Building a Sample of Distant Clusters of Galaxies

Candidate clusters of galaxies drawn from the sample identified from the moderately deep I-band data of the ESO Imaging Survey (EIS), have been used for follow-up optical/infrared imaging and spectroscopic observations. The observations were conducted to assess the nature of these candidates over a large range of redshifts. Currently, 163 EIS candidates have (V-I) colors, 15 have (I-K) and 65 cluster fields have been observed spectroscopically. From a preliminary analysis of these data, we find that > 65% of the candidates studied show strong evidence of being real physical associations, over the redshift range 0.2<z<1.1. The evidence in some cases comes directly from spectroscopic measurements, in others indirectly from the detection of overdensities of objects with either the same color or the same photometric redshift, or from a combination of color and spectroscopic information. Preliminary results also suggest that the redshift derived from the matched-filter algorithm is a reasonable measure of the cluster's redshift, possibly overestimating it by Delta z ~0.1, at least for systems at z<0.7. Overdensities of red objects have been detected in over 100 candidates, 38 of which with estimated redshifts >0.6, and six candidates in the interval 0.45<z<0.81 have either been identified directly from measured redshifts or have been confirmed by the measurement of at least one redshift for galaxies located along a red-sequence typical of cluster early-type galaxies. Lastly, five candidates among those already observed in the infrared have (I-Ks) colors consistent with them being in the redshift interval 0.8<z<1.1. The sample of "confirmed" clusters, already the largest of its kind in the southern hemisphere, will be further enlarged by ongoing observations.Comment: To appear in "Large Scale Structure in the X-ray Universe", ed. M. Plionis and I. Georgantopoulos (Paris: Editions Frontieres), in pres

Combinatorial formulation of Ising model revisited

In 1952, Kac and Ward developed a combinatorial formulation for the two dimensional Ising model which is another method of obtaining Onsager's formula for the free energy per site in the thermodynamic limit of the model. Feynman gave an important contribution to this formulation conjecturing a crucial mathematical relation which completed Kac and Ward ideas. In this paper, the method of Kac, Ward and Feynman for the free field Ising model in two dimensions is reviewed in a selfcontained way.Comment: 27 pages, 17 figure

Fast Community Identification by Hierarchical Growth

A new method for community identification is proposed which is founded on the analysis of successive neighborhoods, reached through hierarchical growth from a starting vertex, and on the definition of communities as a subgraph whose number of inner connections is larger than outer connections. In order to determine the precision and speed of the method, it is compared with one of the most popular community identification approaches, namely Girvan and Newman's algorithm. Although the hierarchical growth method is not as precise as Girvan and Newman's method, it is potentially faster than most community finding algorithms.Comment: 6 pages, 5 figure

Statistical Mechanics Characterization of Neuronal Mosaics

The spatial distribution of neuronal cells is an important requirement for achieving proper neuronal function in several parts of the nervous system of most animals. For instance, specific distribution of photoreceptors and related neuronal cells, particularly the ganglion cells, in mammal's retina is required in order to properly sample the projected scene. This work presents how two concepts from the areas of statistical mechanics and complex systems, namely the \emph{lacunarity} and the \emph{multiscale entropy} (i.e. the entropy calculated over progressively diffused representations of the cell mosaic), have allowed effective characterization of the spatial distribution of retinal cells.Comment: 3 pages, 1 figure, The following article has been submitted to Applied Physics Letters. If it is published, it will be found online at http://apl.aip.org

Neuromorphometric characterization with shape functionals

This work presents a procedure to extract morphological information from neuronal cells based on the variation of shape functionals as the cell geometry undergoes a dilation through a wide interval of spatial scales. The targeted shapes are alpha and beta cat retinal ganglion cells, which are characterized by different ranges of dendritic field diameter. Image functionals are expected to act as descriptors of the shape, gathering relevant geometric and topological features of the complex cell form. We present a comparative study of classification performance of additive shape descriptors, namely, Minkowski functionals, and the nonadditive multiscale fractal. We found that the proposed measures perform efficiently the task of identifying the two main classes alpha and beta based solely on scale invariant information, while also providing intraclass morphological assessment