Statistics of finite-time Lyapunov exponents in the Ulam map

The statistical properties of finite-time Lyapunov exponents at the Ulam point of the logistic map are investigated. The exact analytical expression for the autocorrelation function of one-step Lyapunov exponents is obtained, allowing the calculation of the variance of exponents computed over time intervals of length $n$. The variance anomalously decays as $1/n^2$. The probability density of finite-time exponents noticeably deviates from the Gaussian shape, decaying with exponential tails and presenting $2^{n-1}$ spikes that narrow and accumulate close to the mean value with increasing $n$. The asymptotic expression for this probability distribution function is derived. It provides an adequate smooth approximation to describe numerical histograms built for not too small $n$, where the finiteness of bin size trimmes the sharp peaks.Comment: 6 pages, 4 figures, to appear in Phys. Rev.

Bias Analysis in Entropy Estimation

We consider the problem of finite sample corrections for entropy estimation. New estimates of the Shannon entropy are proposed and their systematic error (the bias) is computed analytically. We find that our results cover correction formulas of current entropy estimates recently discussed in literature. The trade-off between bias reduction and the increase of the corresponding statistical error is analyzed.Comment: 5 pages, 3 figure

Finite-sample frequency distributions originating from an equiprobability distribution

Given an equidistribution for probabilities p(i)=1/N, i=1..N. What is the expected corresponding rank ordered frequency distribution f(i), i=1..N, if an ensemble of M events is drawn?Comment: 4 pages, 4 figure

Genome Biol.

Background Whole genome sequencing of marine cyanobacteria has revealed an unprecedented degree of genomic variation and streamlining. With a size of 1.66 megabase-pairs, Prochlorococcus sp. MED4 has the most compact of these genomes and it is enigmatic how the few identified regulatory proteins efficiently sustain the lifestyle of an ecologically successful marine microorganism. Small non-coding RNAs (ncRNAs) control a plethora of processes in eukaryotes as well as in bacteria; however, systematic searches for ncRNAs are still lacking for most eubacterial phyla outside the enterobacteria. Results Based on a computational prediction we show the presence of several ncRNAs (cyanobacterial functional RNA or Yfr) in several different cyanobacteria of the Prochlorococcus-Synechococcus lineage. Some ncRNA genes are present only in two or three of the four strains investigated, whereas the RNAs Yfr2 through Yfr5 are structurally highly related and are encoded by a rapidly evolving gene family as their genes exist in different copy numbers and at different sites in the four investigated genomes. One ncRNA, Yfr7, is present in at least seven other cyanobacteria. In addition, control elements for several ribosomal operons were predicted as well as riboswitches for thiamine pyrophosphate and cobalamin. Conclusion This is the first genome-wide and systematic screen for ncRNAs in cyanobacteria. Several ncRNAs were both computationally predicted and their presence was biochemically verified. These RNAs may have regulatory functions and each shows a distinct phylogenetic distribution. Our approach can be applied to any group of microorganisms for which more than one total genome sequence is available for comparative analysis

Small-world networks: Evidence for a crossover picture

Watts and Strogatz [Nature 393, 440 (1998)] have recently introduced a model for disordered networks and reported that, even for very small values of the disorder $p$ in the links, the network behaves as a small-world. Here, we test the hypothesis that the appearance of small-world behavior is not a phase-transition but a crossover phenomenon which depends both on the network size $n$ and on the degree of disorder $p$. We propose that the average distance $\ell$ between any two vertices of the network is a scaling function of $n / n^*$. The crossover size $n^*$ above which the network behaves as a small-world is shown to scale as $n^*(p \ll 1) \sim p^{-\tau}$ with $\tau \approx 2/3$.Comment: 5 pages, 5 postscript figures (1 in color), Latex/Revtex/multicols/epsf. Accepted for publication in Physical Review Letter

Entropy estimates of small data sets

Estimating entropies from limited data series is known to be a non-trivial task. Naive estimations are plagued with both systematic (bias) and statistical errors. Here, we present a new 'balanced estimator' for entropy functionals Shannon, R\'enyi and Tsallis) specially devised to provide a compromise between low bias and small statistical errors, for short data series. This new estimator out-performs other currently available ones when the data sets are small and the probabilities of the possible outputs of the random variable are not close to zero. Otherwise, other well-known estimators remain a better choice. The potential range of applicability of this estimator is quite broad specially for biological and digital data series.Comment: 11 pages, 2 figure

Transition to Stochastic Synchronization in Spatially Extended Systems

Spatially extended dynamical systems, namely coupled map lattices, driven by additive spatio-temporal noise are shown to exhibit stochastic synchronization. In analogy with low-dymensional systems, synchronization can be achieved only if the maximum Lyapunov exponent becomes negative for sufficiently large noise amplitude. Moreover, noise can suppress also the non-linear mechanism of information propagation, that may be present in the spatially extended system. A first example of phase transition is observed when both the linear and the non-linear mechanisms of information production disappear at the same critical value of the noise amplitude. The corresponding critical properties can be hardly identified numerically, but some general argument suggests that they could be ascribed to the Kardar-Parisi-Zhang universality class. Conversely, when the non-linear mechanism prevails on the linear one, another type of phase transition to stochastic synchronization occurs. This one is shown to belong to the universality class of directed percolation.Comment: 21 pages, Latex - 14 EPS Figs - To appear on Physical Review

Systems biologists seek fuller integration of systems biology approaches in new cancer research programs

Systems biology takes an interdisciplinary approach to the systematic study of complex interactions in biological systems. This approach seeks to decipher the emergent behaviors of complex systems rather than focusing only on their constituent properties. As an increasing number of examples illustrate the value of systems biology approaches to understand the initiation, progression, and treatment of cancer, systems biologists from across Europe and the United States hope for changes in the way their field is currently perceived among cancer researchers. In a recent EU-US workshop, supported by the European Commission, the German Federal Ministry for Education and Research, and the National Cancer Institute of the NIH, the participants discussed the strengths, weaknesses, hurdles, and opportunities in cancer systems biology

Correlation property of length sequences based on global structure of complete genome

This paper considers three kinds of length sequences of the complete genome. Detrended fluctuation analysis, spectral analysis, and the mean distance spanned within time $L$ are used to discuss the correlation property of these sequences. The values of the exponents from these methods of these three kinds of length sequences of bacteria indicate that the long-range correlations exist in most of these sequences. The correlation have a rich variety of behaviours including the presence of anti-correlations. Further more, using the exponent $\gamma$, it is found that these correlations are all linear ($\gamma=1.0\pm 0.03$). It is also found that these sequences exhibit $1/f$ noise in some interval of frequency ($f>1$). The length of this interval of frequency depends on the length of the sequence. The shape of the periodogram in $f>1$ exhibits some periodicity. The period seems to depend on the length and the complexity of the length sequence.Comment: RevTex, 9 pages with 5 figures and 3 tables. Phys. Rev. E Jan. 1,2001 (to appear