Correlation studies of open and closed states fluctuations in an ion channel: Analysis of ion current through a large conductance locust potassium channel

Ion current fluctuations occurring within open and closed states of large conductance locust potassium channel (BK channel) were investigated for the existence of correlation. Both time series, extracted from the ion current signal, were studied by the autocorrelation function (AFA) and the detrended fluctuation analysis (DFA) methods. The persistent character of the short- and middle-range correlations of time series is shown by the slow decay of the autocorrelation function. The DFA exponent $\alpha$ is significantly larger than 0.5. The existence of strongly-persistent long-range correlations was detected only for closed-states fluctuations, with $\alpha=0.98\pm0.02$. The long-range correlation of the BK channel action is therefore determined by the character of closed states. The main outcome of this study is that the memory effect is present not only between successive conducting states of the channel but also independently within the open and closed states themselves. As the ion current fluctuations give information about the dynamics of the channel protein, our results point to the correlated character of the protein movement regardless whether the channel is in its open or closed state.Comment: 12 pages, 5 figures; to be published in Phys. Rev.

Entropy of seismic electric signals: Analysis in natural time under time-reversal

Electric signals have been recently recorded at the Earth's surface with amplitudes appreciably larger than those hitherto reported. Their entropy in natural time is smaller than that, $S_u$, of a ``uniform'' distribution. The same holds for their entropy upon time-reversal. This behavior, as supported by numerical simulations in fBm time series and in an on-off intermittency model, stems from infinitely ranged long range temporal correlations and hence these signals are probably Seismic Electric Signals (critical dynamics). The entropy fluctuations are found to increase upon approaching bursting, which reminds the behavior identifying sudden cardiac death individuals when analysing their electrocardiograms.Comment: 7 pages, 4 figures, copy of the revised version submitted to Physical Review Letters on June 29,200

1/f Noise and Extreme Value Statistics

We study the finite-size scaling of the roughness of signals in systems displaying Gaussian 1/f power spectra. It is found that one of the extreme value distributions (Gumbel distribution) emerges as the scaling function when the boundary conditions are periodic. We provide a realistic example of periodic 1/f noise, and demonstrate by simulations that the Gumbel distribution is a good approximation for the case of nonperiodic boundary conditions as well. Experiments on voltage fluctuations in GaAs films are analyzed and excellent agreement is found with the theory.Comment: 4 pages, 4 postscript figures, RevTe

Dynamical model and nonextensive statistical mechanics of a market index on large time windows

The shape and tails of partial distribution functions (PDF) for a financial signal, i.e. the S&P500 and the turbulent nature of the markets are linked through a model encompassing Tsallis nonextensive statistics and leading to evolution equations of the Langevin and Fokker-Planck type. A model originally proposed to describe the intermittent behavior of turbulent flows describes the behavior of normalized log-returns for such a financial market index, for small and large time windows, both for small and large log-returns. These turbulent market volatility (of normalized log-returns) distributions can be sufficiently well fitted with a $\chi^2$-distribution. The transition between the small time scale model of nonextensive, intermittent process and the large scale Gaussian extensive homogeneous fluctuation picture is found to be at $ca.$ a 200 day time lag. The intermittency exponent ($\kappa$) in the framework of the Kolmogorov log-normal model is found to be related to the scaling exponent of the PDF moments, -thereby giving weight to the model. The large value of $\kappa$ points to a large number of cascades in the turbulent process. The first Kramers-Moyal coefficient in the Fokker-Planck equation is almost equal to zero, indicating ''no restoring force''. A comparison is made between normalized log-returns and mere price increments.Comment: 40 pages, 14 figures; accepted for publication in Phys Rev

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

Roughness distributions for 1/f^alpha signals

The probability density function (PDF) of the roughness, i.e., of the temporal variance, of 1/f^alpha noise signals is studied. Our starting point is the generalization of the model of Gaussian, time-periodic, 1/f noise, discussed in our recent Letter [T. Antal et al., PRL, vol. 87, 240601 (2001)], to arbitrary power law. We investigate three main scaling regions, distinguished by the scaling of the cumulants in terms of the microscopic scale and the total length of the period. Various analytical representations of the PDF allow for a precise numerical evaluation of the scaling function of the PDF for any alpha. A simulation of the periodic process makes it possible to study also non-periodic signals on short intervals embedded in the full period. We find that for alpha=<1/2 the scaled PDF-s in both the periodic and the non-periodic cases are Gaussian, but for alpha>1/2 they differ from the Gaussian and from each other. Both deviations increase with growing alpha. That conclusion, based on numerics, is reinforced by analytic results for alpha=2 and alpha->infinity. We suggest that our theoretical and numerical results open a new perspective on the data analysis of 1/f^alpha processes.Comment: 12 pages incl. 6 figures, with RevTex4, for A4 paper, in v2 some references were correcte