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

Temporal regulation of murine cytomegalovirus transcription and mapping of viral RNA synthesized at immediate early times after infection

The replication of murine cytomegalovirus strain Smith in murine embryonic fibroblasts was investigated at immediate early, early, and late times after infection. Cloned subgenomic HindIII fragments of murine cytomegalovirus DNA served to define the regions of transcription. At immediate early times viral RNA classes ranging in size from 5.1 to 1.05 kilobases (kb) were transcribed mainly from the fragments HindIII-K and -L, whereas low levels of transcription were detected from the two termini HindIII-E and HindIII-N. A characteristic pattern of proteins could be translated from immediate early RNA in vitro. At early and late times after infection transcription from all HindIII fragments occurred, but different patterns of transcripts and proteins could be identified. Inhibitors of DNA synthesis induced differences in the late transcription pattern, located in the HindIII-F fragment. The coding region for abundant immediate early transcription could be located at between 0.769 and 0.817 map units. A plasmic clone containing the main part (0.769 to 0.815 map units) of this region was constructed. This region coded for six polyadenylated immediate early RNA species of 5.1, 2.75, 2.0, 1.75, 1.65, and 1.05 kb in size. Only the 1.75-kb RNA originated entirely from the HindIII-L fragment. The 5.1- and 2.75-kb RNA species were encoded by both the HindIII-L and HindIII-K fragments, and the 2.0-, 1.65-, and 1.05-kb RNA species were entirely transcribed within HindIII-K

Location, transcripts, and translation products

Cloned genomic fragments from the region (0.769 to 0.818 map units) coding for immediate-early (IE) transcripts of murine cytomegalovirus (MCMV) were used to analyze the physical organization of this region, the direction of transcription, and the proteins synthesized in vitro. Three IE transcription units could be identified. From IE coding region 1 (ie1; 0.781 to 0.796 map units) a dominant 2.75-kilobase (kb) RNA was transcribed from right to left on the prototype arrangement of the MCMV genome which directed the synthesis of an 89,000-molecular-weight polypeptide (89K polypeptide), the major IE protein. This phosphoprotein (pp89) has been shown to be active in the regulation of transcription. Upstream of ie1 and separated by the MCMV enhancer sequence was a second IE coding region, ie2, which was mapped at 0.803 to 0.817 map units. From ie2 a 1.75-kb RNA of moderate abundance was transcribed in the direction opposite to that of the ie1 RNA. After hybrid selection of the ie2 transcript, a 43,000-molecular-weight translation product was detected. A third coding region, ie3, was located directly downstream of ie1 (0.773 to 0.781 map units). The series of RNAs with low abundance, terminating in ie3, probably used the ie1 transcription start site and ranged from 1.0 to 5.1 kb in size. The 5.1-kb RNA apparently represents the nonspliced transcript from both coding regions ie1 and ie3. A 15K polypeptide was translated in vitro from RNA that was hybrid selected by ie3 sequences. Immunoprecipitation with monoclonal antibody revealed that 31K to 67K polypeptides were related to pp89. Some of these proteins were translated from RNAs that were smaller than 2.75 kb. Polypeptides related to pp89 were also synthesized in vivo. Because polypeptides unrelated to pp89 that were translated from RNA that was selected by ie2 and ie3 sequences were not immunoprecipitated by murine antisera, we assumed that the amount of these proteins synthesized in vivo during infection was probably very lo

The evolution of the cluster X-ray scaling relations in the WARPS sample at 0.6<z<1.0

The X-ray properties of a sample of 11 high-redshift (0.6<z<1.0) clusters observed with Chandra and/or XMM are used to investigate the evolution of the cluster scaling relations. The observed evolution of the L-T and M-L relations is consistent with simple self-similar predictions, in which the properties of clusters reflect the properties of the universe at their redshift of observation. When the systematic effect of assuming isothermality on the derived masses of the high-redshift clusters is taken into account, the high-redshift M-T and Mgas-T relations are also consistent with self-similar evolution. Under the assumption that the model of self-similar evolution is correct and that the local systems formed via a single spherical collapse, the high-redshift L-T relation is consistent with the high-z clusters having formed at a significantly higher redshift than the local systems. The data are also consistent with the more realistic scenario of clusters forming via the continuous accretion of material. The slope of the L-T relation at high-redshift (B=3.29+/-0.38) is consistent with the local relation, and significantly steeper then the self-similar prediction of B=2. This suggests that the non-gravitational processes causing the steepening occurred at z>1 or in the early stages of the clusters' formation, prior to their observation. The properties of the intra-cluster medium at high-redshift are found to be similar to those in the local universe. The mean surface-brightness profile slope for the sample is 0.66+/-0.05, the mean gas mass fractions within R2500 and R200 are 0.073+/-0.010 and 0.12+/-0.02 respectively, and the mean metallicity of the sample is 0.28+/-0.16 solar.Comment: 23 pages, 17 figures. Accepted for publication in MNRAS. Revised to match accepted version: reanalysed data with latest calibrations, several minor changes. Conclusions unchange

An algebraic formula for the index of a vector field on an isolated complete intersection singularity

Let (V,0) be a germ of a complete intersection variety in \CC^{n+k}, n>0, having an isolated singularity at 0 and X be the germ of a holomorphic vector field on \CC^{n+k} tangent to V and having on V an isolated zero at 0. We show that in this case the homological index and the GSV-index coincide. In the case when the zero of X is also isolated in the ambient space \CC^{n+k} we give a formula for the homological index in terms of local linear algebra.Comment: 18 pages; added an example which is not quasi homogeneous. A script calculating this example can be found at http://www.iag.uni-hannover.de/~bothmer/gobelin/ or at the and of the source file of this articl