Entropy and Long range correlations in literary English

Recently long range correlations were detected in nucleotide sequences and in human writings by several authors. We undertake here a systematic investigation of two books, Moby Dick by H. Melville and Grimm's tales, with respect to the existence of long range correlations. The analysis is based on the calculation of entropy like quantities as the mutual information for pairs of letters and the entropy, the mean uncertainty, per letter. We further estimate the number of different subwords of a given length $n$. Filtering out the contributions due to the effects of the finite length of the texts, we find correlations ranging to a few hundred letters. Scaling laws for the mutual information (decay with a power law), for the entropy per letter (decay with the inverse square root of $n$) and for the word numbers (stretched exponential growth with $n$ and with a power law of the text length) were found.Comment: 8 page

Guessing probability distributions from small samples

We propose a new method for the calculation of the statistical properties, as e.g. the entropy, of unknown generators of symbolic sequences. The probability distribution $p(k)$ of the elements $k$ of a population can be approximated by the frequencies $f(k)$ of a sample provided the sample is long enough so that each element $k$ occurs many times. Our method yields an approximation if this precondition does not hold. For a given $f(k)$ we recalculate the Zipf--ordered probability distribution by optimization of the parameters of a guessed distribution. We demonstrate that our method yields reliable results.Comment: 10 pages, uuencoded compressed PostScrip

Reconstruction of a first-order phase transition from computer simulations of individual phases and subphases

We present a new method for investigating first-order phase transitions using Monte Carlo simulations. It relies on the multiple-histogram method and uses solely histograms of individual phases. In addition, we extend the method to include histograms of subphases. The free energy difference between phases, necessary for attributing the correct statistical weights to the histograms, is determined by a detour in control parameter space via auxiliary systems with short relaxation times. We apply this method to a recently introduced model for structure formation in polypeptides for which other methods fail.Comment: 13 pages in preprint mode, REVTeX, 2 Figures available from the authors ([email protected], [email protected]

A measurement of large-scale peculiar velocities of clusters of galaxies: results and cosmological implications

Peculiar velocities of clusters of galaxies can be measured by studying the fluctuations in the cosmic microwave background (CMB) generated by the scattering of the microwave photons by the hot X-ray emitting gas inside clusters. While for individual clusters such measurements result in large errors, a large statistical sample of clusters allows one to study cumulative quantities dominated by the overall bulk flow of the sample with the statistical errors integrating down. We present results from such a measurement using the largest all-sky X-ray cluster catalog combined to date and the 3-year WMAP CMB data. We find a strong and coherent bulk flow on scales out to at least > 300 h^{-1} Mpc, the limit of our catalog. This flow is difficult to explain by gravitational evolution within the framework of the concordance LCDM model and may be indicative of the tilt exerted across the entire current horizon by far-away pre-inflationary inhomogeneities.Comment: Ap.J. (Letters), in press. 20 Oct issue (Vol. 686

The spatial distribution of galaxies of different spectral types in the massive intermediate-redshift cluster MACSJ0717.5+3745

We present the results of a wide-field spectroscopic analysis of the galaxy population of the massive cluster MACSJ0717.5+3745 and the surrounding filamentary structure (z=0.55), as part of our systematic study of the 12 most distant clusters in the MACS sample. Of 1368 galaxies spectroscopically observed in this field, 563 are identified as cluster members; of those, 203 are classified as emission-line galaxies, 260 as absorption-line galaxies, and 17 as E+A galaxies (defined by $\frac{H_{\delta}+H_{\gamma}}{2}>6$\AA and no detection of [OII] and $H_{\beta}$ in emission). The variation of the fraction of emission- and absorption-line galaxies as a function of local projected galaxy density confirms the well-known morphology-density relation, and becomes flat at projected galaxy densities less than $\sim 20Mpc^{-2}. Interestingly, 16 out of 17 E+A galaxies lie (in projection) within the ram-pressure stripping radius around the cluster core, which we take to be direct evidence of ram-pressure stripping being the primary mechanism that terminates star-formation in the E+A population of galaxy clusters. This conclusion is supported by the rarity of E+A galaxies in the filament which rules out galaxy mergers as the dominant driver of evolution for E+A galaxies in clusters. In addition, we find the 42 e(a) and 27 e(b) member galaxies, i.e., the dusty-starburst and starburst galaxies respectively, to be spread out across almost the entire study area. Their spatial distribution, which shows a strong preference for the filament region, suggests that starbursts are triggered in relatively low-density environments as galaxies are accreted from the field population.Comment: 16 pages, 15 figures, accepted by Ap

A New Radio - X-Ray Probe of Galaxy Cluster Magnetic Fields

Results are presented of a new VLA-ROSAT study that probes the magnetic field strength and distribution over a sample of 16 ``normal'' low redshift (z < 0.1) galaxy clusters. The clusters span two orders of magnitude in X-ray luminosity, and were selected to be free of (unusual) strong radio cluster halos, and widespread cooling flows. Consistent with these criteria, most clusters show a relaxed X-ray morphology and little or no evidence for recent merger activity. Analysis of the rotation measure (RM) data shows cluster-generated Faraday RM excess out to ~0.5 Mpc from cluster centers. The results, combined with RM imaging of cluster-embedded sources and ROSAT X-ray profiles indicates that the hot intergalactic gas within these ``normal'' clusters is permeated with a high filling factor by magnetic fields at levels of = 5-10 (l/10 kpc)^{-1/2} microGauss, where l is the field correlation length. These results lead to a global estimate of the total magnetic energy in clusters, and give new insight into the ultimate energy origin, which is likely gravitational. These results also shed some light on the cluster evolutionary conditions that existed at the onset of cooling flows.Comment: 6 pages, 1 figure, uses emulateapj5.sty, accepted by ApJ

ROSAT PSPC Observations of the Richest (R≥2R \geq 2) ACO Clusters

We have compiled an X-ray catalog of optically selected rich clusters of galaxies observed by the PSPC during the pointed GO phase of the ROSAT mission. This paper contains a systematic X-ray analysis of 150 clusters with an optical richness classification of $R \geq 2$ from the ACO catalog (Abell, Corwin, and Olowin 1989). All clusters were observed within 45' of the optical axis of the telescope during pointed PSPC observations. For each cluster, we calculate: the net 0.5-2.0 keV PSPC count rate (or $4 \sigma$ upper limit) in a 1 Mpc radius aperture, 0.5-2.0 keV flux and luminosity, bolometric luminosity, and X-ray centroid. The cluster sample is then used to examine correlations between the X-ray and optical properties of clusters, derive the X-ray luminosity function of clusters with different optical classifications, and obtain a quantitative estimate of contamination (i.e, the fraction of clusters with an optical richness significantly overestimated due to interloping galaxies) in the ACO catalog