AUTOMATED MORPHOLOGICAL CLASSIFICATION OF APM GALAXIES BY SUPERVISED ARTIFICIAL NEURAL NETWORKS

We train Artificial Neural Networks to classify galaxies based solely on the morphology of the galaxy images as they appear on blue survey plates. The images are reduced and morphological features such as bulge size and the number of arms are extracted, all in a fully automated manner. The galaxy sample was first classified by 6 independent experts. We use several definitions for the mean type of each galaxy, based on those classifications. We then train and test the network on these features. We find that the rms error of the network classifications, as compared with the mean types of the expert classifications, is 1.8 Revised Hubble Types. This is comparable to the overall rms dispersion between the experts. This result is robust and almost completely independent of the network architecture used.Comment: The full paper contains 25 pages, and includes 22 figures. It is available at ftp://ftp.ast.cam.ac.uk/pub/hn/apm2.ps . The table in the appendix is available on request from [email protected]. Mon. Not. R. Astr. Soc., in pres

Bayesian `Hyper-Parameters' Approach to Joint Estimation: The Hubble Constant from CMB Measurements

Recently several studies have jointly analysed data from different cosmological probes with the motivation of estimating cosmological parameters. Here we generalise this procedure to take into account the relative weights of various probes. This is done by including in the joint \chi^2 function a set of `Hyper-Parameters', which are dealt with using Bayesian considerations. The resulting algorithm (in the case of uniform priors on the log of the Hyper-Parameters) is very simple: instead of minimising \sum \chi_j^2 (where \chi_j^2 is per data set j) we propose to minimise \sum N_j \ln (\chi_j^2) (where N_j is the number of data points per data set j). We illustrate the method by estimating the Hubble constant H_0 from different sets of recent CMB experiments (including Saskatoon, Python V, MSAM1, TOCO and Boomerang).Comment: submitted to MNRAS, 6 pages, Latex, with 3 figures embedde

Combining cosmological datasets: hyperparameters and Bayesian evidence

A method is presented for performing joint analyses of cosmological datasets, in which the weight assigned to each dataset is determined directly by it own statistical properties. The weights are considered in a Bayesian context as a set of hyperparameters, which are then marginalised over in order to recover the posterior distribution as a function only of the cosmological parameters of interest. In the case of a Gaussian likelihood function, this marginalisation may be performed analytically. Calculation of the Bayesian evidence for the data, with and without the introduction of hyperparameters, enables a direct determination of whether the data warrant the introduction of weights into the analysis; this generalises the standard likelihood ratio approach to model comparison. The method is illustrated by application to the classic toy problem of fitting a straight line to a set of data. A cosmological illustration of the technique is also presented, in which the latest measurements of the cosmic microwave background power spectrum are used to infer constraints on cosmological parameters.Comment: 12 pages, 6 figures, submitted to MNRA

Cosmological Parameters from Velocities, CMB and Supernovae

We compare and combine likelihood functions of the cosmological parameters Omega_m, h and sigma_8, from peculiar velocities, CMB and type Ia supernovae. These three data sets directly probe the mass in the Universe, without the need to relate the galaxy distribution to the underlying mass via a "biasing" relation. We include the recent results from the CMB experiments BOOMERANG and MAXIMA-1. Our analysis assumes a flat Lambda CDM cosmology with a scale-invariant adiabatic initial power spectrum and baryonic fraction as inferred from big-bang nucleosynthesis. We find that all three data sets agree well, overlapping significantly at the 2 sigma level. This therefore justifies a joint analysis, in which we find a joint best fit point and 95 per cent confidence limits of Omega_m=0.28 (0.17,0.39), h=0.74 (0.64,0.86), and sigma_8=1.17 (0.98,1.37). In terms of the natural parameter combinations for these data sigma_8 Omega_m^0.6 = 0.54 (0.40,0.73), Omega_m h = 0.21 (0.16,0.27). Also for the best fit point, Q_rms-ps = 19.7 muK and the age of the universe is 13.2 Gyr.Comment: 8 pages, 5 figures. Submitted to MNRA

On virialization with dark energy

We review the inclusion of dark energy into the formalism of spherical collapse, and the virialization of a two-component system, made of matter and dark energy. We compare two approaches in previous studies. The first assumes that only the matter component virializes, e.g. as in the case of a classic cosmological constant. The second approach allows the full system to virialize as a whole. We show that the two approaches give fundamentally different results for the final state of the system. This might be a signature discriminating between the classic cosmological constant which cannot virialize and a dynamical dark energy mimicking a cosmological constant. This signature is independent of the measured value of the equation of state. An additional issue which we address is energy non-conservation of the system, which originates from the homogeneity assumption for the dark energy. We propose a way to take this energy loss into account.Comment: 15 pages, 5 figures. Accepted for publication in JCA

The SBF Survey of Galaxy Distances. II. Local and Large-Scale Flows

We present analysis of local large scale flows using the Surface Brightness Fluctuation (SBF) Survey for the distances to 300 early-type galaxies. Our models of the distribution function of mean velocity and velocity dispersion at each point in space include a uniform thermal velocity dispersion and spherical attractors whose position, amplitude, and radial shape are free to vary. Our fitting procedure performs a maximum likelihood fit of the model to the observations. We obtain a Hubble constant of Ho = 77 +/- 4 +/- 7 km/s/Mpc, but a uniform Hubble flow is not acceptable fit to the data. Inclusion of two attractors, one of whose fit location coincides with the Virgo cluster and the other whose fit location is slightly beyond the Centaurus clusters nearly explain the peculiar velocities, but the quality of the fit can be further improved by the addition of a quadrupole correction to the Hubble flow. Although the dipole and quadrupole may be genuine manifestations of more distant density fluctuations, we find evidence that they are more likely due to non-spherical attractors. We find no evidence for bulk flows which include our entire survey volume (R < 3000 km/s); our volume is at rest with respect to the CMB. The fits to the attractors both have isothermal radial profiles (v ~ 1/r) over a range of overdensity between about 10 and 1, but fall off more steeply at larger radius. The best fit value for the small scale, cosmic thermal velocity is 180 +/- 14 km/s.Comment: 37 pages, AASTeX Latex, including 30 Postscript figures, submitted to Astrophysical Journal, July 2, 199

On library correctness under weak memory consistency: specifying and verifying concurrent libraries under declarative consistency models

Concurrent libraries are the building blocks for concurrency. They encompass a range of abstractions (locks, exchangers, stacks, queues, sets) built in a layered fashion: more advanced libraries are built out of simpler ones. While there has been a lot of work on verifying such libraries in a sequentially consistent (SC) environment, little is known about how to specify and verify them under weak memory consistency (WMC). We propose a general declarative framework that allows us to specify concurrent libraries declaratively, and to verify library implementations against their specifications compositionally. Our framework is sufficient to encode standard models such as SC, (R)C11 and TSO. Additionally, we specify several concurrent libraries, including mutual exclusion locks, reader-writer locks, exchangers, queues, stacks and sets. We then use our framework to verify multiple weakly consistent implementations of locks, exchangers, queues and stacks

Neural computation as a tool for galaxy classification : methods and examples

We apply and compare various Artificial Neural Network (ANN) and other algorithms for automatic morphological classification of galaxies. The ANNs are presented here mathematically, as non-linear extensions of conventional statistical methods in Astronomy. The methods are illustrated using different subsets Artificial Neural Network (ANN) and other algorithms for automatic morphological classification of galaxies. The ANNs are presented here mathematically, as non-linear extensions of conventional statistical methods in Astronomy. The methods are illustrated using different subsets from the ESO-LV catalogue, for which both machine parameters and human classification are available. The main methods we explore are: (i) Principal Component Analysis (PCA) which tells how independent and informative the input parameters are. (ii) Encoder Neural Network which allows us to find both linear (PCA-like) and non-linear combinations of the input, illustrating an example of unsupervised ANN. (iii) Supervised ANN (using the Backpropagation or Quasi-Newton algorithms) based on a training set for which the human classification is known. Here the output for previously unclassified galaxies can be interpreted as either a continuous (analog) output (e.g. $T$-type) or a Bayesian {\it a posteriori} probability for each class. Although the ESO-LV parameters are sub-optimal, the success of the ANN in reproducing the human classification is 2 $T$-type units, similar to the degree of agreement between two human experts who classify the same galaxy images on plate material. We also examine the aspects of ANN configurations, reproducibility, scaling of input parameters and redshift information.Comment: uuencoded compressed postscript. The preprint is also available at http://www.ast.cam.ac.uk/preprint/PrePrint.htm

Morphological Classification of galaxies by Artificial Neural Networks

We explore a method for automatic morphological classification of galaxies by an Artificial Neural Network algorithm. The method is illustrated using 13 galaxy parameters measured by machine (ESO-LV), and classified into five types (E, S0, Sa + Sb, Sc + Sd and Irr). A simple Backpropagation algorithm allows us to train a network on a subset of the catalogue according to human classification, and then to predict, using the measured parameters, the classification for the rest of the catalogue. We show that the neural network behaves in our problem as a Bayesian classifier, i.e. it assigns the a posteriori probability for each of the five classes considered. The network highest probability choice agrees with the catalogue classification for 64 percent of the galaxies. If either the first or the second highest probability choice of the network is considered, the success rate is 90 per cent. The technique allows uniform and more objective classification of very large extragalactic data sets

Observational Tests of FRW World Models

Observational tests for the Cosmological Principle are reviewed. Assuming the FRW metric we then summarize estimates of cosmological parameters from various data sets, in particular the Cosmic Microwave Background and the 2dF galaxy redshift survey. These and other analyses suggest a best-fit Lambda-Cold Dark Matter model with Omega_m = 1 - Omega_lambda = 0.3 and H_0 = 70 km/sec/Mpc. It is remarkable that different measurements converge to this `concordance model', although it remains to be seen if the two main components of this model, the dark matter and the dark energy, are real entities or just `epicycles'. We point out some open questions related to this fashionable model.Comment: 11 pages with 3 figures included. Invited review at ``The Early Universe and Cosmological Observations: a Critical Review'', UCT, Cape Town, July 2001, to appear in "Classical and Quantum Gravity