Oracle-Based Robust Optimization via Online Learning

Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set. In the robust optimization framework the problem solved is a min-max problem where a solution is judged according to its performance on the worst possible realization of the parameters. In many cases, a straightforward solution of the robust optimization problem of a certain type requires solving an optimization problem of a more complicated type, and in some cases even NP-hard. For example, solving a robust conic quadratic program, such as those arising in robust SVM, ellipsoidal uncertainty leads in general to a semidefinite program. In this paper we develop a method for approximately solving a robust optimization problem using tools from online convex optimization, where in every stage a standard (non-robust) optimization program is solved. Our algorithms find an approximate robust solution using a number of calls to an oracle that solves the original (non-robust) problem that is inversely proportional to the square of the target accuracy

Searching for a Gravitational Heating Signature in Nearby Luminous Ellipticals

We present a new deep optical study of a luminosity limited sample of nearby elliptical galaxies, attempting to observe the effects of gravitational interactions on the ISM of these objects. This study is motivated by recent observations of M86, a nearby elliptical galaxy that shows possible evidence for gas heating through a recent gravitational interaction. The complete sample includes luminous ellipticals in clusters, groups and the field. For each of the galaxies we objectively derive a tidal parameter which measures the deviation of the stellar body from a smooth, relaxed model and find that 73% of them show tidal disturbance signatures in their stellar bodies. This is the first time that such an analysis is done on a statistically complete sample and it confirms that elliptical galaxies continue to grow and evolve through gravitational interactions even in the local Universe. Our study of ellipticals in a wide range of interaction stages, along with available ISM data will attempt to shed light on this possibly alternative mechanism for maintaining the observed ISM temperatures of elliptical galaxies.Comment: To appear in proceedings of The Monster's Fiery Breath: Feedback in Galaxies, Groups, and Clusters (AIP conference series

Mass growth and mergers: direct observations of the luminosity function of LRG satellite galaxies out to z=0.7 from SDSS and BOSS images

We present a statistical study of the luminosity functions of galaxies surrounding luminous red galaxies (LRGs) at average redshifts =0.34 and =0.65. The luminosity functions are derived by extracting source photometry around more than 40,000 LRGs and subtracting foreground and background contamination using randomly selected control fields. We show that at both studied redshifts the average luminosity functions of the LRGs and their satellite galaxies are poorly fitted by a Schechter function due to a luminosity gap between the centrals and their most luminous satellites. We utilize a two-component fit of a Schechter function plus a log-normal distribution to demonstrate that LRGs are typically brighter than their most luminous satellite by roughly 1.3 magnitudes. This luminosity gap implies that interactions within LRG environments are typically restricted to minor mergers with mass ratios of 1:4 or lower. The luminosity functions further imply that roughly 35% of the mass in the environment is locked in the LRG itself, supporting the idea that mass growth through major mergers within the environment is unlikely. Lastly, we show that the luminosity gap may be at least partially explained by the selection of LRGs as the gap can be reproduced by sparsely sampling a Schechter function. In that case LRGs may represent only a small fraction of central galaxies in similar mass halos.Comment: ApJ accepted versio

The faint stellar halos of massive red galaxies from stacks of more than 42000 SDSS LRG images

We study the properties of massive galaxies at an average redshift of z~0.34 through stacking more than 42000 images of Luminous Red Galaxies from the Sloan Digital Sky Survey. This is the largest dataset ever used for such an analysis and it allows us to explore the outskirts of massive red galaxies at unprecedented physical scales. Our image stacks extend farther than 400 kpc, where the r-band profile surface brightness reaches 30 mag arcsec-2. This analysis confirms that the stellar bodies of luminous red galaxies follow a simple Sersic profile out to 100 kpc. At larger radii the profiles deviate from the best-fit Sersic models and exhibit extra light in the g, r, i and z-band stacks. This excess light can probably be attributed to unresolved intragroup or intracluster light or a change in the light profile itself. We further show that standard analyses of SDSS-depth images typically miss 20% of the total stellar light and underestimate the size of LRGs by 10% compared to our best fit r-band Sersic model of n=5.5 and r_e=13.1 kpc. If the excess light at r>100 kpc is considered to be part of the galaxy, the best fit r-band Sersic parameters are n=5.8 and r_e=13.6 kpc. In addition we study the radially dependent stack ellipticity and find an increase with radius from e=0.25 at r=10 kpc to e=0.3 at r=100 kpc. This provides support that the stellar light that we trace out to at least 100 kpc is physically associated with the galaxies themselves and may confirm that the halos of individual LRGs have higher ellipticities than their central parts. Lastly we show that the broadband color gradients of the stacked images are flat beyond roughly 40 kpc, suggesting that the stellar populations do not vary significantly with radius in the outer parts of massive ellipticals.Comment: Accepted for publication in Ap

The Frequency of Tidal Features Associated with Nearby Luminous Elliptical Galaxies from a Statistically Complete Sample

We present a deep broadband optical imaging study of a complete sample of luminous elliptical galaxies (M_B<-20) at distances 15 Mpc - 50 Mpc, selected from the Tully catalog of nearby galaxies. The images are flat to ~0.35% across the 20' field and reach a V band depth of 27.7 mag arcsec^-2. We derive an objective tidal interaction parameter for all galaxies and find that 73% of them show tidal disturbance signatures in their stellar bodies. This is the first time that such an analysis is done on a statistically complete sample and it confirms that tidal features in ellipticals are common even in the local Universe. From the dynamical time of the sample galaxies at the innermost radius where tidal features are detected we estimate the mass assembly rate of nearby ellipticals to be dM/M 0.2 per Gyr with large uncertainty. We explore the relation between gravitational interaction signatures and the galaxy environment and find that galaxies in clusters are less disturbed than group and field galaxies. We also study how these interactions affect the broadband colors of ellipticals and find a moderate correlation, suggesting that the mergers are not accompanied by significant star-formation. Lastly, we find no correlation between AGN activity, as measured by 6cm radio emission, and large scale tidal distortions. This implies that gravitational interactions are not the only, and perhaps not the most important, trigger of nuclear activity. In summary, we find that elliptical galaxies in groups and low density environments continue to grow at the present day through mostly "dry" mergers involving little star formation.Comment: Accepted for publication in AJ. Appendix and full dataset available online at: http://www.astro.yale.edu/obe

Determination of the Beta Ray Energy Spectrum from the Absorption Curves of Beta Rays

<p>(a) The decrease in food-discovery time between the first tests on two successive days; (b) the positive correlation between colony size and the number of workers searching (mean values for the first tests on the two successive days are presented). The asterisk indicates a significant difference.</p

DeepSTORM3D: dense three dimensional localization microscopy and point spread function design by deep learning

Localization microscopy is an imaging technique in which the positions of individual nanoscale point emitters (e.g. fluorescent molecules) are determined at high precision from their images. This is the key ingredient in single/multiple-particle-tracking and several super-resolution microscopy approaches. Localization in three-dimensions (3D) can be performed by modifying the image that a point-source creates on the camera, namely, the point-spread function (PSF). The PSF is engineered using additional optical elements to vary distinctively with the depth of the point-source. However, localizing multiple adjacent emitters in 3D poses a significant algorithmic challenge, due to the lateral overlap of their PSFs. Here, we train a neural network to receive an image containing densely overlapping PSFs of multiple emitters over a large axial range and output a list of their 3D positions. Furthermore, we then use the network to design the optimal PSF for the multi-emitter case. We demonstrate our approach numerically as well as experimentally by 3D STORM imaging of mitochondria, and volumetric imaging of dozens of fluorescently-labeled telomeres occupying a mammalian nucleus in a single snapshot.Comment: main text: 9 pages, 5 figures, supplementary information: 29 pages, 20 figure

A Spectacular Hα\alpha Complex in Virgo: Evidence for a Collision Between M86 and NGC 4438 and Implications for Collisional ISM Heating of Ellipticals

Deep wide-field H$\alpha$+[NII] imaging around the Virgo cluster giant elliptical galaxy M86 reveals a highly complex and disturbed ISM/ICM. The most striking feature is a set of H$\alpha$ filaments which clearly connect M86 with the nearby disturbed spiral NGC 4438 (23$'$=120 kpc projected away), providing strong evidence for a previously unrecognized collision between them. Spectroscopy of selected regions show a fairly smooth velocity gradient between M86 and NGC 4438, consistent with the collision scenario. Such a collision would impart significant energy into the ISM of M86, probably heating the gas and acting to prevent the gas from cooling to form stars. We propose that cool gas stripped from NGC 4438 during the collision and deposited in its wake is heated by shocks, ram pressure drag, or thermal conduction, producing most of the H$\alpha$ filaments. Some H$\alpha$ filaments are associated with the well-known ridge of bright X-ray emission to the NW of the nucleus, suggesting that the collision is responsible for peculiarities of M86 previously ascribed to other effects. M86 is radio-quiet, thus AGN heating is unlikely to play a significant role. The M86 system has implications for understanding the role of gravitational interactions in the heating of the ISM in ellipticals, and how collisions in clusters transform galaxies.Comment: 6 pages, 2 figures. For high-resolution images, see http://www.astro.yale.edu/tal/research/index.htm