galaxy images for several hundred faint AGN. This paper provides an overview of the science goals, the experiment design, the data reduction and the science analysis plan for GEMS.Comment: 24 pages, TeX with 6 eps Figures; to appear in ApJ Supplement. Low resolution figures only. Full resolution at http://zwicky.as.arizona.edu/~rix/Misc/GEMS.ps.g