Nonlinear Volatility of River Flux Fluctuations

We study the spectral properties of the magnitudes of river flux increments, the volatility. The volatility series exhibits (i) strong seasonal periodicity and (ii) strongly power-law correlations for time scales less than one year. We test the nonlinear properties of the river flux increment series by randomizing its Fourier phases and find that the surrogate volatility series (i) has almost no seasonal periodicity and (ii) is weakly correlated for time scales less than one year. We quantify the degree of nonlinearity by measuring (i) the amplitude of the power spectrum at the seasonal peak and (ii) the correlation power-law exponent of the volatility series.Comment: 5 revtex pages, 6 page

Common Scaling Patterns in Intertrade Times of U. S. Stocks

We analyze the sequence of time intervals between consecutive stock trades of thirty companies representing eight sectors of the U. S. economy over a period of four years. For all companies we find that: (i) the probability density function of intertrade times may be fit by a Weibull distribution; (ii) when appropriately rescaled the probability densities of all companies collapse onto a single curve implying a universal functional form; (iii) the intertrade times exhibit power-law correlated behavior within a trading day and a consistently greater degree of correlation over larger time scales, in agreement with the correlation behavior of the absolute price returns for the corresponding company, and (iv) the magnitude series of intertrade time increments is characterized by long-range power-law correlations suggesting the presence of nonlinear features in the trading dynamics, while the sign series is anti-correlated at small scales. Our results suggest that independent of industry sector, market capitalization and average level of trading activity, the series of intertrade times exhibit possibly universal scaling patterns, which may relate to a common mechanism underlying the trading dynamics of diverse companies. Further, our observation of long-range power-law correlations and a parallel with the crossover in the scaling of absolute price returns for each individual stock, support the hypothesis that the dynamics of transaction times may play a role in the process of price formation.Comment: 8 pages, 5 figures. Presented at The Second Nikkei Econophysics Workshop, Tokyo, 11-14 Nov. 2002. A subset appears in "The Application of Econophysics: Proceedings of the Second Nikkei Econophysics Symposium", editor H. Takayasu (Springer-Verlag, Tokyo, 2003) pp.51-57. Submitted to Phys. Rev. E on 25 June 200

Effect of nonstationarities on detrended fluctuation analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to quantify long-range power-law correlations in signals. Many physical and biological signals are ``noisy'', heterogeneous and exhibit different types of nonstationarities, which can affect the correlation properties of these signals. We systematically study the effects of three types of nonstationarities often encountered in real data. Specifically, we consider nonstationary sequences formed in three ways: (i) stitching together segments of data obtained from discontinuous experimental recordings, or removing some noisy and unreliable parts from continuous recordings and stitching together the remaining parts -- a ``cutting'' procedure commonly used in preparing data prior to signal analysis; (ii) adding to a signal with known correlations a tunable concentration of random outliers or spikes with different amplitude, and (iii) generating a signal comprised of segments with different properties -- e.g. different standard deviations or different correlation exponents. We compare the difference between the scaling results obtained for stationary correlated signals and correlated signals with these three types of nonstationarities.Comment: 17 pages, 10 figures, corrected some typos, added one referenc

Characterization of Sleep Stages by Correlations of Heartbeat Increments

We study correlation properties of the magnitude and the sign of the increments in the time intervals between successive heartbeats during light sleep, deep sleep, and REM sleep using the detrended fluctuation analysis method. We find short-range anticorrelations in the sign time series, which are strong during deep sleep, weaker during light sleep and even weaker during REM sleep. In contrast, we find long-range positive correlations in the magnitude time series, which are strong during REM sleep and weaker during light sleep. We observe uncorrelated behavior for the magnitude during deep sleep. Since the magnitude series relates to the nonlinear properties of the original time series, while the signs series relates to the linear properties, our findings suggest that the nonlinear properties of the heartbeat dynamics are more pronounced during REM sleep. Thus, the sign and the magnitude series provide information which is useful in distinguishing between the sleep stages.Comment: 7 pages, 4 figures, revte

Effect of Trends on Detrended Fluctuation Analysis

Detrended fluctuation analysis (DFA) is a scaling analysis method used to estimate long-range power-law correlation exponents in noisy signals. Many noisy signals in real systems display trends, so that the scaling results obtained from the DFA method become difficult to analyze. We systematically study the effects of three types of trends -- linear, periodic, and power-law trends, and offer examples where these trends are likely to occur in real data. We compare the difference between the scaling results for artificially generated correlated noise and correlated noise with a trend, and study how trends lead to the appearance of crossovers in the scaling behavior. We find that crossovers result from the competition between the scaling of the noise and the ``apparent'' scaling of the trend. We study how the characteristics of these crossovers depend on (i) the slope of the linear trend; (ii) the amplitude and period of the periodic trend; (iii) the amplitude and power of the power-law trend and (iv) the length as well as the correlation properties of the noise. Surprisingly, we find that the crossovers in the scaling of noisy signals with trends also follow scaling laws -- i.e. long-range power-law dependence of the position of the crossover on the parameters of the trends. We show that the DFA result of noise with a trend can be exactly determined by the superposition of the separate results of the DFA on the noise and on the trend, assuming that the noise and the trend are not correlated. If this superposition rule is not followed, this is an indication that the noise and the superimposed trend are not independent, so that removing the trend could lead to changes in the correlation properties of the noise.Comment: 20 pages, 16 figure

Coevolved mutations reveal distinct architectures for two core proteins in the bacterial flagellar motor

Switching of bacterial flagellar rotation is caused by large domain movements of the FliG protein triggered by binding of the signal protein CheY to FliM. FliG and FliM form adjacent multi-subunit arrays within the basal body C-ring. The movements alter the interaction of the FliG C-terminal (FliGC) "torque" helix with the stator complexes. Atomic models based on the Salmonella entrovar C-ring electron microscopy reconstruction have implications for switching, but lack consensus on the relative locations of the FliG armadillo (ARM) domains (amino-terminal (FliGN), middle (FliGM) and FliGC) as well as changes during chemotaxis. The generality of the Salmonella model is challenged by the variation in motor morphology and response between species. We studied coevolved residue mutations to determine the unifying elements of switch architecture. Residue interactions, measured by their coevolution, were formalized as a network, guided by structural data. Our measurements reveal a common design with dedicated switch and motor modules. The FliM middle domain (FliMM) has extensive connectivity most simply explained by conserved intra and inter-subunit contacts. In contrast, FliG has patchy, complex architecture. Conserved structural motifs form interacting nodes in the coevolution network that wire FliMM to the FliGC C-terminal, four-helix motor module (C3-6). FliG C3-6 coevolution is organized around the torque helix, differently from other ARM domains. The nodes form separated, surface-proximal patches that are targeted by deleterious mutations as in other allosteric systems. The dominant node is formed by the EHPQ motif at the FliMMFliGM contact interface and adjacent helix residues at a central location within FliGM. The node interacts with nodes in the N-terminal FliGc α-helix triad (ARM-C) and FliGN. ARM-C, separated from C3-6 by the MFVF motif, has poor intra-network connectivity consistent with its variable orientation revealed by structural data. ARM-C could be the convertor element that provides mechanistic and species diversity.JK was supported by Medical Research Council grant U117581331. SK was supported by seed funds from Lahore University of Managment Sciences (LUMS) and the Molecular Biology Consortium

GUIDANCE: a web server for assessing alignment confidence scores

Evaluating the accuracy of multiple sequence alignment (MSA) is critical for virtually every comparative sequence analysis that uses an MSA as input. Here we present the GUIDANCE web-server, a user-friendly, open access tool for the identification of unreliable alignment regions. The web-server accepts as input a set of unaligned sequences. The server aligns the sequences and provides a simple graphic visualization of the confidence score of each column, residue and sequence of an alignment, using a color-coding scheme. The method is generic and the user is allowed to choose the alignment algorithm (ClustalW, MAFFT and PRANK are supported) as well as any type of molecular sequences (nucleotide, protein or codon sequences). The server implements two different algorithms for evaluating confidence scores: (i) the heads-or-tails (HoT) method, which measures alignment uncertainty due to co-optimal solutions; (ii) the GUIDANCE method, which measures the robustness of the alignment to guide-tree uncertainty. The server projects the confidence scores onto the MSA and points to columns and sequences that are unreliably aligned. These can be automatically removed in preparation for downstream analyses. GUIDANCE is freely available for use at http://guidance.tau.ac.il

Time correlations and 1/f behavior in backscattering radar reflectivity measurements from cirrus cloud ice fluctuations

The state of the atmosphere is governed by the classical laws of fluid motion and exhibits correlations in various spatial and temporal scales. These correlations are crucial to understand the short and long term trends in climate. Cirrus clouds are important ingredients of the atmospheric boundary layer. To improve future parameterization of cirrus clouds in climate models, it is important to understand the cloud properties and how they change within the cloud. We study correlations in the fluctuations of radar signals obtained at isodepths of winter and fall cirrus clouds. In particular we focus on three quantities: (i) the backscattering cross-section, (ii) the Doppler velocity and (iii) the Doppler spectral width. They correspond to the physical coefficients used in Navier Stokes equations to describe flows, i.e. bulk modulus, viscosity, and thermal conductivity. In all cases we find that power-law time correlations exist with a crossover between regimes at about 3 to 5 min. We also find that different type of correlations, including 1/f behavior, characterize the top and the bottom layers and the bulk of the clouds. The underlying mechanisms for such correlations are suggested to originate in ice nucleation and crystal growth processes.Comment: 33 pages, 9 figures; to appear in the Journal of Geophysical Research - Atmosphere

Green functions for generalized point interactions in 1D: A scattering approach

Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities which may hide important physical aspects of the problem. In this work we present a new method to calculate the exact Green functions for general point interactions in 1D. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients, $R$ and $T$, to construct $G$. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of $N$ general point interactions; on a line; on a half-line; under periodic boundary conditions; and confined in a box.Comment: Revtex, 9 pages, 3 EPS figures. To be published in PR

Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals

We investigate how various coarse-graining methods affect the scaling properties of long-range power-law correlated and anti-correlated signals, quantified by the detrended fluctuation analysis. Specifically, for coarse-graining in the magnitude of a signal, we consider (i) the Floor, (ii) the Symmetry and (iii) the Centro-Symmetry coarse-graining methods. We find, that for anti-correlated signals coarse-graining in the magnitude leads to a crossover to random behavior at large scales, and that with increasing the width of the coarse-graining partition interval $\Delta$ this crossover moves to intermediate and small scales. In contrast, the scaling of positively correlated signals is less affected by the coarse-graining, with no observable changes when $\Delta1$ a crossover appears at small scales and moves to intermediate and large scales with increasing $\Delta$. For very rough coarse-graining ($\Delta>3$) based on the Floor and Symmetry methods, the position of the crossover stabilizes, in contrast to the Centro-Symmetry method where the crossover continuously moves across scales and leads to a random behavior at all scales, thus indicating a much stronger effect of the Centro-Symmetry compared to the Floor and the Symmetry methods. For coarse-graining in time, where data points are averaged in non-overlapping time windows, we find that the scaling for both anti-correlated and positively correlated signals is practically preserved. The results of our simulations are useful for the correct interpretation of the correlation and scaling properties of symbolic sequences.Comment: 19 pages, 13 figure