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

Statistical keyword detection in literary corpora

Understanding the complexity of human language requires an appropriate analysis of the statistical distribution of words in texts. We consider the information retrieval problem of detecting and ranking the relevant words of a text by means of statistical information referring to the "spatial" use of the words. Shannon's entropy of information is used as a tool for automatic keyword extraction. By using The Origin of Species by Charles Darwin as a representative text sample, we show the performance of our detector and compare it with another proposals in the literature. The random shuffled text receives special attention as a tool for calibrating the ranking indices.Comment: Published version. 11 pages, 7 figures. SVJour for LaTeX2

Thermodynamics of hot dense H-plasmas: Path integral Monte Carlo simulations and analytical approximations

This work is devoted to the thermodynamics of high-temperature dense hydrogen plasmas in the pressure region between $10^{-1}$ and $10^2$ Mbar. In particular we present for this region results of extensive calculations based on a recently developed path integral Monte Carlo scheme (direct PIMC). This method allows for a correct treatment of the thermodynamic properties of hot dense Coulomb systems. Calculations were performed in a broad region of the nonideality parameter $\Gamma \lesssim 3$ and degeneracy parameter $n_e \Lambda^3 \lesssim 10$. We give a comparison with a few available results from other path integral calculations (restricted PIMC) and with analytical calculations based on Pade approximations for strongly ionized plasmas. Good agreement between the results obtained from the three independent methods is found.Comment: RevTex file, 21 pages, 5 ps-figures include

Statistical Mechanics of Canonical-Dissipative Systems and Applications to Swarm Dynamics

We develop the theory of canonical-dissipative systems, based on the assumption that both the conservative and the dissipative elements of the dynamics are determined by invariants of motion. In this case, known solutions for conservative systems can be used for an extension of the dynamics, which also includes elements such as the take-up/dissipation of energy. This way, a rather complex dynamics can be mapped to an analytically tractable model, while still covering important features of non-equilibrium systems. In our paper, this approach is used to derive a rather general swarm model that considers (a) the energetic conditions of swarming, i.e. for active motion, (b) interactions between the particles based on global couplings. We derive analytical expressions for the non-equilibrium velocity distribution and the mean squared displacement of the swarm. Further, we investigate the influence of different global couplings on the overall behavior of the swarm by means of particle-based computer simulations and compare them with the analytical estimations.Comment: 14 pages incl. 13 figures. v2: misprints in Eq. (40) corrected, ref. updated. For related work see also: http://summa.physik.hu-berlin.de/~frank/active.htm

Canonical active Brownian motion

Active Brownian motion is the complex motion of active Brownian particles. They are active in the sense that they can transform their internal energy into energy of motion and thus create complex motion patterns. Theories of active Brownian motion so far imposed couplings between the internal energy and the kinetic energy of the system. We investigate how this idea can be naturally taken further to include also couplings to the potential energy, which finally leads to a general theory of canonical dissipative systems. Explicit analytical and numerical studies are done for the motion of one particle in harmonic external potentials. Apart from stationary solutions, we study non-equilibrium dynamics and show the existence of various bifurcation phenomena.Comment: 11 pages, 6 figures, a few remarks and references adde

Excitation of solitons in hexagonal lattices and ways of controlling electron transport

This is a post-peer-review, pre-copyedit version of an article published in Philosophical Transactions A: Mathematical, Physical and Engineering Sciences. The final authenticated version is available online at: http://dx.doi.org/10.1007/s40435-017-0383-x.We construct metastable long-living hexagonal lattices with appropriately modified Morse interactions and show that highly-energetic solitons may be excited moving along crystallographic axes. Studying the propagation, their dynamic changes and the relaxation processes it appears that lump solitons create in the lattice running local compressions. Based on the tight-binding model we investigate the possibility that electrons are trapped and guided by the electric polarization field of the compression field of one soliton or two solitons with crossing pathways. We show that electrons may jump from a bound state with the first soliton to a bound state with a second soliton and changing accordingly the direction of their path. We discuss the possibility to control by this method the path of an excess electron from a source at a boundary to a selected drain at another chosen boundary by following straight pathways on crystallographic axes.DFG, 163436311, SFB 910: Kontrolle selbstorganisierender nichtlinearer Systeme: Theoretische Methoden und Anwendungskonzept

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