Detecting periodicity in experimental data using linear modeling techniques

Fourier spectral estimates and, to a lesser extent, the autocorrelation function are the primary tools to detect periodicities in experimental data in the physical and biological sciences. We propose a new method which is more reliable than traditional techniques, and is able to make clear identification of periodic behavior when traditional techniques do not. This technique is based on an information theoretic reduction of linear (autoregressive) models so that only the essential features of an autoregressive model are retained. These models we call reduced autoregressive models (RARM). The essential features of reduced autoregressive models include any periodicity present in the data. We provide theoretical and numerical evidence from both experimental and artificial data, to demonstrate that this technique will reliably detect periodicities if and only if they are present in the data. There are strong information theoretic arguments to support the statement that RARM detects periodicities if they are present. Surrogate data techniques are used to ensure the converse. Furthermore, our calculations demonstrate that RARM is more robust, more accurate, and more sensitive, than traditional spectral techniques.Comment: 10 pages (revtex) and 6 figures. To appear in Phys Rev E. Modified styl

Test your surrogate data before you test for nonlinearity

The schemes for the generation of surrogate data in order to test the null hypothesis of linear stochastic process undergoing nonlinear static transform are investigated as to their consistency in representing the null hypothesis. In particular, we pinpoint some important caveats of the prominent algorithm of amplitude adjusted Fourier transform surrogates (AAFT) and compare it to the iterated AAFT (IAAFT), which is more consistent in representing the null hypothesis. It turns out that in many applications with real data the inferences of nonlinearity after marginal rejection of the null hypothesis were premature and have to be re-investigated taken into account the inaccuracies in the AAFT algorithm, mainly concerning the mismatching of the linear correlations. In order to deal with such inaccuracies we propose the use of linear together with nonlinear polynomials as discriminating statistics. The application of this setup to some well-known real data sets cautions against the use of the AAFT algorithm.Comment: 14 pages, 15 figures, submitted to Physical Review

Using Topological Statistics to Detect Determinism in Time Series

Statistical differentiability of the measure along the reconstructed trajectory is a good candidate to quantify determinism in time series. The procedure is based upon a formula that explicitly shows the sensitivity of the measure to stochasticity. Numerical results for partially surrogated time series and series derived from several stochastic models, illustrate the usefulness of the method proposed here. The method is shown to work also for high--dimensional systems and experimental time seriesComment: 23 RevTeX pages, 14 eps figures. To appear in Physical Review

Critical and Near-Critical Branching Processes

Scale-free dynamics in physical and biological systems can arise from a variety of causes. Here, we explore a branching process which leads to such dynamics. We find conditions for the appearance of power laws and study quantitatively what happens to these power laws when such conditions are violated. From a branching process model, we predict the behavior of two systems which seem to exhibit near scale-free behavior--rank-frequency distributions of number of subtaxa in biology, and abundance distributions of genotypes in an artificial life system. In the light of these, we discuss distributions of avalanche sizes in the Bak-Tang-Wiesenfeld sandpile model.Comment: 9 pages LaTex with 10 PS figures. v.1 of this paper contains results from non-critical sandpile simulations that were excised from the published versio

PeroxiBase: a database with new tools for peroxidase family classification

Peroxidases (EC 1.11.1.x), which are encoded by small or large multigenic families, are involved in several important physiological and developmental processes. They use various peroxides as electron acceptors to catalyse a number of oxidative reactions and are present in almost all living organisms. We have created a peroxidase database (http://peroxibase.isb-sib.ch) that contains all identified peroxidase-encoding sequences (about 6000 sequences in 940 organisms). They are distributed between 11 superfamilies and about 60 subfamilies. All the sequences have been individually annotated and checked. PeroxiBase can be consulted using six major interlink sections ‘Classes’, ‘Organisms’, ‘Cellular localisations’, ‘Inducers’, ‘Repressors’ and ‘Tissue types’. General documentation on peroxidases and PeroxiBase is accessible in the ‘Documents’ section containing ‘Introduction’, ‘Class description’, ‘Publications’ and ‘Links’. In addition to the database, we have developed a tool to classify peroxidases based on the PROSITE profile methodology. To improve their specificity and to prevent overlaps between closely related subfamilies the profiles were built using a new strategy based on the silencing of residues. This new profile construction method and its discriminatory capacity have been tested and validated using the different peroxidase families and subfamilies present in the database. The peroxidase classification tool called PeroxiScan is accessible at the following address: http://peroxibase.isb-sib.ch/peroxiscan.php

Quantitative analysis by renormalized entropy of invasive electroencephalograph recordings in focal epilepsy

Invasive electroencephalograph (EEG) recordings of ten patients suffering from focal epilepsy were analyzed using the method of renormalized entropy. Introduced as a complexity measure for the different regimes of a dynamical system, the feature was tested here for its spatio-temporal behavior in epileptic seizures. In all patients a decrease of renormalized entropy within the ictal phase of seizure was found. Furthermore, the strength of this decrease is monotonically related to the distance of the recording location to the focus. The results suggest that the method of renormalized entropy is a useful procedure for clinical applications like seizure detection and localization of epileptic foci.Comment: 10 pages, 5 figure

A Multifractal Analysis of Asian Foreign Exchange Markets

We analyze the multifractal spectra of daily foreign exchange rates for Japan, Hong-Kong, Korea, and Thailand with respect to the United States Dollar from 1991 to 2005. We find that the return time series show multifractal spectrum features for all four cases. To observe the effect of the Asian currency crisis, we also estimate the multifractal spectra of limited series before and after the crisis. We find that the Korean and Thai foreign exchange markets experienced a significant increase in multifractality compared to Hong-Kong and Japan. We also show that the multifractality is stronge related to the presence of high values of returns in the series

Magnitude and Sign Correlations in Heartbeat Fluctuations

We propose an approach for analyzing signals with long-range correlations by decomposing the signal increment series into magnitude and sign series and analyzing their scaling properties. We show that signals with identical long-range correlations can exhibit different time organization for the magnitude and sign. We find that the magnitude series relates to the nonlinear properties of the original time series, while the sign series relates to the linear properties. We apply our approach to the heartbeat interval series and find that the magnitude series is long-range correlated, while the sign series is anticorrelated and that both magnitude and sign series may have clinical applications.Comment: 4 pages,late

Radial localization of edge modes in Alcator C-Mod pedestals using optical diagnostics

Dedicated experiments in ion cyclotron range heated enhanced D-alpha (EDA) H-mode and I-mode plasmas have been performed on Alcator C-Mod to identify the location of edge fluctuations inside the pedestal and to determine their plasma frame phase velocity. For this purpose, measurements from gas puff imaging (GPI) and gas puff charge exchange recombination spectroscopy (GP-CXRS) have been collected using the same optical views. The data suggest that the EDA H-mode-specific quasi-coherent mode (QCM) is centered near the radial electric field (E r) well minimum and propagates along the ion diamagnetic drift direction in the plasma frame. The weakly coherent mode (WCM) and the geodesic acoustic mode observed in I-mode, on the other hand, are found to be located around the outer shear layer of the E r well. This results in a weak plasma frame phase velocity mostly along the electron diamagnetic drift direction for the WCM. The findings in these EDA H-mode plasmas differ from probe measurements in ohmic EDA H-mode (LaBombard et al 2014 Phys. Plasmas 21 056108), where the QCM was identified as an electron drift-wave located several mm outside the E r well minimum in a region of positive E r. To explore if instrumental effects of the optical diagnostics could be the cause of the difference, a synthetic diagnostic for GPI is introduced. This diagnostic reproduces amplitude ratios and relative radial shifts of the mode profiles determined from poloidally and toroidally oriented optics and, if instrumental effects related to GP-CXRS are also included, indicates that the measured location of the QCM and WCM relative to the E r well reported here is only weakly affected by instrumental effects