Asymptotic dimension and uniform embeddings

We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the lamplighter group $Z\wr Z$, which has infinite asymptotic dimension.Comment: 17 pages, no figure

Euler characteristic of the configuration space of a complex

A closed form formula (generating function) for the Euler characteristic of the configuration space of $\scriptstyle n$ particles in a simplicial complex is given.Comment: 6 pages, no figure

The Luminosity Function of 81 Abell Clusters from the CRoNaRio catalogues

We present the composite luminosity function (hereafter LF) of galaxies for 81 Abell clusters studied in our survey of the Northern Hemisphere, using DPOSS data processed by the CRoNaRio collaboration. The derived LF is very accurate due to the use of homogeneous data both for the clusters and the control fields and to the local estimate of the background, which takes into account the presence of large-scale structures and of foreground clusters and groups. The global composite LF is quite flat down to $M^*+5$ has a slope $\alpha\sim-1.0\pm0.2$ with minor variations from blue to red filters, and $M^*\sim-21.8,-22.0,-22.3$ mag ($H_0=50$ km s$^{-1}$ Mpc$^{-1}$) in the $g, r$ and $i$ filters, respectively (errors are detailed in the text). We find a significant difference between rich and poor clusters thus arguing in favour of a dependence of the LF on the properties of the environment.Comment: 8 pages, 5 figures. Contribution to the IAP 2000 Conference "Constructing the Universe with Clusters of Galaxies", Paris, July 200

Data-Mining a Large Digital Sky Survey: From the Challenges to the Scientific Results

The analysis and an efficient scientific exploration of the Digital Palomar Observatory Sky Survey (DPOSS) represents a major technical challenge. The input data set consists of 3 Terabytes of pixel information, and contains a few billion sources. We describe some of the specific scientific problems posed by the data, including searches for distant quasars and clusters of galaxies, and the data-mining techniques we are exploring in addressing them. Machine-assisted discovery methods may become essential for the analysis of such multi-Terabyte data sets. New and future approaches involve unsupervised classification and clustering analysis in the Giga-object data space, including various Bayesian techniques. In addition to the searches for known types of objects in this data base, these techniques may also offer the possibility of discovering previously unknown, rare types of astronomical objects.Comment: Invited paper, to appear in Applications of Digital Image Processing XX, ed. A. Tescher, Proc. S.P.I.E. vol. 3164, in press; 10 pages, a self-contained TeX file, and 3 separate postscript figure

Photometric validation of a model independent procedure to extract galaxy clusters

By means of CCD photometry in three bands (Gunn g, r, i) we investigate the existence of 12 candidate clusters extracted via a model independent peak finding algorithm (\cite{memsait}) from DPOSS data. The derived color-magnitude diagrams allow us to confirm the physical nature of 9 of the cluster candidates, and to estimate their photometric redshifts. Of the other candidates, one is a fortuitous detection of a true cluster at z~0.4, one is a false detection and the last is undecidable on the basis of the available data. The accuracy of the photometric redshifts is tested on an additional sample of 8 clusters with known spectroscopic redshifts. Photometric redshifts turn out to be accurate within z~0.01 (interquartile range).Comment: A&A in pres

An automatic procedure to extract galaxy clusters from CRoNaRio catalogs

We present preliminary results of a simple peak finding algorithm applied to catalogues of galaxies, extracted from the Second Palomar Sky Survey in the framework of the CRoNaRio project. All previously known Abell and Zwicky clusters in a test region of 5x5 sq. deg. are recovered and new candidate clusters are also detected. This algorithm represents an alternative way of searching for galaxy clusters with respect to that implemented and tested at Caltech on the same type of data (Gal et al. 1998).Comment: in the proceeding of the XLIII SAIt national conference Mem. Soc. Astr. It., in pres