Effect of nonlinear filters on detrended fluctuation analysis

We investigate how various linear and nonlinear transformations affect the scaling properties of a signal, using the detrended fluctuation analysis (DFA). Specifically, we study the effect of three types of transforms: linear, nonlinear polynomial and logarithmic filters. We compare the scaling properties of signals before and after the transform. We find that linear filters do not change the correlation properties, while the effect of nonlinear polynomial and logarithmic filters strongly depends on (a) the strength of correlations in the original signal, (b) the power of the polynomial filter and (c) the offset in the logarithmic filter. We further investigate the correlation properties of three analytic functions: exponential, logarithmic, and power-law. While these three functions have in general different correlation properties, we find that there is a broad range of variable values, common for all three functions, where they exhibit identical scaling behavior. We further note that the scaling behavior of a class of other functions can be reduced to these three typical cases. We systematically test the performance of the DFA method in accurately estimating long-range power-law correlations in the output signals for different parameter values in the three types of filters, and the three analytic functions we consider.Comment: 12 pages, 7 figure

Long range correlations in DNA : scaling properties and charge transfer efficiency

We address the relation between long range correlations and charge transfer efficiency in aperiodic artificial or genomic DNA sequences. Coherent charge transfer through the HOMO states of the guanine nucleotide is studied using the transmission approach, and focus is made on how the sequence-dependent backscattering profile can be inferred from correlations between base pairs.Comment: Submitted to Phys. Rev. Let

Delocalization in harmonic chains with long-range correlated random masses

We study the nature of collective excitations in harmonic chains with masses exhibiting long-range correlated disorder with power spectrum proportional to $1/k^{\alpha}$, where $k$ is the wave-vector of the modulations on the random masses landscape. Using a transfer matrix method and exact diagonalization, we compute the localization length and participation ratio of eigenmodes within the band of allowed energies. We find extended vibrational modes in the low-energy region for $\alpha > 1$. In order to study the time evolution of an initially localized energy input, we calculate the second moment $M_2(t)$ of the energy spatial distribution. We show that $M_2(t)$, besides being dependent of the specific initial excitation and exhibiting an anomalous diffusion for weakly correlated disorder, assumes a ballistic spread in the regime $\alpha>1$ due to the presence of extended vibrational modes.Comment: 6 pages, 9 figure

Crecimiento y contenido de larvas de atún rojo (Thunnus thynnus) y atún blanco (Thunnus alalunga)

The waters surrounding the Balearic archipelago are considered to be prime spawning habitats of the bluefin tuna (Thunnus thynnus) and other tuna species such as albacore (T. alalunga) in the Mediterranean. During the 2003 bluefin and albacore spawning season, a tuna larval survey (TUNIBAL 0703) was carried out to assess the distribution of bluefin larvae in relation to hydrographic mesoscale features. Tuna larvae were collected by means of surface plankton tows with a bongo gear with a quadrangular mouth measuring 1 m diagonally. The otolith microstructure of 157 and 71 field-captured larvae of Mediterranean bluefin and albacore, respectively, were analyzed to estimate the daily growth pattern. Furthermore, biochemical analysis to estimate DNA, RNA and protein content was done on another batch of 114 bluefin and 132 albacore larvae. The size range included pre-flexion to post-flexion larvae, from 2.8 to 8.6 mm in body length. bluefin and albacore larvae grew linearly in standard length (0.35 and 0.33 mm/day, respectively) and potentially with respect to dry weight. No significant differences between species were observed in the size-weight relationship, or in the allometric relationship of body size and weight to otolith radius. However, the relationship of DNA and RNA to body size and weight showed a significant difference between species. Bluefin tuna larvae showed a greater nucleic acid content than albacore larvae. Protein content showed no significant differences with respect to body length.Las aguas de las Islas Baleares representan una de las zonas más importantes de puesta del atún rojo (Thunnus thynnus) y de otras especies asociadas, como el atún blanco albacore (T. alalunga). En julio del 2003, época de puesta del atún, se realizó la campaña TUNIBAL, con el fin de delimitar las zonas de puesta del atún rojo, así como su relación con el modelo de circulación en el área. Las larvas de atunes se muestrearon mediante arrastres superficiales con una red Bongo de boca cuadrangular (1 m en diagonal). Para el estudio del crecimiento diario, 157 larvas de atún rojo y 71 larvas de atún blanco fueron analizadas. Para el estudio de la condición larvaria (DNA, RNA y proteínas), 119 larvas de atún rojo y 138 larvas de atún blanco fueron analizadas. Se analizaron larvas desde estados de pre-flexión a post-flexión, desde 2.8 a 8.6 mm de longitud estándar. Las larvas de atún rojo y atún blanco crecen linealmente en longitud estándar (0.35 y 0.33 mm/día respectivamente) y potencialmente en peso seco. No se encontraron diferencias significativas en la relación talla-peso, o en la relación del radio del otolito con talla o peso. Sin embargo, la relación entre DNA y RNA con talla o peso mostró diferencias significativas entre especies, siendo el atún rojo el que mostró mayores contenidos en ácidos nucleicos. No obstante, el contenido en proteínas no mostró diferencias significativas con la talla entre especies

Generalization of entropy based divergence measures for symbolic sequence analysis

Entropy based measures have been frequently used in symbolic sequence analysis. A symmetrized and smoothed form of Kullback-Leibler divergence or relative entropy, the Jensen-Shannon divergence (JSD), is of particular interest because of its sharing properties with families of other divergence measures and its interpretability in different domains including statistical physics, information theory and mathematical statistics. The uniqueness and versatility of this measure arise because of a number of attributes including generalization to any number of probability distributions and association of weights to the distributions. Furthermore, its entropic formulation allows its generalization in different statistical frameworks, such as, non-extensive Tsallis statistics and higher order Markovian statistics. We revisit these generalizations and propose a new generalization of JSD in the integrated Tsallis and Markovian statistical framework. We show that this generalization can be interpreted in terms of mutual information. We also investigate the performance of different JSD generalizations in deconstructing chimeric DNA sequences assembled from bacterial genomes including that of E. coli, S. enterica typhi, Y. pestis and H. influenzae. Our results show that the JSD generalizations bring in more pronounced improvements when the sequences being compared are from phylogenetically proximal organisms, which are often difficult to distinguish because of their compositional similarity. While small but noticeable improvements were observed with the Tsallis statistical JSD generalization, relatively large improvements were observed with the Markovian generalization. In contrast, the proposed Tsallis-Markovian generalization yielded more pronounced improvements relative to the Tsallis and Markovian generalizations, specifically when the sequences being compared arose from phylogenetically proximal organisms.publishedVersionFil: Ré, Miguel Ángel. Universidad Tecnológica Nacional. Facultad Regional Córdoba. Centro de Investigación en Informática para la Ingeniería. Departamento de Ciencias Básicas; Argentina.Fil: Ré, Miguel Ángel. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Azad, Rajeev K. University of North Texas. College of Science. Department of Biological Sciences; Estados Unidos de América.Fil: Azad, Rajeev K. University of North Texas. College of Science. Department of Mathematics; Estados Unidos de América.Ciencias de la Información y Bioinformática (desarrollo de hardware va en 2.2 "Ingeniería Eléctrica, Electrónica y de Información" y los aspectos sociales van en 5.8 "Comunicación y Medios"

Crecimiento y contenido bioquímico comparativo de larvas en postflexión de sardina de tres zonas del Mediterráneo Occidental (Ebro, bahías de Almaría y Málaga)

Late larval stages of sardine (16-23 mm) were sampled during the 2003 spawning season in their nursery grounds located off the Ebro river mouth, on the Catalan coast, and in two bays of the Alborán Sea coasts, the Bay of Almería and the Bay of Málaga. The daily growth analysis of each sampled population revealed faster growth in the Ebro sardine larvae than in both of the Alboran Sea larval populations. This fact is supported by their greater content with age of DNA, RNA and protein. However, the significantly higher carbohydrate content of the Bay of Almería sardine larvae and a higher Fulton’s index, indicative of energy storage of individuals, in both of the sardine populations sampled in the Bays of Almería and Málaga show evident differences in the daily growth of the Alborán Sea larvae from those originating in the Ebro region. Late larval growth in the Alborán Sea sardine tends to favour an increase in body mass rather than in body length. This study hypothesises that the productivity pulses off the Alboran Sea coasts induced by the north and northwestern wind regimes may be responsible for the growth pulses observed in the otolith microstructure.Estados avanzados de larvas de sardina (de 16 a 23 mm) fueron muestreados durante el invierno de 2003 en zonas de alevinaje situadas en la desembocadura del río Ebro, en la costa catalana, y en las bahías de Almería y de Málaga, en las costas del Mar de Alborán. El análisis del crecimiento diario de cada población larvaria muestreada, evidencia un mayor crecimiento en las larvas procedentes del Ebro respecto a las nacidas en el Mar de Alborán. Esta observación se corrobora con un mayor incremento con la edad de los contenidos en DNA, RNA y proteínas de la población larvaria de sardina del río Ebro. Sin embargo, un contenido significativamente mayor de carbohidratos en la población de Almería, así como un mayor índice de Fulton, indicador de energía almacenada en un individuo, en ambas poblaciones del Mar de Alborán, evidencia una estrategia diferenciada de crecimiento de estas poblaciones larvarias con respecto a las procedentes del río Ebro. En consecuencia, las larvas de sardina del Mar de Alborán muestran una tendencia a crecer más en masa que en longitud, como lo evidencia el crecimiento relativo del peso seco, DNA, RNA y proteínas en relación con su longitud estándar. En este estudio se plantea la hipótesis de que los pulsos productivos en el Mar de Alborán, inducidos por el régimen de vientos de norte y poniente, pueden ser responsables de los pulsos de crecimiento larvario, como se evidencia en las microestructuras de los otolitos

New stopping criteria for segmenting DNA sequences

We propose a solution on the stopping criterion in segmenting inhomogeneous DNA sequences with complex statistical patterns. This new stopping criterion is based on Bayesian Information Criterion (BIC) in the model selection framework. When this stopping criterion is applied to a left telomere sequence of yeast Saccharomyces cerevisiae and the complete genome sequence of bacterium Escherichia coli, borders of biologically meaningful units were identified (e.g. subtelomeric units, replication origin, and replication terminus), and a more reasonable number of domains was obtained. We also introduce a measure called segmentation strength which can be used to control the delineation of large domains. The relationship between the average domain size and the threshold of segmentation strength is determined for several genome sequences.Comment: 4 pages, 4 figures, Physical Review Letters, to appea

Spectral Statistics of Instantaneous Normal Modes in Liquids and Random Matrices

We study the statistical properties of eigenvalues of the Hessian matrix ${\cal H}$ (matrix of second derivatives of the potential energy) for a classical atomic liquid, and compare these properties with predictions for random matrix models (RMM). The eigenvalue spectra (the Instantaneous Normal Mode or INM spectra) are evaluated numerically for configurations generated by molecular dynamics simulations. We find that distribution of spacings between nearest neighbor eigenvalues, s, obeys quite well the Wigner prediction $s exp(-s^2)$, with the agreement being better for higher densities at fixed temperature. The deviations display a correlation with the number of localized eigenstates (normal modes) in the liquid; there are fewer localized states at higher densities which we quantify by calculating the participation ratios of the normal modes. We confirm this observation by calculating the spacing distribution for parts of the INM spectra with high participation ratios, obtaining greater conformity with the Wigner form. We also calculate the spectral rigidity and find a substantial dependence on the density of the liquid.Comment: To appear in Phys. Rev. E; 10 pages, 6 figure

Onset of Delocalization in Quasi-1D Waveguides with Correlated Surface Disorder

We present first analytical results on transport properties of many-mode waveguides with rough surfaces having long-range correlations. We show that propagation of waves through such waveguides reveals a quite unexpected phenomena of a complete transparency for a subset of propagating modes. These modes do not interact with each other and effectively can be described by the theory of 1D transport with correlated disorder. We also found that with a proper choice of model parameters one can arrange a perfect transparency of waveguides inside a given window of energy of incoming waves. The results may be important in view of experimental realizations of a selective transport in application to both waveguides and electron/optic nanodevices.Comment: RevTex, 4 pages, no figures, few references are adde

WordCluster: detecting clusters of DNA words and genomic elements

<p>Abstract</p> <p>Background</p> <p>Many <it>k-</it>mers (or DNA words) and genomic elements are known to be spatially clustered in the genome. Well established examples are the genes, TFBSs, CpG dinucleotides, microRNA genes and ultra-conserved non-coding regions. Currently, no algorithm exists to find these clusters in a statistically comprehensible way. The detection of clustering often relies on densities and sliding-window approaches or arbitrarily chosen distance thresholds.</p> <p>Results</p> <p>We introduce here an algorithm to detect clusters of DNA words (<it>k-</it>mers), or any other genomic element, based on the distance between consecutive copies and an assigned statistical significance. We implemented the method into a web server connected to a MySQL backend, which also determines the co-localization with gene annotations. We demonstrate the usefulness of this approach by detecting the clusters of CAG/CTG (cytosine contexts that can be methylated in undifferentiated cells), showing that the degree of methylation vary drastically between inside and outside of the clusters. As another example, we used <it>WordCluster </it>to search for statistically significant clusters of olfactory receptor (OR) genes in the human genome.</p> <p>Conclusions</p> <p><it>WordCluster </it>seems to predict biological meaningful clusters of DNA words (<it>k-</it>mers) and genomic entities. The implementation of the method into a web server is available at <url>http://bioinfo2.ugr.es/wordCluster/wordCluster.php</url> including additional features like the detection of co-localization with gene regions or the annotation enrichment tool for functional analysis of overlapped genes.</p