A Formal Framework for Speedup Learning from Problems and Solutions

Speedup learning seeks to improve the computational efficiency of problem solving with experience. In this paper, we develop a formal framework for learning efficient problem solving from random problems and their solutions. We apply this framework to two different representations of learned knowledge, namely control rules and macro-operators, and prove theorems that identify sufficient conditions for learning in each representation. Our proofs are constructive in that they are accompanied with learning algorithms. Our framework captures both empirical and explanation-based speedup learning in a unified fashion. We illustrate our framework with implementations in two domains: symbolic integration and Eight Puzzle. This work integrates many strands of experimental and theoretical work in machine learning, including empirical learning of control rules, macro-operator learning, Explanation-Based Learning (EBL), and Probably Approximately Correct (PAC) Learning.Comment: See http://www.jair.org/ for any accompanying file

Supermassive black hole formation during the assembly of pre-galactic discs

In this paper we discuss the evolution of gravitationally unstable pre-galactic discs that result from the collapse of haloes at high redshift $z \approx 10$ or so, which have not yet been enriched by metals. In cases where molecular hydrogen formation is suppressed the discs are maintained at a temperature of a few thousand degrees Kelvin. However, when molecular hydrogen is present cooling can proceed down to a few hundred degrees Kelvin. Analogous to the case of the larger scale proto-galactic discs, we assume that the evolution of these discs is mainly driven by angular momentum redistribution induced by the development of gravitational instabilities in the disc. We also properly take into account the possibility of disc fragmentation. We thus show that this simple model naturally predicts the formation of supermassive black holes in the nuclei of such discs and provides a robust determination of their mass distribution as a function of halo properties. We estimate that roughly 5% of discs resulting from the collapse of haloes with $M\approx 10^7 M_{\odot}$ should host a massive black hole with a mass $M_{\rm BH}\approx 10^5 M_{\odot}$. We confirm our arguments with time-dependent calculations of the evolution of the surface density and of the accretion rate in these primordial discs. This mechanism offers an efficient way to form seed black holes at high redshift. The predicted masses for our black hole seeds enable the comfortable assembly of $10^9 M_{\odot}$ black holes powering the luminous quasars detected by the Sloan Digital Sky Survey at $z = 6$ for a concordance cosmology. (abridged)Comment: 12 pages, 8 figures, submitted to MNRA

Galaxy Galaxy Lensing as a Probe of Galaxy Dark Matter Halos

Gravitational lensing has now become a popular tool to measure the mass distribution of structures in the Universe on various scales. Here we focus on the study of galaxy's scale dark matter halos with galaxy-galaxy lensing techniques: observing the shapes of distant background galaxies which have been lensed by foreground galaxies allows us to map the mass distribution of the foreground galaxies. The lensing effect is small compared to the intrinsic ellipticity distribution of galaxies, thus a statistical approach is needed to derive some constraints on an average lens population. An advantage of this method is that it provides a probe of the gravitational potential of the halos of galaxies out to very large radii, where few classical methods are viable, since dynamical and hydrodynamical tracers of the potential cannot be found at this radii. We will begin by reviewing the detections of galaxy-galaxy lensing obtained so far. Next we will present a maximum likelihood analysis of simulated data we performed to evaluate the accuracy and robustness of constraints that can be obtained on galaxy halo properties. Then we will apply this method to study the properties of galaxies which stand in massive cluster lenses at z~0.2. The main result of this work is to find dark matter halos of cluster galaxies to be significantly more compact compared to dark matter halos around field galaxies of equivalent luminosity, in agreement with early galaxy-galaxy lensing studies and with theoretical expectations, in particular with the tidal stripping scenario. We thus provide a strong confirmation of tidal truncation from a homogeneous sample of galaxy clusters. Moreover, it is the first time that cluster galaxies are probed successfully using galaxy-galaxy lensing techniques from ground based data.Comment: 8 pages, 5 figures, to appear in Moriond Proceedings, From Dark Halos to Ligh

The Gamma Ray Burst Luminosity Function in the Light of the Swift 2-year Data

We compute the luminosity function (LF) and the formation rate of long gamma ray bursts (GRBs) by fitting the observed differential peak flux distribution obtained by the BATSE satellite in three different scenarios: i) GRBs follow the cosmic star formation and their LF is constant in time; ii) GRBs follow the cosmic star formation but the LF varies with redshift; iii) GRBs form preferentially in low-metallicity environments. We find that the differential peak flux number counts obtained by BATSE and by Swift can be reproduced using the same LF and GRB formation rate, indicating that the two satellites are observing the same GRB population. We then check the resulting redshift distributions in the light of Swift 2-year data, focusing in particular on the relatively large sample of GRBs detected at z>2.5. We show that models in which GRBs trace the cosmic star formation and are described by a constant LF are ruled out by the number of high-z Swift detections. This conclusion does not depend on the redshift distribution of bursts that lack of optical identification, nor on the existence of a decline in star formation rate at z>2, nor on the adopted faint-end of the GRB LF. Swift observations can be explained by assuming that the LF varies with redshift and/or that GRB formation is limited to low-metallicity environments.Comment: 7 pages, 3 figures, ApJ Letter in pres

New observational Constraints on the Growth of the First Supermassive Black Holes

We constrain the total accreted mass density in supermassive black holes at z>6, inferred via the upper limit derived from the integrated X-ray emission from a sample of photometrically selected galaxy candidates. Studying galaxies obtained from the deepest Hubble Space Telescope images combined with the Chandra 4 Msec observations of the Chandra Deep Field South, we achieve the most restrictive constraints on total black hole growth in the early Universe. We estimate an accreted mass density <1000Mo Mpc^-3 at z~6, significantly lower than the previous predictions from some existing models of early black hole growth and earlier prior observations. These results place interesting constraints on early black growth and mass assembly by accretion and imply one or more of the following: (1) only a fraction of the luminous galaxies at this epoch contain active black holes; (2) most black hole growth at early epochs happens in dusty and/or less massive - as yet undetected - host galaxies; (3) there is a significant fraction of low-z interlopers in the galaxy sample; (4) early black hole growth is radiatively inefficient, heavily obscured and/or is due to black hole mergers as opposed to accretion or (5) the bulk of the black hole growth occurs at late times. All of these possibilities have important implications for our understanding of high redshift seed formation models.Comment: ApJ Accepted, 10 pages, 7 figures, 1 table, in emulateapj forma

Redescription of the flat fish Pardachirus marmoratus (Lacepede) from Indian waters

The note describes Pardachirus marmoratus (Lacepede) (Ordcr : Pleronectiformes, Family : Soleidae)occuring in the Gulf of Mannar along the Indian Coast