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The process of ion transport through a locust potassium channel is described by means of the Fokker-Planck equation (FPE). The deterministic and stochastic components of the process of switching between various conducting states of the channel are expressed by two coefficients, $D^{(1)}$ and $D^{(2)}$, a drift and a diffusion coefficient, respectively. The FPE leads to a Langevin equation. This analysis reveals beside the well known deterministic aspects a turbulent, cascade type of action. The (noisy-like) switching between different conducting states prevents the channel from staying in one, closed or open state. The similarity between the hydrodynamic flow in the turbulent regime and hierarchical switching between conducting states of this biochannel is discussed. A non-trivial character of $D^{(1)}$ and $D^{(2)}$ coefficients is shown, which points to different processes governing the channel's action, asymetrically depending on the history of the previously conducting states. Moreover, the Fokker-Planck and Langevin equations provide information on whether and how the statistics of the channel action change over various time scales., Comment: submitted to physica A text : 12 pages + 8 figures

The classical technical analysis methods of financial time series based on the moving average and momentum is recalled. Illustrations use the IBM share price and Latin American (Argentinian MerVal, Brazilian Bovespa and Mexican IPC) market indices. We have also searched for scaling ranges and exponents in exchange rates between Latin American currencies ($ARS$, $CLP$, $MXP$) and other major currencies $DEM$, $GBP$, $JPY$, $USD$, and $SDR$s. We have sorted out correlations and anticorrelations of such exchange rates with respect to $DEM$, $GBP$, $JPY$ and $USD$. They indicate a very complex or speculative behavior., Comment: 21 pages, 14 figures; to be published in Rev. Braz. Phys. on the occasion of D. Stauffer 60th birthday

The evolution of the probability distributions of Japan and US major market indices, NIKKEI 225 and NASDAQ composite index, and $JPY/DEM$ and $DEM/USD$ currency exchange rates is described by means of the Fokker-Planck equation (FPE). In order to distinguish and quantify the deterministic and random influences on these financial time series we perform a statistical analysis of their increments $\Delta x(\Delta(t))$ distribution functions for different time lags $\Delta(t)$. From the probability distribution functions at various $\Delta(t)$, the Fokker-Planck equation for $p(\Delta x(t), \Delta(t))$ is explicitly derived. It is written in terms of a drift and a diffusion coefficient. The Kramers-Moyal coefficients, are estimated and found to have a simple analytical form, thus leading to a simple physical interpretation for both drift $D^{(1)}$ and diffusion $D^{(2)}$ coefficients. The Markov nature of the indices and exchange rates is shown and an apparent difference in the NASDAQ $D^{(2)}$ is pointed out., Comment: 8 pages, 5 figures; to appear in the Proceedings of the Proceedings of the Second Nikkei Symposium: Toward control of Economic Change -- Application of Econophysics, Nov 12-14, 2002, Tokyo, Japan

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 - Atmospheres

We generalize the momentum indicator idea taking into account the volume of transactions as a multiplicative factor. We compare returns obtained following strategies based on the classical or the generalized technical analysis, taking into account a sort of risk investor criterion., Comment: 8 pages, 7 figures; to appear in the Proceedings of the Second Nikkei Symposium: Toward control of Economic Change -- Application of Econophysics, Nov 12-14, 2002, Tokyo, Japan

How to distinguish and quantify deterministic and random influences on the statistics of turbulence data in meteorology cases is discussed from first principles. Liquid water path (LWP) changes in clouds, as retrieved from radio signals, upon different delay times, can be regarded as a stochastic Markov process. A detrended fluctuation analysis method indicates the existence of long range time correlations. The Fokker-Planck equation which models very precisely the LWP $fluctuation$ empirical probability distributions, in particular, their non-Gaussian heavy tails is explicitly derived and written in terms of a drift and a diffusion coefficient. Furthermore, Kramers-Moyal coefficients, as estimated from the empirical data, are found to be in good agreement with their first principle derivation. Finally, the equivalent Langevin equation is written for the LWP increments themselves. Thus rather than the existence of hierarchical structures, like an energy cascade process, {\it strong correlations} on different $time$ $scales$, from small to large ones, are considered to be proven as intrinsic ingredients of such cloud evolutions., Comment: 17 pages, 6 figures; to be published in Journal of Geophysical Research - Atmospheres

The dynamics of the S&P500 price signal is studied using a moving average technique. Particular attention is paid to intersections of two moving averages with different time horizons. The distributions of the slopes and angle between two moving averages at intersections is analyzed, as well as that of the waiting times between intersections. In addition, the distribution of maxima and minima in the moving average signal is investigated. In all cases, persistent patterns are observed in these probability measures and it is suggested that such variables be considered for better analysis and possible prediction of the trends of the signal., Comment: 17 pages, 9 figures; to be published in Physica A

Classical technical analysis methods of stock evolution are recalled, i.e. the notion of moving averages and momentum indicators. The moving averages lead to define death and gold crosses, resistance and support lines. Momentum indicators lead the price trend, thus give signals before the price trend turns over. The classical technical analysis investment strategy is thereby sketched. Next, we present a generalization of these tricks drawing on physical principles, i.e. taking into account not only the price of a stock but also the volume of transactions. The latter becomes a time dependent generalized mass. The notion of pressure, acceleration and force are deduced. A generalized (kinetic) energy is easily defined. It is understood that the momentum indicators take into account the sign of the fluctuations, while the energy is geared toward the absolute value of the fluctuations. They have different patterns which are checked by searching for the crossing points of their respective moving averages. The case of IBM evolution over 1990-2000 is used for illustrations., Comment: 13 pages, 13 figures; presented at the Third EPS Conference on Application of Physics in Financial Analysis, London, UK, Dec. 3-7, 2001

The complex structure of a typical stratus cloud base height (or profile) time series is analyzed with respect to the variability of its fluctuations and their correlations at all experimentally observed temporal scales. Due to the underlying processes that create these time series, they are expected to have multiscaling properties. For obtaining reliable measures of these scaling properties, different methods of statistical analysis are used herein : power spectral density, detrended fluctuation analysis, and multifractal analysis. This broad set of diagnostic techniques is applied to a typical stratus cloud base height (CBH) data set; data were obtained from the Southern Great Plains site of the Atmospheric Radiation Measurement Program of the Department of Energy from a Belfort Laser Ceilometer. First, we demonstrate that this CBH time series is a nonstationary signal with stationary increments. Further, two scaling regimes are found, although the characteristic laws are quite similar ones. Next, the multi-affine scaling properties are confirmed. The scaling properties of the cloud base height profile of such a continental stratus are found to be similar to those of the marine cloud base height profiles studied by us previously. Some physical interpretation in terms of anomalous diffusion (or fractional random walk) is given for the continental case., Comment: 17 pages, 7 figures; to appear in Physica A

The scaling ranges of time correlations in the cloud base height records of marine boundary layer stratocumulus are studied applying the Detrended Fluctuation Analysis statistical method. We have found that time dependent variations in the evolution of the $\alpha$ exponent reflect the diurnal dynamics of cloud base height fluctuations in the marine boundary layer. In general, a more stable structure of the boundary layer corresponds to a lower value of the $\alpha$ - indicator, i.e. larger anti-persistence, thus a set of fluctuations tending to induce a greater stability of the stratocumulus. In contrast, during periods of higher instability in the marine boundary, less anti-persistent (more persistent like) behavior of the system drags it out of equilibrium, corresponding to larger $\alpha$ values. From an analysis of the frequency spectrum, the stratocumulus base height evolution is found to be a non-stationary process with stationary increments. The occurrence of these statistics in cloud base height fluctuations suggests the usefulness of similar studies for the radiation transfer dynamics modeling., Comment: 12 pages, 6 figures; to appear in Int. J. Mod. Phys. C, Vol. 13, No. 2 (2002)

Cloud base height profiles measured with laser ceilometer are studied using multifractal approach. The irregular structure of the signals is a benchmark for nonlinear dynamical processes. A hierarchy of generalized dimensions determines the intermittency of the signal. The multi-affine properties are described by the $h(\gamma)$ function., Comment: 4 pages, 3 figures; to be presented as poster at: Conference on Computational Physics 2001, Sept 5-8, Aachen, Germany

The multifractal structure of the temporal dependence of the Deutsche Aktienindex (DAX) is analyzed. The $q$-th order moments of the structure functions and the singular measures are calculated. The generalized Hurst exponent $H(q)$ and the $h(\gamma(q))$ curve indicate a hierarchy of power law exponents. This approach leads to characterizing the nonstationarity and intermittency pertinent to such financial signals, indicating differences with turbulence data. A list of results on turbulence and financial markets is presented for asserting the analogy., Comment: 6 pages, 3 figures; an invited talk at: Conference on Computational Physics 2001, Sept 5-8, Aachen, Germany

Time series both of microwave radiometer brightness temperature measurements at 23.8 and 31.4 GHz and of retrievals of water vapor and liquid water path from these brightness temperatures are evaluated using the detrended fluctuation analysis method. As quantified by the parameter $\alpha$, this method (i) enables identification of the time scales over which noise dominates the time series and (ii) characterizes the temporal range of correlations in the time series. The more common spectral analysis method is also used to assess the data and its results are compared with those from detrended fluctuation analysis method. The assumption that measurements should have certain scaling properties allows the quality of the measurements to be characterized. The additional assumption that the scaling properties of the measurements of an atmospheric quantity are preserved in a useful retrieval provides a means for evaluating the retrieval itself. Applying these two assumptions to microwave radiometer measurements and retrievals demonstrates three points. First, the retrieved water vapor path during cloudy-sky periods can be dominated by noise on shorter than ~30~min time scales ($\alpha$-exponent = 0.1) and exhibits no scaling behavior at longer time scales. However, correlations in the brightness temperatures and liquid water path retrievals are found to be consistent with a power-law behavior for time scales up to 3 hr with an $\alpha$-exponent equal to approximately 0.3, as in other geophysical phenomena. Second, clear-sky, moist atmospheres show the expected scaling for both measurements and retrievals of the water vapor path. Third, during clear-sky, dry atmospheric days, instrument noise from the 31.4 GHz channel compromises the quality of the water vapor path retrieval., Comment: 21 pages, 11 figures; to be published in the Journal of Applied Meteorology

Specific aspects of time series analysis are discussed. They are related to the analysis of atmospheric data that are pertinent to clouds. A brief introduction on some of the most interesting topics of current research on climate/weather predictions is given. Scaling properties of the liquid water path in stratus clouds are analyzed to demonstrate the application of several methods of statistical physics for analyzing data in atmospheric sciences, and more generally in geophysics. The breaking up of a stratus cloud is shown to be related to changes in the type of correlations in the fluctuations of the signal that represents the total vertical amount of liquid water in the stratus cloud. It is demonstrated that the correlations of the liquid water path fluctuations exist indeed in a more complex way than usually known through their multi-affine dependence., Comment: 19 pages, 6 figures; to appear in: New Vistas in Statistical Physics -- Applications in Econophysics, Bioinformatics, and Pattern Recognition, Delray Beach, Florida, May 9-12, 2001, Proc. Ed. L.T. Wille (Springer Verlag, Berlin, 2002)

Specialized topics on financial data analysis from a numerical and physical point of view are discussed. They pertain to the analysis of crash prediction in stock market indices and to the persistence or not of coherent and random sequences in fluctuations of foreign exchange currency rates. A brief historical introduction to crashes is given, including recent observations on the DJIA and the S&P500. Daily data of the DAX index are specifically used for illustration. The method for visualizing the pattern thought to be the precursor signature of financial crashes is outlined. The log-periodicity of the pattern is investigated. Comparison of patterns before and after crash days is made through the power spectrum. The corresponding fractal dimension of the signal looks like that of a percolation backbone. Next the fluctuations of exchange rates (XR) of currencies forming $EUR$ with respect to $USD$ are analyzed. The XR power spectra are calculated before and after crashes. A detrended fluctuation analysis is performed. The characteristic exponents $\beta$ and $\alpha$ respectively, are compared, including the time dependence of each $\alpha$, found to be singular near crash dates., Comment: 22 pages, 11 figures; to appear in: New Vistas in Statistical Physics -- Applications in Econophysics, Bioinformatics, and Pattern Recognition, Delray Beach, Florida, USA, May 9-12, 2001, Proceedings, L.T. Wille. Ed. (Springer Verlag, Berlin, 2002)

The British Pound (GBP) is not part of the Euro (EUR) monetary system. In order to find out arguments on whether GBP should join the EUR or not correlations are calculated between GBP and EUR, including a reconstructed EUR for the time interval from 1993 till June 30, 2000. The distribution of fluctuations of the exchange rates is Gaussian for the central part of the distribution, but has fat tails for the large size fluctuations. Within the Detrended Fluctuation Analysis (DFA) statistical method the power law behaviour describing the root-mean-square deviation of the exchange rate fluctuations is obtained as a function of time for the time interval of interest. The time-dependent exponent evolution of the exchange rate fluctuations is given. Statistical considerations imply that the GBP is already behaving as a true EUR., Comment: 10 pages, 5 figures

On Jan. 1, 1999 the European Union introduced a common currency Euro ($EUR$), to become the legal currency in all eleven countries which form the $EUR$. In order to test the $EUR$ behavior and understand various features, the $EUR$ exchange rate is artificially extrapolated back to 1993 by a linear superposition of the exchange rates of the 11 currencies composing $EUR$ with respect to several currencies not belonging to the $EUR$, i.e. Swiss Franc ($CHF$), Danish Kroner ($DKK$), British Pound ($GBP$), Japanese Yen ($JPY$) and U.S. Dollar ($USD$) of interest for reasons given in the text. The distribution of fluctuations of the exchange rates is shown to be Gaussian for the central part of the distribution, and having fat tails for the large size fluctuations. Within the {\it Detrended Fluctuation Analysis} ($DFA$) statistical method we have obtained the power law behavior describing the root-mean-square deviation of the exchange rate fluctuations as a function of time. For the period between Jan. 1995 and Jan. 1999 we have compared the time-dependent exponent of these exchange rate fluctuations for $EUR$ and that of the 11 currencies which form the $EUR$. The German Mark ($DEM$) and the French Franc ($FRF$) have been the currencies primarily leading the fluctuations of the exchange rates, while Italian Lira ($ITL$) and ($PTE$) Portuguese Escudo are the less relevant currencies from this point of view. Technical considerations for the $EUR$ implementation are given as conclusions. The cases of exchange rates with $DKK$ appear quite different from the other four major currencies., Comment: 30 pages, 8 figures; to appear in Intrn J Modern Phys

A brief historical perspective is first given concerning financial crashes, - from the 17th till the 20th century. In modern times, it seems that log periodic oscillations are found before crashes in several financial indices. The same is found in sand pile avalanches on Sierpinski gaskets. A discussion pertains to the after shock period with illustrations from the DAX index. The factual financial observations and the laboratory ones allow us some conjecture on symptoms and remedies for discussing financial crashes along econophysics lines., Comment: 15 pages, 5 figures; to appear in Empirical Science of Financial Fluctuations, Tokyo, Japan, Nov. 15-17, 2000 Proceedings} (Springer Verlag, Berlin, 2001) corrected misprint in Ref. 21

The southern oscillation index (SOI) is a characteristic of the El Nino phenomenon. SOI monthly averaged data is analyzed for the time interval 1866-2000. The tail of the cumulative distribution of the fluctuations of SOI signal is studied in order to characterize the amplitude scaling of the fluctuations and the occurrence of extreme events. Large fluctuations are more likely to occur than the Gaussian distribution would predict. The time scaling of fluctuations is studied by applying the energy spectrum and the Detrended Fluctuation Analysis (DFA) statistical method. Self-affine properties are found to be pertinent to the SOI signal and therefore suggest power law correlations of fluctuations of the signal. Antipersistent type of correlations exist for a time interval ranging from about 4 months to about 6 years. This leads to favor specific physical models for El Nino description., Comment: 7 pages, 4 figures; to appear in Phys. Rev. E

The Euro (EUR) has been a currency introduced by the European Community on Jan. 01, 1999. This implies eleven countries of the European Union which have been found to meet the five requirements of the Maastricht convergence criteria. In order to test EUR behavior and understand various features, we have extrapolated the EUR backwards and therefore have obtained a {\it false euro} (FEUR) dating back to 1993. We have derived the exchange rates of the FEUR with respect to several currencies of interest not belonging to the EUR, i.e., Danish Kroner (DKK), Swiss Franc (CHF), Japanese Yen (JPY) and U.S. Dollar (USD). We have first observed the distribution of fluctuations of the exchange rates. Within the {\it Detrended Fluctuation Analysis} (DFA) statistical method, we have calculated the power law behavior describing the root-mean-square deviation of these exchange rate fluctuations as a function of time, displaying in particular the JPY exchange rate case. In order to estimate the role of each currency making the EUR and therefore in view of identifying whether some of them mostly influences its behavior, we have compared the time-dependent exponent of the exchange rate fluctuations for EUR with that for the currencies that form the EUR. We have found that the German Mark (DEM) has been leading the fluctuations of EUR/JPY exchange rates, and Portuguese Escudo (PTE) is the farthest away currency from this point of view., Comment: 10 pages, 5 figures; to be published in Empirical sciences of financial fluctuations, Tokyo, Japan, Nov. 15-17, 2000 Proceedings (Springer Verlag, Berlin, 2001)